The Chapter 1 of this thesis is aimed to provide an overview of the state of the art regarding nowadays photoelectrochemical research. In this chapter, the theoretical foundations of the models existing so far are presented, in order to determine the charge transfer and recombination kinetics at illuminated semiconducting photoelectrodes.

Furthermore, a detailed theoretical presentation of the electrochemical techniques used to determine the dynamics characteristics in photoelectrodes is provided. Additionally, an overview of the main characterization techniques used throughout the thesis is presented. Finally, comments on the methods regarding the computations carried out by DFT and the fitting of EXAFS spectra is also provided.

In Chapter 2, the materials and methods are presented. The procedures for the preparation of photoelectrodes and details on the experimental parameters to perform the photoelectrochemical determinations are explained. The apparatus employed and their particular experimental setup are commented. Furthermore, the necessary detailed explanations on the DFT computations, EXAFS fitting and Matlab treatment of photoelectrochemical data is provided, joined to the presentation of representative input files that would allow the reproduction of the work presented herein. On the other hand, the kinetics of the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) at the surface of semiconducting electrodes is of wide interest nowadays.

These reactions are known to be multistep. There is a need to identify the ratedetermining step (rds) and to develop alternative electrocatalysts to overcome the observed severe kinetic limitations in order to promote the use of clean fuels.

Rh:SrTiO3 was selected as an interesting semi-conducting material in view of water photo-dissociation. Results are reported in Chapter 3. Rh:SrTiO3 is a p-type semiconductor with a band-gap of 2.4 eV. The semiconductor was surface-modified by una respuesta en forma de espiral en la representación de Nyquist. Hasta donde sabemos, esta tesis constituye el primer reporte de dicha observación, en fotoelectrodos semiconductores estudiados en una celda fotoelectroquimica. De hecho, es interesante como después de 30 años de invención de las espectroscopías fotoelectroquímicas de luz modulada, solo existe un reporte de IMVS en un sistema fotoelectroquímico para la disociación del agua. Con el propósito de dar una explicación para esta observación experimental, el modelo clásico de cinética fotoelectroquímica heterogénea en la superficie de electrodos semiconductores iluminados, se implementó en Matlab. Esos cálculos permitieron reproducir todas las características observadas en la respuesta experimental de IMVS. Ello permitió concluir que dicho patrón en espiral se debió a la dinámica no estacionaria de la interfase fotoelectrodo|electrolito. Este descubrimiento abriría una nueva puerta

Even though he had not met me and all our contact was a phone call back in 2015, he pursued the collaboration and it is because of him that I could make the thesis in France. I'll always keep in my mind the scientific discussions we had. I learned his way to analyze results, to patiently listening to my frequent (sometimes bizarre) theoretical disquisitions and wisely putting them in practical ground through smart questions, thank you very much… for all. I also want to thank Mme. Annie Millet for her kindness to me and her permanent availability for poster printing and link with Pierre.

I would want to thank Prof. Dr. Akihiko Kudo and Prof. Dr. Yan Z. Voloshin for precious scientific collaboration. I want to thank the Directors of the École Doctorale 2MIB, who acceded to an unusual Ph.D. contest by phone and still giving me the grant. I also thank Dr. Loïc Assaud and Dr. Alireza Ranjbari, because of innumerable pleasant days in the laboratory, and their help with personal affairs, such as changing home and full support in everyday life. I am also thankful to Prof. Dr. Sylvain Franger for his refined sense of humor and for always answering my frequent doubts regarding electrochemical impedance spectroscopy.

Thanks a lot too to my Ph.D. partners, Dr. Ángel Villagrá and Joumada Al-Cheikh, who worked next to me and shared the curious world of experimental electrochemistry. I am also grateful to Nicolas Gautier and Jean-Pierre Baltaze for all the tennis we played together and moments of much fun. I am further grateful to Anshuman Agrawal, who has always been nice and invited me several times to hang out with his numerous friends.

I should also mention the personal of the experimental platform at the Institute, who were always available to fulfill my frequent and continuous measurement requirements.

These are, Jean-Pierre Baltaze (NMR), Diana Dragoë (XPS), Romuald Saint-Martin (powder XRD), Jérémy Forté (thin film XRD), Sandra Mazérat (AFM), Cristian Herrero (EPR), François Brisset (SEM). Many thanks too to Rodolphe Adam and Bernard Massot for precious help for establishing good computational conditions. I also appreciate the help of Mme. Corinne Ruello, who introduced me (joined to Ángel Villagrá as well) to the new world of French administration. I am grateful to Prof. Dr. Julien Bachmann who received me one month in his research group at Friedrich-Alexander Universität (Erlangen-Nürnberg), where I learned useful experimental procedures that were completely new for me. I am thankful to my Cuban Professors of Chemistry at the University of Havana and to the Cuban educational system, who contributed to my early formation as a chemist; I am indebted to them because of my ground studies.

From the family side, I am thankful to my grandparents for their love, also to all my uncles and aunts, my brother, some dozes of cousins, and all my friends. I am thankful too to my mother-in-law, father-in-law and sister-in-law, who received me in a happy family.

A particular place in my acknowledgements is for my Mother Mery and my Father Manolo. I will never forget their hard work and sacrifice for me to have a happy childhood during the tough 90s in Cuba: the chickens grown inside the house for eating and the bicycle rides to the school. Their permanent encouragement to study and prepare myself for the future, their profound love and support has been very important.

This thesis is devoted to them.

Finally, to my person, my wife Karen, my love for her came in a thunder at the first sight. Ever since, all my goals and wishes are for her to be happy, and for us, to build a family. This thesis is devoted to you.

Most sincerely, Manuel addition of catalytic species, e.g. sorption of the Co(Cl2Gm)3(B-CH3)2 clathrochelate, or deposition of metallic Cu and Pt. The unmodified and surface-modified Rh:SrTiO3 samples were characterized by X-ray Photoelectron Spectroscopy, X-ray Diffraction analysis and other techniques, in order to determine the chemical nature of each element.

Scanning Electron Microscopy was also used to assess the rough morphology of the surface of each photoelectrode. The heterogeneous hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) on unmodified and surface-modified Rh:SrTiO3 samples were initially studied by Open Circuit Photovoltage Decay (OCPD), Linear Sweep Voltammetry (LSV) and Photoelectrochemical Impedance Spectroscopy (PEIS). The potential range of investigation was from -1.30 up to -1.00 V (vs. SCE) for the HER, and from +1.50 V down to +1.00 V (vs SCE) for the OER. Light intensities varied from 60 mW/cm 2 to 530 mW/cm 2 . The behavior of the photoelectrodes could be classified into two groups: the first one contains pristine Rh:SrTiO3, and Rh:SrTiO3 -Co(Cl2Gm)3(B-CH3)2. For this group, kinetic parameters were found independent of light intensity and electrode potential. The second group contains the Rh:SrTiO3 -Cu and Rh:SrTiO3 -Pt photoelectrodes: they exhibited a Tafel-like behavior for the charge transfer and the recombination processes. From such dependence, it was possible to calculate a transfer coefficient, suggesting that either the Volmer step or the Heyrovsky step (in the high surface coverage region, i.e.θH > 0.6) are the rds for the HER mechanism. When these photoelectrodes were used for the OER, they all exhibited very slow charge transfer kinetics.

Results reported in Chapter 4 pertain to the hydrogen evolution reaction (HER) in the homogeneous phase. The HER mechanism is analyzed using the Co(Cl2Gm)3(B-CH3)2 clathrochelate (considered as a model catalyst of the clathrochelate family) dissolved in an electrolyte as electrocatalyst. The study was made by Density Functional Theory analysis. Indeed the HER is the focus of much attention by the scientific community because hydrogen of electrolytic grade is considered as the energy carrier of the future.

Molecular complexes of 3d-transition metals, such as cobalt, are potential alternative candidates to platinum for the HER in acidic media. Among these, cage complexes such as tris-dioximate metal clathrochelates have shown high HER catalytic properties.

However, a full theoretical mechanistic study of such reaction has not been undertaken yet. This is why in this chapter, we report on a DFT study of the HER mechanism catalyzed by the model cobalt clathrochelate. For all species involved, high spin and low spin configurations were calculated. The structure of the clathrochelate was determined by Extended X-ray Absorption Fine Structure Spectroscopy (EXAFS). For the fitting of EXAFS spectra, the XRD and the DFT geometries were employed. Both geometries differed slightly, but EXAFS proved to be highly sensitive to these small structural variations because the adequate fitting of EXAFS employing the DFT optimized geometry needed more variables than the XRD geometry. In order to study the mechanism of the HER, several protonation sites located in the cage formed by the ligand framework and in the metal, were investigated. Protonation was found to be possible in various positions of the ligand structure, but direct protonation of cobalt was found to be the most energetically favored, enabling partial electron transfer to the coordinated proton. Several combinations of double protonation were further calculated.

However, a structural and energetic analysis of relevant protonated intermediates and the calculated transition state for HER, with a η 2 character, suggested that the proposed ECCE mechanism was not favored. Instead, an ECEC mechanism was considered, but a transition state connecting reactants and products could not be found, which lead to a proposition of a Proton Coupled Electron Transfer for the last step of the HER mechanism.

Results reported in Chapter 5 are related to the dynamic characterization of Rh:SrTiO3 and Rh:SrTiO3 -Pt photoelectrodes performed by Intensity Modulated Photovoltage Spectroscopy (IMVS). The IMVS response obtained for these photoelectrodes was completely unexpected, when compared to previous results reported in the scientific literature. Indeed, instead of recording conventional IMVS responses (that would resemble to typical electrochemical impedance spectra), spiral-like shapes were observed in the complex plane (Nyquist representation). To the best of our knowledge, this thesis constitutes a first report of such observation in semiconducting photoelectrodes studied in a photoelectrochemical cell. As a matter of fact, it is notable that after 30 years after the invention of light modulated photoelectrochemical spectroscopy, there is only one report of water splitting studied by IMVS. In order to provide an explanation for such experimental finding, the classical model of heterogeneous photoelectrochemical kinetics at the surface of illuminated semiconducting electrodes was implemented and solved numerically in Matlab. Such calculations allowed us to reproduce all the features observed in the experimental IMVS response, leading us to the conclusion that such spiral-like observations are due to nonsteady state dynamics at the photoelectrode|electrolyte interfaces. These findings open new understanding on the complex dynamic behavior of illuminated semiconducting photoelectrodes.

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RÉSUMÉ

Dans le Chapitre 1 de cette thèse, nous présentons une analyse bibliographique relative à l'état actuel des connaissances en photo-électrochimie. Dans ce chapitre, nous présentons la théorie et les modèles qui permettent d'expliquer les dynamiques de transfert de charge et de recombinaison à la surface d'électrodes semi-conductrices sous illumination. Nous présentons également une description théorique détaillée des techniques électrochimiques utilisées et une description des méthodes de caractérisation employées lors de cette thèse. Finalement, nous décrivons les procédés de calcul utilisés pour les analyses DFT et EXAFS.

Dans le Chapitre 2, nous décrivons les matériaux et les méthodologies utilisées au cours de notre travail. Les procédés de préparation des photo-électrodes sont décrits et les détails des paramètres expérimentaux utilisés pour les mesures électrochimiques sont fournis. Des explications détaillées sont fournies à propos de l'appareillage utilisé pour la caractérisation des matériaux, et au sujet de la mise en oeuvre pratique des calculs DFT et EXAFS. De même, les méthodes utilisées pour le traitement des données électrochimiques sous Matlab sont décrites, de manière à faciliter la reproduction de ce travail de recherche. Les réactions de dégagement d'hydrogène (HER pour l'acronyme anglais) et de dégagement d'oxygène (OER pour l'acronyme anglais) présentent un fort intérêt sociétal. Ces réactions possèdent des mécanismes complexes, à étapes multiples, et les étapes cinétiquement limitantes présentent des limitations cinétiques sévères. Ces caractéristiques doivent être étudiées en détail afin de guider la recherche de catalyseurs plus performants. Rh:SrTiO3 a été sélectionné en tant que matériau semi-conducteur performant pour la photo-dissocation de l'eau. Les résultats rapportés dans le Chapitre 3 concernent l'étude de ce matériau, qui possède une conduction de type p et une énergie de bande interdite de 2,4 eV. Ce semi-conducteur a été modifié en surface par addition de co-catalyseurs destinés à améliorer la cinétique de transfert de charge, par exemple par sorption d'un clathrochélate tel que Co(Cl2Gm)3(B-CH3)2, ou par déposition de nanoparticules métalliques de Cu ou du Pt. Les matériaux obtenus (Rh:SrTiO3 non-modifié ou modifié) ont été caractérisés par Spectroscopie de Photoélectrons X (XPS pour l'acronyme anglais), par Diffraction des Rayons X (XRD, pour l'acronyme anglais) et par d'autres techniques qui ont permis leur caractérisation chimique et structurale. La morphologie de la surface a été déterminée par Microscopie à Balayage Électronique (SEM pour l'acronyme anglais) : elle révèle la rugosité de tous ces matériaux. Les réactions d'HER et d'OER ont été étudiées par la méthode dite de la Chute du Photo-potentiel Libre (OCPD, pour l'acronyme anglais), par Voltammetrie à Balayage Linéaire de Potentiel (LSV, pour l'acronyme anglais) et par Spectroscopie d'Impédance Photo-électrochimique (PEIS, pour l'acronyme anglais). Les mesures ont été réalisées dans le domaine de potentiel allant de -1.30 à -1.00 V (vs. SCE) pour l'HER, et de +1.50 V et +1.00 V pour l'OER. L'intensité lumineuse utilisée varie entre 60 mW/cm 2 et 530 mW/cm 2 . Le comportement des photo-électrodes vis-à-vis de l'HER nous a permis de les classer en deux groupes. Le premier groupe rassemble Rh:SrTiO3 et Rh:SrTiO3 -Co(Cl2Gm)3(B-CH3)2. Dans ce cas, les paramètres cinétiques mesurés sont indépendants du potentiel d'électrode et de l'intensité de la source lumineuse utilisée. Le second groupe rassemble Rh:SrTiO3 -Cu et Rh:SrTiO3 -Pt, deux photoélectrodes pour lesquelles les constantes de vitesse suivent un comportement de type plutôt métallique. Cette observation nous a permis de calculer le coefficient de transfert de la réaction qui suggère que l'étape cinétiquement limitante (rds) est soit l'étape de Volmer, soit l'étape de Heyrovsky (à haute densité de courant, lorsque le taux de recouvrement en surface en ad-atomes d'hydrogène adsorbés est tel que θH > 0,6). En ce qui concerne l'OER, toutes les photo-électrodes utilisées ont une cinétique très lente.

Les résultats rapportés dans le Chapitre 4 concernent la réaction de dégagement d'hydrogène en phase homogène : il s'agit d'une étude mécanistique utilisant la Théorie du Fonctionnel de la Densité (DFT, pour l'acronyme anglais), et portant sur un clathrochélate de cobalt dissout en solution. En effet, l'HER est l'objet de nombreuses recherches au sein de la communauté scientifiques car l'hydrogène électrolytique issu de l'eau est considéré comme le vecteur énergétique de l'avenir. Les complexes des métaux de transition 3-d, comme le cobalt, présentent des alternatives intéressantes au platine pour l'HER en milieux acide. Parmi une grande variété de complexes possibles, les complexes de type cage (le cation métallique actif est placé au centre d'une cage ligantaire) utilisant des ligands tris-dioximate, connus sous le nom de clathrochélates, ont montré propriétés électrocatalytiques très intéressantes vis-à-vis de l'HER. Pourtant, une étude théorique complète du mécanisme d'HER n'a pas encore été réalisée. C'est la raison pour laquelle nous nous sommes attaqués à ce problème. Dans ce Chapitre, nous présentons une description théorique du mécanisme d'HER, catalysé par le clahtrochélate modèle Co(Cl2Gm)3(B-CH3)2. Pour toutes les espèces chimiques possibles, les configurations bas-spin et haut-spin ont été calculées. La structure du clathrochélate a été déterminée par Spectroscopie d'Absorption X (EXAFS, pour l'acronyme anglais). Pour parvenir à effectuer le calcul EXAFS, la géométrie déterminée par XRD et par optimisation DFT a été employée. Les deux géométries sont légèrement différentes, mais l'EXAFS est sensible à ces petites différences puisque la simulation du spectre EXAFS expérimental à partir de la géométrie DFT a nécessité plus de paramètres. Dans le but d'étudier le mécanisme de l'HER, l'énergie de plusieurs sites de protonation (sur le ligand organique et sur le centre métallique) a été calculée.

Nos calculs montrent que la protonation du ligand est possible à plusieurs endroits, mais que la protonation directe du cobalt reste énergétiquement favorisée. Plusieurs combinaisons de double protonation ont été calculées. Cependant, l'analyse structurelle et énergétique, et l'état de transition (avec des caractéristiques η 2 ) suggèrent que le mécanisme ECCE n'est pas favorisé. Il a été donc considéré un mécanisme ECEC.

Toutefois, il n'a pas été possible d'identifier un état de transition, ce qui pourrait signifier que la dernière étape du mécanisme pourrait être concertée. Les résultats présentés dans le Chapitre 5 concernent la caractérisation dynamique des photoélectrodes à base de Rh:SrTiO3 et de Rh:SrTiO3 -Pt, par IMVS (Intensity Modulated photoVoltage Spectroscopy). Les réponses expérimentales obtenues par IMVS sont très différentes de celles auxquelles nous nous attendions compte tenu des résultats disponibles dans la littérature. En effet, au lieu d'obtenir des réponses typiques d'IMVS (c'est-à-dire des diagrammes habituels qui ressemblent ceux de spectroscopie d'impédance électrochimique), nous avons mesuré des diagrammes ayant une forme en spirale (graphe tracés dans le plan complexe en coordonnées de Nyquist) inattendue.

Après avoir regardé en détail la littérature disponible à ce sujet, nous sommes arrivés à la conclusion que c'est la première fois qu'un comportement de ce type est rapporté pour des photo-électrodes semi-conductrices illuminées à l'aide de cellules photoélectrochimiques. Environ 30 ans après l'invention de la spectroscopie photoélectrochimique de lumière modulée, il est étonnant de réaliser qu'il n'existe dans la littérature qu'un seul article discutant de la photo-dissociation de l'eau par IMVS. Pour expliquer nos observations expérimentales, nous avons résolu sous Matlab les équations différentielles classiques, qui rendent compte de la dynamique de transfert et de recombinaison de charge dans les photo-électrodes semi-conductrices sous illumination.

Ces calcules nous ont permis de simuler complètement des caractéristiques en spirale observées expérimentalement par IMVS. Cela nous a permis de tirer la conclusion que ce comportement est dû à une dynamique non-stationnaire de l'interface semi-conducteur|électrolyte.

RESUMEN

El Capítulo 1 de esta tesis presenta la revisión del estado del arte en fotoelectroquímica. Dicho capítulo presenta los fundamentos teóricos necesarios para comprender los modelos existentes para determinar la cinética de transferencia y recombinación de carga en fotoelectrodos iluminados. Además, se describen detalladamente las técnicas electroquímicas empleadas con este fin. Adicionalmente, se presenta una visión general de las técnicas de caracterización más importantes que fueron empleadas en esta tesis. Finalmente, se realizan comentarios acerca de los métodos de cómputo relacionados con los cálculos DFT y el ajuste de espectros EXAFS.

En el Capítulo 2 se describen los materiales y métodos. Se explican los procedimientos de preparación de los fotoelectrodos, así como detalles que conciernen los parámetros experimentales empleados para realizar las determinaciones fotoelectroquímicas. Los equipos de caracterización y sus particularidades de trabajo se explican además. Se tratan también en detalle (i) la metodología de cálculo DFT, (ii) el tratamiento para ajustar los espectros EXAFS, (iii) y el tratamiento de los datos fotoelectroquímicos realizados en Matlab. Se proveen también los ficheros de entrada típicos, con el propósito de facilitar una eventual repetición del trabajo presentado a continuación. La cinética de la reacción de evolución de hidrógeno (HER, por sus siglas en inglés) y de la reacción de evolución de oxígeno (OER, por sus siglas en inglés) en la superficie de fotoelectrodos sometidos a iluminación es de vital importancia en la actualidad. Se conoce que estas reacciones poseen un mecanismo complejo de múltiples pasos, y por ello presentan grandes limitaciones cinéticas que deben estudiarse para desarrollar fuentes alternativas y renovables de energía. Precisamente, el Capítulo 3 trata sobre el estudio del material semiconductor Rh:SrTiO3, que posee conductividad tipo p y un band-gap de 2.4 eV. El semiconductor se modificó con especies catalíticas, como el clatroquelato Co(Cl2Gm)3(B-CH3)2, y con Pt y Cu metálicos. Los materiales se caracterizaron mediante Espectroscopía de Fotoelectrones X (XPS, por sus siglas en inglés), Difracción de Rayos X (XRD, por sus siglas en inglés), que permitieron su identificación química. Adicionalmente, se realizaron mediciones de Microscopía Electrónica de Barrido (SEM, por sus siglas en inglés) que permitieron poner en evidencia la naturaleza rugosa de la superficie de todos los materiales. Los estudios fotoelectroquímicos de la HER y la OER se realizaron mediante Caída del Fotopotencial a Circuito Abierto (OCPD, por sus siglas en inglés), Voltametría de Barrido Lineal (LSV, por sus siglas en inglés), y Espectroscopía de Impedancia Fotolectroquímica (PEIS, por sus siglas en inglés). Los estudios se realizaron en el rango de -1,30 V a -1,00 V (vs. SCE) para la HER, y de 1.50 V a 1.00 V (vs SCE) para la OER, y con intensidades de luz desde 60 mW/cm 2 hasta 530 mW/cm 2 . El comportamiento de los fotoelectrodos se pudo clasificar en dos grupos, uno formado por Rh:SrTiO3 y el otro por Rh:SrTiO3 -Co(Cl2Gm)3(B-CH3)2. En este caso, los parámetros cinéticos no dependieron del potencial de electrodo ni de la intensidad de iluminación. En cambio, los parámetros cinéticos de los fotoelectrodos formados por Rh:SrTiO3 -Cu and Rh:SrTiO3 -Pt exhibieron un comportamiento tipo Tafel. Dicha dependencia permitió calcular el coeficiente de transferencia, que sugirió ya sea la reacción de Volver, o la reacción de Heyrovsky en el límite de alta densidad de hidrógeno adsorbido, como posible paso determinante en el mecanismo de HER.

En el Capítulo 4 se estudió la HER electrocatalizada por el clatroquelato modelo Co(Cl2Gm)3(B-CH3)2, mediante métodos relacionados con la Teoría de los Funcionales de la Densidad (DFT, por sus siglas en inglés). De hecho, la HER recibe gran atención por la comunidad científica debido a la demanda social por nuevas fuentes de energía limpia y renovable. Los complejos moleculares de metales de transición 3-d, como el cobalto, son candidatos potenciales al platino para la HER en medio ácido. Entre esos complejos, los clatroquelatos metálicos han mostrado propiedades catalíticas respecto a la HER. Sin embargo, un tratamiento teórico completo del mecanismo de dicha reacción no se ha realizado aún. Es por ello que en este capítulo se realizó un cálculo DFT para estudiar el mecanismo de la HER catalizada por un clatroquelato modelo. Para todas las especies involucradas, se calcularon las configuraciones de alto espín y de bajo espín.

La estructura del clatroquelato se determinó por espectroscopía EXAFS. El ajuste de los espectros EXAFS se realizó mediante el empleo de las geometrías obtenidas por XRD y por DFT. Ambas geometrías fueron ligeramente diferentes, pero el EXAFS demostró ser muy sensible a estas pequeñas variaciones estructurales pues el ajuste adecuado de la señal EXAFS con la geometría obtenida mediante optimización DFT, necesitó más variables de las que se emplearon con la geometría XRD. Para estudiar el mecanismo de la HER, se calcularon varios sitios de protonación en el ligando orgánico y en el centro metálico. Los resultados mostraron que la protonación fue posible en varios sitios del ligando, sin embargo, la protonación directa en el cobalto fue la más favorecida energéticamente. Varias combinaciones de doble protonación se calcularon además. Sin embargo, el análisis estructural y energético de los diversos intermediarios permitió concluir que dicho mecanismo no estaba favorecido. En su lugar, se exploró un mecanismo ECEC, que llevó a proponer que la última etapa en la evolución de dihidrógeno es un paso concertado.

Por otra parte, el Capítulo 5 está consagrado a determinaciones dinámicas en fotoelectrodos compuestos por Rh:SrTiO3 y Rh:SrTiO3 -Pt, realizados por Espectroscopía de Fotovoltaje de Intensidad Modulada (IMVS, por sus siglas en inglés).

La respuesta obtenida en IMVS fue completamente inesperada, si se le compara con los resultados esperados según la literatura científica. De hecho, en lugar de la respuesta típica en IMVS, que parece la de un espectro de impedancia electroquímcia, se obtuvo

INTRODUCTION AND OBJECTIVES OF THE DOCTORAL THESIS

The context of the 21 st century demands for a rapid change of the energetic matrix which is currently based on fossil non-renewable fuels, towards renewable sources that will not harm the ecosystem and will be available indefinitely.

Hence, a widely explored alternative is the transformation of solar energy into electric energy by means of photovoltaic devices, which comprises semiconducting p-n junction cells, or more recently Dye Sensitized Solar Cells.

Another possibility is the use photoelectrochemical cells that can harvest solar energy to transform chemicals into other chemicals that could be used as renewable fuels. For example, water splitting into both dihydrogen and dioxygen. Indeed, the whole body of this work is devoted to the thorough study of photoelectrochemical cells for water splitting based on the Rh:SrTiO3 semiconducting material.

In a photoelectrochemical cell, a common approach is to employ semiconductors that can absorb visible light. However, to find an adequate semiconducting material is not a straightforward task because not only its band gap should be less than 3 eV (to harvest visible light), but also the band edges must be satisfactorily placed so that the targeted reaction can proceed from a thermodynamic perspective.

A material that has been shown to be active for water splitting is Rh-doped SrTiO3.

Pristine SrTiO3 is an n-type material with a rather large band-gap lying in the UV region of the electromagnetic spectrum. However, doping with Rh changes the conductivity type of the material to p-type, and therefore has been applied successfully as a photocathode in a water splitting cell, to target the hydrogen evolution reaction (HER).

Another important issue to address in photoelectrochemical systems is the kinetics of charge transfer and recombination at the surface of photoelectrodes. Indeed, water splitting is a heterogeneous multistep processes that has revealed serious kinetic limitations. Hence, co-catalysts should be incorporated at the surface of semiconductors, with the ideal purpose to accelerate the rate of charge transfer, and decrease the rate of recombination of charge carriers.

The chemical nature of such catalysts is wide since it may be either metallic nanoparticles or appropriate molecular complexes. As a matter of fact, there is a family of organometallic compounds that have been shown to be active molecular catalysts for the HER, but have never been tested as heterogeneous catalysts in the surface of semiconducting photoelectrodes. Such family is known as clathrochelates, which consist in a polymacrocyclic cage of organic ligands that encapsulate a central metal atom (typically Fe or Co).

Consequently, the need to find efficient photoelectrochemical systems for water splitting, that can function assisted by visible light was the main scientific problem that motivated this thesis.

Therefore, the main objective of this thesis was to determine the dynamic behavior for heterogeneous visible-light driven water splitting at the surface of Rh:SrTiO3 photoelectrodes, modified with suitable catalysts comprising metallic Pt and Cu and the Co(Cl2Gm)3(B-CH3)2 molecular clathrochelate, in order to provide insights that could allow to build efficient photoelectrochemical devices.

The specific objectives of this thesis can be summarized as follows:

-To characterize by means of spectroscopic and microscopic techniques the -To solve a system of differential equations and to perform numeric simulations in Matlab, in order to describe the non-steady state photoelectrochemical response of Rh:SrTiO3 and Rh:SrTiO3 -Pt photoelectrodes observed in IMVS.

CHAPTER 1. Bibliographic overview

Introduction

Contemporary energetic and climatic context has urged the scientific community to find clean and renewable energy sources that could solve the growing needs of modern societies. In particular, water splitting [1][2][3][START_REF] Yengantiwar | Direct Liquid Injection Chemical Vapor Deposition of Molybdenum-Doped Bismuth Vanadate Photoelectrodes for Efficient Solar Water Splitting[END_REF][START_REF] Pham | Modelling heterogeneous interfaces for solar water splitting[END_REF] has attracted much attention, as demonstrated by the large amount of research efforts aiming to transform scientific fundamental knowledge into useful, reasonably cheap, and therefore widely available technologies. 6- 24 Another widely explored alternative is related to the development of photovoltaic devices able to transform photon energy into electricity. [START_REF] Izaki | Hybrid ZnO/phthalocyanine photovoltaic device with highly resistive ZnO intermediate layer[END_REF][START_REF] Zhang | A novel research approach on the dynamic properties of photogenerated charge carriers at Ag2S quantumdots-sensitized TiO2 films by a frequency-modulated surface photovoltage technology[END_REF][START_REF] Krüger | Charge Transport and Back Reaction in Solid-State Dye-Sensitized Solar Cells : A Study Using Intensity-Modulated Photovoltage and Photocurrent Spectroscopy[END_REF][START_REF] Liu | Analysis on dye-sensitized solar cells based on Fe-doped TiO 2 by intensity-modulated photocurrent spectroscopy and Mott -Schottky[END_REF][START_REF] Du | Zn-Cu-In-Se Quantum Dot Solar Cells with a Certified Power Conversion Efficiency of 11[END_REF][START_REF] Okhay | Photovoltage Study of Graphene Oxide with Ni Nanoparticles[END_REF][START_REF] Petrozza | Electron Transport and Recombination in Dye-Sensitized Mesoporous TiO2 Probed by Photoinduced Charge-Conductivity Modulation Spectroscopy with Monte Carlo Modeling[END_REF][START_REF] Schlichthörl | Band Edge Movement and Recombination Kinetics in Dye-Sensitized Nanocrystalline TiO2 Solar Cells : A Study by Intensity Modulated Photovoltage Spectroscopy[END_REF][START_REF] Osterloh | Photochemical Charge Separation in Poly(3-hexylthiophene) (P3HT) Films Observed with Surface Photovoltage Spectroscopy[END_REF][START_REF] Roelofs | Increased Quantum Dot Loading by pH Control Reduces Interfacial Recombination in Quantum-Dot-Sensitized Solar Cells[END_REF][START_REF] Bisquert | Simulation of Steady-State Characteristics of Dye-Sensitized Solar Cells and the Interpretation of the Diffusion Length[END_REF][START_REF] Bisquert | On Voltage, Photovoltage, and Photocurrent in Bulk Heterojunction Organic Solar Cells[END_REF] In a recent book related to water splitting, [START_REF] Lewerenz | Photoelectrochemical Water Splitting Materials, Processes and Architectures[END_REF] extensive considerations were made regarding "The Potential Contribution of Photoelectrochemistry in the Global Energy Future". [START_REF] Parkinson | Photoelectrochemical Water Splitting Materials, Processes and Architectures[END_REF] The authors commented on the commercial viability of carbon dioxide reduction and water photoelectrolysis, and reached the conclusion that the most promising target for solar energy conversion is the development of water splitting systems, but there is still a long way to travel to improve materials for effective photoelectrolysis.

The current challenge is to move forward in the development of materials with adequate properties for light harvesting and the development of catalysts, preferably without the use of precious metals, which would allow for the scaling of this technology aiming to realistic practical applications. The strong scientific interest in photoelectrocatalysis in contemporary research is undisputed, [1][2][3][START_REF] Yengantiwar | Direct Liquid Injection Chemical Vapor Deposition of Molybdenum-Doped Bismuth Vanadate Photoelectrodes for Efficient Solar Water Splitting[END_REF][START_REF] Pham | Modelling heterogeneous interfaces for solar water splitting[END_REF][START_REF] Hossain | Solution Combustion Synthesis, Characterization, and Photocatalytic Activity of CuBi2O4 and Its Nanocomposites with CuO and α-Bi2O3[END_REF][START_REF] Zhou | Photocatalysis with TiO2 Nanotubes: 'Colorful' Reactivity and Designing Site-Specific Photocatalytic Centers into TiO2 Nanotubes[END_REF][START_REF] Li | Graphene with Atomic-Level In-Plane Decoration of h-BN Domains for Efficient Photocatalysis[END_REF][START_REF] Kuang | Facile Construction of Dual p-n Junctions in CdS/Cu2O/ZnO Photoanode with Enhanced Charge Carrier Separation and Transfer Ability[END_REF][START_REF] Chen | Enhanced photogenerated carrier separation in CdS quantum dot sensitized ZnFe2O4/ZnIn2S4 nanosheet stereoscopic films for exceptional visible light photocatalytic H2 evolution performance[END_REF][START_REF] Zachäus | Photocurrent of BiVO4 is limited by surface recombination, not surface catalysis[END_REF][START_REF] Mckone | Solar energy conversion, storage, and release using an integrated solar-driven redox flow battery[END_REF][START_REF] Lin | Modifying photocatalysts for solar hydrogen evolution based on the electron behavior[END_REF][START_REF] Wu | Band-gap tailoring and visible-light-driven photocatalytic performance of porous (GaN)1-x(ZnO)x solid solution[END_REF][START_REF] Wei | Loading of Co3O4 onto Ptmodified nitrogen-doped TiO2 nanocomposites promotes photocatalytic hydrogen production[END_REF][START_REF] Robinson | Photocatalytic photosystem I/PEDOT composite films prepared by vapor-phase polymerization[END_REF][START_REF] Gao | A Facile One-Step Synthesis of Fe-Doped g-C3N4 Nanosheets and Their Improved Visible-Light Photocatalytic Performance[END_REF][START_REF] Hu | Bi2WO6 Nanosheets Decorated with Au Nanorods for Enhanced Near-Infrared Photocatalytic Properties Based on Surface Plasmon Resonance Effects and Wide-Range Near-Infrared Light Harvesting[END_REF] and such research rhythm should guarantee on the mid to long term the necessary progress required for a transition towards alternative and renewable energy sources.

Dye sensitized solar cells (DSSC) vs. Photoelectrochemical cells (PEC)

There are several configurations for systems that convert light into useful electrical or chemical energy. [START_REF] Sivula | Photoelectrochemical Water Splitting Materials, Processes and Architectures[END_REF] In order to illustrate the underlying principles, we shall comment here two of the most important ones.

In the first place, we shall consider the Dye Sensitized Solar Cells (DSSC, Fig. 1-1). [START_REF] Du | Zn-Cu-In-Se Quantum Dot Solar Cells with a Certified Power Conversion Efficiency of 11[END_REF][START_REF] Roelofs | Increased Quantum Dot Loading by pH Control Reduces Interfacial Recombination in Quantum-Dot-Sensitized Solar Cells[END_REF][START_REF] Bisquert | Simulation of Steady-State Characteristics of Dye-Sensitized Solar Cells and the Interpretation of the Diffusion Length[END_REF][START_REF] Bisquert | On Voltage, Photovoltage, and Photocurrent in Bulk Heterojunction Organic Solar Cells[END_REF][START_REF] Barea | Properties of Chromophores Determining Recombination at the TiO2 -Dye -Electrolyte Interface[END_REF][START_REF] Wang | Enhanced Carrier Transport Distance in Colloidal PbS Quantum-Dot-Based Solar Cells Using ZnO Nanowires[END_REF] Such cells are composed by two electrodes that are put face-to-face and close together (the distance is in the μm range), while the void space in-between is filled by a solution containing a solvent (usually water) and a dissolved redox active electrolyte. In such cells, there is usually one photoelectrode and one conventional metallic electrode. The working photoelectrode is composed by a mesoporous semiconducting material with photoactive particles at the nanometer size, with TiO2 being by far the most extensively used semiconducting material. However, TiO2 has a large band-gap, slightly larger than 3 eV, which lies in the UV region of the electromagnetic spectrum, and therefore does not absorb visible light. In order to obtain visible light excitation, a monolayer of a specific dye that absorbs in the visible region is sorbed at the surface of the semiconducting particles. Thus, upon light excitation of the DSSC, the dye absorbs light and consequently electrons from the HOMO are excited to the LUMO of the molecule (photons must have an energy at least equal to the difference of energy between the LUMO and the HOMO of the dye). Energetically, the LUMO of the molecule must have a higher energy level than the conduction band of the semiconducting material, so that charge injection from the excited dye to the conduction band of the semiconductor can occur. When this is achieved, then the electrons diffuse through the nanoparticles of the semiconductor to reach a transparent conducting substrate (typically Indium Tin Oxide, ITO), and the electrons are transported through an external circuit down to the cathode (also known as back-contact). At the cathode, the electrons reduce the oxidized form of the electrolyte (typically I3 to I -), then the reduced form of the electrolyte diffuses towards the working photo-electrode and reacts with the cationic dye, to regenerate the dye (Fig. 1-1). Extensive research has been done in the domain of DSSC, and still continues. DSSCs offer a promising alternative to harvest light and thus profit from the electric energy these devices can generate.

A second device of interest for light energy conversion is the Photoelectrochemical Cells (PEC). The experimental setup based on a conventional three electrode configuration, comprising a working photoelectrode (photoanode or photocathode, sometimes both), a counter electrode and a reference electrode, as depicted in Fig. 12.

The purpose of the PEC is usually to obtain H2 and O2 separately from water photodissociation. In the PEC, the absorbing material is often the semiconductor itself. [START_REF] Shinde | Onset potential behavior in α-Fe2O3 photoanodes: the influence of surface and diffusion Sn doping on the surface states[END_REF][START_REF] Klotz | Empirical in operando analysis of the charge carrier dynamics in hematite photoanodes by PEIS, IMPS and IMVS[END_REF] However, it is worth noting that photoelectrode architectures exhibiting a dye as the absorber have been reported, [START_REF] Swierk | Design and development of photoanodes for water-splitting dye-sensitized photoelectrochemical cells[END_REF] for example, the recent report on NiO-dye Mo3S4 catalyst PEC for the HER, [START_REF] Click | Membrane-Inspired Acidically Stable Dye-Sensitized Photocathode for Solar Fuel Production[END_REF] where light absorption is not performed by the CHAPTER 1 29 semiconductor but by an organic dye. Another possibility is the surface modification of semiconducting materials with molecular organometallic catalysts having adequate band gap for visible light excitation, [START_REF] Krawicz | Photofunctional Construct That Interfaces Molecular Cobalt-Based Catalysts for H2 Production to a Visible-Light-Absorbing Semiconductor[END_REF] aiming to the HER.

Depending on the conductivity type of the semiconductor used in the PEC, the photoelectrode is either the seat of the OER that forms O2 by water oxidation (in such cases n-type semiconductors, such as hematite [START_REF] Klahr | Water oxidation at hematite photoelectrodes: The role of surface states[END_REF][START_REF] Klotz | Empirical in operando analysis of the charge carrier dynamics in hematite photoanodes by PEIS, IMPS and IMVS[END_REF][START_REF] Dunn | Tin doping speeds up hole transfer during light-driven water oxidation at hematite photoanodes[END_REF] or BiVO4 [START_REF] Liang | Improving BiVO4 photoanodes for solar water splitting through surface passivation[END_REF][START_REF] Trzesniewski | Photocharged BiVO4 photoanodes for improved solar water splitting[END_REF][START_REF] Ma | Dynamics of photogenerated holes in undoped BiVO4 photoanodes for solar water oxidation[END_REF][START_REF] Xiao | Synthesis of a monoclinic BiVO4 nanorod array as the photocatalyst for efficient photoelectrochemical water oxidation[END_REF] as typical examples, are required), or the seat of the HER that forms H2 from water reduction (in such cases, p-type semiconductors such as Rh:SrTiO3, [START_REF] Iwashina | Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation[END_REF] for example, are required). Usual laboratory measurements are performed in cells specially designed for photoelectrochemistry. These cells contain a visible light permeable quartz window, form where illumination goes to the photoelectrode. Besides, the cell is a closed volume and the determinations are constantly performed under inert atmosphere of argon.

In PEC cells, the semiconductor may be in the bulk solid form, and not necessarily in the form of nanoparticles as in DSSC. Bulk semiconductors, when in contact with an electrolyte solution, develop a space charge inside the semiconductor, where an electric field is developed. This is because the concentration of charge carriers is significantly less than in metals. Consequently, after light excitation, the photogenerated exciton separates into electron/hole pairs which are driven apart by the electric field inside the semiconductor. The process is therefore different from the charge separation processes in DSSC, where the nano-size of the semiconducting particles does not allow the development of a space charge, and therefore charge separation occurs by diffusion of photogenerated carriers. [START_REF] Lewerenz | Photoelectrochemical Water Splitting Materials, Processes and Architectures[END_REF] This thesis is completely devoted to the analysis of PEC systems, and not to the development of DSSC. Given the importance of heterogeneous processes in PEC for this thesis, a detailed discussion of these issues shall be developed in the next section.

Electrochemistry of bulk semiconducting photoelectrodes

In this section, the behavior of p-type semiconductors shall be described (the behavior of n-type semiconductors is analogous in an opposite manner). When an interface between a semiconducting electrode and a solution is formed, the Fermi levels (EF) in both phases are not equal. This is the driving force that leads to charge transfer, in order to equalize the EF (equilibrium). Consequently, there is a bending of the energy bands in the semiconductor close to the interface. In the case of a p-type semiconductor, the EF of the semiconductor is usually lower than the EF of electrons in solution (determined by the redox couple in solution), causing an electron transfer from the solution to the semiconductor. The excess of electrons at the surface of the p-type semiconductor causes a downwards band bending. In these conditions, the surface of the semiconductor is depleted from majority carriers (holes for p-type semiconductors) and the region where this happens is commonly called the depletion layer. In the depletion layer there is an electric field. The region inside the semiconductor where an electric field exists is known as the space charge region, and has an associated capacitance (𝐶 𝑠𝑐 ).

On the other hand, the region of the solution close to the interface where the electric potential drops is called the Helmholtz layer and has an associated capacitance (𝐶 𝐻 ).

Excluding heavily doped semiconductors, 𝐶 𝐻 is much higher than 𝐶 𝑠𝑐 . Therefore, most of the overall applied potential across the interface, drops in the space charge region and not in the solution side of the interface, i.e. 𝜙 𝑠𝑐 ≫ 𝜙 𝐻 , where 𝜙 𝑠𝑐 stands for the potential drop within the space charge, and 𝜙 𝐻 represents the potential drop in the Helmholtz layer.

When an external electric bias is applied to a semiconductor|electrolyte interface, the band-edges in contact with the electrolyte are pinned (phenomenon referred to as Fermi level pinning), while the bands in the bulk of the material move depending on the applied bias. Therefore, band bending can be modified depending on the applied electrode potential. When a semiconducting electrode is illuminated by light with energy ℎ𝜈 higher than its band gap, charge separation occurs and an electron-hole pair is consequently generated. [START_REF] Fabian | Particle Suspension Reactors and Materials for Solar-Driven Water Splitting[END_REF][START_REF] Hisatomi | Recent advances in semiconductors for photocatalytic and photoelectrochemical water splitting[END_REF][START_REF] Ran | Earth-abundant cocatalysts for semiconductor-based photocatalytic water splitting[END_REF][START_REF] Hamann | Measurement of the driving force dependence of interfacial charge-transfer rate constants in response to pH changes at n-ZnO/H2O interfaces[END_REF] The direction of the photoexcited electrons depends on band bending.

For example, at the electrode potential where there is no net electric field inside the semiconductor, the material is in flat-band conditions (Fig. 123) and no photocurrent is observed because there is no electric field to drive electron-hole separation. Conversely, if a positive potential is applied, there is an accumulation of majority carriers at the interface (holes for a p-type semiconductor) and an accumulation layer is formed. Under these conditions, p-type semiconductors behave as dark anodes. [START_REF] Memming | Semiconductor Electrochemistry[END_REF] Photoexcitation by light with energy larger than the band-gap is possible, but the photogenerated current of minority carriers (electrons for p-type semiconductors) flows to the bulk due to band bending. On the other hand, at electrode potentials more negative than the flat-band potential, there is a depletion of majority carriers (holes for p-type semiconductors) and a downwards band bending. Consequently, minority carriers (electrons for p-type semiconductors) can tranfer to the electrolyte to react with redox species in the nearby (Fig. 123). There is another possibility (Fig. 123), when very negative potentials are applied to the photoelectrode, beyond the extrinsic level, the depletion of majority carriers is so strong, that minority carriers themselves can promote charge transfer reactions, in addition to the characteristic photocurrents under illumination. Such condition is known as inversion layer, and has the particularity that the surface of a ptype semiconductors behaves like an n-type semiconductor. [START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF] This fact shall be extensively discussed during the presentation of the results of Chapter 3.

Kinetic model of Photoelectrochemical Impedance

𝑍 = 𝑈 Ĩ ̃ (1-1)
EIS analysis has been extended to photo-electrochemical interfaces. The heterogeneous kinetics of charge transfer in semiconducting photoelectrodes can be analyzed by Photoelectrochemical Impedance Spectroscopy (PEIS) which is also a powerful technique. The purpose of PEIS is to record a usual EIS spectrum at a constant level of illumination (Fig. 1234). Therefore, besides the real and imaginary parts of the impedance, light intensity is another experimental variable to control.

In the case where 𝐶 𝑠𝑐 ≪ 𝐶 𝐻 , PEIS spectra may be fitted to eq. 1-2 and therefore to obtain semiquantitative evaluation of relevant charge transfer and recombination kinetic parameters (Fig. 12345). [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF][START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF]

𝑍(𝜔) = 𝑅 + 1 𝑖𝜔𝐶 𝑠𝑐 +( 𝑞 𝑘 𝐵 𝑇 )𝐼 0 ( 𝑘 𝑟 𝑘 𝑟 +𝑘 𝑡 )( 𝑘 𝑡 +𝑖𝜔 𝑘 𝑟 +𝑘 𝑡 +𝑖𝜔 ) (1-2)
In eq. 1-2 𝑍(𝜔) represents the impedance, 𝑅 corresponds to the solution resistance, 𝑖 is the imaginary unit, 𝜔 stands for the angular frequency of the ac perturbation, 𝐶 𝑠𝑐 is the

𝑓 𝐿𝐹 𝑀𝐴𝑋 = 𝑘 𝑡 (1-3)
The low and high frequency limits of the impedance in the low frequency relaxation are given by eqs. 1-4 and 1-5, respectively (Fig. 1-6 b, right pannel). Therefore, the ratio (𝑍 1 -𝑅)/(𝑍 2 -𝑅) (eq. 1-6) allows the determination of 𝑘 𝑟 once 𝑘 𝑡 is known. Besides the kinetic description of heterogeneous charge transfer at illuminated semiconducting electrodes described in the prvious section, the analysis of PEIS spectra can be performed by means of electric (equivalent circuit). In general, it is possible to find analogies between kinetic and electric treatments of PEIS data because the value of a circuit element (a resistance or capacitance, for example) can be composed of several charge transfer and recombination parameters. [START_REF] Lewerenz | Photoelectrochemical Water Splitting Materials, Processes and Architectures[END_REF][START_REF] Bertoluzzi | Charge transfer processes at the semiconductor / electrolyte interface for solar fuel production: insight from impedance spectroscopy[END_REF][START_REF] Bertoluzzi | Equivalent Circuit of Electrons and Holes in Thin Semiconductor Films for Photoelectrochemical Water Splitting Applications[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF] Current literature regarding the interpretation of PEIS in the framework of illuminated semiconducting photoelectrodes does not show preferences for a particular approach. Therefore, both kinetic and electric treatments are completely valid and can offer a coherent interpretation of the complex phenomena regarding heterogeneous charge transfer kinetics.

Some equivalent circuit models available in the literature are shown in Fig. 1-7. 17,69-72 A detailed discussion of each equivalent circuit is outside the scope of this thesis, because the analysis of PEIS was performed using a kinetic model only. Nevertheless, the meaning of each of the equivalent circuits shall be commented succinctly. Fig. 1234567a represents an equivalent circuit which is entirely alike to the kinetic model presented in the previous section. The relation between kinetic and electric parameters is given by the following equations.

𝐶 𝐻𝐹 = 𝐶 𝑆𝐶 (1-11)
Where 𝑅 𝐿𝐹 and 𝐶 𝐿𝐹 represent the resistance and capacitance associated to the low frequency relaxation; 𝑅 𝐻𝐹 and 𝐶 𝐻𝐹 stand for the resistance and capacitance associated to the high frequency relaxation. The meaning of all other symbols was discussed in the previous section. A Nyquist plot showing the high and low frequency relaxations is depicted in Fig. 12345678.

It is important to note that the capacitance associated to the low frequency relaxation does not correspond to the capacitance of the Helmholtz layer (CH). However, the seminal work of Scheffold makes such association, [START_REF] Schefold | Impedance and intensity modulated photocurrent spectroscopy as complementary differential methods in photoelectrochemistry[END_REF] an interpretation that has been abandoned today. [START_REF] Lewerenz | Photoelectrochemical Water Splitting Materials, Processes and Architectures[END_REF][START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF] Fig states is relevant. [START_REF] Klahr | Water oxidation at hematite photoelectrodes: The role of surface states[END_REF] The equivalent circuit shown in Fig. 1-7 e describes three relaxations instead of two. [START_REF] Bertoluzzi | Equivalent Circuit of Electrons and Holes in Thin Semiconductor Films for Photoelectrochemical Water Splitting Applications[END_REF] The relaxation at the highest frequencies has been attributed to the reversible trappingdetrapping process of holes and electrons by surface states, while the middle and low frequency relaxations were associated to charge transfer and recombination from the surface states band and valence band, respectively. [START_REF] Bertoluzzi | Equivalent Circuit of Electrons and Holes in Thin Semiconductor Films for Photoelectrochemical Water Splitting Applications[END_REF] The equivalent circuit depicted in Fig. 1234567f is the Randles circuit, and has also been employed to treat illuminated semiconducting photoelectrodes. [START_REF] Memming | Semiconductor Electrochemistry[END_REF] However, such circuit is far too simplistic to obtain a global view of heterogeneous charge transfer and recombination processes occurring at illuminated semiconductors.

From a chemical perspective, it is easier and more intuitive to make a kinetic analysis based on rate constants than based on resistances. Furthermore, several equivalent circuits can produce the same relaxation pattern. Thus, the same PEIS data can be treated in several manners, which contributes to the richness, flexibility, and perhaps ambiguity in electric analysis of PEIS. Consequently, the choice of an electric model is crucial to make a consistent interpretation of experimental results. A typical example of this can be appreciated in a recent publication, [START_REF] Bertoluzzi | Charge transfer processes at the semiconductor / electrolyte interface for solar fuel production: insight from impedance spectroscopy[END_REF] where the authors discuss two different (but related) interpretations of the same circuit model, to describe heterogeneous dynamics in thin film semiconducting photoelectrodes.

The equivalent circuit interpretation of PEIS is so rich that, in a short period of time, the same authors analyze their data with similar electric models while giving different names to the fitting parameters. [START_REF] Bertoluzzi | Charge transfer processes at the semiconductor / electrolyte interface for solar fuel production: insight from impedance spectroscopy[END_REF][START_REF] Bertoluzzi | Equivalent Circuit of Electrons and Holes in Thin Semiconductor Films for Photoelectrochemical Water Splitting Applications[END_REF] For example, some interfacial capacitances have been referred to as chemical capacitance (Cμ) [START_REF] Bertoluzzi | Charge transfer processes at the semiconductor / electrolyte interface for solar fuel production: insight from impedance spectroscopy[END_REF] or bulk capacitances (Cbulk). [START_REF] Klahr | Water oxidation at hematite photoelectrodes: The role of surface states[END_REF] HER at open circuit conditions, at the surface of p-type Si. [START_REF] Babenko | Kinetics of the photoelectrochemical evolution of hydrogen at p-type Si[END_REF] Certainly, the kinetics of charge transfer and recombination can be estimated through the following equations [START_REF] Babenko | Kinetics of the photoelectrochemical evolution of hydrogen at p-type Si[END_REF][START_REF] Ponomarev | Theoretical analysis of the laser-induced phototransient response of semiconductor | electrolyte circuits with 'currentdoubling' reactions[END_REF] (

1 𝑈 0 𝑑𝑈 𝑑𝑡 ) 𝑡=0 = 𝑘 𝑡 𝐶 𝑆𝐶 𝐶 𝐻 -𝑘 𝑟 (1-12) 𝑈 𝑓 𝑈 0 = 𝑘 𝑡 𝑘 𝑡 +𝑘 𝑟 (1-13)
Where 𝑈 0 is the photopotential when the light is switched off, 𝑈 𝑓 is the final potential after the decay with the light switched off, and A complete discussion of the differential equations leading to these results is not the purpose of this work, and the interested reader may consult the original publications. [START_REF] Babenko | Kinetics of the photoelectrochemical evolution of hydrogen at p-type Si[END_REF][START_REF] Ponomarev | Theoretical analysis of the laser-induced phototransient response of semiconductor | electrolyte circuits with 'currentdoubling' reactions[END_REF] It is sufficient to say that the kinetic scheme discussed for PEIS (Fig. 12345) is the same employed for this derivation. It is interesting to note that the OCPD method has not been frequently employed to unravel the photoelectrochemical kinetics at open circuit conditions for illuminated semiconducting electrodes in a PEC configuration. In contrast, photopotential decays have been much more employed to study the carrier dynamics in DSSC. [START_REF] Krüger | Charge Transport and Back Reaction in Solid-State Dye-Sensitized Solar Cells : A Study Using Intensity-Modulated Photovoltage and Photocurrent Spectroscopy[END_REF][START_REF] Schlichthörl | Band Edge Movement and Recombination Kinetics in Dye-Sensitized Nanocrystalline TiO2 Solar Cells : A Study by Intensity Modulated Photovoltage Spectroscopy[END_REF][START_REF] Bisquert | Determination of Rate Constants for Charge Transfer and the Distribution of Semiconductor and Electrolyte Electronic Energy Levels in Dye-Sensitized Solar Cells by Open-Circuit Photovoltage Decay Method[END_REF]

Intensity Modulated Photovoltage Spectroscopy (IMVS)

Intensity modulated photovoltage spectroscopy (IMVS) has been a ubiquitous technique used mostly for the characterization of dye-sensitized solar cells. [START_REF] Krüger | Charge Transport and Back Reaction in Solid-State Dye-Sensitized Solar Cells : A Study Using Intensity-Modulated Photovoltage and Photocurrent Spectroscopy[END_REF][START_REF] Schlichthörl | Band Edge Movement and Recombination Kinetics in Dye-Sensitized Nanocrystalline TiO2 Solar Cells : A Study by Intensity Modulated Photovoltage Spectroscopy[END_REF][START_REF] Bisquert | Determination of Rate Constants for Charge Transfer and the Distribution of Semiconductor and Electrolyte Electronic Energy Levels in Dye-Sensitized Solar Cells by Open-Circuit Photovoltage Decay Method[END_REF][START_REF] Set | Analytical modeling of intensity-modulated photovoltage spectroscopic responses of organic bulk-heterojunction solar cells[END_REF][START_REF] Liu | Characterization of Photocurrent Generation Dynamics in Polymer Solar Cells Based on ZnO / CdS-Core / Shell Nanoarrays by Intensity Modulated Photocurrent Spectroscopy : Theoretical Modeling[END_REF] IMVS consists in illuminating a photoelectrode, kept at open-circuit, with constant bias light while a small level of illumination is periodically modulated ( Φ ̃) at different frequencies. Such periodic irradiation causes the development of an oscillating photopotential (𝑈 ̃). IMVS data is thus analyzed through a transfer function as shown in eq. 1-14

𝐻 = 𝑈 Φ ̃ (1-14)
Where 𝐻 stands for the transfer function for IMVS, 𝑈 ̃ is the modulated photovoltage, and Φ ̃= 𝐼 0 (1 + 𝑒 -𝑖𝜔𝑡 ) is the modulation of light, while 𝐼 0 represents the current of photoexcited minority carriers, which depends on the width of the space charge and the level of illumination.

A scheme of the experimental setup used to perform IMVS measurements is depicted in Fig. 1-10 a. Indeed, there is a led that is connected to an ac generator that allows the modulation of light. The modulated light arrives to a beam splitter that splits the light intensity, and delivers half for the PEC and half for a photodetector that is located outside the PEC. Note that the light intensity that is actually being measured is at the photodetector, and not at the photoelectrode surface. Therefore, it is expected that the light intensity actually felt by the working photoelectrode will be lower, due to reflection losses caused by the quartz window of the PEC.

Inside the PEC, the photosensitive working electrode then receives the modulated light, and therefore an oscillating photovoltage (𝑈 ̃) is thus measured through the external wiring.

Fig. 1-10 b depicts a scheme of a typical IMVS response, obtained in our laboratory with a solaronix test cell. [START_REF]Titanium dioxide[END_REF][START_REF][END_REF][80] Observe how the IMVS response is very similar to a PEIS response, at least for DSSC.

In the context of DSSC systems, IMVS offers information regarding the electron lifetime in the cell ( 𝜏 𝑛 , Fig. 1 Surprisingly, the use of IMVS in the framework of PEC has been very limited over the last 30 years of development of light modulated photoelectrochemical spectroscopy. To the best of our knowledge, there is only one report of IMVS applied to PEC for water oxidation with hematite photoelectrodes. [START_REF] Klotz | Empirical in operando analysis of the charge carrier dynamics in hematite photoanodes by PEIS, IMPS and IMVS[END_REF] In such study, the authors employed an empirical method to analyze IMVS, called Distribution of Relaxation Times (DRT). In this bibliographic overview we shall no devote further space to describe such DRT theory because we did not employ this method to analyze our experimental data.

Advancing some of the results obtained in this thesis with IMVS, it is worth to comment that our results are completely different to those reported up until now, and its explanation and theoretical justification was performed by using the classical kinetic model based on differential equations.

Heterogeneous mechanisms of the Hydrogen Evolution Reaction (HER) and the Oxygen Evolution Reaction (OER)

Photoelectrodes in PEC cells are used mainly for two reactions of utmost interest, At neutral pH, the HER has been proposed to proceed via a discharge step (Volmer reaction) followed either by an electrochemical desorption step (Heyrovsky reaction) or a recombination step (Tafel reaction). [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF] Volmer reaction

𝐻 2 𝑂 + 𝑒 -+ 𝑀 = 𝑀 -𝐻 + 𝑂𝐻 - (1-15)
Heyrovsky reaction

𝑀 -𝐻 + 𝐻 2 𝑂 + 𝑒 -= 𝐻 2 + 𝑂𝐻 -+ 𝑀 (1-16)
Tafel reaction

2𝑀 -𝐻 = 𝐻 2 + 2𝑀 (1-17)
Where M represents an active site at the surface, and all other symbols have their usual meaning.

If the Volmer reaction is the rate determining step (rds), then the observed Tafel slope shall be of 120 mV/dec. However, if the rds is the Heyrovsky reaction, the displayed Tafel slope will be 40 mV/dec, and if the Tafel reaction is the rds, the appreciated Tafel slope will be 30 mV/dec. Currently, the scientific community has a general agreement regarding the heterogeneous mechanism for the HER. Though, the recent microkinetic analysis has shown that a Tafel slope of 120 mV/dec may be also obtained when the Heyrovsky reaction is rate determining, [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF] and there is a high surface density of adsorbed H atoms. As a consequence, a slope of 120 mV/dec may originate either if the Volmer reaction is the rds, or if the Heyrovsky reaction, in the high coverage region of H (𝜃 𝐻 > 0.6), is the rds.

Conversely, the OER has been studied for over 70 years. [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF][START_REF] Bockris | Kinetics of activation controlled consecutive electrochemical reactions: anodic evolution of oxygen[END_REF][START_REF] Lyons | Mechanism of oxygen reactions at porous oxide electrodes. Part 2 -Oxygen evolution at RuO2, IrO2 and IrxRu1-xO2 electrodes in aqueous acid and alkaline solution[END_REF][START_REF] Defaria | Electrocatalytic properties of ternary oxide mixtures of composition Ru0.3Ti(0.7-x)CexO2: oxygen evolution from acidic solution[END_REF][START_REF] Hu | Oxygen evolution reaction on IrO2-based DSA type electrodes: kinetics analysis of Tafel lines and EIS[END_REF][START_REF] Riddiford | Mechanisms for the evolution and ionization of oxygen at platinum electrodes[END_REF][START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF][START_REF] Bockris | Mechanism of Oxygen Evolution on Perovskites[END_REF] , and still recently there are contributions regarding the multistep mechanism of the OER. For example, two recent publications present different mechanisms for this multistep reaction. [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF][START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF] One of these publications proposes the following sequence in alkaline solutions [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF] 𝑀 + 𝑂𝐻 -= 𝑀𝑂𝐻 + 𝑒 - (1-18)

𝑀𝑂𝐻 + 𝑂𝐻 -= 𝑀𝑂 + 𝐻 2 𝑂 + 𝑒 - (1-19) 𝑀𝑂 + 𝑂𝐻 -= 𝑀𝑂𝑂𝐻 + 𝑒 - (1-20) 𝑀𝑂𝑂𝐻 + 𝑂𝐻 -= 𝑀𝑂𝑂 -+ 𝐻 2 𝑂 (1-21) 𝑀𝑂𝑂 -= 𝑀 + 𝑂 2 + 𝑒 - (1-22)
This mechanism is complex, and it has been clearly shown through simulation that the observed Tafel slopes depend on the surface coverage of the intermediates and on the applied overpotential. Simulation results show that Tafel plots may have 21, 22, 30, 40 or 120 mV/dec, depending on the overpotential and the rds of the reaction, as depicted in Figure 4 (a) to (f) of reference 81. For its relevance to the analysis of the OER in this thesis, it is worth to mention that this model is also able to account for a Tafel slope of 60 mV/dec, but in very specific conditions and within a multi-slope current-voltage curve, as depicted in Figure 4 d of reference 81.

In the other recent publication [START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF] the authors based their analysis on a seminal publication of John Bockris. [START_REF] Bockris | Kinetics of activation controlled consecutive electrochemical reactions: anodic evolution of oxygen[END_REF] In such study [START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF] the following steps are proposed without mentioning the pH. Though, the presence of water in the reactants of the chemical equations suggests that this mechanism applies for neutral pH.

𝑀 + 𝐻 2 𝑂 = 𝑀𝑂𝐻 + 𝐻 + + 𝑒 - (1-23) 𝑀𝑂𝐻 = 𝑀𝑂 + 𝐻 + + 𝑒 - (1-24) 2𝑀𝑂 = 𝑂 2 + 2𝑀 (1-25)
In this case, the simulation study revealed that a Tafel slope of 120 mV/dec is obtained when reaction 1-23 is rds, while a slope of 40 mV/dec is appreciated when reaction 1-24 is rds. Also, dual Tafel slopes can be observed, when the rds switches from reaction 1-24 at low overpotentials to reaction 1-23 at higher overpotentials (see Figure 1 in reference 87). On the other hand, when reaction 1-25 is the rds, the observed Tafel slope depends on the surface coverage of the intermediates. Indeed, when 𝜃 𝑂𝐻 and 𝜃 𝑂 ≈ 0, simulation predicts a Tafel slope of 30 mV/dec, but when 𝜃 𝑂𝐻 ≈ 1 and 𝜃 𝑂 ≈ 0, a Tafel slope of 60 mV/dec is predicted. This mechanism has many other subtleties, for example, depending on the rate parameters a dual Tafel slope of 30 and 60 mV/dec can be obtained if surface coverages give 𝜃 𝑂𝐻 and 𝜃 𝑂 ≈ 0 at low overpotentials and 𝜃 𝑂𝐻 ≈ 1 and 𝜃 𝑂 ≈ 0 at high overpotentials. The authors further note that it is possible to obtain a Tafel slope of 40 mV/dec (which is more typical when the rds is reaction 1-24, if reaction 1-23 is rds and 𝜃 𝑂𝐻 is high. For the cases where reaction 1-25 is the rds and 𝜃 𝑂 ≈ 1, a limiting current was observed in the simulations.

General characteristics of SrTiO3 and Rh:SrTiO3 semiconducting materials

The SrTiO3 material, thoroughly employed in this thesis, presents cubic perovskite structure, as shown in Fig. 1-12 a and b (space group P m -3 m; a = b = c = 3.905 Å; α = β = γ = 90°, cell volume = 59.547 Å 3 ). 101 Non-doped SrTiO3 possesses n-type conductivity and has a band gap of 3.2 eV. [102][103][104] Such band gap lies in the UV region of the electromagnetic spectrum, therefore, much experimental and theoretical work can be found in current literature concerning the photocatalytic properties of SrTiO3 with different dopants [START_REF] Iwashina | Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation[END_REF][START_REF] Jia | BiVO4-Ru/SrTiO3:Rh composite Z-scheme photocatalyst for solar water splitting[END_REF][START_REF] Chen | Theoretical Investigation of the Metal-Doped SrTiO 3 Photocatalysts for Water Splitting[END_REF][102][103][104][105][106][107][108][109][110][111][112] with the purpose to decrease the band gap of the material. To the best of our knowledge, there is no previous study devoted to the determination of the photoelectrochemical kinetics of the heterogeneous reaction occurring at the surface of SrTiO3based photoelectrodes.

These facts prompted us to utilize in this thesis the novel advanced semiconducting material (Rh doped SrTiO3) that absorbs visible light, and has been shown to act as a hydrogen evolving photo-catalyst [START_REF] Iwashina | Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation[END_REF][START_REF] Jia | BiVO4-Ru/SrTiO3:Rh composite Z-scheme photocatalyst for solar water splitting[END_REF][START_REF] Wang | Scalable water splitting on particulate photocatalyst sheets with a solar-to-hydrogen energy conversion efficiency exceeding 1%[END_REF][START_REF] Zhang | Photoelectrochemical Water Splitting System-A Study of Interfacial Charge Transfer with Scanning Electrochemical Microscopy[END_REF] because the absolute energy of its conduction band is around 0.7 eV higher than the redox potential of the couple H2|H2O (see Figure 10 within reference 104).

Interestingly, it has been shown that doping changes not only the band gap of the material, but also can tune the type of conductivity in the material. For example, doping of SrTiO3 with Ir keeps n-type conductivity with the characteristic anodic photocurrent, 102 while doping with Rh switches the properties of the SrTiO3 material to display p-type conductivity and therefore cathodic photocurrents. [START_REF] Iwashina | Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation[END_REF] This behavior is due to the fact that in-band Ir energetic levels are around 0.5 eV higher in energy than Rh inband states. Consequently, the Fermi level of Ir:SrTiO3 is closer to the conduction band, thereby the n-type conductivity in the material. 102 In this thesis, the Rh:SrTiO3 material shall be employed extensively. In such material the energy difference between Rh in-gap states and the conduction band is 2.4 eV, as observed before in soft X-ray spectroscopy, 103 which lies well in the visible region of the electromagnetic spectrum. In the resting state, Rh:SrTiO3 material possesses Rh in the +4 oxidation state in the form of a dark grey solid, 103,112 but during the HER, a photoreduction occurs and Rh exists therefore in the +3 oxidation state, which is a yellow solid that is more active towards the HER. 102,103 In the context of this work it is instructive to review previously published EIS results of SrTiO3based photoelectrodes. 113,114 In both studies a relaxation was fully observed at high frequencies while at low frequencies the authors observed an increase in the impedance but the LF semicircle did not appear. Unfortunately, the reported EIS data 113,114 are depicted only in the Nyquist representation and with no frequency indications, and Bode plots were not represented. An inspection of the experimental part revealed that in reference 113 the frequency window was between 100 kHz and 10 mHz.

However in reference 114 the authors did not provide the range of frequencies tested.

The extraction of qualitative conclusions from these two studies is further troubling since the axes in the Nyquist representations ( These studies did not apply neither a kinetic model nor an electric model to fit the EIS responses. The authors limited their conclusions about EIS to the interpretation of the usual Randles circuit. Such interpretation, as recognized by Rüdiger Memming, is valid in the context of semiconducting electrodes, [START_REF] Memming | Semiconductor Electrochemistry[END_REF] but is far too limited to exploit all the information that EIS can give regarding the heterogeneous processes occurring at the interface of illuminated semiconductors. [START_REF] Klahr | Water oxidation at hematite photoelectrodes: The role of surface states[END_REF][START_REF] Shinde | Onset potential behavior in α-Fe2O3 photoanodes: the influence of surface and diffusion Sn doping on the surface states[END_REF][START_REF] Klotz | Empirical in operando analysis of the charge carrier dynamics in hematite photoanodes by PEIS, IMPS and IMVS[END_REF][START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF][START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF][START_REF] Bertoluzzi | Equivalent Circuit of Electrons and Holes in Thin Semiconductor Films for Photoelectrochemical Water Splitting Applications[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF][START_REF] Schefold | Impedance and intensity modulated photocurrent spectroscopy as complementary differential methods in photoelectrochemistry[END_REF]115 In any case, if EIS results already reported 113 were to be analyzed in the framework of a kinetic model (Fig. 12345), it could be said that the LF relaxation did not fully develop in a frequency sweep down to 10 mHz, and therefore the phenomenological charge transfer rate constant reflects a slow process and should be smaller than 0.01 s -1 . Certainly, in order to fully observe the LF relaxation, it should be necessary to descend to lower frequencies to fully appreciate the LF relaxation, as will be shown in Chapter 3.

General characteristics of clathrochelates

Molecular electrocatalysis aiming at energy relevant reactions is nowadays a hot research topic due to the urgent need to find clean and renewable sources of energy. 116 The possible utilization of dihydrogen as an energy carrier is tempting and promising.

So far, a truly efficient process to evolve dihydrogen from acidic electrolytes without platinum-based electrocatalysts has not been discovered. That is the cause of the numerous efforts devoted to develop electrocatalysts based on diverse materials such as Fe, Ni, Ru, Re, Mo etc. 117-123 Among the various alternatives explored as possible molecular catalysts for the hydrogen evolution reaction (HER) in the homogeneous phase, there are several Co, Ni and Fe based diglyioxyme complexes 124 or Ni dithiolenes 125 that demonstrated interesting properties.

Tris-dioximate metal clathrochelates such as the cobalt species shown in Fig. 1-13 are a family of metal complexes that have been shown to be efficient homogeneous electrocatalysts for the HER, and have been shown to be pre-catalysts for the deposition of active Co-based particles in glassy carbon electrodes under bulk electrolysis conditions. [126][127][128][129] Clathrochelates are basically polymacrocyclic cage compounds which are able to stabilize the low oxidation states of transition metals (e.g. Co or Fe), thereby offering interesting possibilities to act as hydrogen-producing catalysts with an appealing potential as molecular electrocatalysts. 126,127 In this context, the clathrochelate family of organometallic compounds is very versatile from a chemical and electrochemical perspective. [130][131][132][133] The physical nature of clathrochelates at room temperature is in the form of a stable brown-red solid. This has allowed its analysis by XRD. and I. Nevertheless, it has been long recognized that the Co I species is catalytically active and responsible for the observed hydrogen evolution activity. 127,130 These facts have led to their successful implementation in practical devices such as polymer exchange membrane (PEM) cells. [134][135][136] Though, a systematic approach to elucidate the impact of different substituents in the organic cage upon the electrochemical characteristics of the clathrochelates is still somewhat incomplete. Even though DFT studies of the geometric and electronic structures of these molecules have already been reported in the literature, 129,137 a thorough exploration of the HER mechanism has received scarce attention from a theoretical perspective. The only attempt to rationalize HER catalyzed by cobalt clathrochelates was presented few years ago. 129 In such study, DFT calculations on the reduced form of a model complex was reported, considering single protonation either on Co or on the iminic C, while neglecting other possible protonation sites, double protonation, or bimolecular pathways.

In summary, the qualitative prove for the electrocatalytic capabilities of clathrochelates is well established. [126][127][128] Some previous experimental work has been performed with inorganic acids dissolved in water, 126,128 consequently, any mechanistic analysis is obscured by the two proton sources present in the system. Future experimental mechanistic studies on clathrochelates should be performed with defined organic acids of varying strength, in order to provide experimental support for the mechanistic possibilities discussed in this thesis. Where 𝐸 𝑘 represents the kinetic energy of the photoelectron, ℎ𝜈 is the energy of the Xrays, 𝐸 𝑏 is the binding energy of the core-electron that was ejected by the X-ray, and 𝑊 is a work function that is characteristic of the instrument.

The XPS technique is sensitive to the element type, because each element has a characteristic binding energy, which permits its identification in the sample.

Furthermore, X-rays are able to penetrate deeply in the sample, however, the photoelectrons that are actually able to escape from the sample come from no deeper than around 10 nm, 138 therefore, XPS is a technique for surface analysis and does not provide information of the chemical composition in the bulk.

Trends in binding energy (BE) can be established. For example, an electron in an atom shall be more strongly bound (i.e., will possess higher BE) if it is closer to the nucleus.

Consequently, for the same element, photoelectrons coming from a K shell will have a greater BE than photoelectrons coming from L shells. Moreover, for different elements and equal atomic shell, the greater BE shall be observed in the element with larger atomic number (Z), due to the greater electrostatic interaction between the nucleus and the electrons in the shell. Furthermore, when a certain atom is bound to another atom of greater electronegativity, then the molecular orbitals localized in the former will be stabilized, and the observed BE will be larger. Therefore, oxidation and reduction are easily observed in XPS because when an atom is oxidized, it loses electron density and the remaining electrons feel the nuclear charge to a greater extent, which is observed by an increase in BE. The opposite holds for reduction.

X-ray photoelectron spectroscopy has been performed on powders of several clathrochelates in order to analyse their chemical composition. Furthermore, the XPS spectra of all the studied Co clathrochelates contained weak additional peaks assigned to the shake-up satellites associated with molecular paramagnetism. 144 These results indicated that the studied clathrochelates contained an encapsulated Co II ion as the central atom.

X-ray diffraction

Crystalline solid materials possess a structure where the atoms are set in periodic spatial (1-27)

X-ray diffraction is the main means to determine the structure of crystalline materials.

The simplest model to explain X-ray diffraction was proposed by Bragg in 1913. Bragg assumed that the X-rays were scattered by a set of parallel planes of atoms. Each plane is a source of scattered radiation and the diffraction pattern is observed when the spacing between planes is in the order of the wavelength of the radiation. Indeed, when the phases of scattered X-rays coming from different planes differ in an integer number of X-ray wavelengths, these two scattered beams interfere in a constructive manner and a diffraction peak is thus observed. Following geometric considerations, the path Where 𝑑 ℎ𝑘𝑙 is the distance between parallel planes in the lattice, defined by (hkl) Miller indices, λ corresponds to the wavelength of the X-ray, while 𝜃 ℎ𝑘𝑙 corresponds to the angle of the scattered radiation.

In summary, different sets of planes in a particular crystal lattice, cause a unique diffraction patter, which is typical of the compound.

X-ray absorption spectroscopy (XAS)

X-ray absorption spectroscopy comprises several techniques, the most common being X-ray Absorption Near Edge Structure (XANES) and Extended X-ray Absorption Fine XAS is analogous to UV-Vis optical spectroscopy, in the sense that in both cases the absorption coefficient 𝜇(𝐸), which is a function of the energy of the electromagnetic wave, is experimentally measured. In XAS, there is a Lambert-Beer type relation, analogous to UV-Vis spectroscopy (eq. 1-29)

𝐼 𝐼 0 ∝ exp (-𝜇(𝐸)) (1-29)
Where 𝐼 is the transmitted photon flux, 𝐼 0 stands for the incident photon flux, 𝜇(𝐸)

represents the energy dependent absorption coefficient. In is worth noting that XAS can be also measured in fluorescence mode, but the treatment described here does not change.

Optical UV-Vis spectroscopy and X-ray Absorption Near Edge Structure (XANES) have a similar ground since the absorption coefficient is determined by Fermi's golden Conversely, in EXAFS spectroscopy the electromagnetic wave spans various keV beyond the absorption edge. Therefore, such high energies are able to excite core electron levels (commonly K (1s), L1 (2s) or L2 (2p) shells), which is the initial bounding state Ψ 𝑖 . Certainly, the X-ray energy is large enough so that the electron is ejected from the molecule and travels through the material in the form of a photoelectron wave that is not a bound level, but continuum levels with large kinetic energy ( Ψ 𝑓 ), furthermore a core vacancy remains, which interacts with the photoelectron.

Thus, the main difference between UV-Vis and EXAFS spectroscopy is the nature of the initial and final states. Indeed, in UV-Vis spectroscopy the energy of the electromagnetic wave is never higher than around 3.4 eV, which determines that both Ψ 𝑖 and Ψ 𝑓 are bound molecular states close to the valence orbitals. Therefore, UV-Vis and XANES spectroscopies possess similar selection rules.

In the case of EXAFS, the outgoing photoelectron travels through the material as a wave, and scatters back toward the photoabsorber atom when it strikes nuclei of neighboring atoms. The complex quantum interference between the outgoing photoelectron wave and the back-scattered photoelectron wave originates an oscillatory behavior of the absorption coefficient 𝜇.

The travel of the photoelectron wave can be from the photoabsorber directly to a neighbor, and then back to the photoabsorber. In such case, the path is referred to as single scattering. Moreover, the travel of the photoelectron wave can be from the photoabsorber, to a neighbor 1, then to a neighbor 2, and then back to the photoabsorber.

Those scattering paths, involving more than one neighbor, are referred to as multiple scattering paths.

Thus, oscillatory signal that occurs at around 0.1 keV beyond the edge step is the actual EXAFS signal 𝜒, which is extracted from the absorption coefficient according to eq. 1-

31

𝜒(𝐸) = 𝜇(𝐸)-𝜇 0 (𝐸) Δ𝜇 (1-31)
Where 𝜒(𝐸) is the normalized oscillatory part of the absorption coefficient is, 𝜇(𝐸) is the measured absorption coefficient, 𝜇 0 (𝐸) stands for the absorption coefficient without the contribution of scattering by neighboring atoms (this quantity is approximated by a spline function), and Δ𝜇, which is the edge step.

The EXAFS spectrum is analyzed according to the general EXAFS equation (eq. 1-32) 147

𝜒(𝑘) = 𝑆 0 2 ∑ 𝑁 |𝑓 𝑒𝑓𝑓 (𝑘)| 𝑘𝑅 2 sin (2𝑘𝑅 + 𝜙 𝑘 )exp (-2𝑘𝑅/𝜆 𝑘 )exp (-2𝜎 2 𝑘 2 ) 𝑅 (1-32)
Where 𝜒(𝑘) is the EXAFS amplitude; 𝑘 is the wave-vector calculated according to 𝑘 = CHAPTER 1 61 √(2𝑚 𝑒 (𝐸 -𝐸 0 ))/ħ 2 , with 𝑚 𝑒 being the mass of the electron, 𝐸 0 the energy of the edge and 𝐸 the energy of the X-ray; 𝑆 0 2 represents the amplitude factor, the summation Σ 𝑅 extends over all scattering paths, 𝑁 stands for the number of scatterers for a given scattering path, |𝑓 𝑒𝑓𝑓 (𝑘)| represents the effective scattering amplitude, 𝑅 is the distance between the absorber atom and the back-scatterer neighbor, 𝜎 2 stands for the Debye-Wäller (DW) factor, 𝜆 𝑘 is the mean free path of the photoelectron, 𝜙 𝑘 is the total phase shift, whose origin resides in the interaction of the photoelectron wave with the absorber and the scatterer.

The transformation of the EXAFS signal in k-space towards the R-space is performed by means of Fourier transform analysis using equation 1-33

𝜒(𝑅) = 𝐹𝑇{𝜒(𝑘)} = 1 √2𝜋 ∫ exp (2𝑘𝑖𝑅)𝑘 𝑤 𝜒(𝑘)Ω(𝑘)𝑑𝑘 ∞ -∞ (1-33)
Where 𝜒(𝑅) is the EXAFS signal in the R-space (after Fourier transform), 𝜒(𝑘) is the EXAFS oscillating data in k-space, 𝐹𝑇 represents the Fourier transform, applied to 𝜒(𝑘), 𝑖 is the imaginary number, 𝑘 stands for the wave vector, Ω(𝑘) is a window function, and 𝑤 is the k-weight. However, the actual numerical implementation employs the discrete Fast Fourier (do not confuse with the EXAFS signal 𝜒) and correlation coefficient R can be read in the specialized literature. 146 The above comments clearly show that EXAFS is a local probe spectroscopy. Indeed, the nature of the initial state Ψ 𝑖 , usually K or L edges is highly localized in the photoabsorber atom. Furthermore, the electron mean free path (𝜆 𝑘 ) and the dependence of 𝜒(𝑘) with 𝑅 -2 , determine that the useful EXAFS analysis is restricted, at most, to 5 Å from the photoabsorber.

Considering the physical interpretation of the parameters obtained through the fitting of EXAFS data, the most important are R and 𝜎 2 . It may be said that 𝑅 values, for single scattering paths, corresponds to the photoabsorberneighbor distance. Actually, ARTEMIS provides a value of Δ𝑅, which is the difference between the atomic distances in the input model, and the effective length of the single scattering path. The DW factor ( 𝜎 2 ) represents both thermal and static disorder present in the sample. The static disorder refers to multiple atoms of the same nature being located at effectively the same distance of the photoabsorber. The thermal disorder is related to atomic vibrations of atoms around their equilibrium positions. 147 Therefore, the DW factor is the standard deviation in the determination of 𝑅.

Typical values for Δ𝑅 should be less than 0.5 Å, 𝛥𝐸 should be less than 10 eV, 𝑆 0 2 should be within the 0.80 and 1.10 range and DW factors usually in the range from 0.003 to 0.020 Å 2 .

CHAPTER 1 64

To the best of our knowledge, there is only one study devoted to the study of the XANES spectra of a series of clathrochelates, in a combined study with XPS determinations. 130 The XANES results already published and those analyzed in this thesis shall be analyzed and compared during the results and discussion. However, it is worth noting that currently there is no published report regarding the EXAFS analysis of clathrochelates.

Density Functional Theory (DFT) calculations of molecular structure

Density Functional Theory (DFT) is very useful to predict the behavior of molecular systems. DFT is based on the fact that the electronic energy of the ground states is determined by the electron density 𝜌. 150 In the first place, it is worth to comment what a functional is. For example, in mathematics, a function usually takes as the input a number, and gives another number as the output. For the function 𝑓(𝑥) = 2𝑥 , if 𝑥 = 3 the output result is 𝑓 = 6 .

Conversely, a functional 𝐹 takes as the input variable a function, and gives a number as the output. Indeed, a simple functional may be written in the following way: 𝐹[𝑦(𝑥)] = ∫ 𝑦(𝑥)𝑑𝑥 3 0 , in this case, the input variable is the function 𝑦(𝑥), consequently, if 𝑦(𝑥) = 2𝑥, then 𝐹[2𝑥] = 9. In this way, it may be appreciated that a functional is the function of another function. According to DFT, the energy of the system is a functional of the electronic density ( 𝜌 ) (eq. 1-36), and the properties of the molecular system are univocally determined if 𝜌 is known.

𝐹[𝜌] = 𝐸

(1-36)

The DFT foundations reside in the Hohenberg -Kohn theorems. 150,151 Hohenberg -Kohn treatment was developed for an electron cloud in the presence of an external potential. For its application to molecular modeling, the electrons are treated as a charged gas, while the external potential is originated by the fields of the nucleus.

The Hohenberg -Kohn theorems can be stated as follows: (i) for molecules with a nondegenerate ground state, the molecular energy of the ground state, the wave function, and all other electronic properties are determined univocally by the electron density of the ground state 𝜌(𝑥, 𝑦, 𝑧), which is a function of only three variables; therefore, the electronic energy of the ground state is a functional of the electron density; (ii) there is a universal and exact functional 𝐹[𝜌] that establishes the dependence of observables from the electron density, nevertheless, the form of such universal and exact functional is unknown; (iii) the exact energy of the ground state can be obtained only if the exact electronic density is substituted in the functional of the total energy, while any other electron density that is substituted in the functional of the electronic energy shall give a greater energy than the real, so that 𝐹[𝜌 𝑡𝑟𝑢𝑒 ] = 𝐸 𝑡𝑟𝑢𝑒 < 𝐹[𝜌] = 𝐸, where the subscript "true" indicates the true electron density and electronic energy. In other words, the true electron density of the ground state minimizes the functional of the electronic energy.

The application of DFT to computational chemistry came with the introduction of orbitals to DFT, as proposed by Kohn and Sham. 150,151 A disadvantage of DFT is that the actual form of the functional linking 𝜌 with 𝐸 is not known, therefore, approximate functionals should be used. The actual form of the functionals may be intimidating; a thorough discussion of it is not the purpose of this thesis. The interested reader is referred to the specialized literature. In the equation of the STO, the spherical harmonic describes the angular dependence of the orbital. Conversely, the radial part reveals an exponential dependence on the nucleus-electron distance ( 𝜒 𝑖 ∼ 𝑒 -𝑟 ). Such type of function is quite inefficient for computational implementation.

In order to accelerate computation, the exponential function is substituted by Gaussian functions (eq. 1-39)

𝜒 𝑛,𝑙,𝑚 (𝑟, 𝜃, 𝜑) = 𝑁𝑌 𝑙,𝑚 (𝜃, 𝜑)𝑟 2𝑛-2-1 𝑒 -𝜁𝑟 2 (1-39)

Whose dependence on the nucleus-electron distance is 𝑒 -𝜁𝑟 2 , and a the molecular orbital is approximated by a linear combination of GTO.

In addition to spatial functions, a spin function should be added to the description of In particular, the use of UHF spin-orbitals has a drawback known as "spin contamination". The extent of spin contamination can be assessed through the expectation value of the 𝑺 𝟐 operator, 〈𝑺 𝟐 〉. Theoretically, 〈𝑺 𝟐 〉 = 𝑆 𝑍 (𝑆 𝑍 + 1), therefore, for a singlet 𝑆 𝑍 = 0 and 〈𝑺 𝟐 〉 = 0, for a triplet 𝑆 𝑍 = 1 and 〈𝑺 𝟐 〉 = 2. For its relevance to this thesis, it is interesting to mention that clathrochelates have been treated

theoretically by means of unrestricted wave functions, 137 124,125,152,155,156,[158][159][160][161][161][162][163][164][165][166][167][168][169][170] and in heterogeneous photoelectrodes based on SrTiO3. [START_REF] Chen | Theoretical Investigation of the Metal-Doped SrTiO 3 Photocatalysts for Water Splitting[END_REF]104,106,108,109 Concerning coordination compounds as catalysts for the hydrogen evolution reaction, DFT investigations have aimed to find the most stable pathways for various reaction mechanisms. This approach is fully thermodynamic, and does not give information on the kinetics of various paths. Certainly, it has been recognized that the whole picture to address a catalytic mechanism should be given by a combined thermodynamic and kinetic analysis. 169 In this respect, Brian H. Solis and Sharon H. Schiffer have outlined the methodology to perform a kinetic analysis of the homogeneous electrocatalytic mechanisms. 163 An CHAPTER 1 69 electrocatalytic mechanism comprises several electron transfer and proton transfer reactions, and the activation energy for each step has to be calculated. In the case of electron transfer reactions, the activation barrier is given by the Marcus relation 171-173

Δ𝐺 ≠ = (Δ𝐺 0 +𝜆) 2 4𝜆
(1-40)

Where Δ𝐺 ≠ is the activation barrier for electron transfer, Δ𝐺 0 is the driving force, and 𝜆

is the reorganization energy.

The calculation of Δ𝐺 0 for an electron transfer reaction is equivalent to calculating the standard redox potential because Δ𝐺 0 = -𝑛𝐹Δ𝐸 0 , where 𝑛 is the amount of exchanged electrons, 𝐹 represents the Faraday's constant and Δ𝐸 0 stands for the standard redox potential.

There are several alternatives described in the literature aiming to estimate the redox potential from ab-initio quantum chemistry. 163,169,[174][175][176][177] The most usual manner is through the calculation of Born-Haber cycles, consisting in optimizing the relevant redox states in gas phase and in a certain solvent. In another manner, the relevant redox states may be directly optimized in the relevant solvent. 169 In that manner, through Hessian calculations, the thermodynamic quantities of the calculated molecules can be estimated, thereby giving access to the value of Δ𝐺 𝑎𝑏𝑠 0 and Δ𝐸 𝑎𝑏𝑠 0 . However, redox potentials are experimentally obtained against a reference electrode. To solve this, a common approach is to employ a reference electrochemical reaction (e.g. the ferrocene|ferrocenium redox couple), that is calculated at the same level of theory than the molecule of interest, and the Δ𝐸 𝑎𝑏𝑠 0 is referred to such reference reaction, thus providing a means to compare calculations with experiments.

Moreover, there are theoretical approaches to calculate the reorganization energies for electron transfer based on DFT. [178][179][180][181][182][183][184][185][186][187][188][189][190] In order to calculate the barrier for proton transfer, the possibility of hydrogen tunneling must be treated, and when water is present (besides a Brønsted acid), proton transfer from the solvent should be taken into account.

Additionally, the overall rates of each reaction path shall depend additionally on the concentrations of the acid and the molecular electrocatalyst.

CHAPTER 2. Experimental section

Synthesis of Rh doped strontium titanate (Rh:SrTiO3)

SrTiO3 powder doped with 1 mol % Rh at Ti sites was prepared by a solid-state reaction. The starting materials, SrCO3 (Kanto Chemical; 99.9%), TiO2 (Soekawa Chemical; 99.9%), and Rh2O3 (Wako Pure Chemical), were mixed in a Sr:Ti:Rh ratio of 1.07:(1 -x):x. The mixture was calcined in air at 1173 K for 1 h and then at 1373 K for 10 h in an aluminum crucible. [START_REF] Iwashina | Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation[END_REF] This material was kindly supplied by Prof. Dr. Akihiko Kudo, from the Tokyo University of Science.

Synthesis of Rh doped strontium titanate modified with Pt (Rh:SrTiO3 -Pt)

The Rh:SrTiO3 -Pt photocatalyst was prepared by a photodeposition method. 500 mg of Rh:SrTiO3 were dispersed in an aqueous methanol solution (10 vol. %, 120 mL) in an ultrasonic bath. Subsequently, 0.385 mL of an aqueous solution of H2PtCl6 (20 mM) was added to the suspension. After removing dissolved air by evacuation through N2 bubbling, the suspension was irradiated for 3 hours with visible light (λ > 420 nm) using a 300 W-Xe lamp and a cutoff filter. The resulting Rh:SrTiO3 -Pt photocatalyst was then collected by filtration and washed with abundant water. This material was kindly supplied by Prof. Dr. Akihiko Kudo, from the Tokyo University of Science.

Synthesis of the clathrochelate hexachlorine containing cobalt(II) trisdioximate (Co(Cl2Gm)3(B-CH3)2)

The procedure for the synthesis of Co(Cl2Gm)3(B-CH3)2 has been reported elsewhere. 132 Briefly, dichloroglyoxime (2.78 mmol), methylboronic acid (1.85 mmol), and CoCl2 (0.93 mmol) were dissolved/suspended in dry nitromethane (20 mL) under argon, and then the solvent (10 mL) was partially distilled off. The reaction mixture was cooled down to room temperature, and the dark-brown precipitate was filtered off and successively washed with 4 M aqueous hydrochloric acid, water, ethanol, diethyl ether, and hexane. The product was recrystallized from hot chlorobenzene and then extracted with chlorobenzene, and the extract was flash-chromatographically separated on silica gel (0.035-0.070 mm, 30-mm layer). The filtrate was evaporated to a small volume and precipitated with hexane. The precipitate was washed with hexane and dried in vacuo.

Yield: 0.55 g (60%). This solid was kindly supplied by Prof. Dr. Yan Z. Voloshin, from the Russian Academy of Sciences in Moscow.

X-ray Photoelectron spectroscopy

XPS measurements were performed at ICMMO in a Thermo Fisher Scientific apparatus with base pressure in the low 10 -9 mbar range. The spectrometer was equipped with a monochromatic aluminium source (Al Kα, 1486.7 eV) using a spot size of 400 µm (corresponding to an irradiated zone of approximately 1 mm 2 ). The hemispherical analyzer was operated at 0° take off angle in the constant analyzer energy mode, with a step of 1 eV for the acquisition of survey scans and a step of 0.1 eV for the acquisition of narrow windows.

Electron Paramagnetic Resonance spectroscopy

X-band EPR measurements were performed at ICMMO (Institut de Chimie Moléculaire et des Matériaux d'Orsay) using a Bruker Elexsys E 500 EPR spectrometer equipped with an Oxford ESR9 liquid helium flow cryostat. A gold-chromel thermocouple was placed directly below the sample position. The complexes were dissolved to a concentration of 1 mM and transferred to an EPR tube. Dioxygen was purged 5 times under vacuum. The EPR tube was then cooled down to 77 K in liquid nitrogen before being transferred to the resonance chamber.

Optical spectroscopy

Ultraviolet Visible (UV-Vis) spectra were obtained at ICMMO using a Perkin Elmer precisely Lambda 35 instrument.

Emission spectrum of the LED was obtained with an Avantes Starline instrument, model Avaspec-204L-USB2-BB-50.

Scanning Electron Microscopy

Scanning Electron Microscopy images and Energy Dispersive spectra were recorded at ICMMO using a SEM-EDS Cambridge equipment and electron microprobe measurements (EPMA) (microprobe SX 100 CAMECA).

Powder X-ray Diffraction

Photoelectrode preparation

Photoelectrodes of Rh:SrTiO3 were prepared at ICMMO by drop-casting 10 μL of an isopropanol suspension containing Rh:SrTiO3 (30 mg in 0.5 mL) on top of an ITO surface. Next, 10 μL of Nafion (50 μL to a final volume of 1 mL in isopropanol) were put on top of the surface through the same methodology, and let dry for three hours. In all cases, the solvent was let to evaporate at room temperature. Before measurements, photoelectrodes were put into Na2SO4 (0.1 M) solution and allowed to wet and equilibrate overnight.

For the incorporation of the clathrochelate Co(Cl2Gm)2(B-CH3)2 (M = 575.81 g/mol), after the drop-casting of Rh:SrTiO3, 0.5 mL of 10 -2 M mother solution of the clathrochelate was prepared in DMF, then 10 μL of this solution was dropped immediately onto the surface. The total amount of clathrochelate at the surface of the Rh:SrTiO3 photoelectrode was thus 10 -2 μmol (5.8 μg). The evaporation of DMF was performed with the aid of a vacuum primary pump for two hours. The dissolution of the clathrochelate in DMF was not preserved, and was freshly prepared any time the photoelectrodes were prepared. Next, 10 μL of Nafion (50 μL to a final volume of 1 mL in isopropanol) were added onto the surface using the same methodology, and let dry for one hour. In all cases, the solvent was allowed to evaporate slowly at room temperature. Before measurements, photoelectrodes were put into an electrolyte solution and allowed to wet and equilibrate overnight.

For the electrodeposition of Cu, a copper wire was connected to the working electrode (ITO-Rh:SrTiO3-Nafion), and the electrode potential was alternatively polarized in the anodic region in decreasing potential steps from +1.5 down to +1.0 V (steps of 0.1 V vs. SCE) and in the cathodic region (from -1.3 up to +1.0 V, steps of 0.1 V vs. SCE).

Rh:SrTiO3 -Pt photoelectrodes were prepared by drop-casting 10 μL of an isopropanol suspension containing Rh:SrTiO3 -Pt (30 mg in 0.5 mL) on top of an ITO surface.

Next, 10 μL of Nafion (50 μL to a final volume of 1 mL in isopropanol) were put on top of the surface using the same methodology, and let dry at ambient conditions for three hours. In all cases, the solvent was let to evaporate at room temperature. Before measurements, photoelectrodes were put into Na2SO4 (0.1 M) solution and allowed to wet and equilibrate overnight.

The geometric area of all these photoelectrodes was always set to ≈ 1.5 cm 2 .

Electrochemical measurements

All electrochemical measurements were performed in aqueous Na2SO4 (0.1 M) in a three electrode cell configuration employing Indium Tin Oxide (ITO) surfaces modified with the semiconducting materials and the catalysts as the working electrodes. Saturated calomel electrode (SCE) and a carbon plaque were employed as reference and counter electrodes, respectively. MilliQ water (remaining resistivity of ≈ 10 M.cm) was used for all tests, and was obtained from a Merck Millipore device.

All photoelectrochemical measurements were performed using a Modulab Solartron Analytical potentiostat, model 2100A. The light source was controlled with a calibrated optical bench (Thorlabs Inc. DC2100), equipped with a 450 nm LED light source. The intensity of light (in mW/cm 2 ) was measured with a calibrated silicon detector coupled to the optical bench, as provided by Thorlabs Inc.

Open circuit photovoltage decay

For the open-circuit photovoltage decay measurements, the photoelectrodes were kept at open-circuit conditions throughout the whole experiment. Initially, the photoelectrodes were illuminated for 60 s, then the LED was switched off and the open-circuit photopotential decay was recorded for further 120 s. Different light intensities were tested, in the power density range of 150 to 400 mW/cm 2 (values of light power employed in each experiment are specified in each particular plot).

Intensity modulated photovoltage spectroscopy

IMVS determinations were performed at open-circuit conditions. The small ac perturbation of light was always 10 % of the dc bias light. The frequency range explored was typically between 20 Hz and 10 mHz (the detailed frequency ranges are carefully specified in the Bode representations of IMVS spectra reported during the discussion), as provided in the discussion chapters. Likewise, the precise light intensities employed for these determinations are indicated in each particular graph.

An important experimental parameter to adjust in order to clearly observe the nonsteady state spiral pattern in IMVS was the number of points per decade being measured. The default value of 10 must be increased to at least 60, so that clean IMVS non-steady state spectra can be obtained.

Linear potential sweep voltammetry

Cyclic Voltammetry and Linear Sweep Voltammetry experiments were performed at the scan rate of 1 mV/s. The potential and the light power ranges over which each experiment was performed are specified in each particular case in the results and discussion Chapters.

Photoelectrochemical Impedance Spectroscopy

Photoelectrochemical impedance (PEIS) determinations were performed using a quartz photoelectrochemical cell from Pine Research Instrument Company. PEIS spectra were recorded under potentiostatic control. The amplitude of the sinusoidal potential perturbation was 10 mV in all cases. The frequency range explored was comprised between the kHz to the mHz region. Further specific details concerning LED powers are given in each particular case during the discussion of the results. Fitting of experimental PEIS spectra was performed using Peter's kinetic model, [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF] which was implemented in Matlab R2014b using home-made code.

Matlab treatment of photoelectrochemical data

The treatment of all photoelectrochemical data obtained in this thesis was automatized with Matlab codes. A thorough explanation of the functioning of the scripts is secondary in the context of this thesis, because the main scientific results are in the domain of photoelectrochemistry and the programs to import, simulate, and fit photoelectrochemical data are common programming routines. Examples of a working Matlab program, developed during the thesis in order to import data from the potentiostat output, and then perform all the treatment in the case of OCPD measurements are provided below.

These codes can be useful for other interested researchers or PhD students who might need either a template or some guidance in Matlab programming, oriented to rather simple physical chemistry problems.

Just below, a script is provided that allows all kinetic treatment of OCPD, and finally, there is a Matlab function that works concomitantly with the script for the numerical estimation of time derivatives. The script and the function operate in different .m files.

The Matlab codes for fitting PEIS are much more tangled. These are composed by five different programs that work simultaneously, and all together comprise slightly more than 1200 lines of codes. Likewise, the numerical simulation of IMVS is composed by four different Matlab programs that function as an ensemble, and comprise around 600 lines of codes. For space reasons, these programs are not given explicitly in this Chapter.

Theoretical calculations on clathrochelates

All calculations made to study clathrochelates were performed in GAMESS. 191 Visualization of molecular orbitals was performed with Macmolplt. 192 Main geometry optimizations and Hessian calculations were accomplished with the B3LYP exchange correlation functional. Other functionals, such as M06-L, TPSS, BP86, PBE and PBE0, were also tested for geometry optimizations, which is discussed in the next section.

Basis sets were included manually after being downloaded from the Basis Set Exchange website. 193 For geometry optimizations the LANL2DZ basis set was employed, with effective core potentials for Co and Cl. [194][195][196] Electronic energies and molecular orbitals were further refined by the all-electron basis cc-pVTZ for Co and cc-pVDZ for all other atoms. 197,198 For the single point calculations, the group $dft and the keyword nrad=125

were included. This is related to the grid selection in DFT calculations (nrad governs the number of radial grid points in Euler-Maclaurin quadrature whose default value is 96). Below, a typical GAMESS input to perform geometry optimization for a molecule of water is presented. In order to clarify different parts of the input file, these are highlighted with different colors. For example, the main instructions of the input described just above, are put at the beginning of the file, and highlighted here in blackbold letters.

$contrl runtyp=optimize scftyp=rhf icharg=0 mult=1 MAXIT=200 dfttyp=b3lyp $end $SYSTEM MWORDS=850 MEMDDI=800 $END $scf dirscf=.f. diis=. -The type of calculation to be performed (an optimization, as expressed in runtyp=optimize) -The kind of "self-consistent field" wavefunction to be used (in this example, it is scftyp=rhf, which stands for "restricted hartree-fock") -The charge and the multiplicity of the molecule (this is specified through the keywords icharg=0 mult=1)

-The maximum number of allowed iterations (in our calculations we set MAXIT=200, which is the maximum allowed by GAMESS).

-The DFT functional to be used (dfttyp=b3lyp).

The $SYSTEM group governs (among other things):

-The amount of memory allocated to each calculation (MWORDS=850 MEMDDI=800).

The $scf group is related to the "self-consistent field" calculation, for example:

-The keyword dirscf=.f. has been set to "false" (.f.), which stores the numeric integrals on disk. Instead, if its value were set to "true" (.t.), then the integrals would not have been stored, but calculated each time. The impact of this on the speed of calculation depends on the specific hardware, i.e., if it is faster to for GAMESS to calculate an integral, or to find it on the computer's memory.

-The keywords diis (Direct Inversion in the Iterative Subspace) damp (Davidson's damping of the Fock matrix), directly affect the rate of convergence. It was observed that without inclusion of these keywords, the scf calculations on clathrochelates did not converge. Therefore, these were included in all calculations.

-The keyword ethrsh = 10 forces diis when the energetic difference between two iterations is less than 10 Hartrees. 10 Hartrees is an enormous amount of energy, equivalent to 272.114 eV. In practical terms, this forces diss almost from the beginning of the calculation, thus speeding and stabilizing scf convergence.

The group $STATPT controls the parameters for the search of a stationary point. For example:

-The keyword OPTTOL=0.0005 is the tolerance for the gradient convergence in units of Hartree/Bohr. The default is 0.0001, but this is indeed a strict condition, and was enlarged given the structural complexity of clathrochelates.

-The keyword NSTEP=99 specifies the maximum number of steps to make the geometry optimization.

-The keyword HSSEND=.T. set to "true" (.T.) is essential in each geometry optimization because it instructs the calculation of the Hessian matrix (or the normal vibrational modes) at the end of the optimization process. All calculated frequencies must be real and positive, otherwise the stationary point is not a minimum and the calculation should be restarted to find a true minimum.

The group $pcm sets the use of a solvent during the calculation -The specific solvent is specified trhough solvnt=WATER -The smd flag set to true (.t.) selects the "Solvation Model Density", which has a database of 178 organic and inorganic solvents.

Note that GAMESS is not case-sensitive, so keywords may be written in capital letters or not. A broader description of all keywords and groups may be found in the GAMESS website, in reference 200.

Next, in the $DATA section, it is observed a commentary line, then the symmetry group of the molecule. Rigorously speaking, water is known to belong to the C2v symmetry group, however, if the symmetry is specified, then GAMESS forces the geometry optimization to follow the indicated symmetry, which is not a problem for water whose geometry is well known. Commonly, no symmetry constrains are set through a C1 group, with the intention to evaluate whether the theoretical model gives the adequate geometry without pre-established constraints. In the next line, this is the oxygen element symbol (O) followed by the atomic number (8.0) and the Cartesian coordinates, highlighted in bold-red letters. Just below, written in blue, the LANL2DZ basis set may be observed, as it was manually introduced. In the same manner, the two hydrogen atoms along with its basis set are also specified.

The following lines specify the input for a single-point energy calculation. The $DATA group is similar to the one just presented for the geometry optimization of water, and it is not fully included here because, for the Co(Cl2Gm)2(B-CH3)2 clathrochelate, the basis set specification spans over 24 pages in a word document (Times New Roman, 10, single spacing).

$CONTRL SCFTYP=ROHF RUNTYP=ENERGY MAXIT=200 ICHARG=0 MULT=2 dfttyp=b3lyp $END $SYSTEM MWORDS=250 MEMDDI=100 $END $scf dirscf=.f. diis=.t. damp=.t. ethrsh=10 $end $dft nrad=125 $end $pcm solvnt=dmf smd=.true. $end

$DATA $END

In order to find a transition state, a saddle point search has to be performed, and a single imaginary frequency needs to be found to assess its correct determination. Saddle point searches may be performed in GAMESS, specifying RUNTYP=SADPOINT.

Cartesian coordinates of the optimized molecules at B3LYP/LANL2DZ level with effective core potentials for Co, Cl and Fe

The reproduction of the theoretical results reported in this thesis cannot be performed with ease without the Cartesian coordinates of the complexes. Therefore, we present them in (x,y,z) format, after geometry optimization. Having this information, any interested reader can view the molecules referred in Chapter 4 directly in any molecular modeling program and to run other calculations based on the molecules reported in the annex section at the end of this thesis.

Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy

The EXAFS spectrum was treated with ATHENA, ARTEMIS and FEFF 7.0. The calculations using FEFF 7.0 were performed with the parameters that can be observed below in the input file. The calculations were set to consider only single scattering (2 legs paths) and multiple scattering of 3 legs paths. Scattering paths were calculated until 6 Å farther apart from the Co photoabsorber.

The EXAFS amplitude was given by equation 2-1 147

𝜒(𝑘) = 𝑆 0 2 ∑ 𝑁 |𝑓 𝑒𝑓𝑓 (𝑘)| 𝑘𝑅 2 sin (2𝑘𝑅 + 𝜙 𝑘 )exp (-2𝑘𝑅/𝜆 𝑘 )exp (-2𝜎 2 𝑘 2 ) 𝑅 (2-1)
Where 𝜒(𝑘) denotes the EXAFS amplitude; 𝑘 is the wave-vector 𝑘 = CHAPTER 2 85 √(2𝑚 𝑒 (𝐸 -𝐸 0 ))/ħ 2 , where 𝑚 𝑒 is the mass of the electron, 𝐸 0 the energy of the edge and 𝐸 the energy of the X-ray; 𝑆 0 2 stands for the amplitude factor, the summation Σ 𝑅 extends over all scattering paths, 𝑁 is the degeneracy of a given scattering path,

|𝑓 𝑒𝑓𝑓 (𝑘)| denotes the effective scattering amplitude, 𝑅 is the distance between the absorber atom and the back-scatterer neighbor, 𝜎 2 is for the Debye-Wäller (DW) factor, 𝜆 𝑘 is the mean free path of the photoelectron, 𝜙 𝑘 is the total phase shift.

This equation is identical to the one presented during the EXAFS presentation in the Bilbiographic Overview. Nevertheless, it is repeated here to facilitate the reading.

During the fitting, the XRD structure and DFT optimized geometry (B3LYP/LANL2DZ) were used. The following variables were allowed to refine: R, DW factors, 𝐸 0 and 𝑆 0 2 .

The degeneracy for each scattering path was not allowed to refine because in this analysis the structure of the molecule was known. Different DW factors were grouped according to chemical sense, with the purpose to limit the number of parameters. This is extensively treated during the discussion of EXAFS results.

The fitting was accomplished in R-space (k range from 3.000 to 11.886 Å -1 , R range from 1.000 to 4.627 Å). During the analysis, whenever not specified, k 2 -weighting was used, and a Hanning window function was employed throughout.

The fitting was performed to minimize the statistical variable chi-squared, given by the equation 2-2 147

𝜒 2 = ∑ ( 1 𝑠 𝑖 ) 𝑁𝑜.𝑜𝑓 𝑝𝑜𝑖𝑛𝑡𝑠 1 (𝜒 𝑒𝑥𝑝 (𝑘 𝑖 )-𝜒 𝑐𝑎𝑙𝑐 (𝑘 𝑖 )) 2 𝑁𝑜.𝑜𝑓 𝑝𝑜𝑖𝑛𝑡𝑠-𝑁𝑜.𝑜𝑓 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 (2-2)
Where 𝜒 𝑒𝑥𝑝 (𝑘 𝑖 ) denotes the measured amplitude of EXAFS in point "i", and 𝜒 𝑐𝑎𝑙𝑐 (𝑘 𝑖 )

represents the calculated EXAFS amplitude at point "i", calculated by FEFF 7.0.

The normalization factor 𝑠 𝑖 is given by the following equation 2-3 147

𝑠 𝑖 = ∑ 𝑘 𝑗 3 |𝜒 𝑒𝑥𝑝 (𝑘 𝑖 )| 𝑁𝑜.𝑜𝑓 𝑝𝑜𝑖𝑛𝑡𝑠 𝑗 𝑘 𝑖 3 (2-3)
A typical input file for FEFF (as implemented in ARTEMIS) is presented just below. ). 101 The XRD determination should permit to establish if the doping process would be a source of appreciable distortion in the crystal lattice or not. Fig. 3-1 shows the comparison between the experimental XRD pattern of Rh:SrTiO3 and a prediction of the SrTiO3 pattern. There is an excellent match between experimental and predicted data. This is the indication that the incorporation of Rh at 1% in Ti(IV) sites does not disturb substantially the hosting crystal structure, which is essentially the same as for nondoped SrTiO3. Fig. 3-1 further confirms that the procedure described in this work is appropriate to obtain a single phase of Rh:SrTiO3 that was not contaminated by excess of precursors such as TiO2, Rh2O3 or SrCO3. Though, XRD analysis was not able to put into evidence the presence of Rh in the sample due to its low content.

In order to assess the presence of Rh as a dopant, XPS spectra were obtained. In addition to the typical Ti and Sr profiles, the presence of Rh in the compound was undoubtedly determined (Fig. 3-2 a). XPS was further employed to obtain information on the energetics of the valence band with respect to the Fermi level (EF). In XPS, the zero in the binding energy (BE) scale corresponds to the energy of the EF. [START_REF] Izaki | Hybrid ZnO/phthalocyanine photovoltaic device with highly resistive ZnO intermediate layer[END_REF] Consequently, the energy difference between EF and the maximum of the valence band can be directly estimated by this technique. A value of 1.2 eV was obtained for Rh:SrTiO3.

With the purpose to obtain deeper insights into the band energetics of the photoelectrode, diffuse reflectance spectroscopy was also employed. In Fig. 3-3 we observed a strong absorption in the UV region, which is associated to inter-band transitions of SrTiO3 consistent with the reported band gap of 3.2 eV for this material. 102-104 Fig. 3-3 shows that Rh doping produced in-gap states, observed in the diffuse reflectance spectra with an absorption band with a maximum at 560 nm, lying well in the visible region. Such absorption suggests that the energy difference between Rh in-gap states and the conduction band is approximately 2.7 eV, as observed before using soft X-ray spectroscopy. 103 There is a weak absorption beyond 1000 nm that may be attributed to d-d transitions in the material. defined, and the Si K-shell is observed as well, which originates from the glass substrate on top of which ITO is deposited. In the case of the photoelectrode assembly, EDS revealed the presence of F at the surface, from the Nafion film. Additionally, the Sr and Rh L-shells, and Ti K-shell were consistent with the identity of the semiconducting material. The presence of Rh is indicated in Fig. 34, but with a notably weak intensity, related to the small loading of such atom whose role is the doping of SrTiO3. The trend observed in such photopotential experiments indicates, as expected, that the Rh:SrTiO3 photoelectrodes have a p-type conductivity. [START_REF] Iwashina | Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation[END_REF][START_REF] Jia | BiVO4-Ru/SrTiO3:Rh composite Z-scheme photocatalyst for solar water splitting[END_REF]103,112 On the other hand, Fig.

Photoelectrochemical characteristics of

3-5 b shows the charge transfer and recombination rate constants, calculated by open-

circuit photovoltage decay (OCPD) as explained in the Bibliographic Overview (chapter 1 of this thesis) and in appropriate literature. [START_REF] Babenko | Kinetics of the photoelectrochemical evolution of hydrogen at p-type Si[END_REF][START_REF] Ponomarev | Theoretical analysis of the laser-induced phototransient response of semiconductor | electrolyte circuits with 'currentdoubling' reactions[END_REF] For this measurement, dioxygen was extensively purged with Ar gas, and the cell was kept closed in Ar atmosphere during the measurements.

The charge transfer with the electrolyte is expected to occur with the solvent, since it is highly unlikely that an electrochemical reaction with either sodium or sulfate ions can take place in these experimental conditions. Thus, the charge transfer and recombination rate constants displayed in Fig. 3-5 b should correspond to the HER, which is notably slow. Both rate constants proved to be independent of light intensity, even at high levels of illumination (≈ 500 mW/cm 2 ). Overall, the rate of charge transfer was larger (kt = 0.035 s -1 ) than the rate of recombination (kr = 0.003 s -1 ).

It is worth to comment here that there is a possible accumulation of sodium ions within the Nafion film and at the interfaces, and that this could modify the Helmholtz capacitance. However, since all experiments were made using similar Nafion layers, such possible effects are assumed to be constant and do not change the interpretation of the ensemble of results herein presented and the associated conclusions. material was modest (10 μA/cm 2 ), which is not a record but is consistent with previous reports on Rh:SrTiO3 photoelectrodes. [START_REF] Iwashina | Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation[END_REF] It is worth noting that such photocurrent values are better than those obtained with other recent photoelectrode assemblies. 203 Fig. 3-6 a inset shows that, under illumination, the reduction current starts before the thermodynamic potential of the HER. Indeed, without illumination, the only driving force available to carry out the HER is the applied potential and no HER can occur at potentials more positive than its thermodynamic potential. When the photoelectrode is illuminated, a part of the necessary driving force is supplied by photons, therefore the needed driving force for the HER can be attained at an electrode potential that is more positive than the thermodynamic potential for the HER. [START_REF] Thorne | Energetics at the surface of photoelectrodes and its influence on the photoelectrochemical properties[END_REF] In order to gain insights into the mechanism of the HER, the Tafel slope was extracted (Fig. 3456), and a value of 157 mV/dec was obtained. Such value of the Tafel slope rules out the possibility of both the Tafel and Heyrovsky (in the low surface coverage region of H atoms) reactions as possible rds. [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF]204 Nevertheless, 157 mV/dec is slightly larger than the 120 mV/dec predicted for either the Volmer step or the Heyrovsky step (high coverage of H atoms); but the similarity between these values allows to suggest that any of the Volmer step or the Heyrovsky step (high coverage of H atoms) might be the rds at the surface of Rh:SrTiO3.

On the other hand, the linear sweep voltammogram under anodic polarization is presented in Fig. 3456b. In this case, no photocurrents were detected (i.e., dark and illuminated currents were the same), which is normal for p-type semiconductors under positive bias. In such conditions, there is an upwards band bending that forces the photoexcited electrons towards the bulk of the semiconductor. Hence, the anodic reaction (OER) occurs by transfer of majority carriers (holes). Indeed, the photoexcitation process does not change much the amount of majority carriers at the CHAPTER 3 96 interface and the current density is therefore unperturbed by illumination. Additionally, it may be appreciated that this system displays notoriously low performance for the OER, since appreciable anodic currents start to flow only at +1.3 V (vs. SCE), showing an enormous overpotential of 720 mV.

The Tafel slope of the OER for the Rh:SrTiO3 material was determined to be 60 mV/dec (Fig. 3456). Currently, the mechanism of the OER is much more controversial than that of the HER. Indeed, a recent microkinetic analysis [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF] 22 with the rds given by equation 1-21 as a plausible mechanism in this case. On the other hand, it has been shown that avoiding the quasi-equilibrium assumption for the OER within the Bockris' oxide mechanism, such Tafel slope can be accounted for. [START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF] Certainly, a Tafel slope of 60 mV/dec is obtained when the rds is the reaction 𝑀 -𝑂 = 𝑀 + 1/2𝑂 2 (eq. 1-25) and 𝜃 𝑂 ≈ 0 and 𝜃 𝑂𝐻 ≈ 1. Henceforward, the mechanism of the OER shall be interpreted in terms of the contemporary revision of Bockris' oxide mechanism (eq. 1-23 to 1-25). 87

Photoelectrochemical kinetics of the HER at the surface of Rh:SrTiO3

photoelectrodes PEIS is a powerful technique since it provides information not only on the charge transfer and recombination rate constants but also on interfacial capacitances associated to the system. [START_REF] Klahr | Water oxidation at hematite photoelectrodes: The role of surface states[END_REF][START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF][START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF][START_REF] Schefold | Impedance and intensity modulated photocurrent spectroscopy as complementary differential methods in photoelectrochemistry[END_REF]115 Previous optical characterization of Rh:SrTiO3 revealed that Rh existed in the form of Rh 4+ (dark grey solid). 103 However, it has been shown that Rh 4+ may be reduced to Rh 3+ (yellow solid), which is more active towards the HER. 102,103 During all photoelectrochemical experiments, the photoelectrode was observed to turn yellow, indicating that the active material actually being measured was Rh 3+ :SrTiO3. The yellow color disappeared from the surface of the electrodes after one minute of contact with air, indicating that Rh 3+ was easily oxidized to Rh 4+ by dioxygen when in contact with the photoelectrode. In any case, all kinetic analysis presented henceforward correspond to the stable PEIS response of the photoelectrode, associated to the Rh 3+ oxidation state. The effect of light intensity on PEIS spectra (Fig. 34567) was more marked when the potential was more negative. In fact, the effect of light power was evidenced only at -1.30 and -1.25 V (vs. SCE) while at less negative potentials a change in light intensity did not change the shape of PEIS spectra.

Interestingly, the frequency at which the maximum of the LF relaxation occurred did not change, neither with the electrode potential (Fig. 34567) nor with the light intensity (Fig. 34567), indicating that 𝑘 𝑡 was independent of these experimental parameters. Such behavior is consistent with an ideal semiconductor|electrolyte interface, where most of the potential drops inside the space charge and not in the Helmholtz layer, causing 𝑘 𝑡 to have a fixed value at any applied potential. 205 However, the behavior of the recombination rate constant was non-ideal, since its value is expected to decrease with increased band bending. The independence of the recombination rate constant on the electrode potential has been reported before, for example in Figure 7 of reference 66. Such behavior has been attributed to the presence of surface states. Overall, charge transfer and recombination kinetic constants had nearly the same value at open-circuit and under cathodic polarization. Therefore, the HER in this material is notably slow over a wide potential window.

Since over the -1.30 V to -1.20 V range the kinetic parameters did not change, the mean value was calculated, providing numeric results of 𝑘 𝑡 = (0.020 ± 0.007) 𝑠 -1 , 𝑘 𝑟 = (0.004 ± 0.002) 𝑠 -1 . The percentage of photogenerated electrons (calculated according to 𝜂 = 𝑘 𝑡 /(𝑘 𝑟 + 𝑘 𝑡 ), eq. 1-7) being transferred to the Helmholtz layer was estimated to be 𝜂 = (78 ± 2) %.

Furthermore, the increase (towards more positive) of the electrode potential caused PEIS spectra to expand. Such fact may be explained through a widening of the space charge region related to an increase in band bending. This would allow higher light absorption with the concomitant increase in the photogenerated flux of minority carriers (I0, Table within the annex section at the end of this thesis). [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF] It is worth to comment here on the dependence of the space charge capacitance (derived from the HF relaxation) upon the electrode potential. However, it is necessary to be aware that the phase angle for the HF relaxation was at most -67°, a value which is quite farther apart from the ideal (-90°) value to consider the capacitance associated to the HF relaxation as a pure capacitance. Instead, the HF relaxation may contain contributions from surface roughness, surface states and the Nafion film that covers the photoelectrode.

Under depletion conditions, the space charge capacitance usually follows the Mott-Schottky equation 206

𝐶 𝑠𝑐 -2 = 2 𝑞𝜀𝜀 0 𝑁𝐴 2 (𝐸 -𝐸 𝐹𝐵 - 𝑘 𝐵 𝑇 𝑞 ) (3-1)
Where 𝐶 𝑠𝑐 stands for the space charge capacitance, 𝐸 𝐹𝐵 is the flat-band potential, 𝐸 is the applied potential, 𝜀 stands for the relative permittivity of the semiconducting material, 𝜀 0 represents the permittivity of free space, 𝑁 is the doping density of the semiconductor, 𝐴 stands for the area of the electrode, 𝑘 𝐵 represents the Boltzmann constant, 𝑞 is the elemental charge, and 𝑇 is the absolute temperature.

Consequently, a plot of Csc -2 vs E would give a straight line and extrapolation towards the potential axis would give the flat band potential and the slope allows estimating the doping density of the semiconductor. However, Mott-Schottky analysis can be misleading in some cases because the theory has been developed for flat semiconductors, without surface states 207 and most real photoelectrodes do not comply with these requisites. Despite these simplifying assumptions, the Mott-Schottky plot for Rh:SrTiO3 presents a linear shape that is slightly dependent on light intensity (Fig. 345678).

Interestingly, the positive slope of this graph contrasts not only with the wellestablished p-type nature of the photoelectrode 9,13 but also with the photopotential measurements presented in Fig. 345. Indeed, such figure indicates two things: (i) the flat band potential for this semiconductor is located at electrode potentials greater than 0.28 V (vs. SCE), and (ii) the semiconductor is p-type. However, the positive slope in Fig. 3-8 is characteristic of an n-type semiconductor. caused strong depletion conditions so that the inversion conditions were achieved. [START_REF] Memming | Semiconductor Electrochemistry[END_REF][START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF]206,208 In the inversion region, the space charge is so heavily depleted from majority carriers, that minority carriers (electrons for a p-type semiconductor) themselves can promote electron transfer reactions. Under these conditions, the bulk behaves like a p-type semiconductor, while the surface displays n-type conductivity, [START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF] which explains the observed positive slope in the Mott-Schottky plot within the potential window from -1.3 to -1.2 V (vs. SCE).

Photoelectrochemical kinetics of the OER at the surface of Rh:SrTiO3 photoelectrodes

The photoelectrochemical study of p-type semiconductors under forward bias is seldom performed and reported in the literature because most p-type semiconductors suffer from corrosion at positive potentials. 115 Nevertheless, Rüdiger Memming recently presented various interesting reports on measuring dark currents in semiconductorelectrolyte interfaces. [START_REF] Memming | Semiconductor Electrochemistry[END_REF] Considering the stability of Rh:SrTiO3 photoelectrodes under anodic polarization, we undertook the study of this p-type material under forward bias.

PEIS spectra recorded on Rh:SrTiO3 at positive potentials presented two relaxations.

The LF relaxation was found at notably low frequencies; with the need to go down to 0.282 mHz to truly observe such relaxation. Clearly, the kinetics of this system towards the OER was very slow, as suspected from the high overpotential of 720 mV determined during the analysis of LSV (Fig. 3456). Fig. 3-9 a indicates that, when the electrode potential is made less positive, the Nyquist representation expands, preserving the ratios between the two relaxations, suggesting that rate constants do not vary with the electrode potential.

Structural, chemical and spectroscopic characterization of SrTiO3 photoelectrodes modified with the hexachlorine containing cobalt(II) trisdioximate (Co(Cl2Gm)3(B-CH3)2)

Results reported in the previous section are related to pristine Rh:SrTiO3 photoelectrodes. In this section, we report on our attempts to improve the performance of the semiconducting material by surface sorption of a model organometallic compound selected from a well-known family of electrocatalysts of the HER in the homogeneous phase. Indeed, the hexachlorine containing cobalt(II) tris-dioximate clathrochelate Co(Cl2Gm)3(B-CH3)2, (Fig. 345678910) was impregnated at the surface of Rh:SrTiO3 photoelectrodes by drop-casting. From now on, this system shall be referred to as Rh:SrTiO3 -Ch.

In the first characterization step, the X-ray photoelectron spectrum of the organometallic compound was recorded on the powder. which is in agreement for Co II complexes reported earlier 130,[140][141][142][143] . It should be noted

here that SOS values depend on the oxidation state of the encapsulated Co ion centre in the ligand cage. 130 Furthermore, the XPS spectra of this clathrochelate contained weak additional peaks assigned to the shake-up satellites associated with molecular paramagnetism. 144 These results suggest that the clathrochelate contains a Co II The super-hyperfine interaction with N would be observed in EPR as a further signal splitting as a triplet (nuclear spin for N; 𝐼 = 1 ). 139 However, such superhyperfine interaction is not resolved in the experimental spectrum, indicating that the unpaired electron is localized essentially on the metallic center. As will be described in Chapter 4, DFT calculations were performed on the low spin and high spin configurations for the Co(II) oxidation state of the clathrochelate, and the low spin doublet was calculated to be 154 kJ/mol more stable than the high spin quartet state, which is in agreement with the EPR results.

For the quantitative description of the EPR spectrum, a fitting procedure was undertaken using the free software easyspin, which is based on Matlab. 209 The shape of the EPR spectrum, caused by the anisotropic structure of the molecule, suggested the use of g and A tensors with three contributions, i.e., g = [gx gy gz] and A = [Ax Ay Az].

Previous EPR fitting of other clathrochelates has been performed with easyspin (see, for example, Figure 1 of the supporting information in reference 127). A look at the EPR spectrum obtained in this work (Fig. 3-11 a) reveals that there is no small splitting due to the super-hyperfine interaction with N. Therefore, the effect of unresolved superhyperfine interactions, as well as any other contributions to line broadening caused by relaxation, or distributions in g and A tensors was considered by the inclusion of an anisotropic strain tensor (H) as implemented in easyspin, so that H = [Hx Hy Hz]. The fit parameters of the EPR spectrum are shown in Table 3-1, and the comparison between experimental and fitted EPR spectra is depicted in Fig. 3-11 a. Once the clathrochelate complex was characterized, it was subsequently coated onto the surface of Rh:SrTiO3 photoelectrodes and a thin layer of Nafion was put atop the interface, as described in the Experimental Section of chapter 2. The interaction between the semiconducting substrate and the clathrochelate was assessed by XPS.

Unlike other modified photoelectrodes that shall be shown in next sections, in this case open-circuit conditions, charge transfer and recombination rate constants were found quite small and proved to be independent of light intensity. Furthermore, the presence of the clathrochelate at the surface did not change appreciably the rate of charge transfer and recombination at open circuit, when compared to bare Rh:SrTiO3 (Fig. 3-5 b). towards the HER in the homogeneous phase. [126][127][128]139 Moreover, previous electrochemical studies on various clathrochelates evidenced that these molecules may act as precatalysts for the deposition of cobalt-based nanoparticles, which are also active towards the HER. 129 Nevertheless, the authors of such report recognized that the chemical nature of the cobalt particles formed after electrolysis was unknown, but EDX analysis showed the presence mainly of Co and O. 129 In the Rh:SrTiO3 -Ch system studied here, we observed that the electrochemical response under cathodic polarization evolved upon cycling, so that the performance towards the HER increased (increase of the current densities and decrease of the overpotential, Fig. 34567891011121314). We speculate that such electrochemical evolution during testing under cathodic polarization might be due either to a better coating of the complex at the surface of the semiconductor or to the transformation of the clathrochelate into another cobalt containing species which is a more active electrocatalyst, by analogy to a previous report. 129 When the photoelectrode was illuminated, the inherent evolution of CV did not allow to clearly determine whether the current density increase was due to incoming light or to the chemical transformation of the clathrochelate. The effect of light was better observed by PEIS, as shall be discussed below.

Current potential characteristics of Rh:SrTiO3 -Ch photoelectrodes

At this point, it is worth to note that electrode activation by tiny deposition of Pt and Au coming from the counter electrode has been reported. 210 In order to avoid such interfering effect, a graphite plaque was always employed in this work as the counter electrode. Thus, any evolution in electrochemical responses was due to chemical transformations of the working electrode and not to modifications originated from the counter electrode. (eq. 1-25) is the rds and 𝜃 𝑂 ≈ 0 and 𝜃 𝑂𝐻 ≈ 1. [START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF] Considering the notable overpotential that still remains for the OER, and the absence of photocurrent, the effect of electrochemical cycling upon the anodic response of this photoelectrode under forward bias was not further investigated.

Photoelectrochemical kinetics of the HER at the surface of Rh:SrTiO3 -Ch photoelectrodes

In the previous section it was observed that the electrochemical response was varying upon electrode cycling. In order to have an insight into the effect that such potential cycling had on the kinetic parameters, CV and PEIS were measured alternatively at the same time, i.e., one PEIS after each CV cycle. The trend in CV was already shown in Fig. 3-15 a, while the trend in PEIS is depicted in Fig. 3-15 a and b, for the first and last (70 th ) cycles, respectively.

Overall, the Nyquist representations of PEIS spectra showed a tendency to shrink upon cycling, a fact which is consistent with the increasing slope of current-potential curves obtained by LSV (Fig. 3-14 b) given that the total resistance of the photoelectrode measured in PEIS equals 𝑅 𝑡𝑜𝑡𝑎𝑙 = 𝑍(𝜔 → 0) = (𝑑𝑗/𝑑𝑉) -1 . 17

In both the first and last cycles of PEIS analysis, it was found that under high illumination conditions, instead of the two characteristic relaxations in PEIS, [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF]115 only one relaxation was observed (Fig. 3-15 a and b). Indeed, the two relaxations may appear close in frequency and are consequently merged, or any of both relaxations might lie outside the range of experimentally explored frequencies, or any of both relaxations could present very small impedance and could be a small shoulder at either HF or LF.

However, at lower illumination levels (129.57 mW/cm 2 ) the two typical relaxations of semiconducting photoelectrodes were observed (Fig. 3 To determine the kinetic parameters for all PEIS spectra (including those for which the two relaxations were not resolved i.e. those obtained at high illumination), kinetic parameters determined at the lower illumination intensity were used as initial guess for the fitting. The fact that PEIS obtained at 129.57 mW/cm 2 and at potentials of -1.25 and -1.10 V (vs. SCE) displayed the same maximum of the LF relaxation in the Bode plot of -Z", indicated that charge transfer rate was not altered in this potential range.

The results of the fitting of experimental PEIS spectra obtained for the Rh:SrTiO3 -Ch photoelectrode are shown in Table (within the annex section at the end of this thesis).

The charge transfer kinetics measured on the clathrochelate-modified semiconductor was found to be 10 times larger than the kinetics measured on the pristine semiconductor, thus showing evidence of the electrocatalytic effect that was observed also in CV under cathodic bias. However, the recombination rate was also found to be faster on the Rh:SrTiO3 -Ch photoelectrode. Therefore, the fraction of photoexcited electrons transferred to the electrolyte is almost the same, with and without the modification of the semiconductor with the clathrochelate (compare the values of η in The effect of the electrode potential on the PEIS spectra follows the usual trend reported in the systems discussed so far, i.e., the Nyquist representations of PEIS spectra expand as the potential is made less negative. Such fact is attributed to a decreasing value of the photogenerated flux of minority carriers (I0) associated to the shrinking of the space charge region and the decreasing band bending when the potential goes less negative (see Table within the annex section at the end of this thesis). [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF] Finally, it is worth to comment on the behavior of the space charge capacitance. The Nevertheless, the Mott-Schottky analysis performed to Rh:SrTiO3 -Ch photoelectrodes revealed a straight line with a positive slope (Fig. 3-17). Such slope was also encountered in pristine Rh:SrTiO3 photoelectrodes (Fig. 345678), and was attributed to the strong negative bias applied to the system, causing such strong depletion that inversion conditions were attained, [START_REF] Memming | Semiconductor Electrochemistry[END_REF][START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF]206,208 and therefore the surface of a p-type semiconductor behaved with n-type conductivity. [START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF] Indeed, the presence of the clathrochelate does not modify the potential range where inversion occurs in this semiconductor (compare Fig. The effect of the electrode potential on PEIS spectra is better appreciated in the Bode representation of -Z". Fig. 3-18 b shows that the frequency position of the LF relaxation does not change with applied bias, suggesting a constant value of kt no matter the electrode potential. However, the electrode potential shifted the HF relaxation down to lower frequencies, an indication that the space charge capacitance is changing (Table within the annex section at the end of this thesis). Regarding the effect of light power on PEIS spectra, we found that the charge transfer and recombination rate constants were not affected by light intensity, as observed in the LF relaxation (Fig. 3456789101112131415161718). This may be due to the fact that, under accumulation conditions, the concentration of majority carriers, responsible for the charge transfer reactions, is not considerably affected by photoexcitation.

Surface characterization after photoelectrochemical testing

The observation that the electrochemical response was varying with the number of cycles under cathodic polarization was not surprising, because of the previous report mentioned above showing that, under strong cathodic polarization, clathrochelates can be decomposed into another active form of Co at the surface of the electrodes. In principle the evolution observed here under cathodic polarization could be due to the same fact. This observation confirms clathrochelates as versatile molecules that can act themselves as electrocatalysts, [126][127][128]139 or can be transformed into other active compounds under electrolysis conditions. 129 In the previous report on the First of all, the fact we were able to observe Co through the Nafion film at the surface indicates that this film was very thin, with a thickness of at most 10 nm. The intensity of the XPS spectra was found to be quite low, due to the blocking effect of Nafion and to the low loading of the catalyst. After electrochemical testing, it was found that the Co 2p signals shifted to higher binding energies, suggesting that Co was now present with a higher oxidation state, in agreement to a recent report. 211 Additionally, the shake-up satellites were still observed after electrochemical testing, suggesting that the Co species was still paramagnetic. We note that the electrodeposited species reported previously is not necessarily the same as the one we have encountered here. system revealed that the XRD pattern showed only reflections coming from the predominating semiconducting substrate which is due to the small catalyst loading. 212 Likewise, the SEM micrograph (Fig. 3-20) presented the same characteristics as all other micrographs presented so far, i.e., the presence of important surface roughness, and the inability to reveal the presence of neither Nafion nor the Cu catalyst. For this material, SEM images before and after electrochemical testing were indistinguishable.

Therefore, we decided that XPS would more likely be the appropriate technique to provide not only convincing proofs for the existence of Cu at the surface, but also to assess its chemical nature. Indeed, the presence of Cu at the surface of Rh:SrTiO3 was have not been attained. Nevertheless, it is possible to affirm that the flat-band potential for this system is somewhere above 0.28 V (vs. SCE).

Additionally, OCPD measurements gave access to the kinetics of charge transfer under open-circuit conditions. [START_REF] Babenko | Kinetics of the photoelectrochemical evolution of hydrogen at p-type Si[END_REF][START_REF] Ponomarev | Theoretical analysis of the laser-induced phototransient response of semiconductor | electrolyte circuits with 'currentdoubling' reactions[END_REF] The behavior is similar to those of other systems discussed so far: charge transfer and recombination rate constants are notably small and nearly independent of light power. For Rh:SrTiO3 -Cu, kt is around 0.04 s -1 and kr is around 0.01 s -1 . CHAPTER 3 123 concentration at the surface according to eq. 3-2. As a result, an important amount of the potential drop probably appears in the Helmholtz layer (Fermi level pinning). [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF][START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF] 𝑘 𝑟 = 𝑘 𝑟 0 exp (

-𝛽𝑞𝜙 𝑠𝑐 𝑘𝑇 ) (3-2)
Where 𝑘 represents Boltzman's constant, 𝑇 is the absolute temperature, 𝑞 is the elemental charge, 𝜙 𝑠𝑐 is the potential drop in the space charge, and 𝛽 is an empirical parameter related to surface non-ideality caused by Fermi level pinning. In this context, 𝑘 𝑟 is treated as a pseudo first order rate constant.

The potential dependence of the recombination rate constant depends on the nonideality factor (referred here to as β), while the potential dependence of the charge transfer rate constant depends on the transfer coefficient (herein referred to as α). This nomenclature is usual in published research. 115,213,214 It should be noted here that there is a dispersion of the parameter's nomenclature in published literature; hence, the electrochemical literature can be confusing, because these two letters (α and β) have been sometimes exchanged to refer to the opposite parameter. [START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF] Returning to the qualitative analysis of PEIS spectra, Fig. 3 more electrons go to the surface while the holes remaining inside the material create an opposing electric field that continually reduces the band bending (𝜙 𝑠𝑐 ). According to eq. V (vs. SCE) is attributed to the strong polarization applied to the electrode, that allowed to reach inversion conditions, [START_REF] Memming | Semiconductor Electrochemistry[END_REF][START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF]206,208 where the bulk of the material behaves as a ptype semiconductor while the surface as a n-type character. [START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF] As mentioned before, for an ideal semiconductor-electrolyte junction, the whole of the applied potential drops in the space charge and there is almost no potential drop in the Helmholtz layer, therefore, 𝑘 𝑡 is independent of the electrode potential. 205 However, in this case, we observed a decrease of 𝑘 𝑡 as the electrode potential was made more positive, indicating that the photoelectrode did not behave ideally and that there is a potential drop in the Helmholtz layer that influences the rate of charge transfer.

Assuming that the Tafel equation describes the HER reaction (eq. 3-4) [START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF] 𝑘 𝑡 = 𝑘 𝑡 0 exp (

𝛼𝑞𝜙 𝐻 𝑘𝑇 ) (3-4) CHAPTER 3 127
Where 𝛼 is the transfer coefficient and 𝜙 𝐻 is the potential drop in the Hemholtz layer,

and considering that the applied potential is the sum of the drops in the space charge and the Helmhotz layer (eq. 3-5)

𝑉 = 𝜙 𝐻 + 𝜙 𝑠𝑐 (3-5)
a plot of the logarithm of 𝑘 𝑡 and 𝑘 𝑟 vs. applied bias should give a straight line, which is in excellent agreement with our experimental results (Fig. 3-26 b). From a mechanistic perspective, the slope of the plot of ln 𝑘 𝑡 vs 𝑉 gives the charge transfer coefficient for the HER as determined to be α = 0.28 in this material.

On the other hand, the slope of the plot of the logarithm of 𝑘 𝑟 vs. E gives a measure of β.

For an ideal semiconductor|electrolyte junction β = 1, and departure of this ideal value is related to the presence of surface states, and their influence in the potential distribution across the interface. In some recent literature, such non-ideality factor was just ignored and PEIS spectra were fitted and analyzed without considering this effect, even though the presence of surface states is established through the dependence of rate constants upon the applied potential. [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF]215 However, there are some other publications where this parameter is effectively determined. 115,214 Values of β have been determined

for TiO2 plane (011) and plane (100) to be 0.11 and 0.21, 214 and for CdS values ranging from 0.43 to 0.67 have been determined, 115 with a clear dependence on the nature of the semiconductor|electrolyte interface. It is interesting indeed to see how the same authors can neglect this non-ideality factor [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF]215 after having considered and determined it more than a decade before. 115 Perhaps the origin of this was expressed by the authors, who established that their publication [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF] was devoted to a phenomenological analysis only.

In the case of Rh:SrTiO3 -Cu photoelectrodes, we found that β = 0.48, indicating that this junction behaved non-ideally. behavior is consistent with previous determinations in other photoelectrocatalytic systems. [START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF] The fitted results of PEIS spectra, used to construct Fig. 3-25 a to e are reported in Table (within the annex section at the end of this thesis).

Photoelectrochemical kinetics of the OER at the surface of Rh:SrTiO3 -Cu photoelectrodes

The kinetic parameters and interfacial capacitances of Rh:SrTiO3 -Cu photoelectrodes during the OER were determined by PEIS analysis. [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF][START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF] Typical PEIS spectra are reported in Fig. 3-27. The Rh.SrTiO3 -Cu system displays the two characteristic relaxation constants that have already been discussed for Rh:SrTiO3 and Rh:SrTiO3 - Fitting results of PEIS spectra are compiled in Table (within the annex section at the end of this thesis).

The kinetic information was determined by fitting PEIS spectra. Results (Fig. 3-27 a to c) show the effect of applied potential and illumination level. Fig. 3-27 a shows the the capacitance associated to the HF semi-circle for two different light power values at constant electrode potential. The physical meaning of the capacitance associated to the HF relaxation must be discussed carefully because the phase angle (-43°) is far away from the (-90°) value expected for a pure capacitance (Fig. 3-27 c). The capacitance of the HF relaxation can be considered as a true interfacial capacitance for phase angles between -90° and -80°. This is obviously not the case for this system. As discussed above, the capacitances experimentally determined contain contributions from surface roughness, surface states and the Nafion polymer.

Structural, chemical and morphological characterization of the Rh:SrTiO3 -

Pt photoelectrodes

Measurements on the HER and OER at Rh:SrTiO3 -Pt photoelectrodes have also been made. Following the same characterization methodology employed so far, we have obtained the XRD pattern of the material. The XRD pattern of the Rh:SrTiO3 -Pt powder was found indistinguishable from pristine Rh:SrTiO3. Fig. 3-28 shows that main diffraction peaks correspond to reflections coming from the typical perovskite structure of SrTiO3 that was already discussed. The most likely explanation for not observing any diffraction peak from Pt is the relatively low loading of the surface co-catalyst.

Likewise, the SEM image revealed no differences with that of pristine Rh:SrTiO3, indicating that surface loading of platinum does not change the morphology of the semiconductor (Fig. 34) which was not a surprise. These two observations have been reported before in similar photoelectrocatalytic systems. 212 XPS analysis has proven to be sensitive enough to put in evidence relatively small amounts of catalysts. For the Rh:SrTiO3 -Pt solid, the XPS spectrum of Pt 4f is shown in Fig. 3-29 c, displaying an asymmetric shape which is characteristic of metallic Pt. 216

Photoelectrochemical characteristics of Rh:SrTiO3 -Pt photoelectrodes at open-circuit

The first photoelectrochemical experiment performed on the Rh:SrTiO3 -Pt photoelectrodes was to illuminate and to observe the increase of the electrode potential (Fig. 3-30 a). The trend observed with Rh:SrTiO3 -Pt is similar to what was observed for the different photoelectrodes tested so far. This is the indication that the material kept its p-type conductivity with the presence of Pt at the surface. The photopotential was around 1 V, which was the largest value obtained for all the materials studied in this work.

Photoelectrochemical kinetic studies performed under open circuit conditions [START_REF] Babenko | Kinetics of the photoelectrochemical evolution of hydrogen at p-type Si[END_REF][START_REF] Ponomarev | Theoretical analysis of the laser-induced phototransient response of semiconductor | electrolyte circuits with 'currentdoubling' reactions[END_REF] revealed that the charge transfer and recombination rate constants displayed similar values and were nearly independent of light intensity. Fig. 3-30 b might induce the thought that kt increases linearly with light power, while kr decreases. However, the variations are so small that it is not possible to affirm the existence of a true dependence of kinetic parameters upon illumination intensity. to high applied overpotentials. However, published models concerning the OER do not predict Tafel slopes greater than 120 mV/dec. [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF][START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF][START_REF] Bockris | Mechanism of Oxygen Evolution on Perovskites[END_REF] Considering this, the Tafel analysis for current-potential curves obtained for Rh:SrTiO3 -Pt photoelectrodes towards the OER shall not be further performed. Suffice it to say that a dual Tafel slope suggests the coexistence of two mechanisms running in parallel, as supposed for the HER. Evidently, nowadays models for the OER are still limited and require further improvements. The cause behind the discrepancies between observed and predicted Tafel slopes might be that the surface is likely to present different sites with distinct reactivity, in contrast to model assumptions. [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF][START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF][START_REF] Bockris | Mechanism of Oxygen Evolution on Perovskites[END_REF] In the case of semiconducting photoelectrodes, another cause CHAPTER 3 136 could be that a fraction of the applied potential falls in the space charge region 66 thereby justifying a weaker potential dependence of the current density.

Photoelectrochemical kinetics of the HER at Rh:SrTiO3 -Pt photoelectrodes

The electrochemical HER kinetics on Rh:SrTiO3 -Pt was also studied by PEIS analysis and interpreted with the same kinetic model used so far. [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF][START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF]115 Typical Nyquist plots recorded between -1.30 V and -1.10 V (vs. SCE) are shown in Fig. 3-32 a. For this system, the two characteristic semi-circles were clearly resolved. Fig. 3-32 a and b show that the HF time constant was nearly independent of the electrode potential, which is typical of photoelectrodes presenting Fermi level pinning. [START_REF] Lewerenz | Photoelectrochemical Water Splitting Materials, Processes and Architectures[END_REF] Fermi level pinning can be qualitatively assessed by the fact that the maximum of the LF relaxation depended on the applied potential (Fig. 3-32 b, highlighted with dashed lines). It was also found that the recombination rate constant increased as the applied potential was made less negative, because the LF relaxation tends to expand.

For this system, light had virtually no effect on any of the kinetic parameters, as observed in Fig. 3-32 c. This is perhaps due to the strong contribution of dark currents to the overall response. As a final comment for the qualitative interpretation of PEIS spectra, it may be seen that the phase of the HF relaxation is never larger than -55°.

Again, this is the indication that the fitted capacitance associated to this relaxation should not be considered as a pure capacitance, where the phase angle should be preferably -80 ° (or even closer to the ideal -90°). 202 As a consequence, the discussion of the space charge capacitance that follows should be considered carefully, because, as expressed before, the HF relaxation should contain contributions not only from the space charge capacitance, but also from surface roughness and the polymeric Nafion as well. photoelectrodes, and is attributed again to the inversion of the semiconductor due to the high applied driving force, [START_REF] Memming | Semiconductor Electrochemistry[END_REF][START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF]208 that makes that the semiconductor behaves as a p-type in the bulk and as a n-type at the surface. 65 c shows the evolution of the recombination rate constant, which decreases slightly as the electrode potential is made more negative (observe that the potential axis in Fig. 3-33 c has been inversed for the sake of clarity): this is consistent with eq. 3-2. The effect of electrode potential on rate parameters is opposed, i.e., kt increases when kr decreases, which is a usual behavior for photoelectrodes displaying Fermi level pinning.

The increasing value of kt when the applied potential is made more negative is related to the increasing driving force in the Helmholtz layer, while the decreasing value of kr with more negative potential is associated to a decrease of the surface concentration of majority carriers. Therefore, the efficiency of the transfer of photoexcited electrons in this photoelectrode increased with band bending, and attained a value close to 50% at -1.30 V (vs. SCE).

Both kr and kt are shown in a Tafel plot in Fig. 3-34 b. As already discussed, the linear relationship observed on this Tafel plot is expected from theory, [START_REF] Leng | Investigation of the Kinetics of a TiO2 Photoelectrocatalytic Reaction Involving Charge Transfer and Recombination through Surface States by Electrochemical Impedance Spectroscopy[END_REF] but the mechanistic complexity of multistep charge transfer during the HER and the presence of surface states can cause the potential dependence of kinetic constants to be quite odd in frequent cases. [START_REF] Upul Wijayantha | Kinetics of oxygen evolution at α-Fe2O3 photoanodes: a study by photoelectrochemical impedance spectroscopy[END_REF]215 For the Rh:SrTiO3 -Pt photoelectrode, the slope of ln(kt) vs. E provided a Butler-Volmer transfer coefficient of α = 0.21, in reasonable agreement with the Rh:SrTiO3 -Cu material. On the other hand, the slope of the ln(kr) vs. E plot gave a very low value for the ideality factor (β = 0.04). This value indicates that the presence of Pt at the surface makes the photoelectrode highly non-ideal, suggesting a very high density of surface states with the concomitant Fermi level pinning. Apparently, the highly nonideal behavior of the interface can be a consequence of the important dark current baseline of the LSV (Fig. 3-31 a), which dominates the current-potential characteristics of the photoelectrode, while the photocurrent is quite small compared to such background current in the dark, and hence the negligible effect of light on PEIS spectra (Fig. 3-32).

The kinetic parameters obtained after the fitting of PEIS spectra for Rh:SrTiO3 -Pt under cathodic polarization are compiled in Table , within the annex section at the end of this thesis. The fact that the OER is a multistep heterogeneous process involving the exchange of four electrons makes not surprising the observed slow kinetics. These values follow the trend observed so far for all other photoelectrodes. Interestingly, the presence of Pt at the surface of Rh:SrTiO3 did not improve the kinetics of charge transfer towards the OER, in contrast with the notable increase in the rate for the HER.

There is another interesting difference in the behavior of this material under positive and negative potentials. Indeed, when we studied the HER, the HF relaxation (which should possess an important contribution from Csc) did not depend much upon applied potential, suggesting an almost constant interfacial capacitance, which is a cause of Fermi level pinning. Such Fermi level pinning causes an important drop of potential in the Helmholtz layer and therefore the maximum of the LF semicircle (kt) depended on the applied potential. In contrast, Fig. 3-35 b clearly shows that the HF relaxation was significantly affected by electrode potential, while the LF relaxation looks nearly the same, no matter the applied potential was. This indicated that the charge transfer rate was constant and independent of applied potential (which again is normal for an ideal semiconductor|electrolyte junction) and the absence of Fermi level pinning, hence the stronger influence of the applied potential upon the HF relaxation (i.e., upon Csc).

The limited effect of light intensity upon PEIS spectra can be appreciated on Fig. 3

Kinetic comparison of the different photoelectrodes studied in Chapter 3

The first kinetic determinations reported in this chapter were performed under opencircuit conditions. The four photoelectrodes did not present significant differences among them. In general, the charge transfer rate constant possessed values of approximately 0.04 s -1 and was larger than the recombination rate constant, which displayed values of approximately 0.01 s -1 , excepting the case of Rh:SrTiO3 -Pt photoelectrodes, where both kt and kr presented similar values. Overall, the kinetics of charge transfer at open-circuit was notably slow without applied bias.

Mechanistic insights into both the HER and OER were discussed in terms of a Tafel analysis. Table 3-2 summarizes the Tafel slopes obtained for each photoelectrode, towards the HER and the OER. Rh: SrTiO3 -Pt 107 89 a 163 b a determined in the potential range from 1.5 to 1.4 V (vs. SCE); b determined in the potential range between 1.3 and 1.2 V (vs. SCE).

For the HER, the systems Rh:SrTiO3, Rh: SrTiO3 -Ch and Rh: SrTiO3 -Pt displayed Tafel slopes fairly close to 120 mV/dec, suggesting that either the Volmer step [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF]217 or the Heyrovsky step (in the region of high surface density of adsorbed H) [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF] are possible rds in the multistep mechanism. Conversely, the OER at Rh:SrTiO3, Rh: SrTiO3 -Ch and Rh: SrTiO3 -Cu exhibited Tafel slopes fairly close to 60 mV/dec, suggesting that the reaction 𝑀 -𝑂 = 𝑀 + 1/2𝑂 2 is the rds, with 𝜃 𝑂 ≈ 0 and 𝜃 𝑂𝐻 ≈ 1. [START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF] Additionally we observed Tafel slopes of 202 mV/dec for the SrTiO3 -Cu system towards the HER, and a dual Tafel behavior for SrTiO3 -Pt for the OER. It is worth mentioning that current mechanistic models do not account for these observations. [START_REF] Shinagawa | Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion[END_REF][START_REF] Marshall | Avoid the quasi-equilibrium assumption when evaluating the electrocatalytic oxygen evolution reaction mechanism by Tafel slope analysis[END_REF][START_REF] Bockris | Mechanism of Oxygen Evolution on Perovskites[END_REF] The dynamics of both the HER and the OER of the four different illuminated holes) in the p-type semiconductor. Moreover, the kinetics of charge transfer in these systems was extremely low and showed no difference from one system to the other, as observed in the LF relaxation in Fig. 3-36 a.

Much more interesting was the study of the HER. Both the charge transfer and the recombination rate constants can be ordered in the following increasing way: Rh:SrTiO3 < Rh:SrTiO3 -Ch < Rh:SrTiO3 -Cu < Rh:SrTiO3 -Pt, which is highlighted in Fig. In the case of photoelectrodes modified with either Pt or Cu as the catalysts, the HF relaxation occurred at a higher frequency when compared to the other two photoelectrodes, and therefore, Rh:SrTiO3 -Pt and RhSrTiO3 -Cu photoelectrodes had a lower space charge capacitance.

Another striking difference encountered was the dependence of the rate constant upon applied potential (Fig. 3-37). Indeed, for metal modified semiconductors, kt exhibited an exponential dependence on the electrode potential, indicating the presence of surface states and therefore, Fermi level pinning. Such dependence is depicted in a Tafel plot in Fig. 3-37, which allowed to calculate a transfer coefficient for the HER at the surface of Rh:SrTiO3 -Cu and Rh:SrTiO3 -Pt, displaying values of 0.28 and 0.21, respectively.

Conversely, for Rh:SrTiO3 and Rh:SrTiO3 -Ch photoelectrodes, 201 the charge transfer rate constant did not change with the applied potential (Fig. 3-37), a behavior that is consistent with an ideal semiconductor|electrolyte junction. Though, the surface of Rh:SrTiO3 and Rh:SrTiO3 -Ch was far from being ideal, because the recombination rate constant should decrease with increasing (i.e., more negative) bias. However, for these two electrodes, the recombination rate constant kept a constant value. We speculate that such behavior is related to the presence of surface states but with a lower surface density when compared to the metal-modified photoelectrodes. Indeed, a lower density of surface states should not significantly modify the potential drop across the Helmholtz layer, so that the charge transfer rate constant would not be affected, but the presence of surface states could explain surface non-ideality in the behavior of kr.

On the other hand, the recombination rate constant of the metal-modified photoelectrodes varied exponentially with the applied potential. Such dependence (Fig. surface states in the performance of these photoelectrodes, and further demonstrating that the modification of the semiconductor with Pt lead to the most non-ideal surface, where the recombination rate constant was only slightly dependent on the electrode potential.

The potential dependence of Csc deserves a special comment. Indeed, the p-nature of this material is beyond doubts, not only because of multiple previous reports, [START_REF] Iwashina | Rh-Doped SrTiO3 Photocatalyst Electrode Showing Cathodic Photocurrent for Water Splitting under Visible-Light Irradiation[END_REF][START_REF] Jia | BiVO4-Ru/SrTiO3:Rh composite Z-scheme photocatalyst for solar water splitting[END_REF]103 but also due to the determinations of open-circuit potential vs. light power, and the photocurrents under cathodic bias reported in this Thesis. Despite this, Mott-Schottky analysis showed a positive slope throughout this work, in open contrast with the nature of the semiconductor (i.e., p-type semiconductors exhibit negative Mott-Schottky slopes). This fact was explained in terms of an inverted region in the semiconductorelectrolyte interface. [START_REF] Memming | Semiconductor Electrochemistry[END_REF][START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF]206,208 The behavior of the space charge capacitance in the inverted region has been poorly investigated in semiconductor electrochemistry. Indeed, references to this can be found mostly in books [START_REF] Memming | Semiconductor Electrochemistry[END_REF]202 or in relatively old papers. [START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF]208 Only recently, B. Fabre described it in a Chemical Reviews paper. 206 The quantitative behavior of semiconducting electrodes under inversion conditions has been described in specialized books, [START_REF] Memming | Semiconductor Electrochemistry[END_REF] though. The literature presents contradictory explanations regarding its qualitative behavior. Some authors express that under inverted conditions, the photoelectrode behaves metal-like, 208 while others note that p-type semiconductors in inverted conditions behave as n-type at the surface and as p-type in the bulk. [START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF] The experimental results obtained in this thesis support the early opinion of Hagfeldt and Grätzel, [START_REF] Hagfeldt | Light-Induced Redox Reactions in Nanocrystalline Systems[END_REF] because at sufficiently negative potentials, the positive slope in Mott-Schottky plots indicates that the surface of the p-type photoelectrodes behaves as n-type.

Conclusions for Chapter 3

In this Chapter we have reported thorough photoelectrochemical determinations of four photoelectrodes employing visible light irradiation. The photoelectrodes are Rh:SrTiO3, Rh:SrTiO3 modified with the hexachlorine cobalt(II) tris-dioximate (Co(Cl2Gm)3(B-CH3)2) (referred to as Rh:SrTiO3 -Ch), and Rh:SrTiO3 modified with metallic Cu and Pt.

All photoelectrodes and materials were characterized by different techniques including XRD, XPS, SEM, EDS, DRS, EPR. This allowed us to verify that the crystallographic structure of SrTiO3 was not appreciably distorted by the inclusion of Rh as a dopant.

The presence of Rh was confirmed by Diffuse Reflectance Spectroscopy and by X-ray Photoelectron Spectroscopy (XPS). XPS was the technique of choice for the characterization of the interface, since it provided conclusive proof for the presence of metallic copper (atomic ratio Sr:Cu at the surface 87:13) and metallic platinum (atomic ratio Sr:Pt at the surface 90:10) at the surface of Rh:SrTiO3.

The morphology analysis of all these systems was carried out by Scanning Electron Microscopy (SEM), revealing the polycrystalline nature of the semiconducting material.

On the other hand, the presence of surface catalysts could not be appreciated by SEM, probably because of the low loading. The rate of charge transfer on Rh:SrTiO3 photoelectrodes during the HER is slower than on several other materials. [START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF][START_REF] Babenko | Kinetics of the photoelectrochemical evolution of hydrogen at p-type Si[END_REF]205 However, surface modification with a Co(II) containing clathrochelate, metallic Cu and Pt, systematically increased the charge transfer rate constant. Consequently, this work identifies (Co(Cl2Gm)3(B-CH3)2) and copper as possible heterogeneous catalysts to improve the performance of Rh:SrTiO3 photoelectrodes for the HER.

It should be noted that the External Quantum Efficiency (EQE) of all these photoelectrodes could be estimated considering the LED power of the incident light, its energy, related to the measured photocurrent density. Overall, a value of EQE below 0.01 % was estimated, which was not ameliorated by any of the catalysts tested.

Therefore, the model clathrochelate, and Cu and Pt were electrocatalysts that improved the dark current in all cases, but did not contribute to increase the photocurrent. Hence, the photon to current efficiency was not increased by the presence of the surface catalysts studied in this thesis.

CHAPTER 4. The Hydrogen Evolution Reaction Catalyzed by a Model Clathrochelate: Insights from Density Functional Theory analysis

Introduction

Molecular hydrogen of electrolytic grade (obtained by water electro-, photo-or photoelectro-dissociation) is considered as a promising energy carrier. In terms of technology, engineers tend to prefer acidic electrolytes of larger ionic conductivity. In acidic media, iridium dioxide nanoparticles are used for the oxyen evolution reaction (OER) and platinum nanoparticles (usually supported by carbon black) are used for the hydrogen evolution reaction (HER). Platinum is the most efficient catalyst of the HER but as a result of its scarcity and high sensitivity to trace amounts of pollutants, catalysts based on abundant and cheap transition metals are required. Several candidates have been investigated from experimental and theoretical points of view. 125,152,155,156,159,162,163,166,169 The ultimate goal is to incorporate such materials in electrolysis or PEC cells to transform visible light into useful chemical fuels, as discussed in Chapter 3. Regarding electrocatalysis engineering (i.e. the design of customized catalytic sites from both the energetic and geometrical viewpoints), there is still a deficit of theoretical developments, in order to go beyond mere empirical approaches. Theoretical investigations reported so far in the literature on the HER catalyzed by transition metal complexes have been directed to identify stable pathways in the catalytic cycle. 125,155,156,160,162,163,166,168,169 Tris-dioximate metal clathrochelates such as the cobalt species shown in Fig. 4-1 are a family of cage-type metal complexes that have been shown to be efficient catalysts for the HER. [126][127][128] Clathrochelates are basically polymacrocyclic cage compounds which are able to stabilize the low oxidation states of transition metals (e.g. Fe, Co or Ni), thereby offering interesting possibilities to act as hydrogen-producing catalysts with an appealing potential as molecular electrocatalysts. 126,127 Even though DFT studies of the geometric and electronic structures of these molecules have already been reported in the literature, 129,137

Selection of DFT functional and basis set for geometry optimizations

Current literature regarding DFT calculations on clathrochelates, reveals that most calculations have been performed with the B3LYP exchange correlation functional. 129,132,137,139,218 Though, it has been recognized that transition metal complexes can be described by several other functionals. 169 Therefore, the first step in Cl is less elaborated (and less expensive from a computational perspective), it provides a good geometric description of the complex. Therefore, for the present study, we selected the B3LYP functional and the basis 1 to run the geometry optimizations and hessian calculations, and we selected basis 2 to refine the calculated energy through single point calculations. The choice of B3LYP functional and LANL2DZ basis set as an adequate choice is further supported by several publications describing the behavior of various organometallic compounds 157,219,220 including a phthalo-cyaninoclathrochelate. 218 Another important effect considered in these calculations is the presence of solvent. In order to describe the contribution of solvent molecules, we have utilized the PCM-SMD model. To provide an evaluation of the impact of different solvents on the theoretical results, we performed optimization and energy calculations of some significant intermediates in acetonitrile and dimethylformamide. Table 4-2 indicates that, at least from a computational perspective, the trend regarding the stability of different intermediates was not affected by the choice of the solvent. According to this, the full computational study of the mechanism was performed considering DMF as the solvent.

X-ray Near Edge (XANES) and Extended X-ray Absorption Fine Structure (EXAFS) analysis of the Co K-edge in the Co(Cl2Gm)3(B-CH3)2 clathrochelate

X-ray absorption spectroscopy is a very precise technique to determine molecular structures. Indeed, it is interesting to investigate XANES and EXAFS for this complex, and to establish whether the known XRD geometry and the optimized DFT geometry could reproduce adequately the spectroscopic observations. The process of extracting the EXAFS signal is depicted in Fig. 4-2. After the absorption coefficient is obtained (Fig. 4-2 a), a smooth pre-edge is subtracted in order to eliminate instrumental background or absorption from other edges (Fig. 4-2 b).

The similarities between optical UV-Vis and X-ray absorption spectroscopy (XAS) explained in Chapter 1 devoted to the Bibliographic Overview indicates that the selection rules for the transitions are the same in both spectroscopies governed by Fermi's golden rule. 146 Indeed, transitions are allowed between sates whose variation in the magnetic quantum number is ∆𝑚 = ±1. Therefore, transitions between 𝑠 and 𝑝 orbitals are allowed, likewise transitions between p and d orbitals. Conversely, electronic transitions between s and d orbitals are forbidden. In a molecule, there is always a mixture of atomic orbitals to form molecular orbitals. That is why, when there is some extent of mixing (hybridization) between 𝑝 and 𝑑 orbitals, the forbidden 𝑠 → 𝑑 transition can be weakly observed because the 𝑑 orbital have a partial 𝑝 character. Such analysis allows to interpret the XANES part of the XAS for the Co(Cl2Gm)3(B-CH3)2 clathrochelate (Fig. 4-3). Fig. 4-3 shows that the spectrum is dominated by the 1𝑠 → 4𝑝 transition, which constitutes the edge-step. Rigorously speaking, the edge step should be regarded as a combination of 1𝑠 → 4𝑝 transition, with the emission of the photoelectron wave. Moreover, a magnification of the pre-edge region of the spectrum, between 7.68 and 7.72 keV shows a weak pre-edge absorption attributable to a forbidden 1𝑠 → 3𝑑 transition. 130 The apparition of such transition with such a low intensity indicates a certain degree of mix between 𝑝 and 𝑑 electronic levels in the clathrochelate molecule. 201 In the energy range that begins at approximately 0.1 keV beyond the edge step, the Extended X-ray Absorption Fine Structure (EXAFS) can be observed. EXAFS spectroscopy has been notoriously employed for precise structural determinations in the framework of material science and electrocatalysis. [START_REF] Subbaraman | Enhancing Hydrogen Evolution Activity in Water Splitting by Tailoring Li+-Ni(OH)2-Pt Interfaces[END_REF][START_REF] Shinde | Onset potential behavior in α-Fe2O3 photoanodes: the influence of surface and diffusion Sn doping on the surface states[END_REF]130,162,[221][222][223][224][225] Fig. 4 third shell there are Cl and C sp3 atoms. Given the fact that scattering amplitudes are more intense when the atomic number (Z) of the back-scatterer is larger, it is presumed that this third shell shall be predominantly due to Co-Cl single scattering rather than Co-C(sp3). A way to support such presumption is to plot the normalized FT of the spectrum with different k-weights, so that the FT of the first neighbor has the same intensity (Fig. 45). The FT-EXAFS signal scattered from different atoms has different dependencies on k-weight; shells that decrease with increasing k-weight may contain atoms with lower Z. Conversely, shells that grow with increasing k-weight may be composed by atoms with larger Z. [START_REF] Shinde | Onset potential behavior in α-Fe2O3 photoanodes: the influence of surface and diffusion Sn doping on the surface states[END_REF]146 Consequently, Fig. 45suggests that the EXAFS signal appearing at approximately 2 Å could be due to light atoms (corresponding to the second shell of O C sp2 and B), while the EXAFS signal beyond 3 Å could belong to atoms with larger Z (probably Cl from the third shell).

Once such qualitative interpretation of the experimental EXAFS was performed, the EXAFS signal was fitted by using the XRD geometry as a first approach. It is convenient to recall here that the spectrum is fitted according to the EXAFS equation 147

𝜒(𝑘) = 𝑆 0 2 ∑ 𝑁 |𝑓 𝑒𝑓𝑓 (𝑘)| 𝑘𝑅 2 sin (2𝑘𝑅 + 𝜙 𝑘 )exp (-2𝑘𝑅/𝜆 𝑘 )exp (-2𝜎 2 𝑘 2 ) 𝑅 (4-1)
Where 𝜒(𝑘) is the EXAFS amplitude, 𝑆 0 2 represents the amplitude factor, the summation Σ 𝑅 extends over all scattering paths, 𝑁 stands for the number of scatterers for a given scattering path, |𝑓 𝑒𝑓𝑓 (𝑘)| represents the effective scattering amplitude, 𝑅 is the distance between the absorber atom and the back-scatterer neighbour, 𝑘 is the wavevector which is directly related to the energy of the X-rays through the expression 𝑘 = √(2𝑚 𝑒 (𝐸 -𝐸 0 ))/ħ 2 , with 𝑚 𝑒 being the mass of the electron, 𝐸 0 the energy of the edge and 𝐸 the energy of the X-ray, 𝜎 2 stands for the Debye-Wäller (DW) factor, 𝜆 𝑘 is the mean free path of the photoelectron, 𝜙 𝑘 is the total phase shift, whose origin resides in the interaction of the photoelectron wave with the absorber and the scatterer.

Initially, the first and second shells were fitted together (Fig. 4 the third shell. Therefore, fitting parameters of the first and second shells were used as initial guess to perform a more complete fit comprising the whole spectrum.

Consequently, the fit was performed from R = 1.000 to 4.627 Å, thus comprising all relevant EXAFS signals in the spectrum. Likewise, all single scattering and multiple scattering paths shorter than 4.627 Å were considered in the fit. All parameters were permitted to refine without any constraint, excepting the amplitude reduction term 𝑆 0 2 , which was restrained to 1.00. 201 The fit was chosen so as to minimize the reduced χ 2 statistical parameter. As a final 4-3).

The rapid oscillations that could not be reproduced with the fit of the first and second shells only, are now nicely reproduced by the inclusion of the third shell. Fig. 456confirms that the signals of the second and third shells do overlap. In a second step, the EXAFS spectrum was fitted using the DFT optimized geometry.

Initially, the strategy was to follow the same procedure employed with the XRD geometry (as shown in Table 4- This strategy led to an acceptable fit of the EXAFS spectrum, as shown in Fig. 4567. As might be expected, the statistical parameters (reduced-χ 2 and R-factor) indicated a better fit when the XRD geometry was employed. Nevertheless, the possibility to reproduce the EXAFS shape with the DFT geometry indicates that the computational procedure allows the finding of structures that are close to the experiment ones. Experimental Fit; DFT geom.

FT magnitude (a.u.)

R (Angstrom)

Experimental Fit;XRD geom. Regarding the second shell, the position of the B atoms was adequately determined.

However, the positions of O and iminic C appear in the fit with a rather large Δ𝑅 value of up to -0.58 Å (see Tables 2 3 and4

Analyses of the three redox states with two spin multiplicities

After the structural characterization by XAS spectroscopy, we proceeded to study the model clathrochelate in different oxidation states. A previous theoretical study on clathrochelates was devoted to the detailed description of a molecule having fluorine and methyl as the apical and ribbed substituents, respectively. 137 The molecule studied here (Fig. 4-1) possesses a methyl and Cl atoms as the apical and ribbed substituents, respectively. Such structural differences imply that all theoretical results between these two works are not directly comparable. Nevertheless, a comparison between the geometric and electronic characteristics obtained for these two systems shall be undertaken, highlighting the differences and similarities between the two complexes.

From the perspective of the computational procedure, both works have employed the same functional (B3LYP), but the previous work used the Aldrich's group all-electron In the previous work, high-spin and low-spin configurations were considered for the [Co] -1 species only, while only the low-spin case was considered for [Co] 0 and [Co] +1 redox states. In this work, we have calculated high-spin and low-spin configuration for all (three) redox states (Table 4567).

It may be appreciated in Overall, our calculations suggest that there are marked geometric differences between each oxidation state in this clathrochelate. However, the structures of the low and high spin species within the same oxidation state resemble quite closely, in contrast with the conclusions of the previous study where the low and high spin configurations of the reduced clathrochelate were predicted to have a very different structure.

Computation of the equilibrium redox potentials for the Co(Cl2Gm)3(B-CH3)2 clathrochelate

The relevant observable under consideration in this Chapter is the equilibrium redox potential. As was mentioned before, clathrochelates possess two well defined redox waves in cyclic voltammetry, associated to the Co III |Co II and Co II |Co I redox couples. 127,128,139 There are several alternatives described in the literature aiming to estimate the redox potential from ab-initio quantum chemistry. 163,169,174-177 A first possibility is through the calculation of Born-Haber cycles: this is done by optimizing the relevant redox states in gas phase and in a certain solvent. In another manner, the relevant redox states may be directly optimized in the solvent, 169 and the absolute free energy difference between oxidized and reduced states can be referred to an absolute electrode potential according to equation 4-2.

𝐸 𝑎𝑏𝑠 0 = -(Δ𝐺 𝑎𝑏𝑠 0 𝑛𝐹 ⁄ ) (4-2)
Where Δ𝐺 𝑎𝑏𝑠 0 is the free energy change of the reaction 𝑂𝑥 + 𝑒 -= 𝑅𝑒𝑑, where 𝑂𝑥 and 𝑅𝑒𝑑 stand for relevant redox states of the clathrochelate. 𝐸 𝑎𝑏𝑠 0 obtained in such a way should be referred to an appropriate reference. We selected the redox couple Fc + |Fc (i.e., Ferrocenium|Ferrocene) as a reference reaction, which was optimized at the same level of theory of the clathrochelate. In equation 4-2, 𝐹 and 𝑛 stand for Faraday's constant and the number of exchanged electrons, respectively.

The experimental results used to compare our theory were found vs. Ag|AgCl(s)|KCl(aq), and can be appreciated in the right-most column of Table 1 in reference 128. Recently, in order to compare theoretically-estimated equilibrium redox potentials as calculated above, with equilibrium potentials found experimentally with the above-mentioned reference electrode, we employed an experimentally determined value for the Fc + |Fc couple, 139 which is in close agreement to the 0.5 V shift that has been applied before. 152 Nevertheless, we note that the use of usual aqueous references in organic electrochemistry is biased by the liquid junction potential (LJP) 226 which depends on electrolyte composition. Therefore, differences between theory and experiment can have their origin not only in the inherent simplifications of theoretical model (e.g. harmonic approximation or continuum solvation etc.), but also on variations in LJP that are difficult to systematize in different experimental conditions. We found a difference of 130 mV for the cathodic wave, and of 30 mV for the anodic response, which is in reasonable agreement with experiment. Strictly speaking, the actual prediction of redox potentials is currently a challenge, with error values ranging from 150 to 170 mV in calculations of small organic molecules or metallocenes 174,176 or up to 200 mV 227 for organometallic complexes relevant to electrocatalysis.

Consequently, it has been recognized that quantum chemistry should be regarded as a powerful tool to assess trends due to the systematic cancellation of computational errors 124 since the accuracy of absolute values is still challenging. Considering these facts, the calculation of equilibrium potentials using the methodology described in this work was found acceptable.

The reliability of theoretical calculations comes from the predictions these can make. So far, the DFT methodology employed has been tested against (i) the structural information from XRD (Table 45678), (ii) EXAFS spectroscopy and (iii) the prediction of the equilibrium potentials. These facts provide a degree of confidence regarding the theoretical results that shall be presented in the following sections.

Explored pathway for the electrocatalytic HER

The experimental cyclic voltammogram of the clathrochelate of Fig. 4-1 128 indicates that the catalytically active species is a [Co] -1 . This fact that had been recognized before 127,128,130,136,139 and the monomolecular catalytic mechanism depicted in Fig. 4-9 has been explicitly proposed elsewhere, 127,130 in agreement with experimental results. We note that the clathrochelate studied experimentally possessed n-butyl moieties as the apical substituents. 128 Nevertheless, for computational rationality, the molecule calculated here possessed methyl groups as the apical substituents, as depicted in Fig.

4-1.

The monomolecular catalytic pathway comprises the one-electron reduction of [Co] The structure of clathrochelates suggests that a second proton could be then incorporated to the structure to form a H-H complex. Four distinct possibilities were investigated for such a second protonation: they are represented as (NCo), (NN), (NC) or (CC). Likewise, the formula [ 1 Co(NN)HH] 1 stands for a complex species in the singlet state, with two H attached to two adjacent N atoms of the organic ligand, with the overall charge of the complex being +1. Dihydrogen could evolve from such doubly protonated species giving rise to [Co] 1 which is then reduced at the electrode to complete the catalytic monomolecular path.

Analysis of main protonated intermediates

As discussed above, the structure of clathrochelates (Fig. 4-1) is such that various protonation sites can be considered for further dihydrogen evolution. We have hence considered single protonation in Co, N and C, and further second protonation. For each case, we have calculated high spin and low spin states. metric data for the most relevant protonated intermediates.

A detailed discussion of the structure of each particular single-protonated intermediate is not necessary, since it may be appreciated that the 4 + 2 coordination scheme holds approximately for all of them with the particularity that, of the two N atoms lying farther apart, there is always one that is more elongated than the other. The quasi square planar geometry for the clathrochelate persists in these intermediates, with ϕ angles below 170°. Additionally, the X-H distance (X stands for the protonated site in the clathrochelate cage) indicates that H is bound to the clathrochelate by a single bond.

The larger X-H bond distance in the case of [Co(Co)H] 0 suggests that H could be more loosely bound in this species and it might be a reactive intermediate in the catalytic cycle. *In the entry X-H, the X stands for the protonation site in the ligand of the clathrochelate.

In the case of doubly protonated complexes, any attempt to optimize η interaction can be viewed as metal-to-ligand charge transfer to achieve a partial reduction of H + in this intermediate.

Energetic analysis of the HER mechanism

After the geometric description of main species in the proposed mechanism, an energetic analysis is presented, in order to support the partial conclusions obtained so far. The full energetic description presented in the main text, was undertaken with B3LYP functional and cc-p-VTZ for Co and cc-p-VDZ for all other atoms. The energy calculations on some relevant intermediates were also calculated with BP86 and PBE0 functionals (Table 4-10 Table 4-13), displaying the same trend as the B3LYP functional.

Total energies for all species calculated in this work are presented in Table andTable (within the annex section at the end of this thesis). The energies of other doubly protonated species were far above the presented scale (See tables Table A9 and Table A10 within the annex section at the end of this thesis, for the numeric values), possibly as a consequence of structural distortions mentioned in the previous sections. Finally, after dihydrogen evolution, the catalytic cycle is closed by the one-electron

reduction from [Co] 1 + 1e -= [Co] 0 .
However, the energetic barrier calculated for the HER is far too high, since typical barriers for the HER catalyzed by organometallic complexes are around 90 kJ/mol, 162 which is in open contrast with the calculated barrier of 691.65 kJ/mol. A revision of the literature indicates that the mechanism in Fig. 4-9 is the only one proposed for clathrochelates, 127,130 therefore it is tacitly assumed that this is the actual operating mechanism. Though, our results suggest that, at least for the Co(Cl2Gm)3(B-CH3)2 complex, the mechanism depicted in Fig. 4 devoted to the investigation of such a putative species and the possibility to find another transition state that would be more energetically favorable than the one depicted in Fig. 456789.

The [ 2 Co(Co)H] -1 species could be optimized. Structurally it was similar to [ 1 Co(Co)H] 0 , with Co-N distances and bond angles presenting close values (Table 4567891011121314). The orbital d manifold for this species is characteristic of a d 9 transition metal (Fig. 4 ECEC or ECCE) but simultaneously, i.e., the proton and the electron are transferred at the same time. Another recent example of a concerted PCET reaction is given by Frank Neese and coworkers in order to explain the up-hill electrochemical reduction of carbon dioxide by Ni cyclam. 227 Considering the possibility of PCET for the last step, the ECEC mechanism appears to be a reasonable option for the HER electrocatalytic mechanism of the Co(Cl2Gm)3(B-CH3)2 clathrochelate.

Conclusions for Chapter 4

In this Chapter we fully addressed the homogeneous reduction of protons by a model cobalt clathrochelate in the homogeneous phase. To the best of our knowledge, such work was done for the first time. First, geometry optimizations were carried out with several functionals and basis sets. An analysis of published literature and the results obtained in this work suggest that B3LYP is the most appropriate functional to perform DFT calculations on clathrochelates. The geometry optimization did not show appreciable differences when the LANL2DZ basis set with effective core potentials for Co and Cl was employed, or when the mixture of the all-electron cc-pVTZ for Co and cc-pVDZ for all other atoms was utilized. Considering that the former basis set being the less expensive from a computational perspective, it was selected for geometry optimizations and Hessian calculations, while the latter was used for refining electronic energies and molecular orbitals.

Second, the DFT and the XRD geometries were employed to fit the experimental EXAFS spectrum of the clathrochelate. Despite the slight differences between both geometries, EXAFS proved to be sensitive to such minor differences, and therefore the adequate fitting of the observed EXAFS using the DFT geometry was possible with more variables than in the case of the XRD geometry. Nevertheless, the DFT optimized geometry was good enough to allow the fitting of the EXAFS spectrum. Besides, another experimental quantity used to test our theory was the DFT calculation of the equilibrium potential for the model clathrochelate, with an error of 170 mV, which can be considered a good result given the inherent simplifications of the methodology employed, for example, the DFT functional which is not the true functional (the true functional is unknown, as explained in the section devoted to DFT in Chapter 1), the incomplete basis set (the use of a complete basis set is impossible, because a complete basis set would have infinite mathematical functions), the continuum treatment of solvation, and the harmonic oscillator approximation to estimate thermodynamic quantities. It is worth to mention that the methodology employed here is the one that is most widely used in nowadays research.

Subsequently, the three redox states of the clathrochelate and their high and low spin configurations were explored. The HER mechanism calculated here was based on a proposition made in previous publications. 127,130 The explored ECCE mechanism consisted in the activation of a [Co] 0 clathrochelate by one-electron reduction to yield the catalytically active [Co] -1 . In such a species, the Co central atom was found to move 0.7 Å within the organic cage, to be more accessible for direct protonation. In the process, two N atoms of the organic cage decoordinated, thus allowing H + binding through a σ bond between the filled dz 2 orbital of Co and the empty 1s orbital of H + .

Doubly protonated species could be optimized, nevertheless, further HER starting from a doubly protonated species, and then involving a transition state with η 2 -[ 1 Co(CoCo)HH] 1 character was considered unlikely, not only because of important structural rearrangements involved, but also because of the high energy of the transition state. Alternatively, we have studied an ECEC mechanism on the basis of the reduction of the singly protonated [ 1 Co(Co)H] 0 . In the case of this mechanism, the [ 2 Co(Co)H] -1 species could be optimized and its structure was rather similar to [ 1 Co(Co)H] 0 . However, neither doubly protonated species, nor an H2 complex directly bound to Co, nor a transition state were found. These facts prompted us to propose that the last step in the HER catalyzed by the Co(Cl2Gm)3(B-CH3)2 clathrochelate should not occur by sequential steps, but as a proton coupled electron transfer.

CHAPTER 5. Non-steady state response observed through IMVS in Rhodium doped Strontium Titanate based photoelectrodes

Introduction

Different experimental techniques and mathematical models have been developed and reported in the literature to account for heterogeneous photoelectrochemical kinetics.

Among these techniques, Intensity Modulated Photovoltage Spectroscopy (IMVS) has been mostly used for the characterization of dye-sensitized solar cells. [START_REF] Krüger | Charge Transport and Back Reaction in Solid-State Dye-Sensitized Solar Cells : A Study Using Intensity-Modulated Photovoltage and Photocurrent Spectroscopy[END_REF][START_REF] Schlichthörl | Band Edge Movement and Recombination Kinetics in Dye-Sensitized Nanocrystalline TiO2 Solar Cells : A Study by Intensity Modulated Photovoltage Spectroscopy[END_REF][START_REF] Bisquert | Determination of Rate Constants for Charge Transfer and the Distribution of Semiconductor and Electrolyte Electronic Energy Levels in Dye-Sensitized Solar Cells by Open-Circuit Photovoltage Decay Method[END_REF][START_REF] Set | Analytical modeling of intensity-modulated photovoltage spectroscopic responses of organic bulk-heterojunction solar cells[END_REF][START_REF] Liu | Characterization of Photocurrent Generation Dynamics in Polymer Solar Cells Based on ZnO / CdS-Core / Shell Nanoarrays by Intensity Modulated Photocurrent Spectroscopy : Theoretical Modeling[END_REF] In addition to PEIS analysis; which we have been using so far to analyze the kinetics of both the HER and the OER at the surface of Rh:SrTiO3 photoelectrodes, surfacemodified by addition of co-catalysts of diverse nature (see previous chapters), we have also characterized our Rh:SrTiO3-based photoelectrodes by means of IMVS. In order to facilitate the discussion, we will first recall the fundamental aspects of IMVS analysis and will briefly compare IMVS with PEIS in order to outline main differences, despite the fact that the topic was already addressed in the Bibliographic Overview (Chapter 1).

As already shown, the purpose of PEIS is to record a usual EIS spectrum at a constant level of illumination. EIS spectra are obtained by applying a small ac current I ̃ (or voltage 𝑈 ̃) perturbation to the stationary system, and by recording the sinusoidal voltage 𝑈 ̃ (or current I ̃) response. EIS data are analyzed through a transfer function known as impedance (𝑍) which is defined according to eq. 5-1, where the ~ symbol on top of the variables indicates the periodic (harmonic) modulation.

𝑍 = 𝑈 Ĩ ̃

(5-1)

In the case of IMVS, the photoelectrode is held at open circuit conditions and a constant level of illumination is applied to the photoelectrode, joined to a small ac perturbation of the illumination level Φ ̃. This causes the development of an oscillating photopotential (𝑈 ̃). IMVS is analyzed through a transfer function as well as EIS, defined in eq. 5-2

𝐻 = 𝑈 Φ ̃
(5-2)

Where 𝐻 stands for the transfer function for IMVS, 𝑈 ̃ is the modulated photovoltage, and Φ ̃= 𝑙𝑒𝑑 0 (1 + 𝑒 -𝑖𝜔𝑡 ) is the modulation of light, while 𝑙𝑒𝑑 0 represents the LED power.

At this stage, it is necessary to discuss the physical meaning of the IMVS transfer function. When an increasing illumination intensity is applied to a photoelectrode, usually a greater photovoltage is measured. This would increase the numerator (𝑈 ̃) in the fraction written in eq. 5-2, causing an increase in the absolute value of 𝐻 .

Conversely, an increased level of illumination will certainly increase the denominator of eq. 5-2 causing a contraction in the absolute value of 𝐻. Which of these two effects predominates will determine whether the IMVS spectrum will shrink or expand upon increased light power.

Experimentally, it is observed that an increasing light power causes a contraction of IMVS, which permits to conclude that the increase in the incident light power dominates the behavior of the absolute value of 𝐻.

The analogy between PEIS and IMVS if even more evident when the transfer function 𝐻 is depicted in the Nyquist and Bode representations (Fig. 5-1, a c e). photoelectrochemical experiments reported in this thesis. In current literature, PEIS and EIS spectra are usually represented as (-Z", Z') plots in Nyquist coordinates; therefore, the information appear in the first quadrant of the complex plane. However, it is also possible to find photoelectrochemical literature (e.g. in the middle of the 90s) where the Nyquist representation was (Z", Z').

In the case of IMVS, apparently there is no current agreement regarding the Nyquist representation [START_REF] Set | Analytical modeling of intensity-modulated photovoltage spectroscopic responses of organic bulk-heterojunction solar cells[END_REF] as it is for EIS, where the imaginary component of the impedance is plotted with the reversed sign. Therefore, in this work the axis of the imaginary component of 𝐻 shall be depicted as is.

A recent publication clearly indicated that the units of 𝐻, which follow directly from its definition (eq. 5-2), is [𝑉/𝑠𝑢𝑛] , [START_REF] Set | Analytical modeling of intensity-modulated photovoltage spectroscopic responses of organic bulk-heterojunction solar cells[END_REF] where 1 sun = 100 mW/cm 2 . For the sake of consistency with the units of light power employed in this thesis, the units of IMVS that shall appear henceforward are [𝑉/ (𝑚𝑊𝑐𝑚 -2 ) ].

The parameter calculated from IMVS spectra when the technique is applied to dyesensitized solar cells is the electron lifetime (τ), which is directly derived from the maximum of 𝐻 " . Indeed, Fig. Nonetheless, the interest of this thesis is not devoted to the kinetic analysis of dye-sensitized solar cells, but to kinetic determinations of water splitting in photoelectrochemical cells (PEC), as shall be presented now.

Comments on the existing analytical models of IMVS

Even though DSSC and PEC systems are characterized using the same photoelectrochemical techniques, the processes taking place in DSSC and PEC are so fundamentally different that the interpretation of the experimental results using either IMVS or PEIS is totally different. More details on these differences were given in Chapter 1 devoted to the Bibliographic Overview.

The photomodulated electrochemical spectroscopy was created by Laurie M. Peter and co-workers in the middle of the 80s. 228 The seminal theoretical foundations to describe mathematically these techniques were developed by the same author and co-workers between 1995 and 1997. [START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF][START_REF] Schefold | Impedance and intensity modulated photocurrent spectroscopy as complementary differential methods in photoelectrochemistry[END_REF]213,229 It is interesting to note that in the case of PEC systems, the development of PEIS and IMPS was carried out in parallel, with several publications aiming to give a comparison between these two techniques. However, it is striking to note the absence of any mention to IMVS for the characterization of PEC systems 30 years after its invention. In contrast, IMVS characterization of DSSC has been widely developed and applied to multiple cells. To the best of our knowledge, there is only one article published in 2016 presenting the analysis of IMVS of a PEC cell which photoelectrode was n-type hematite. [START_REF] Klotz | Empirical in operando analysis of the charge carrier dynamics in hematite photoanodes by PEIS, IMPS and IMVS[END_REF] The authors of this publication explicitly recognized that, to the best of their knowledge, their paper was the first to present a discussion of IMVS analysis of a PEC used for water splitting. The approach of the authors was empirical, and they did not analyze the photoinduced processes with the help of kinetic models.

A thorough revision of the literature revealed only one mention to a possible analysis by IMVS of a PEC cell. The mathematical description employed consisted in the same kinetic model used in this thesis to address the kinetics by PEIS. [START_REF] Dunn | Tin doping speeds up hole transfer during light-driven water oxidation at hematite photoanodes[END_REF][START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF][START_REF] Schefold | Impedance and intensity modulated photocurrent spectroscopy as complementary differential methods in photoelectrochemistry[END_REF]115,213,229 In particular, Ponomarev and Peter described the possibility to measure very fast reactions under coulostatic conditions at low illumination levels, so that the photopotential was no larger than a few millivolts. 229 Under these conditions the complex plane plot of 𝜔𝑈(𝜔) should give a semicircle which low frequency intercept should occur at 𝜔𝑈(𝜔) 𝜔→0 = (I 0 /𝐶)(𝑘 𝑡 /(𝑘 𝑡 + 𝑘 𝑟 )) , which high frequency limit should be 𝜔𝑈(𝜔) 𝜔→∞ = (I 0 /𝐶 𝑆𝐶 ) and the maximum of which should be located at 𝜔 𝑚𝑎𝑥 = (𝑘 𝑡 + 𝑘 𝑟 ). However, such assertion has not been taken into consideration in the following publications, not by the authors or by other researchers. Indeed, in the framework of this thesis, the first analysis of IMVS responses was performed by plotting a Nyquist representation of the product 𝜔𝑈(𝜔), as suggested by Ponomarev and Peter, but such graph did not display any tendency, and certainly not the one predicted (or suggested) by the authors in their original publication.

Experimental IMVS response of Rh:SrTiO3 -Pt photoelectrodes

The experimentally measured IMVS responses of Rh:SrTiO3 -Pt photoelectrodes obtained in this thesis are presented in Fig. 5-2 a to d. The shape of the IMVS response is strikingly different to any previous report obtained with this technique. [START_REF] Krüger | Charge Transport and Back Reaction in Solid-State Dye-Sensitized Solar Cells : A Study Using Intensity-Modulated Photovoltage and Photocurrent Spectroscopy[END_REF][START_REF] Schlichthörl | Band Edge Movement and Recombination Kinetics in Dye-Sensitized Nanocrystalline TiO2 Solar Cells : A Study by Intensity Modulated Photovoltage Spectroscopy[END_REF][START_REF] Klotz | Empirical in operando analysis of the charge carrier dynamics in hematite photoanodes by PEIS, IMPS and IMVS[END_REF][START_REF] Bisquert | Determination of Rate Constants for Charge Transfer and the Distribution of Semiconductor and Electrolyte Electronic Energy Levels in Dye-Sensitized Solar Cells by Open-Circuit Photovoltage Decay Method[END_REF][START_REF] Set | Analytical modeling of intensity-modulated photovoltage spectroscopic responses of organic bulk-heterojunction solar cells[END_REF][START_REF] Liu | Characterization of Photocurrent Generation Dynamics in Polymer Solar Cells Based on ZnO / CdS-Core / Shell Nanoarrays by Intensity Modulated Photocurrent Spectroscopy : Theoretical Modeling[END_REF] The frequency sweep was performed from high to low frequencies, and a spiral shape was repeatably observed in the Nyquist representation (Fig. 5-2 a). The real and imaginary components of 𝐻 begin with zero absolute value: this is consistent with the initial zero photopotential, that further develops as the experiments runs. Then, as the frequency decreases, the real and imaginary components of 𝐻 oscillate while the absolute value of the transfer function increases.

It is worth to note that these spirals can be observed only when the points-per-decade being measured is relatively large. In this work, the number of points per decade being measured was increased form the default value (10) report where the trigonometric functions are directly employed. [START_REF] Schlichthörl | Band Edge Movement and Recombination Kinetics in Dye-Sensitized Nanocrystalline TiO2 Solar Cells : A Study by Intensity Modulated Photovoltage Spectroscopy[END_REF] In any case, both treatments are entirely analogous.

The frequency sweep rate is controlled automatically by the potentiostat. For frequencies below 1 Hz, the measurement of one IMVS point takes more than 1s, for example, and the measurement of one point at 0.1 Hz takes at least 10 s. Therefore, it was experimentally observed that the time elapsed between two measured points was inversely proportional to the corresponding frequency, i.e., 𝑡 ∝ 𝜔 -1 at frequencies below 1 Hz.

Mathematical model of the IMVS response

The origin of the unusual shape of the IMVS spectra reported in this thesis was initially puzzling. In order to provide an explanation for the observed (spiral) behavior, it was hypothesized that the classic model for heterogeneous electrochemical kinetics at illuminated semiconducting electrodes was still valid in our experimental conditions.

The simplest (and the first) kinetic model that we used coincides with the one presented by Ponomarev and Peter. 229 It is described by the following system of differential equations: ). The time evolution of 𝑄 𝑠𝑐 is due to the interplay between (i) the modulated photoexcitation process 𝐼 0 (1 + 𝑒 -𝑖𝜔𝑡 ), which is a positive term because illumination promotes minority carriers (electrons for a p-type semiconductor) to the conduction band; and (ii) the rate of recombination 𝑘 𝑟 (𝑄 𝑠𝑐 -𝑄 𝐻 ), which is negative because recombination removes photoexcited electrons from the space charge. Note that the recombination rate is 𝑘 𝑟 (𝑄 𝑠𝑐 -𝑄 𝐻 ). Indeed, the difference (𝑄 𝑠𝑐 -𝑄 𝐻 ) equals the amount of charge accumulated at the surface (the physical meaning has already been discussed during the analysis of PEIS data), since the recombination rate is proportional to the surface concentration of electrons.

The second differential equation describes the time evolution of 𝑄 𝐻 . Indeed, the charge in the Helmholtz layer increases with the electron transfer; this is taken into account by the term 𝑘 𝑡 (𝑄 𝑠𝑐 -𝑄 𝐻 ), where such electron transfer is also proportional to the charge accumulated at the surface.

The last equation accounts for the sum of potential drops across the system, i.e., the overall measured potential (𝑈) should equal the sum of the potential drop inside the space charge (𝑄 𝑠𝑐 /𝐶 𝑠𝑐 ) plus the potential drop in the Helmholtz layer (𝑄 𝐻 /𝐶 𝐻 ).

Additionally, the dynamic model was extended in order to include the presence of surface states, as described by Ponomarev and Peter, using the following system of differential equations. potential drop in the space charge (𝑄 𝑠𝑐 /𝐶 𝑠𝑐 ) is equal to the sum of the potential drop caused by charge accumulation in surface states ( 𝑄 𝑠𝑠 /𝐶 𝑠𝑠 ) and the potential drop associated to the charging of surface states (𝑗 𝑆𝑆 𝑅 𝑆𝑆 ). The initial conditions for the two systems of differential equations was set so that 𝐻 = 0 at 𝑡 = 0 . A graphical comparison of the physical meaning of both models is presented in Fig. 5-4 a and b.

Comments on the methods employed for the numerical solution of the system of first order ordinary differential equations

The first set of ordinary differential equations was implemented and solved numerically in Matlab, a very versatile program with a wide library of built-in numerical methods that are available for the most diverse applications. In particular, we are interested in the solution of equations 5-3 to 5-5 and equations 5-6 to 5-10, as discussed in the previous section. The numerical methods available in Matlab to solve ordinary differential equations use the acronym "ode" and a number (with or without letters). Overall, there are seven different methods that are candidates to be used for the solution of the present problem, whose names are ode45; ode23; ode113; ode15s; ode23s; ode23t and ode23tb.

The first solver, ode45, is based on the explicit Runge-Kutta (4,5) method. It is a onestep solver in the sense that, for the computation of the solution at 𝑦(𝑡 𝑛 ) it is only required the solution at the previous time 𝑦(𝑡 𝑛-1 ). Matlab documentation suggests that this should be the first solver to attempt for the majority of the problems. 230 The solver ode23 is based on an explicit Rung-Kutta (2,3) method, and presents similar characteristics to the ode45, but may be more efficient than the latter when applied to problems presenting moderate stiffness. 231 The ode113 is an implementation of a variable order Adams-Bashforth-Moulton solver, which is a multi-step solver that needs the solution at various prior times to predict the solution at y(t n ). 232 These three solvers are recommended for non-stiff systems of differential equations.

Other solvers are recommended for stiff systems of differential equations. The solver ode15s is based on numerical differentiation formulas that can use backward differentiation formulas, known as Gear's method, and this is a multi-step solver. 233,234 The solver ode23s is based on a modified Rosenbrock formula of order 2 and is a onestep solution. 234 . The solver ode23t consists in an implementation of the trapezoidal rule that performs an interpolation between various points in the solution. 233 Finally, the solver ode23tb is based on an implicit Runge-Kutta formula that consists in a mixed implementation of various methods. In the first stage it comprises a trapezoidal rule step (TR) and in the second stage uses a second order backward differentiation formula (BDF2). 235 A detailed presentation of the explicit formulation of each of these solvers lies beyond the scope and purposes of this work, which is devoted to utilize the numerical library already built-in in Matlab. Additionally, it may be appreciated that most solvers perform well. Indeed, only small variations were observed from one method to the other, as depicted in Fig. 5-5 a and b.

The only solver that failed completely (mostly at high frequencies) in the reproduction of the IMVS response was the ode23s. Given that all other solvers provide closely similar results, further numerical simulation was carried out by using the ode23t solver, which is an arbitrary choice.

Numerical exploration of non-steady state IMVS response

The experimental photoelectrochemical response is due to non-steady-state dynamics because the time derivatives cannot be equalized to zero. We note that the spiral pattern described here has never been reported before. Therefore, a numerical exploration of the differential equations 5-3 to 5-5 and 5-6 to 5-10 is necessary in order to shed light onto some questions. For example, (i) which is the cause behind the sense of rotation of the spirals, (ii) what is the effect of charge transfer and recombination rate constants on the what is the effect of illumination intensity upon the IMVS response. Indeed, the complexity of the differential equations describing the exciton generation (electron-hole pair) and the heterogeneous kinetics of water splitting is not straightforward and cannot be predicted without the rigorous solution of the dynamic model. The numerical exploration described below aims to provide a physical explanation regarding why the spirals shrink when the illumination power increases, i.e., we intend to determine whether the shrinking of the spirals observed experimentally is due to a dependence of the kinetic parameters upon light intensity, or whether this is due only to the increase in the light power that increases the denominator of transfer function 𝐻.

A common problem of numerical simulations is that different sets of parameters (kt, kr, Csc, CH, I0, CSS, RSS for example) can reproduce similarly the observed experimental response. In order to circumvent this fact, some parameters should be determined experimentally by other means. For example, recombination and charge transfer rate All the experimental IMVS spirals reported in this thesis rotate clock-wise, in the sense of decreasing frequency and increasing absolute 𝐻 value: this is consistent with a negative frequency modulation of the LED (𝑒 -𝑖𝜔𝑡 ).

In the previous section, two sets of differential equations, describing two different models (with and without surface states) were proposed. The numerical exploration shall be undertaken first with the simplest model (equations 5-3 to 5-5), and then shall be extended to the model comprising surface states (equations 5-6 to 5-10).

First, the influence of the charge transfer and recombination rate constants on the observed IMVS response was determined. On the other hand, the increase in Helmholtz capacitance makes the spirals shrink. The shrinking in the spirals has a limit, when CH is around 10 2 times larger than CSC, and The effect of the photogenerated current of minority carriers (I0) was also explored (Fig. 5-9 a to d). It was observed that I0 had a very strong effect on the absolute value of 𝐻.

The observed trend was that a decrease in I0 causes a shrinking in the spirals.

Finally, the effect of the presence of surface states was also evaluated, as depicted in Fig. 5-10. When surface states are present (equations 5-6 to 5-10), the effect in the oscillatory IMVS response of the other parameters is the same as the effect described just above, when the presence of surface states was not considered. For example, the effect of kt and kr is opposite. Furthermore, as observed before, an increase in kt causes and expansion in the spirals and an increase in kr causes a contraction of the spirals. The effect of interfacial capacitances, and the photogenerated current of minority carriers is the same as the one depicted in Figures Fig. 5-7 to Fig. 56789.

However, the presence of surface states does have an impact in the IMVS oscillatory response. We found that the presence of surface states did not change appreciably the absolute value of the transfer function 𝐻. But we observed that surface states make the non-steady-state IMVS oscillations shift to lower frequencies, as observed in the Bode plots 𝐻 and the phase angle (Fig. 5-10 b to d).

Among all kinetic parameters tested so far, the only one that caused a phase shift in the IMVS oscillatory response was the presence of surface states. The other parameters caused either a decrease (shrinking) or increase (expansion) of the transfer function 𝐻 (of the spirals in the Nyquist representation), but did not cause a phase shift.

These simulations put in evidence that more than one kinetic parameter (interfacial capacitance rate constants, or light intensity) may have the same effect in the observed IMVS. At the beginning of this Chapter, it was experimentally demonstrated that an increase in the light power causes a decrease in the absolute value of IMVS transfer function 𝐻 (Fig. 5-1), by increasing the denominator of its definition (eq. 5-2).

However, it is not clear if the shrinking of IMVS when light power increase as observed in this thesis (Fig. 5-2) was due only to the increase in the denominator of the transfer function, or it was also caused to a change in rate constants, interfacial capacitances, surface states charging or changes in photogenerated flux of minority carriers.

In order to separate the effect of putative variations in kinetic parameters with light power from the inherent tendency of IMVS to shrink due to light power increase, IMVS must be analyzed by normalizing 𝐻 against light power.

Of course, if the light-normalized IMVS response is found to be dependent on light intensity, this will mean that there are kinetic parameters which depend on light power.

The simulations just described have indicated that IMVS alone cannot provide a certain The dynamic models employed so far can be considered as successful because they are able to reproduce the main features of the experimental observations. For example, not only the oscillatory nature of IMVS and sense of rotation of the spirals, but also the absolute value of the transfer function, and the behavior of the real and imaginary components of 𝐻 in the Bode representation, which rise from zero when the frequency is swept decreasingly.

The differences that can be noted in Fig. 5-11 show however that the differential equations are not a perfect model to describe the experimental observations. For example, at small values of the transfer function 𝐻 (high frequency) the shape is adequately reproduced. Though, at larger values of 𝐻 (low frequencies) the experimental IMVS response presented a higher absolute value when compared to the simulation. Likewise, in the Bode representation of 𝐻", it may be seen that peaks and valleys of the experimental non-steady-state IMVS do not coincide precisely with the simulation. Probably, this is due to the heterogeneous nature of the photoelectrode surface, which brings as consequence a distribution of kinetic parameters [START_REF] Ponomarev | A comparison of intensity modulated photocurrent spectroscopy and photoelectrochemical impedance spectroscopy in a study of photoelectrochemical hydrogen evolution at p-InP[END_REF] unusual oscillatory IMVS obtained experimentally was correct (Fig. 5-11).

Once the physical origin behind the IMVS spirals has been understood, we proceeded to compare the experimental behavior of Rh:SrTiO3 and Rh:SrTiO3 -Pt photoelectrodes under these experimental conditions. The interpretation of this observation is that, for Rh:SrTiO3 -Pt photoelectrodes at the light power tested, the shrinking in IMVS spirals is essentially due to the increase in photon flux (Φ) that determines an increase in the denominator of 𝐻 (eq. 5-2). This further suggests that none of the kinetic parameters of the system has changed appreciably with the experimental variation of light.

This observation is also supported by the Bode representation of 𝐻" , when it is compared without light normalization (Fig. 56789101112) and with light normalization (Fig.

5-12 d

). Yet, there is an important phase shift between the four experiments presented here that must be explained. Indeed, the phase shift can be suspicioned in the Nyquist representation since the IMVS measurements performed at 0. Previously, we demonstrated that from one IMVS measurement to another, the photodetector voltage (which is outside the PEC cell and is only responsible for the measurement of light modulation) exhibited a phase shift (Fig. 5-3 b and c). Therefore, such effect was verified, as can be appreciated in Fig. 5-13 a and b, where the real (𝐴') and imaginary ( 𝐴" ) components of the light modulation, as measured by the photodetector, are displayed. Fig. 5-13 shows that the observed phase shift in the IMVS spectra is the same as the one measured in the photodetector, which indicates that the phase shift observed in IMVS has an instrumental origin, and is not due to differences in light-induced interfacial effects.

These IMVS determinations performed on the Rh:SrTiO3 -Pt system recall the PEIS determinations performed on the same system. In both cases, a small dependence of the photoelectrochemical response upon light intensity was evidenced (Fig. 3-33). Thus, the decrease in the absolute value of 𝐻 does have its origin in variations of any of the kinetic parameters. The numeric exploration of the IMVS spirals discussed earlier indicated that the shrinking in the spirals may be due to one or more of the following reasons: (i) to a decrease in charge transfer rate, (ii) to an increase in recombination rate, (iii) to an increase in the space charge capacitance, or (iv) to a decrease in the photogenerated flux of minority carriers.

Taking into consideration that the estimation of rate constants at open circuit conditions, obtained from photovoltage decay measurements (Fig. 3-5 b), revealed that these constants were independent of light intensity, it is probable that the decrease in the absolute value of 𝐻 when light increases is an increase in the space charge capacitance, for the case of Rh:SrTiO3 photoelectrodes.

However, variations in the flux of photogenerated minority carriers (I0) should also play a role, but its qualitative description is far less evident because, in one hand it may be argued that increased light power should directly increase I0, but, on the other hand, it is known that if light power is strong enough to diminish appreciably band bending (i.e., the width of the space charge region), I0 could decrease at strong illumination.

Nonetheless, and inspection of the light power employed in these experiments (up to 2.86 mW/cm 2 ) suggests that the low intensity employed makes unlikely any decrease in band bending. Thus, we speculate that, in this low intensity limit of light power, an increase in light power would increase the photogenerated current of minority carriers, that would contribute to an increase in the absolute value of 𝐻 (which is not observed experimentally as depicted in Fig. 567891011121314).

These considerations reinforce the interpretation that the observed decrease in the absolute value of 𝐻 is due to an increase in the space charge capacitance. Additionally, a phase shift of instrumental origin was put into evidence through the analysis of the ac photovoltage measurements of the photodetector which is related to the optical bench.

It is worth to comment why most IMVS responses reported in the literature do have a shape that resemble a typical EIS response, while in this work we have reported on the highly unusual spiral shape that has never been reported before.

One of the most important studies describing a mathematical model for heterogeneous charge transfer and recombination at illuminated semiconducting electrodes was presented by Peter in 1995. 229 Such study was devoted to the theory of IMPS, but we have employed it here for modeling IMVS. In this paper 229 Peter arrives to analytical solutions for IMPS but does not describe under which conditions these solutions hold.

However, two years after, in 1997, the same authors presented another paper 213 (also devoted to IMPS) where it is clear that they employed the steady-state approximation to find the analytical expressions (in reference 213 , it may be appreciated that equations 9, 10 and 11 are the steady-state solution of the differential equations 6 and 7).

Regarding IMVS, other authors have presented theoretical treatments of this lightmodulated technique. In the context of this discussion, it is necessary to highlight two publications that also use the steady state approximation to find analytical expressions for IMVS in the case of DSSC. [START_REF] Schlichthörl | Band Edge Movement and Recombination Kinetics in Dye-Sensitized Nanocrystalline TiO2 Solar Cells : A Study by Intensity Modulated Photovoltage Spectroscopy[END_REF][START_REF] Set | Analytical modeling of intensity-modulated photovoltage spectroscopic responses of organic bulk-heterojunction solar cells[END_REF] The authors obtain expressions that describe an EISlike shape of IMVS. There are other models that employ Fick-type partial differential equations to treat the diffusion of photoexcited electrons, aiming at predicting IMVS. [START_REF] Krüger | Charge Transport and Back Reaction in Solid-State Dye-Sensitized Solar Cells : A Study Using Intensity-Modulated Photovoltage and Photocurrent Spectroscopy[END_REF] Such models are appropriate for nano-structured photoelectrochemical systems where band-bending does not develop because of the reduced size of the semiconducting particles, and also yield EIS-like shape of IMVS.

The numerical approach used during our thesis has not considered the steady-state approximation and therefore, none of the relevant time derivatives was equated to zero.

This allows concluding that the most widely presented and discussed IMVS response (displaying an EIS-like shape) is observed when the system behaves following the steady-state approximation where all time derivatives are zero. Conversely, when the steady-state approach does not hold, a complex spiral-like shape is obtained, as reported in this thesis.

Both observations (EIS-like versus spiral-like) appear strikingly different. However, these are certainly not so different because they originate form a common root obeying to the classical dynamic model for heterogeneous reactions occurring at illuminated semiconducting electrodes, that unifies the description of this beautiful photoelectrochemical technique.

OVERALL CONCLUSIONS

The main findings and conclusions that can be extracted from the results reported in this thesis shall be presented in coherence with the specific objectives expressed at the beginning of this manuscript. For the sake of clarity, the overall conclusions shall be written in concise items.

- μmol at the surface). In all cases, photocurrents around 15 μA/cm 2 were observed. The observation of cathodic photocurrents is characteristic of p-type semiconducting photoelectrodes working under cathodic polarization.

-The estimated incident photon to current efficiency of all photoelectrodes was notably small (below 0.01 %). Hence, all catalysts were electrocatalysts which did not contribute to light harvesting and to increase the absolute photocurrent. -Under cathodic polarization, the Mott-Schottky plots of the space charge capacitance for all photoelectrodes displayed a positive slope, which indicates that at electrode potentials more negative than -1.1 V (vs. SCE), the semiconductor was forced to inversion conditions, where the Fermi level approaches the conduction band (for p-type semiconductors). Under these conditions, p-type semiconductors behave like n-type semiconductors at the surface and p-type in the bulk.

-Concerning the kinetics of the OER, all photoelectrodes displayed slow electron transfer kinetics, indicating that the surface of Rh:SrTiO3, modified or not by the addition of metallic Pt and Cu, or by the molecular Co(Cl2Gm)3(B-CH3)2 clathrochelate, is not suitable for dioxygen evolution.

-The electrocatalytic mechanism of the molecular Co(Cl2Gm)3(B-CH3)2 for the hydrogen evolution reaction (HER) in the homogeneous phase was computed by means of Density Functional Theory (DFT). Several possible protonation sites were identified in the organic ligand cage, according to our calculations.

Additionally, double protonation in two adjacent N atoms was also found In the 4 th Chapter, a theoretical study of the mechanism of hydrogen evolution catalyzed by a model clathrochelate is provided. During the discussion, the EXAFS spectrum of the organometallic complex was thoroughly analyzed and modelled, and the relevant protonated intermediates involved in the mechanism were identified. The 5 th Chapter deals with the photoelectrochemical dynamics of illuminated Rh:SrTiO3-based photo-electrodes, characterized by the light-modulated photovoltage technique. Unusual results were obtained and are reported in this thesis for the first time. This unexpected dynamic behavior has been modelled by a set of classical differential equations usually used to describe such photo-processes.

  photoelectrodes, thereby proposing possible rate determining steps in the

Fig. 1 -

 1 Fig. 1-1 a) Schematic representation of a Dye Sensitized Solar Cell (DSSC). Main processes occurring during illumination are explained in the main text.

Fig. 1 -

 1 Fig. 1-2. a) Schematic representation of a Photoelectrochemical Cell (PEC).

Fig. 1 - 3 .

 13 Fig. 1-3. Schematic energetic diagram of a p-type semiconducting photoelectrode under a) flat-band conditions b) accumulation conditions at applied electrode potentials more positive than the flat-band potential, c) depletion conditions at applied potentials more negative than the flat-band potential; d) inversion conditions applied potentials much more negative than the flat-band potential

  Spectroscopy (PEIS) to study the heterogeneous charge transfer at illuminated semiconducting electrodes Electrochemical and photo-electrochemical interfaces are usually the seat of multi-step reaction paths. Each step has its own kinetics and a characteristic time constant. The determination of these different time constants provides a detailed description of the underlying microscopic processes. The purpose of Electrochemical Impedance Spectroscopy (EIS) is to measure the impedance of such interfaces over an extended range of frequencies. Each reaction step is excited individually at a characteristic frequency and in favorable cases, all time constants are obtained. From a practical viewpoint, the measures are made by applying to the electrochemical interface a sinusoidal voltage (or current) perturbation of varying frequency, and recording the sinusoidal current (or voltage) output. The amplitudes and phase shifts of both excitation/response signals are determined on a frequency-to-frequency basis and the resulting impedance diagram is plotted in the complex plane, usually in either Nyquist or Bode coordinates. The transfer functions thus obtained are electrical impedances (𝑍), calculated as the ratio between the oscillating voltage (𝑈 ̃) and the current (I ̃) as depicted in eq. 1-1

Fig. 1 -

 1 Fig. 1-4. a) Scheme displaying the measurement of PEIS. Such technique consists in recording a usual EIS response under constant illumination. In this drawing, the counter electrode and the reference electrode have not been represented; b) Scheme showing that, besides the usual real and imaginary part of the impedance, light is another relevant variable in PEIS.

  Fig. 1-5. Illuminated p-type photoelectrode under reverse bias. Main kinetic and parameters discussed in the text are presented

Fig. 1 - 6 . 1 . 5 .

 1615 Fig. 1-6. Typical photoelectrochemical impedance spectrum (PEIS), shown as Nyquist (a) and Bode (b) plots, for an illuminated semiconductor. The figure highlights the relation between PEIS the relevant kinetic parameters discussed in the text.

Fig. 1 - 7 .

 17 Fig. 1-7 b to d aims to model illuminated photoelectrodes where the presence of surface

Fig. 1 -

 1 7 b represents a photoelectrode where charge transfer can occur from both the valence band (represented with the superscript "bulk") and from surfaces states (also called traps, and depicted with the superscript "trap"). Fig.1-7 cneglects charge transfer from surface states, while Fig.1-7d neglects charge transfer from the valence band.

Fig. 1 - 8 .

 18 Fig. 1-8. Typical photoelectrochemical impedance spectrum (PEIS) shown as Nyquist plot. High frequency and low frequency relaxations are highlighted.

1 . 6 .

 16 photoelectrodes is the open circuit photovoltage decay (OCPD). In such technique, the

Fig. 1 -

 1 Fig. 1-9. a) Schematic representation of a photoelectrode being measured under open circuit conditions and constant level of light. In this drawing, the counter electrode and the reference electrodes have not been represented; b) Typical OCPD transient for a Rh:SrTiO3 photoelectrode modified with a Co clathrochelate, obtained in this thesis.

  Fig. 1-10. a) Schematic drawing of a photoelectrode in a PEC configuration being measured by IMVS. Light modulation is the applied perturbation and the oscillating photovoltage is thus generated. IMVS is analyzed through a transfer function, as explained in the text. In this drawing, the counter electrode and the reference electrode have not been represented; b) Scheme of the typical IMVS response in the Nyquist representation. The data for this figure were obtained in our laboratory, with the solaronix DSSC test cell. Note that the experimental data depicted in (b) were not obtained with an electrode setup as depicted in (a).

  processes in DSSC and PEC are so different, that the models of the former cannot be used in the latter, and vice versa, which means that the analysis of IMVS in the context of a PEC cell has no relation with the analysis of DSSC.

Fig. 1 -

 1 Fig. 1-11. Typical IMVS response in the Nyquist representation. The data for this figure were obtained in our laboratory, with the solaronix DSSC test cell. Note that the experimental data depicted in were not obtained with an electrode setup as in a PEC.

Fig. 1 -

 1 Fig. 1-12. a) Crystallographic structure of SrTiO3, front view; b) Crystallographic strcture of SrTiO3, perspective view. Color codes: green, Sr; red, O, white, Ti.

Figure 8 b

 8 Figure 3 b within reference 114) are not orthonormal.

  Fig. 1-13. a) Drawing of the Lewis structural motive of clathrochelates. X and R represent apical and ribbed substituents, respectively; b) graphical abstract for a recently published work of our group. The figure highlights two redox couples present in clathrochelates (blue voltammogram) along with the HER electrocatalysis (red voltammograms).

Fig. 1 -

 1 Fig. 1-14. a) Structure of the Co(Cl2Gm)3(B-CH3)2, the unit cell is indicated; b) Packing of Co(Cl2Gm)3(B-CH3)2 in the solid state, within the unit cell.

1. 11 . Overview of the most important experimental techniques employed for the characterization of photoelectrochemical systems used in this thesis 1 . 11 . 1 .

 111111 X-ray photoelectron spectroscopyX-ray Photoelectron spectroscopy consists in probing a surface with X-ray electromagnetic radiation, which is able to eject electrons from core-levels in the atoms.Such photoelectrons are analyzed according to the distribution of their kinetic energy in order to assess the chemical composition and electronic states present at the surface of the sample. The kinetic energy of the photoelectron satisfies the following equation 138 𝐸 𝑘 = ℎ𝜈 -𝐸 𝑏 -𝑊(1-26)

  positions. The periodic arrangement defines various planes of atoms that are identified by means of Miller indices. Miller indices are the reciprocals of the axis intercept of the plane. For example, if the x-intercept of the plane is in the length of the unit cell in such direction, the first Miller index shall be the reciprocal of a/a, which equals 1. If the yintercept of a plane is in the half of the length of the unit cell in such direction, the second Miller index shall be the reciprocal of b/2b which equals 2. Miller indices are written in parentheses and are not separated by commas. This information is summarized in Fig. 1-15 a. Miller indices are relevant, because they can be used to define the inter-planar distances by means of geometric considerations. For example, in the case of a cubic lattice, where the three dimensions of the unit cell are equal (a = b = c) and all angles are of 90 ° (α = β = γ), the relation between planar spacing and Miller indices is given by 145 𝑑 ℎ𝑘𝑙 = 𝑎 √ℎ 2 +𝑘 2 +𝑙 2

  scattered X-rays waves is given by 2𝑑 ℎ𝑘𝑙 𝑠𝑖𝑛𝜃 (Fig.1-15 b) Thus, the Bragg equation governs the scattering of X-rays from a crystal lattice

Fig. 1 -

 1 Fig. 1-15. a) Drawing to represent the Miller indices, and its relation to different planes in crystals; b) geometric justification of Brag's law.

Fig. 1 -

 1 Fig. 1-16. a) Normalized XAS spectrum of the Co K-edge for Co(Cl2Gm)3(B-CH3)2, that shall be discussed further in this work; b) Scheme illustrating the quantum interference occurring during EXAFS, between the outgoing photoelectron and its scattering caused by the neighboring atoms.

  Therefore, when the electron spin is included in the calculation, the function describing the electron is called spin-orbital, and can be written as 𝜙 = 𝜒𝜗, where 𝜙 is the spin-orbital, 𝜒 represents the Cartesian part of the wave function, as expressed by equation 1-38 or 1-39, and 𝜗 represents here the electron spin, which can be either 𝜶or 𝜷. The spin-orbitals can be "restricted", when only one type of spatial function 𝜒 is employed, irrespective of the electron spin. That means that each spatial orbital possesses one electron 𝜶 and one 𝜷, and the wavefunction is called "restricted Hartree-Fock" (RHF) in the framework of HF calculations, and "restricted Kohn Sham" (RKS)if the framework of DFT.152 Likewise, if the molecule has unpaired electrons, the spatial part of the spin-orbital can be forced to be the same, and the wavefunction is called "restricted open-shell Hartree-Fock" (ROHF) for the HF method, and "restricted openshell Kohn Sham" (ROKS) for DFT. Finally, there is another possibility, where different spins are allowed to be described by different spatial functions, which is called "unrestricted Hartree-Fock" (UHF) in the context of HF calculations, and "restricted Kohn Sham" (UKS) if the context of DFT (Fig.1-17).

Fig. 1 -

 1 Fig. 1-17. Difference in restricted, restricted open-shell, and unrestricted wave-functions. Observe how for restricted and restricted open-shell wave functions there is a single spatial function for α and β spins.

  Powder X-ray Diffraction measurements were carried out at ICMMO in a Panalytical PW3040/60 X'Pert MPD Pro diffractometer (θ-2θ Bragg-Brentano type). The apparatus contained a monochromator (Johansson type), equipped with a Ge (111) monocrystal in order to select the Kα1 (λ = 1.54059 Å) line of the Cu emission spectrum. Detection was performed by a fast X'Celerator PW 3015/20 detector of Real Time Multiple Strip technology. The sample, in powder form, was carefully deposited in the sample-holder with a spinner type "Spinner PW3064", thus allowing to average the intensity of the diffracted signal. Measurements were performed between 20 ° and 100 ° with a step of 0.0167 °, and a global acquisition time of 217 s per step.

  Such value was largely increased to 125 in order to increase the accuracy of the energy estimations. Restricted open-shell Kohn-Sham (ROKS) wave functions were employed for open-shell species (species with unpaired electrons), and restricted Kohn-Sham (RKS) for closed-shell species (species with all electrons paired).Solvent effects were taken into account through the PCM-SMD model.199 Harmonic vibrational frequencies were computed for all the species reported in this work. All the minimum energy structures possessed positive eigenvalues of the Hessian matrix, and the transition state had a unique imaginary frequency. Self-Consistent Field (SCF) convergence was controlled through the group $scf. Pulay's Direct Inversion in the Iterative Subspace (DIIS) and Davidson's damping of the Fock matrix were used in order to accelerate and stabilize SCF convergence. DIIS was forced from the beginning of the calculation by increasing the energy threshold for its triggering from the default 0.5 Hartree to 10 Hartree (ethrsh keyword).

CHAPTER 3 . 3 . 1 .

 331 Catalytic tuning of Rhodium doped Strontium Titanate photoelectrodes Structural, chemical and optical characterization of Rh:SrTiO3 The first step in the characterization of the material was achieved by the crystallographic confirmation of Rh:SrTiO3 by X-ray diffraction (XRD). Non-doped SrTiO3 is known to possess a typical cubic perovskite structure (space group P m -3 m; a = b = c = 3.905 Å; α = β = γ = 90°, cell volume = 59.547 Å 3

Fig. 3 - 1 .

 31 Fig. 3-1. Comparison between experimental XRD pattern for Rh:SrTiO 3 and calculated for SrTiO 3

Fig. 3 -

 3 3 b additionally depicts the emission spectrum of the LED employed

Fig. 3 - 3 . 1 . 1 .

 3311 Fig. 3-2 a) XPS spectra of Ti 2p, Sr 3d and Rh 3d and b) Valence band XPS spectrum for the Rh:SrTiO3 material.

Fig. 3 -

 3 Fig. 3-4 b shows an image of the ITO-

  Rh:SrTiO3 at open circuit conditions Once the chemical characterization of the photoelectrode was accomplished, we proceeded to perform the first photoelectrochemical experiments. The evolution of the open-circuit electrode potential with increasing light intensities is shown in Fig. 3-5 a.

  201

3. 1 . 3 . 1 )

 131 Fig. 3-5. a) Open circuit potential vs. led power for the Rh:SrTiO3 material; b) charge transfer and recombination rate constants, determined by open circuit photovoltage decay.

  predicts a Tafel slope of 60 mV/dec only under very specific conditions of intermediates' surface concentrations within a multi-slope curve, when eq. 1-21 is rds (see Figure 4 d in reference 81). The fact that Fig. 3-6 d exhibits a single Tafel slope over a relatively wide potential window (in open contrast to Figure 4 d in reference 81) made us reject the equations 1-18 to 1-

Fig. 3 -

 3 Fig. 3-7 shows typical PEIS results in the Nyquist plot for Rh:SrTiO3; dots are

Fig. 3 -

 3 Fig. 3-7. Typical PEIS spectra for Rh:SrTiO3; dots represent experimental values and straight lines are the best fit to equation 1; a) Nyquist representation; b) Bode representation of -Z"; effect of light intensity; c) Bode representation of -Z"; effect of electrode potential; d) Bode representation of the phase angle.

Fig. 3 -

 3 Fig.3-8 suggests that the high (negative) overpotential applied to the photoelectrode

  Fig. 3-9. Typical PEIS spectra for Rh:SrTiO3; dots represent experimental values and straight lines are the best fit to equation 1; a) Effect of light in the Nyquist representation; b) effect of electrode potential in the Bode plot of -Z"; c) effect of light intensity in the Bode representation of -Z"; d) Bode representation of the phase angle.

Fig. 3 -

 3 Fig. 3-10 a) Chemical structure of the model clathrochelate studied in this work. b) XPS spectrum of the Co 2p core level for the Co(Cl2Gm)3(B-CH3)2 molecule in powder form.

  Fig. 3-11. a) EPR spectrum of the Co(Cl2Gm)3(B-CH3)2 molecule (black), recorded in frozen DMF solution at 20 K; best fit obtained with easyspin free software; b) SOMO of the Co(Cl2Gm)3(B-CH3)2 molecule, calculated with the B3LYP functional and the cc-pVTZ basis for Co and cc-pVDZ for all other atoms.

Fig. 3 - 201 3. 2 . 1 .

 320121 Fig. 3-12. Comparison of XPS spectra of unmodified Rh:SrTiO3 and Rh:SrTiO3 -Ch photoelectrodes for a) Sr 3d and Ti 2p levels.

Fig. 3 -

 3 Fig. 3-14 a and b show the polarization curve under cathodic and anodic bias,

Further

  Fig. 3-14. Polarization curve of Rh:SrTiO3 -Ch photoelectrodes for a) the hydrogen evolution reaction without and with (529.03 mW/cm 2 ) illumination b) the oxygen evolution reaction, no photocurrents were observed. Scan rate = 1 mV/s; c) Tafel plot for the HER; d) Tafel plot for the OER.

  Fig. 3-15. a) Effect of cycling on PEIS in the Nyquist for the Rh:SrTiO3 -Ch photoelectrode a) Nyquist representation b) Bode representation.

Fig. 3 -

 3 Fig. 3-16 . Typical PEIS spectra for Rh:SrTiO3-Ch a) Effect of light in the Nyquist representation; b) effect of electrode potential in the Bode plot of -Z"; c) effect of light intensity in the Bode representation of -Z"; d) Bode representation of the phase angle.

  Fig. 3-17. Mott-Schottky representation for the Rh:SrTiO3 -Ch photoelectrode under cathodic bias.

  vs E should give a straight line). As discussed before, Mott-Schottky analysis can be misleading because the theory has been developed for flat semiconductors, without surface states, and most real photoelectrodes do not account for these conditions.

3- 8 3 . 2 . 4 .

 8324 photoelectrodes

  electrodeposition of Co clathrochelates, the authors did not determine the exact chemical nature of the electrodeposited active compound, but provided a clue by EDX analysis that the surface of their glassy carbon electrode, after electrodeposition, was containing Co, O and C.129 We also performed some specific experiments to characterize the decomposition product of the clathrochelate. An XPS spectrum was recorded at the Co 2p core level before and after electrochemical testing (Fig.3-19).

Fig. 3 -3. 3 .

 33 Fig. 3-19. XPS of the Co 2p core level of the photoelectrode Rh:SrTiO3 -Ch, before (red) and after (blue) electrochemical testing.

Fig. 3 - 1 .

 31 Fig. 3-20. SEM micrograph of the surface of a Rh:SrTiO3 -Cu photoelectrode.

Fig. 3 - 2 ) 3 . 3 . 2 . 87 3. 3 . 3 .

 323328733 Fig. 3-22. a) Photopotential vs. LED power for the SrTiO3 -Cu system; b) Kinetic parameters at open-circuit for the Rh:SrTiO3 -Cu system.

Fig. 3 -

 3 Fig.3-24 a shows that the HF relaxation constant shrinks upon light power increase.

Fig. 3 -

 3 Fig. 3-24. Typical PEIS spectra for Rh:SrTiO3-Cu a) Effect of light in the Nyquist representation; b) effect of electrode potential in the Bode plot of -Z"; c) effect of light intensity in the Bode representation of -Z"; d) Bode representation of the phase angle.

3- 3 ,Fig. 3 -

 33 Fig. 3-25. Relevant kinetic parameters of Rh:SrTiO3-Cu towards the HER, at various electrode potentials and light intensities; a) space-charge capacitance 𝐶 𝑠𝑐 ; b) charge transfer rate constant 𝑘 𝑡 ; c) recombination rate constant 𝑘 𝑟 ; d) efficiency of minority carrier transfer at the photoelectrode.

Fig. 3 -

 3 Fig. 3-25 d shows the dependence of the efficiency in the transfer of photoexcited

Fig. 3 -. 3 -

 33 Fig. 3-26. a) Mott-Schottky plot for the Rh:SrTiO3 -Cu photoelectrode; b) Tafel plot for charge transfer (red) and recombination rate constants (blue) for Rh:SrTiO3 -Cu photoelectrodes.

Fig. 3 -

 3 Fig. 3-27. Typical PEIS spectra for Rh:SrTiO3-Cu a) Effect of light in the Nyquist representation; b) effect of electrode potential in the Bode plot of -Z"; c) effect of light intensity in the Bode representation of -Z".

Fig. 3 -

 3 Fig. 3-28. a) Comparison of the XRD pattern for Rh:SrTiO3 and Rh:SrTiO3 -Pt materials; b) SEM micrograph of the surface of a Rh:SrTiO3 -Pt photoelectrode.

Fig. 3 -

 3 Fig. 3-29. a) XPS spectrum of Pt 4f in Rh:SrTiO3 -Pt; b) comparison of the XPS spectrum of Ti 2p for Rh:SrTiO3 and Rh:SrTiO3 -Pt materials.

Fig. 3 - 2 ) 3 . 4 . 2 .

 32342 Fig. 3-30. a) Photopotential vs. led power for the system Rh:SrTiO3 -Pt b) Kinetic parameters for Rh:SrTiO3 -Pt in open-circuit conditions. Dashed lines have been put as a guide to the eye.

Fig. 3 -

 3 Fig. 3-33 a to d show the kinetic parameters obtained for this system by fitting

Fig. 3 -Fig. 3 -

 33 Fig. 3-32. Photoelectrochemical impedance spectroscopy for Rh:SrTiO3 -Pt under cathodic polarization a) Effect of electrode potential on Nyquist representation) b) effect of the electrode potential on the Bode representation of -Z"; c) effect of light intensity on the Bode representation of -Z";d) Bode representation of the phase angle.

Fig. 3 - 3 . 4 . 4 .

 3344 Fig. 3-34. a) Mott-Schottky plot for Rh:SrTiO3 -Pt; .b) Tafel plot of kt and kr for the Rh:SrTiO3 -Pt photoelectrode.

  Fig. 3-35. Photoelectrochemical impedance spectroscopy for Rh:SrTiO3 -Pt under anodic polarization a) Effect of electrode potential on Nyquist representation) b) effect of the electrode potential on the Bode representation of -Z"; c) effect of light intensity on the Bode representation of -Z";d) Bode representation of the phase angle.

  photoelectrodes was then studied under polarization by PEIS analysis. An adequate way

3- 36 b

 36 by the Bode plot of -Z" with dashed lines. Additionally, the four photoelectrodes studied here can be classified into two groups according to their behavior. One group is composed by Rh:SrTiO3 modified with metals (Pt and Cu) and the other group is formed by unmodified Rh:SrTiO3 and by Rh:SrTiO3 modified with the hexachlorine containing Co clathrochelate.

3- 37 )

 37 Fig. 3-37. a) Charge transfer and recombination rate constants for Rh:SrTiO3 and Rh:SrTiO3 -Ch photoelectrodes; b) Comparison of the Tafel plot for Rh:SrTiO3 -Cu and Rh:SrTiO3 -Pt photoelectrodes.

  Photoelectrochemical determinations under open-circuit conditions confirmed the p-

  Fig. 4-1. Chemical structure of the model clathrochelate studied in this work.

4 155

 4 our theoretical study was to use different functionals in the calculations. In order to accomplish this, geometry optimizations were undertaken with B3LYP, M06-L, TPSS, BP86, PBE and PBE0 functionals. The highly challenging problem caused by the DFT analysis of clathrochelates was put into evidence when the only functional that permitted an adequate optimization of the Co clathrochelate shown in Fig.4-1 was found to be B3LYP. Indeed, M06-L, TPSS and BP86 were unconverged after 21, 26 and 27 iterations, respectively; while PBE and PBE0 yielded chemically unreasonable structures after 100 iterations. It is worth noting that the number of iterations performed for (un)convergence does not give physical information. Instead, it may suggest that the numeric approach (or the DFT functional) used to solve the problem is (in)adequate. This is perhaps the cause behind the fact that B3LYP functional has been the most popular choice in published literature concerning DFT calculations in clathrochelates. CHAPTER Subsequently, two basis sets were employed to perform geometry optimizations in the framework of the B3LYP functional. First, the LANL2DZ with effective core potentials for Co and Cl (basis 1) was employed. Second, a mixture of basis sets comprising the all-electron basis cc-p-VTZ for Co and cc-p-VDZ for all other atoms (basis 2) was utilized. Table4-1 displays a comparison of crystallographic Co-N distances, and metric data calculated with these two basis sets. The structural comparison was performed in terms of (i) the Co-N bound distances; (ii) the Bailar twist angle θ taken as the dihedral between BNN'B' atoms (from here on, the apostrophe differentiates between the two apical extremes of the molecule) and (iii) the angle φ taken between BCoB'. The angle θ expresses the rotation around the pseudo-C3 axis between the N•••N•••N and N'•••N'•••N' triangles, while the φ angle provides a measure of the displacement of the central Co atom inside the organic cage. Equal bond distances and θ = 0° with φ = 180° are characteristic of D3h symmetry, while of θ = 60° and φ = 180° correspond to D3 symmetry.

Fig. 4 - 3 .

 43 Fig. 4-2. a) Absorption coefficient μ(E) vs. X-ray energy of the Co K-edge; b) background-corrected absorption coefficient μ(E) vs. X-ray energy.

  -6 a and b) in the R space from R = 1.0 to 3.1 Å. For such fit, all single scattering and multiple scattering paths below 3.1 Å were included. It may be appreciated that these two shells reproduce acceptably the shape of the EXAFS spectrum. Fig. 4-6 a permits to conclude that the EXAFS signals coming from the second shell do overlap with the signals from the first shell. Consequently, the EXAFS of the third shell might mix with the EXAFS of the second shell as well.

Fig. 4 - 85 Å - 1 (

 4851 Fig. 4-6 b further shows that there is a rapid oscillation around k = 5.15 Å -1 and k = 6.85

Fig. 4 -

 4 Fig. 4-6. a) FT-EXAFS and b) k 2 χ(k) spectrum of the clathrochelate. Fit from R = 1 to 3.1 Å. Main scattering paths are depicted below the spectrum. MS stands for multiple-scattering; c) FT-EXAFS and d) k 2 χ(k) spectrum of the clathrochelate. Fit from R = 1.000 to 4.627 Å. Main scattering paths are depicted below each spectra. The contribution of MS paths was negligible and is not represented, even though it was considered in the fit.

  scheme around the Co central atom. For the second and third shells, a single DW for

  3), i.e., to use a 4 + 2 coordination scheme and two different DW factors for the first shell while for the second and third shells, to group the DW factors per atom type. Unfortunately, such procedure led to poor quality fits, probably due to the fact that the DFT geometry is slightly different than the XRD geometry. To face this issue, the amounts of variables were incremented, by fitting the second shell similarly to the first, i.e., by employing two DW factors for each atom type, in order to differentiate the 4 + 2 coordination around Co. The fitting results may be observed in Table4-4. For reasonable EXAFS fit values of organometallic complexes see reference 147.

Fig. 4 -

 4 Fig. 4-7. a) Comparison of the FT-EXAFS spectra and fit of the clathrochelate using DFT geometry (left) and XRD geometry (right); b) the same fits shown in a), but in k 2 χ(k) form; using the XRD geometry (up) and the DFT geometry (down).

  (-10 ± 5 eV); S0 2 = 1.00 (restrained variable); R-factor = 0.015; reduced-χ 2 = 1020; MS = Multiple-Scattering; r = restrained variable.Numeric results of the fits compiled in Tables2 and 3have a common trend. The structural determination of the first and third shells is excellent with both XRD and DFT geometries, with Δ𝑅 no larger than 0.1 Å and DW factors in the order of 10 -3 Å 2 . For example, Table4-5 shows that the shortest Co-N neighbors are at 1.91 Å according to XRD, while the prediction from the EXAFS fit is at 1.92 Å, showing that the EXAFS fit overestimated the distance by only 0.01 Å, which is exactly the value of ΔR. Likewise, for the farthest Co-Cl distance, it was determined to be 4.63 Å by XRD and predicted to be 4.70 Å by the EXAFS fit, corresponding to a ΔR = 0.07 Å. As expected, all R values of the model (either XRD or DFT) equal the (R + ΔR) of the EXAFS fit.

  ). The meaning of such values is that both the XRD and the DFT models employed to fit the EXAFS spectrum had a difference with the actual position of O and C iminic atoms in the second shell of the clathrochelate. In order to provide an explanation for these high values in Δ𝑅 for these two atoms in the second shell, a thorough inspection of the cif (crystallographic information file, containing XRD information) corresponding to the clathrochelate was performed. It was observed that the cif contained nine different files, each one comprising a slightly different structure for the molecule. Metric distances corresponding to Co-O and Co-C(sp2) distances, obtained with two of these cif files are shown in Table 4-6.

  basis set (TZVP) for Co and the double-ζ split valence (SV) for all other atoms.

  of [1 Co] -1 shown in the left of Fig.4-8). The structures of the[Co] -1 species that we obtained is different to that of the previous work, 137 where lowspin reduced complex had this quasi-square planar structure, with two N considered as decoordinated, but the high-spin counterpart presented a highly symmetric structure. In the context of HER electrocatalysis, the structure of the [Co] -1 obtained in this work is interpreted as favorable because the exposition of the Co should make the coordination of H + more sterically favorable, while the decoordination of two N leaves vacant coordination sites for H + binding to form a reactive intermediate. These facts shall be discussed later in the text.Finally, the oxidation of the initial[Co] 0 leads to[Co] 1 . Both spin states in the[Co] 1 complex display a highly symmetric structure, with Co-N mean values of 1.94 Å for [1 Co] 1 and 2.08 for [[START_REF] Pham | Modelling heterogeneous interfaces for solar water splitting[END_REF] Co] 1 , which is in agreement with the reported value of 1.92 Å for the low-spin oxidized analogue. The φ and θ angles suggest that the [ 1 Co] 1 and [[START_REF] Pham | Modelling heterogeneous interfaces for solar water splitting[END_REF] Co] 1 clathrochelate are very close to the D3 and D3h symmetry groups, respectively.

Fig. 4 - 8 .

 48 Fig. 4-8. View of Co clathrochelate studied in this work. This figure highlights the position of Co inside the organic cage for [Co] -1 (left), [Co] 0 (center) and [Co] 1 (right).

  0 to form the catalytically active [Co] -1 , and then the formation of various protonated intermediates, usually termed in the literature as a "hydride complex". Previous theoretical work on clathrochelates has considered protonation on the iminic C. 129 Thus, we have extended this approach by calculating three possible protonation sites, namely, Co, N and C. In order to clarify the nomenclature herein employed, it may be defined that the formula [ 1 Co(C)H] 0 represents the model clathrochelate of Fig. 4-1, in the singlet state with a proton bound to an iminic C of the ligand, with an overall zero charge of the complex. In the same way, the formula [ 1 Co(Co)H] 0 means that the proton is coordinated directly to Co, with multiplicities and charges being the same as in the first example. Whenever the spin multiplicity is not specified, as in [Co] -1 , we are referring to the redox state only, without distinction between spin states.

Fig. 4 -

 4 Fig. 4-9. Monomolecular catalytic mechanism usually proposed for Co containing clathrochelates.

2 -[Fig. 4 -

 24 Fig. 4-10. Structure of the transition state leading to dihydrogen evolution from the model clathrochelate; a) perspective view, b) side view.

Fig. 4 -

 4 Fig. 4-12 shows an energetic diagram of the electrocatalytic HER mechanism. Our

Fig. 4 -

 4 Fig. 4-12. Energy profile for the hydrogen evolution reaction catalyzed by the model clathrochelate investigated in this work. Blue thin lines represent high spin species, red thick lines stand for the low spin species. Dashed lines connecting different states have been put as a guide to the eye. The figure is composed of four panels. Panel (a) represents the energy evolved upon the one electron reduction of the catalyst, high and low spin energies for the [Co] -1 species are close enough that cannot be appreciated separately in the figure. Panel (b) represents the energy change associated to the first protonation of the catalyst, distinct protonation sites are written near each line. Each state in panel (b) corresponds to an equivalent coordinate of reaction. Panel (c) up, conveys the energy change evolved upon the second protonation and further hydrogen evolution through a transition state (represented in green). Panel (c) down, depicts the one-electron reduction of the clathrochelate with the proton in Co, and the further Proton Coupled Electron Transfer. Panel (d) deals with the reduction of [Co] + to [Co] 0 to regenerate the initial state of the catalyst. It should be kept in mind that panels (a) and (d) depict only the relevant cobalt species; however, the initial state in panel (a) truly corresponds to 2[Co] 0 + 2HA and the final state in panel (d) is 2[Co] 0 + H2 + 2A -, with HA being trifluoroacetic acid.

Fig. 4 -

 4 Fig. 4-13. Alternative ECEC monomolecular catalytic mechanism proposed for the Co(Cl2Gm)3(B-CH3)2 clathrochelate.

- 14 )

 14 Fig. 4-14. Orbital d manifold in [ 2 Co(Co)H] -1 ; we note that these orbitals are not degenerate b) Magnification showing the dz 2 orbital of Co forming a σ bond with the empty 1s orbital of H + .

Fig. 5 -

 5 Fig. 5-1 a c and e show the experimental IMVS response of a dye-sensitized solar cell78-

  Fig. 5-1 d), indicating that the electron lifetime decreases with increasing illumination

Fig. 5 - 3 . 2 Fig. 5 -Fig. 5 -Fig. 5 -

 532555 Fig. 5-2. Experimental IMVS response for a Rh:SrTiO3 -Pt photoelectrode, effect of light intensity; a) Nyquist representation; b) Bode representation of the imaginary component of H; ) Bode representation of the real component of H; d) Bode plot of the phase angle.

  1 + 𝑒 -𝑖𝜔𝑡 ) -𝑘 𝑟 (𝑄 𝑠𝑐 -𝑄 𝐻 ) 𝑄 𝑠𝑐 and 𝑄 𝐻 are the charge located in the space charge and the Helmholtz layer, respectively; 𝑘 𝑡 and 𝑘 𝑟 are the charge transfer and recombination rate constants; 𝑖 is the imaginary number. The first differential equation represents the time variation of the electric charge in the space charge ( 𝑑𝑄 𝑠𝑐 𝑑𝑡

Fig. 5 - 4 .

 54 Fig. 5-4. Comparison of kinetic models employed in this work to simulate non-steadystate IMVS responses; a) without the consideration of surface states; b) considering the contribution of surface states

Fig. 5 -

 5 5 presents the numerical solution of equations 5-3 to 5-5 by using each of the seven methods implemented in Matlab. The first issue to note is that the classical differential equations for heterogeneous photoelectrochemical kinetics at the surface of illuminated semiconducting electrodes are able to account for the observed IMVS response obtained experimentally in this work. Indeed, compare the experimental Bode representation shown in Fig. 5-2 b and c, with the simulation presented in Fig. 5-5 a and b.

Fig. 5 - 5 .

 55 Fig. 5-5. Simulated study of the effect of Matlab built-in solver of ordinary differential equations on the calculated response of IMVS. Calculated data shown in in the Bode representation; a) Imaginary component of 𝐻; b) real component of 𝐻.

Fig. 5 - 6 .

 56 Fig. 5-6. Simulation of the rotation sense of the spirals; a) to d) Nyquist and Bode plots of the simulated IMVS response; e) to h) Nyquist and Bode plots of the simulated light modulation. Blue lines depict a clock-wise rotation, obtained with negative modulation, while red lines show counter-clock-wise rotation, calculated with positive modulation.

Fig. 5 -Fig. 5 -

 55 Fig. 5-7 shows that the charge transfer and recombination rate constants have an

Fig. 5 - 7 .Fig. 5 - 8 .Fig. 5 -

 57585 Fig. 5-7. Simulation of the effect of the charge transfer (a to d) and recombination (e to h) rate constant on the non-linear response of IMVS. Calculations were performed through a logarithmic sweep of the relevant parameter (either kt or kr), therefore figure labels depict the exponent of the actual parameter value, e.g. -2 in the red line of (a) indicates that kt = 0.01 s -1 . Other parameters: Csc = 40 μF; CH = 10 mF; I0 = 10 -8 A; R = 44 Ω; from (a) to (d) kr = 0.01 s -1 ; from (e) to (h) kt = 0.01 s -1 .

Fig. 5 - 9 .

 59 Fig. 5-9. Simulation of the effect of the photogenerated current of minority carriers I0 (a to d) on the non-steady state response in IMVS. Calculations were performed through a logarithmic sweep of the relevant parameter (either I0 or R), therefore figure labels depict the exponent of the actual parameter value, e.g. -8 in the blue line of (a) indicates that I0 = 10 -8 A. Other parameters: kt = kr = 0.01 s -1 ; CH = 10 mF; CSC =40 μF; from (a) to (d) R = 44 Ω from.

Fig. 5 - 5 . 7 .

 557 Fig. 5-10. Simulation of the effect of surface states on the non-linear response of IMVS. The letters SS in the label of this figure stand for "surface states". Common simulation parameters: kt = kr = 0.01 s -1 ; CH = 10 mF; CSC =40 μF; R = 44 Ω; I0 = 10 -8 A. Additional simulation parameters to account for the presence of surface states: Rss = 10 4 Ω; CSS = 10 mF, giving rise to τSS = 10 2 s.

  Fig. 5-11. Comparison of the experimental and simulated non-steady-state IMVS response for the Rh:SrTiO3 -Pt. Parameters employed for the simulation without surface states: kt = kr = 0.01 s -1 ; CH = 10 mF; CSC =40 μF; R = 44 Ω; I0 = 10 -8 A. Simulation parameters to account for the presence of surface states: Rss = 10 4 Ω; CSS = 10 mF, giving rise to τSS = 10 2 s.

5. 8 .Fig. 5 -

 85 photoelectrodes

  Fig. 5-12. Effect of light intensity on the experimental IMVS response for the Rh:SrTiO3 -Pt photoelectrodes; a) Nyquist representation; b) Nyquist representation normalized for the incident led power; c) Bode representation of the imaginary component of H; d) Bode representation of the imaginary component of H normalized for the incident led power.

Fig. 5 - 5 . 9 .

 559 Fig. 5-13. Comparison of the experimental photodetector voltage for the IMVS experiments of Rh:SrTiO3 -Pt photoelectrodes at different light intensities. a) Imaginary component; b) real component. The phase shift observed between both measurements is due to instrumental uncertainties.

Fig. 5 -

 5 Fig. 5-14. Effect of light intensity on the experimental IMVS response for the Rh:SrTiO3 photoelectrodes; a) Nyquist representation; b) Nyquist representation normalized for the incident led power; c) Bode representation of the imaginary component of H; d) Bode representation of the imaginary component of H normalized for the incident led power.

Fig. 5 - 5 . 10 .

 5510 Fig. 5-15 Comparison of the experimental photodetector voltage for the IMVS experiments of Rh:SrTiO3 photoelectrodes at different light intensities. a) Imaginary component; b) real component. The phase shift observed between both measurements is due to instrumental uncertainties.

Fig. 5 -

 5 Fig. 5-16. Comparison of the experimental IMVS response for the Rh:SrTiO3 and Rh:SrTiO3 -Pt photoelectrodes; a) Nyquist representation; b) Nyquist representation normalized for the incident led power; c) Bode representation of the imaginary component of H; d) Bode representation of the imaginary component of 𝐻 normalized for the incident led power.

Fig. 5 - 5

 55 Fig. 5-17. Comparison of the experimental photodetector voltage for the IMVS experiments described above. a) Imaginary component; b) real component. The phase shift observed between both measurements is due to instrumental uncertainties and not to differences in surface kinetics between Rh:SrTiO3 and Rh:SrTiO3 -Pt.

  photocurrents were observed, indicating that the photoelectrodes were working

  Instead, metallic Cu, Pt and the molecular Co(Cl2Gm)3(B-CH3)2 clathrochelate increased the dark currents and decreased the overpotential of the HER.-Tafel slopes obtained from polarization curves were analyzed for both the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) in the four photoelectrodes tested. For the HER, a Tafel slope of approximately 120 mV/dec was obtained, which did not permit to distinguish between the Volmer reaction 𝐻 2 𝑂 + 𝑒 -+ 𝑀 = 𝑀 -𝐻 + 𝑂𝐻 -or the Heyrovsky step 𝑀 -𝐻 + 𝐻 2 𝑂 + 𝑒 -= 𝐻 2 + 𝑂𝐻 -+ 𝑀 (in the limit of high surface density of adsorbed H atoms, 𝜃 𝐻 > 0.6) as rds. For the OER, Tafel slopes close to 60 mV/dec were obtained; this was interpreted in terms of Bockris' oxide mechanism, with reaction 𝑀 -𝑂 = 𝑀 + 1/2𝑂 2 under the conditions 𝜃 𝑂 ≈ 0 and 𝜃 𝑂𝐻 ≈ 1 as a possible rds. Additionally, Tafel slopes deviating from mathematical models were obtained for the Rh:SrTiO3 -Cu towards the HER and for Rh:SrTiO3 -Pt towards the OER.-The kinetic parameters of the hydrogen evolution reaction (HER) at different cathodic applied electrode potentials and illumination levels was determined by means of Photoelectrochemical Impedance Spectroscopy (PEIS), for unmodified Rh:SrTiO3 photoelectrodes, and for photoelectrodes modified with metallic Pt and Cu, and with the molecular Co(Cl2Gm)3(B-CH3)2 clathrochelate. Regarding the HER, the photoelectrodes can be classified into two groups: a first group comprising pristine Rh:SrTiO3, and Rh:SrTiO3 modified with Co(Cl2Gm)3(B-CH3)2, and a second group composed by Rh:SrTiO3 modified with Pt and Cu. In pristine Rh:SrTiO3, and Rh:SrTiO3 modified with Co(Cl2Gm)3(B-CH3)2 photoelectrodes, recombination and charge transfer rate constants were found to be independent of applied potential and light intensity.Conversely, on Rh:SrTiO3 photoelectrodes modified with Pt and Cu, recombination and charge transfer rate constants displayed an exponential dependence with applied electrode potential. These observations can be attributed to the presence of surface states at the surface, which is the origin of such non-ideal behaviors.

  function D = derivada(x,y) Der = diff(y)./diff(x); %plot(x,y) D(1) = Der(1); for i = 1:length(Der)-1 D(i+1) = 0.5*(Der(i)+Der(i+1)); end D(length(Der)+1)=Der(end); end ANNEX II. Kinetic parameters derived from the fitting of PEIS.

Titre:

  Cinétique photo-électrochimique de la photo-dissociation de l'eau assistée par lumière visible sur électrodes à base de Rh:SrTiO3 Mots clés : Photo-électrochimie, cinétique, dissociation de l'eau Résumé : L'étude de la cinétique de la photodissociation de l'eau assistée par lumière visible a été l'objectif principal de ce travail. En tant que matériau photo-excitable, le semiconducteur SrTiO3 dopé au Rh a été utilisé. Le dopage permet l'absorption de lumière visible et donc la transformation d'énergie solaire en combustibles chimiques. Le 1 er Chapitre de cette thèse est consacré à une étude bibliographique couvrant les méthodes de caractérisation et les modèles de la cinétique photo-électrochimique. Le 2 ème Chapitre traite la description des matériaux et méthodes expérimentaux. Le 3 ème Chapitre concerne la caractérisation de la cinétique de la photodissociation de l'eau sur photo-électrodes à base de Rh:SrTiO3, modifiées en surface par ajout d'un clathrochélate modèle, ou avec du Cu ou du Pt métalliques. Le 4 ème Chapitre décrit une étude théorique du mécanisme de la réaction de dégagement d'hydrogène, catalysée par un clathrochélate modèle. Le spectre EXAFS du complexe a été analysé et modélisé, et les intermédiaires importants du mécanisme ont été mis en évidence. Le 5 ème Chapitre est consacré à l'étude dynamique de photo-électrodes à base de Rh:SrTiO3 en utilisant la technique de la photo-tension à lumière modulée. Ce Chapitre présente des résultats inattendus, qui sont rapportés pour la première fois. Ce comportement bizarre a été modélisé par un système d'équations différentielles usuellement utilisées pour décrire ce type de système photoélectrochimique. Title : Photoelectrochemical kinetics of visible-light driven water splitting at Rh:SrTiO3 based electrodes Keywords: Photoelectrochemistry, kinetics, water splitting Abstract: The kinetics of water photo-dissociation assisted by visible light was the main topic of this work. The Rh doped SrTiO3 semiconductor was employed as photo-excitable material. It can absorb visible light and therefore transform solar energy into useful chemical fuels. In this manuscript, a wide bibliographic overview is provided in the 1 st Chapter, covering a description of the characterization methods and current models for photoelectrochemical kinetics. The 2 nd Chapter is devoted to the description of the materials and methods. The 3 rd Chapter deals with the full photoelectrochemical kinetic characterization of water splitting with Rh:SrTiO3 photoelectrodes, surface-modified by addition of a model clathrochelate or with metallic Cu or Pt.

  [START_REF] Lewerenz | Photoelectrochemical Water Splitting Materials, Processes and Architectures[END_REF]

  when the light is off. 𝐶 𝑆𝐶 and 𝐶 𝐻 represent the space charge and the Helmholtz capacitance, respectively. Excepting heavily doped semiconductors, the capacity of the space charge is much lower than the capacity of the Helmholtz capacitance (𝐶 𝐻 ), and therefore 1/𝐶 𝐻 is actually neglected in front of 1/𝐶 𝑆𝐶 .

	𝑑𝑈 𝑑𝑡	denotes the time derivative of the
	open circuit potential

Table 1 -

 1

1 presents a brief summary of experimental Tafel slopes encountered at various electrodes. The main conclusion extracted is that quite often reality is richer than available mathematical models. Considering this, Tafel analysis should be assumed as information allowing to suggest possible rate determining steps.

Table 1 -

 1 1. Succinct compendium of Tafel slopes for the HER and the OER at various materials. These data are summarized in reference 81 with further examples.

		Hydrogen Evolution Reaction (HER)
	Material	Tafel slope	Conditions	Reference
	Pt (bulk)	36-68 (low η) 125 (high η)	H2SO4 0.5 M	89
	Pt (110)	55 (low η) 150 (high η)	KOH 0.1 M	90
	Pt (111)	140-150
	Pt/C	30	H2SO4 0.1 M	91,92
	Pt/C	125	NaOH 0.5 M	89
	Ni	121-142
	Mo	126	NaOH 1 M	93,94
	NiMo	132
	CoP	50		91
	Ni2P	75	H2SO4 0.5 M	92
	C (graphite)	206		95
		Oxygen Evolution Reaction (OER)
	Material	Tafel slope	Conditions	Reference
	Pt (bulk)	110	HClO4 1 M
	Pt (bulk)	60 (low η) 120 (high η)	KOH 1 M	96
	Ir Ir-Pt	85 210	H2SO4 1 M; 80°C	97
	Ni(OH)2 LnBaCo2O5+δ*	65 60	KOH 0.1 M	98 99
	NiCo2O4 (nanoneedle) NiCo2O4 (nanosheet)	292 393	KOH 1 M	100
	SrVO3	235
	LaCoO3	70 (low η) 135 (high η)	NaOH 1 M	88
	* Ln = Pr, Sm, Gd, Ho.

7.6 7.8 8.0 8.2 8.4 EXAFS Normalized (E) (a.u.) Energy (keV) XANES

	rule (eq. 1-30) 146
	𝜇 ∝ |< Ψ 𝑓 |𝜀̂• 𝑟 ⃗ • exp (𝑘 ⃗⃗ 𝑟 ⃗)|Ψ 𝑖 >|	2	𝛿(𝐸 𝑓 -𝐸 𝑖 -ħ𝜔)	(1-30)
	Where 𝜇 is the absorption coefficient, Ψ 𝑓 represents the wave-function for the final state,
	Ψ 𝑖 stands for the wave-function of the initial state, 𝜀̂• 𝑟 ⃗ • exp (𝑘 ⃗⃗ 𝑟 ⃗) represents the
	oscillating electromagnetic wave and 𝛿(𝐸 𝑓 -𝐸 𝑖 -ħ𝜔) is Dirac's jump function, with
	𝐸 𝑓 being the energy of the final state, 𝐸 𝑖 the energy of the initial state, and ħ𝜔 the
	energy of the X-ray. 146
	a)		b)

  𝑌 𝑙,𝑚 (𝜃, 𝜑) represents a spherical harmonic function and 𝜁 is an orbital exponent.

	CHAPTER 1
	molecule may be written as a linear combination of an appropriate basis set of functions.
	𝜓 = ∑ 𝑐 𝑖 𝜒 𝑖 𝑖	(1-37)
	Where 𝑐 𝑖 are coefficients that are optimized during the calculation, 𝜒 𝑖 stands for
	hydrogenoid orbitals, i.e., atomic orbitals (s, p, d, f) known as Slater Type Orbitals
	(STO). STO possess the following mathematical form (eq. 1-38) 150
	𝜒 𝑛,𝑙,𝑚 (𝑟, 𝜃, 𝜑) = 𝑁𝑌 𝑙,𝑚 (𝜃, 𝜑)𝑟 𝑛-1 𝑒 -𝜁𝑟	(1-38)
	Where 𝜒 𝑛,𝑙,𝑚 (𝑟, 𝜃, 𝜑) represents a STO, 𝑛 𝑙 and 𝑚 are the principal, angular and
	magnetic quantum numbers, (𝑟, 𝜃, 𝜑) are spherical coordinates, 𝑁 is a normalization
	factor,
		150,151
	Another approximation used in ab-initio and DFT calculations is related to the wave
	function. Considering that 𝜓 is unknown, it is assumed that the wave function of a
	66

1.12.1. Density Functional Theory as a tool to investigate electrocatalytic mechanisms Quantum

	in particular the reduced form
	of a clathrochelate in the triplet state presented important spin contamination, as
	expressed by a value of 〈𝑺 𝟐 〉 = 2.51. 137 There are few studies where it is considered
	whether spin contamination is important or not, in the study of mechanisms of electron
	transfer. 153 However, most current studies regarding DFT calculations regarding
	electrocatalytic mechanisms involving open-shell transition metal complexes, employ
	UKS methodology and do not consider the effect of spin contamination. 152,154-157 ROHF
	and ROKS wavefunctions do not present spin contamination.

chemical calculations have found a vast application in the study of electrocatalytic mechanisms, both in the homogeneous phase, where organometallic compounds are the protagonist,

Table 3 -

 3

		1. Magnetic parameters for the Co(Cl2Gm)3(B-CH3)2 clathrochelate, as
	obtained by fitting in easyspin.
		z	y	x
	g	2.33	2.03	2.01
	A (MHz)	272	57	186
	H (MHz)	60.0	204.7	180.3
	Another step in the characterization of the Co(Cl2Gm)3(B-CH3)2 complex was

accomplished by XANES and EXAFS spectroscopies. A detailed discussion of the XANES and the fit of EXAFS for this complex in the solid state shall be reported in Chapter 4, in the framework of the analysis of DFT calculations of the mechanism o f the HER catalyzed by Co(Cl2Gm)3(B-CH3)2 in the homogeneous phase.

  Table with those in Table , within the annex section at the end of this thesis).

Table 3 -

 3 2. Tafel slopes determined for each photoelectrode towards the HER and the OER, based on LSV measurements. Tafel slopes reported for the HER were determined in the dark.

	𝜕𝑉/𝜕log (𝑖) (mV/dec)
	HER	OER

Table 4 -

 4 1. Comparison between calculated and experimental metric data for the organic cage of the model clathrochelate studied in this work ([ 2 Co] 0 ). Theoretical calculations were performed with the B3LYP exchange correlation functional. Basis 1 corresponds to the LANL2DZ with effective core potentials for Co and Cl. Basis 2 was cc-pVTZ for Co and cc-p-VDZ for all other atoms. Atomic distances are given in Angstroms. Bond angles are given in degrees. The Bailar twist angle was measured through the N atoms lying farther apart from Co. the results of this work and previously published data137,139 indicate that the B3LYP functional slightly overestimates bond distances. Even though it should be kept in mind that geometry in the solid state is not necessarily the same as in an organic solution. The Jahn-Teller effect leading to a 4 + 2 coordination scheme is adequately reproduced by the B3LYP functional and each of the bases employed (φ angle), while the Bailar twist angle is in reasonable agreement with experiment, in particular for the LANL2DZ (basis 1). In general both basis sets reproduce well the geometry of the clathrochelate. Even though the LANL2DZ basis with ECP forCo and

		XRD	basis 1	basis 2
	Bond distances
	Co-N1	1.91	1.89	1.90
	Co-N2	1.90	1.93	1.96
	Co-N3	1.92	1.94	1.96
	Co-N4	1.92	1.96	1.92
	Co-N5	2.14	2.12	2.16
	Co-N6	2.14	2.15	2.23
	Angles
	θ (BNN'B')	12	20	38
	φ (BCoB')	172	174	171

Table 4 -

 4 2. Total energies in Hartrees of the three different redox states (high and low spin) in acetonitrile (AN) and dimethyl-formamide (DMF). Level of theory B3LYP cc-pVTZ for Co cc-p-VDZ for all other atoms.

	[ 1 Co] -1	[ 3 Co] -1	[ 2 Co] 0	[ 4 Co] 0
	AN -5281.2472991695 -5281.2453638159 -5281.1698643585 -5281.1111792086
	DMF -5281.2472991695 -5281.2453638160 -5281.1698643585 -5281.1111792086
	[ 1 Co] 1	[ 5 Co] 1
	AN -5280.9312627981 -5280.8849278885
	DMF -5280.9312627980 -5280.8849278885

Table 4

 4

		-3. DW factors and path distances for the hexachlorine containing cobalt(II) tris-
	dioximate clathrochelate (Co(Cl2Gm)2(B-CH3)2). Fit performed with the XRD
	geometry. *
	Shell Path	Degeneracy	𝜎 2 (Å 2 ) Error 𝜎 2 (Å 2 ) R (Å)	Δ𝑅 (Å)
	1	Co-N Co-N	4 2	0.007 0.003	0.002 0.002	1.92 2.06	0.01 -0.08
		Co-O Co-O	4 2	0.018	0.003	3.35 3.30	0.45 0.20
	2	Co-C(sp2) 4 Co-C(sp2) 2	0.011	0.004	2.40 2.95	-0.58 0.21
		Co-B (r)	2	0.0003	-	3.04	-0.07
	3	Co-Cl Co-Cl	4	0.003	0.0003	4.32	-0.06

Table 4 -

 4 4. DW factors and path distances for the hexachlorine containing cobalt(II) trisdioximate clathrochelate (Co(Cl2Gm)2(B-CH3)2). Fit performed with the DFT optimized geometry at B3LYP/LANL2DZ level.

	Shell Path	Degeneracy	𝜎 2 (Å 2 ) Error 𝜎 2 (Å 2 ) R (Å)	Δ𝑅 (Å)
	1	Co-N (r) Co-N (r)	4 2	0.007 0.003	--	1.9 2.13	-0.04 -0.1
		Co-O	4	0.015	0.006	2.76	-0.19
		Co-O	2	0.003	0.008	3.32	0.21
	2	Co-C (sp2) 4	0.014	0.008	2.54	-0.23
		Co-C (sp2) 2	0.009	0.005	2.39	-0.58
		Co-B (r)	2	0.0003	-	3	-0.17
	3	Co-Cl Co-Cl	4	0.002	0.001	4.51	0.08

Table 4 -

 4 5. Comparison between metric data derived from XRD, DFT, and their corresponding EXAFS fits. The distances reported here from the 4 + 2 coordination motif, are mean values of the 4 and 2 neighbors, respectively.

			EXAFS (Solid geom.) XRD	EXAFS (DFT geom.) DFT
	Path	Degeneracy	R (Å)	Δ𝑅 (Å)	R (Å)	R (Å)	Δ𝑅 (Å)	R (Å)
	Co-N	4	1.92	0.01	1.91	1.90	-0.04	1.93
	Co-N	2	2.06	-0.08	2.14	2.13	-0.10	2.14
	Co-O	4	3.35	0.45	2.90	2.76	-0.19	2.95
	Co-O	2	3.30	0.20	3.10	3.32	0.21	3.11
	Co-C (sp2) 4	2.40	-0.58	2.74	2.39	-0.23	2.78
	Co-C (sp2) 2	2.95	0.21	2.98	2.54	-0.58	2.97
	Co-B	2	3.04	-0.07	3.10	3.00	-0.17	3.17
	Co-Cl	4	4.32	-0.06	4.38	4.51	0.08	4.49
	Co-Cl	2	4.70	0.07	4.63	4.65	-0.05	4.70

Table 4 -

 4 6. Comparison between Co-O and Co-C(sp2) distances for two different XRD structures of the clathrochelate.

	Distance (Å) cif 1	cif 9	Distance (Å) cif 1	cif 9
	Co-O1	2.87	2.92	Co-C1	2.72	2.79
	Co-O2	2.89	2.92	Co-C2	2.73	2.79
	Co-O3	2.91	2.97	Co-C3	2.77	2.84
	Co-O4	2.95	2.97	Co-C4	2.76	2.84
	Co-O5	3.05	3.01	Co-C5	2.95	2.86
	Co-O6	3.11	3.01	Co-C6	2.97	2.86
	It should be noted that even XRD data display a spreading in the positions of O and

C(sp2) in the second shell of the clathrochelate. Apparently, Co-O and Co-C(sp2) distances are not entirely homogeneous in the solid state, which should be the cause for the slightly elevated values of ΔR obtained in the fit of these two atoms in the second shell of the clathrochelate.

Table 4

 4 -7 that both spin configurations of [Co] 0 display Jahn-Teller distortion (structure of [ 2 Co] 0 shown in the center of Fig. 4-8), clearly observed in a 4 + 2 coordination where four N atoms are nearly equidistant to Co, while two other lie farther apart, and the φ angle departs from 180°. The mean value of the Co-N distance is 2.00 and 2.02 Å for [ 2 Co] 0 and [ 4 Co] 0 , respectively (2.01 in reference 137).

Table 4 -

 4 7. Calculated metric data for the three redox states and two spin multiplicities of the model clathrochelate studied in this work. Theory level B3LYP/ LANL2DZ with ECP for Co and Cl.

		[ 1 Co] -1	[ 3 Co] -1	[ 2 Co] 0	[ 4 Co] 0	[ 1 Co] +1	[ 5 Co] +1
	Bond distances in Å
	Co N1	1.87	1.89	1.89	1.89	1.93	2.07
	Co N2	1.87	1.90	1.93	1.93	1.94	2.07
	Co N3	1.90	1.92	1.94	1.97	1.94	2.07
	Co N4	1.91	1.93	1.96	2.03	1.94	2.08
	Co N5	1.96	2.42	2.12	2.14	1.95	2.09
	Co N6	2.62	2.80	2.15	2.18	1.95	2.09
	Angles in degrees
	θ (BNB'N')	20	44	5	23	71	4
	φ (BCoB')	174	173	171	157	179	179
	After the one-electron reduction, the characteristic 4 + 2 coordination scheme of the
	clathrochelate is predicted to be reinforced, as expressed by the departure of the two N
	atoms that lie farther apart, from 2.12-2.15 Å in [ 2 Co] 0 to 2.42-2.80 Å in [ 3 Co] -1 or 1.96-
	2.62 in [

1

Co] -1 . Such a one-electron reduction provoked a movement of 0.7 Å of Co within the organic cage, so that the central atom is nearly in a square-planar

Table 4 -

 4 8. Comparison of calculated and experimental redox potential of the clathrochelate vs. the Fc + |Fc couple. B3LYP/ LANL2DZ.

	Fc + |Fc	Co II |Co I	Co III |Co II

Table 4

 4

-9 displays selected

Table 4 -

 4 9. Calculated metric data for the relevant protonated intermediates in the HER mechanism. Theory level B3LYP/ LANL2DZ with ECP for Co and Cl.

  1

	Bond distances in Å
	Co N1	1.91	1.88	1.82	1.90	1.78	1.87	1.92	1.93
	Co N2	1.91	1.88	1.91	1.90	1.92	1.92	1.94	1.93
	Co N3	1.92	1.90	1.95	1.94	1.94	1.94	1.94	1.94
	Co N4	1.93	1.92	1.98	2.00	1.98	1.94	1.98	1.94
	Co N5	2.37	2.41	2.09	2.32	2.06	2.37	1.98	2.48
	Co N6	2.65	2.75	2.69	2.82	2.59	2.65	2.06	2.50
	XH *	1.44	1.44	1.04	1.04	1.10	1.09	1.03	1.78
	H---H							2.69	0.785
	Angles in degrees
	θ (BNB'N') 5	18	12	26	6	12	70	3
	ϕ (BCoB') 159	156	164	157	167	159	177	179
	δ (HNN'H')							1

Table 4 -

 4 10. Comparison of the energies obtained with various functionals for the process [1 Co] -1 + HA = [ 1 Co(Co)H] 0 + A -. Calculated with the basis set cc-pVTZ for Co and cc-pVDZ for all other atoms, where HA stands for trifluoroacetic acid, and A -is the trifluoroacetate anion.

	Functional	E(kJ/mol)
	B3LYP	117.85
	PBE0	125.18
	BP86	150.58

Table 4 -

 4 11. Comparison of the total energy (in Hartrees) between some species of the HER mechanism studied here, calculated with different DFT functionals and the basis set cc-pVTZ for Co and cc-pVDZ for all other atoms.

	[ 1 Co] -1	[ 1 Co(Co)H] 0	[ 1 Co(NN)HH] 1	TS
	B3LYP -5281.247299 -5281.746202	-5282.069582	-5282.026552
	BP86 -5282.823112 -5283.309549	-5283.666282	-5283.634031
	PBE0 -5279.831869 -5280.327978	-5280.656901	-5280.605563

Table 4 -

 4 12. Comparison of the total energy (in kJ/mol) between some species of the HER mechanism studied here, calculated with different DFT functionals and the basis set cc-pVTZ for Co and cc-pVDZ for all other atoms.

	[ 1 Co] -1	[ 1 Co(Co)H] 0	[ 1 Co(NN)HH] 1	TS
	B3LYP -13865914.78 -13867224.65	-13868073.69	-13867960.71
	BP86 -13870052.08 -13871329.22	-13872265.82	-13872181.15
	PBE0 -13862198.57 -13863501.11	-13864364.69	-13864229.90

Table 4 -

 4 13. Relative energies (in kJ/mol) between some species of the HER mechanism studied here, calculated with different DFT functionals and the basis set cc-pVTZ for Co and cc-pVDZ for all other atoms.

		[ 1 Co] -1	[ 1 Co(Co)H] 0	[ 1 Co(NN)HH] 1	TS
	B3LYP	1310	0	-849	-736
	BP86	1277	0	-937	-852
	PBE0	1303	0	-864	-729

Table 4 -

 4 14. Comparison of the calculated metric data for the intermediates protonated directly in Co. Theory level B3LYP/ LANL2DZ with ECP for Co and Cl.

		[ 1 Co(Co)H] 0	[ 3 Co(Co)H] 0	[ 2 Co(Co)H] -1
	Bond distances in Å
	Co N1	1.91	1.88	1.88
	Co N2	1.91	1.88	1.89
	Co N3	1.92	1.90	1.88
	Co N4	1.93	1.92	1.89
	Co N5	2.37	2.41	2.71
	Co N6	2.65	2.75	2.82
	Co-H	1.44	1.44	1.47
	Angles in degree
	θ (BNB'N')	5	18	26
	ϕ (BCoB')	159	156	151

  An increase in the space charge capacitance causes a decrease in the absolute value of the transfer function and consequently a shrinking in the spirals. In the same manner, a decrease in I0 causes a shrinking in the spirals. The sole simulation condition that caused a phase shift in the IMVS response was the presence of surface states. All other parameters caused either a decrease (shrinking) or increase (expansion) of the transfer function 𝐻 (i.e., the spirals in the Nyquist representation), but did not cause phase shift.

	possible, but a structural analysis of the involved intermediates suggested that such double protonated species should not participate in the actual HER electrocatalysis. Additionally, the calculated transition state for an ECCE mechanism presented a very high energy. Therefore we considered an alternative ECEC mechanism. In this case, neither a doubly protonated species nor a transition state could be found, which lead us to propose that the last HER step could be a Proton Coupled Electron Transfer. -The structural elucidation of the clathrochelate Co(Cl2Gm)3(B-CH3)2 by means of EXAFS spectroscopy was treated in detail, by using the known XRD geometry was slightly different to the geometry found by XRD. Despite the small difference, the adequate fitting of EXAFS with the DFT geometry required more variables in the second scattering shell. This confirms the sensitivity and accuracy of EXAFS in structural determinations. -Intensity Modulated Photovoltage Spectroscopy was used to characterize photoelectrodes made of pristine Rh:SrTiO3 and Rh:SrTiO3 -Pt. The IMVS response observed at open circuit conditions presented a spiral-like shape in the Nyquist representation. To the best of our knowledge, this is the first report of such behavior in semiconducting photoelectrodes studied by IMVS. -By means of numerical simulations, it was established that the spiral-like shape observed by IMVS analysis was determined by a non-steady state dynamic response. Such non-steady state dynamics was adequately simulated using the classical system of differential equations that describes charge transfer and recombination at the surface of illuminated photoelectrodes. -The numerical simulations permitted to determine the influence of charge transfer and recombination kinetic parameters, interfacial capacitances, and surface states, upon the non-steady state dynamic behavior of the photoelectrodes in IMVS conditions. An increase in charge transfer rate constant causes increase in the absolute value of the IMVS transfer function (𝐻) and therefore an expansion of the spirals. Contrariwise, an increase in kr causes a photo_potential_on = -B.data(LED_power_segments(counter_on)+1:LED_power_segments(counter_on+1),3); LED_Power = B.data(LED_power_segments(counter_on)+1,4); final_results_off(counter_final_results,1:2) = [kt kr]; final_results_on(counter_final_results,1:2) = [LED_Power photo_potential_on(end)]; if export_variable == 1 output_headers = {'time_off' 'photo_potential_off' 'd_ocpd_dt' 'time_on' 'photo_potential_on'}; data1 = [time_off photo_potential_off d_photopot_dt']; data2 = [time_on photo_potential_on]; xlswrite('Results OCPD', output_headers(1),counter_fig -1,'B5'); xlswrite('Results OCPD', output_headers(2),counter_fig -1,'C5'); xlswrite('Results OCPD', output_headers(3),counter_fig -1,'D5'); xlswrite('Results OCPD', output_headers(4),counter_fig -1,'E5'); xlswrite('Results OCPD', output_headers(5),counter_fig -1,'F5'); xlswrite('Results OCPD', data1,counter_fig -1,'B6'); xlswrite('Results OCPD', data2,counter_fig -1,'E6'); clear data end figure(1) plot(time_off, photo_potential_off, color_line, 'linewidth', linewidth_show_lines) title('PHOTOPOTENTIAL DECAY VS TIME') hold on figure(2) plot(time_off, d_photopot_dt, color_line, 'linewidth', linewidth_show_lines) title('dU/dt VS TIME') hold on figure(3) plot(time_off, d_photopot_dt./(photo_potential_off(1)), color_line, 'linewidth', linewidth_show_lines) title('[1/Uo][dU/dt] VS TIME') hold on hold on xlabel('time, s', 'FontSize', font_size_show) ylabel('Photopotential V', 'FontSize', font_size_show) set(gca,'FontSize', font_size_show, 'linewidth',linewidth_show_lines) figure(5) plot(LED_Power, photo_potential_on(end), [color_line 'o--'], 'linewidth', linewidth_show_lines) title('PHOTOPOTENTIAL VS LED POWER') hold on xlabel('Led Power, mW/cm2', 'FontSize', font_size_show) ylabel('Photopotential V', 'FontSize', font_size_show) set(gca,'FontSize', font_size_show, 'linewidth',linewidth_show_lines) counter = counter + 2; end figure(6) plot(final_results_on(:,1), final_results_off(:,1), [color_line 'o-'], 'linewidth', linewidth_show_lines) hold on title('kt vs Led Power') xlabel('Led Power, mW/cm2', 'FontSize', font_size_show) ylabel('kt, s-1', 'FontSize', font_size_show) legend('kt') set(gca,'FontSize', font_size_show, 'linewidth',linewidth_show_lines) figure(7) plot(final_results_on(:,1), final_results_off(:,2), [color_line 'o-'], 'linewidth', linewidth_show_lines) hold on title('kr VS Led Power') xlabel('Led Power, mW/cm2', 'FontSize', font_size_show) ylabel('kr, s-1', 'FontSize', font_size_show) legend('kr') set(gca,'FontSize', font_size_show, 'linewidth',linewidth_show_lines) disp('kt; kr') disp(final_results_off) disp('led power; Photopotential') disp(final_results_on) if export_variable_fit == 1 output_headers = {'led power (mW/cm2)' 'photopotential (V)' 'kt (s-1)' 'kr (s-1)' }; data_fit = [final_results_on final_results_off]; xlswrite('Results OCPD fit', output_headers(1),1,'B5'); xlswrite('Results OCPD fit', output_headers(2),1,'C5'); xlswrite('Results OCPD fit', output_headers(3),1,'D5'); xlswrite('Results OCPD fit', output_headers(4),1,'E5'); xlswrite('Results OCPD fit', data_fit,1,'B6'); clear data end contraction of the spirals. B.data(LED_power_segments(counter_on)+1:LED_power_segments(counter_on+1),2); if export_variable == 1 figure(4) plot(time_on, photo_potential_on, color_line, disp('look for the output files in the folder') 'linewidth', disp(pwd) linewidth_show_lines) title('PHOTOPOTENTIAL VS TIME') end
	counter_on = counter_on + 2; geometry and the DFT optimized geometry as well. Both geometries accounted counter_fig = counter_fig + 1;
	for a satisfactory reproduction of the EXAFS spectrum. Nonetheless, the DFT counter_final_results = counter_final_results + 1;
	clear time photo_potential d_photopot_dt k1 k2

Table A1 .

 A1 Fit parameters of PEIS for the Rh:SrTiO3 system under cathodic polarization.

	kt (s -1 ) kr (s -1 ) Csc (F)	I0 (A)	η	E (V)	LED power (mW/cm 2 )
	0.023	0.005	2.70E-04 6.08E-05 0.82	-1.30	529.03
	0.008	0.003	2.49E-04 2.54E-05 0.74	-1.25	294.13
	0.022	0.006	2.43E-04 3.16E-05 0.78	-1.25	529.03
	0.013	0.003	2.30E-04 1.76E-05 0.80	-1.20	0.49
	0.023	0.006	2.24E-04 1.81E-05 0.78	-1.20	294.13

Table A2 .

 A2 Fit parameters of PEIS for the Rh:SrTiO3 system under anodic polarization.

	kt (s -1 ) kr (s -1 ) Csc (F)	I0 (A)	η	E (V) LED power (mW/cm 2 )
	0.032	0.026	3.45E-05	3.30E-05	0.55 1.40	0.49
	0.029	0.021	3.18E-05	2.26E-05	0.58 1.40	294.13
	0.029	0.020	3.22E-05	2.64E-05	0.60 1.40	529.03
	0.022	0.016	3.75E-05	8.23E-05	0.58 1.50	294.13

Table A3 .

 A3 Fitting results of PEIS for the Rh:SrTiO3 -Ch photoelectrode under cathodic polarization.

	kt (s -1 ) kr (s -1 ) Csc (F)	I0 (A)	η	E (V)	LED power (mW/cm 2 )
	0.28	0.09	1.18E-04 8.84E-05 0.76	-1.30	129.57
	0.28	0.09	1.08E-04 4.90E-05 0.76	-1.30	529.03
	0.15	0.12	1.05E-04 2.41E-05 0.56	-1.15	129.57
	0.28	0.09	9.01E-05 2.98E-05 0.76	-1.25	529.03
	0.19	0.09	8.71E-05 2.09E-05 0.68	-1.20	129.57
	0.28	0.09	7.57E-05 1.84E-05 0.76	-1.20	529.03
	0.16	0.09	7.69E-05 1.01E-05 0.62	-1.15	129.57
	0.28	0.09	6.54E-05 1.17E-05 0.76	-1.15	529.03
	0.28	0.09	5.74E-05 1.16E-05 0.76	-1.10	129.57

Table A4 .

 A4 Fitting results of PEIS for the Rh:SrTiO3 -Ch photoelectrode under anodic polarization.

	kt (s -1 )	kr (s -1 )	Csc (F)	I0 (A)	η	E (V)	LED power (mW/cm 2 )
	0.010	0.015	2.13E-05 9.91E-05 0.40	1.50	294.13
	0.013	0.012	2.13E-05 7.38E-05 0.53	1.50	529.03
	0.014	0.013	2.14E-05 2.09E-05 0.52	1.40	529.03
	0.021	0.008	2.49E-05 3.30E-06 0.74	1.30	294.13
	0.013	0.007	2.38E-05 5.00E-06 0.64	1.30	529.03

Table A5 .

 A5 Fitting results of PEIS data for the Rh:SrTiO3 -Cu under cathodic polarization.

	kt (s -1 ) kr (s -1 ) Csc (F)	I0 (A)	η	E (V)	LED power (mW/cm 2 )
	2.6	4.0	3.55E-07 1.13E-04 0.39	-1.30	67.39
	4.1	5.1	3.35E-07 1.12E-04 0.45	-1.30	185.92
	3.1	4.6	3.31E-07 1.06E-04 0.40	-1.30	294.13
	3.1	4.8	3.20E-07 1.06E-04 0.39	-1.30	393.52
	2.9	4.8	3.13E-07 1.06E-04 0.38	-1.30	485.34
	3.0	5.0	3.04E-07 1.07E-04 0.37	-1.30	529.03
	2.0	5.6	3.01E-07 9.49E-05 0.26	-1.25	67.39
	1.9	5.5	2.96E-07 9.62E-05 0.26	-1.25	185.92
	1.9	5.7	2.89E-07 9.75E-05 0.25	-1.25	294.13
	1.9	5.7	2.82E-07 9.89E-05 0.25	-1.25	393.52
	1.8	5.9	2.77E-07 9.89E-05 0.24	-1.25	485.34
	1.8	5.9	2.70E-07 1.00E-04 0.23	-1.25	529.03
	1.2	6.7	2.70E-07 9.28E-05 0.15	-1.20	67.39
	1.2	6.8	2.65E-07 9.40E-05 0.15	-1.20	185.92
	1.2	7.1	2.61E-07 9.50E-05 0.14	-1.20	294.13
	1.2	6.9	2.58E-07 9.58E-05 0.14	-1.20	393.52
	1.2	7.2	2.54E-07 9.63E-05 0.14	-1.20	485.34
	1.1	7.1	2.52E-07 9.70E-05 0.14	-1.20	529.03
	0.7	7.6	2.52E-07 9.13E-05 0.08	-1.15	67.39
	0.7	7.7	2.50E-07 9.13E-05 0.08	-1.15	185.92
	0.7	7.7	2.48E-07 9.13E-05 0.08	-1.15	294.13
	0.7	7.7	2.46E-07 9.16E-05 0.08	-1.15	393.52
	0.7	7.7	2.44E-07 9.16E-05 0.08	-1.15	485.34
	0.7	7.8	2.43E-07 9.23E-05 0.08	-1.15	529.03
	0.4	7.8	2.42E-07 8.91E-05 0.05	-1.10	67.39
	0.4	7.8	2.40E-07 8.97E-05 0.04	-1.10	185.92
	0.4	8.0	2.39E-07 9.12E-05 0.04	-1.10	294.13
	0.4	8.3	2.38E-07 9.27E-05 0.04	-1.10	393.52
	0.4	8.5	2.38E-07 9.61E-05 0.04	-1.10	485.34
	0.4	8.8	2.38E-07 9.93E-05 0.04	-1.10	529.03
	0.2	9.0	2.38E-07 1.03E-04 0.02	-1.05	67.39
	0.2	9.3	2.37E-07 1.06E-04 0.02	-1.05	185.92
	0.2	9.9	2.36E-07 1.09E-04 0.02	-1.05	294.13
	0.2	9.8	2.35E-07 1.10E-04 0.02	-1.05	393.52
	0.2	10.1	2.34E-07 1.11E-04 0.02	-1.05	485.34
	0.2	10.1	2.33E-07 1.12E-04 0.02	-1.05	529.03

Table A6 .

 A6 Fitting results of PEIS data for the system Rh:SrTiO3 -Cu under anodic polarization.

	kt (s -1 )	kr (s -1 )	Csc (F)	I0 (A)	η	E (V)	LED power (mW/cm 2 )
	0.021	0.017	2.48E-05 5.43E-05 0.54	1.40	0.49
	0.017	0.016	2.64E-05 6.21E-05 0.52	1.40	294.13

Table A7 .

 A7 Kinetic parameters obtained from the fitting of PEIS data under cathodic polarization for Rh:SrTiO3 -Pt photoelectrodes.

	1.2	12.9	6.03E-08	3.06E-05 0.09	-1.05	393.52
	1.2	13.5	5.95E-08	3.15E-05 0.08	-1.05	485.34
	1.2	12.6	6.11E-08	3.05E-05 0.09	-1.05	529.03
	kt (s -1 ) kr (s -1 ) Csc (F)	I0 (A)	η	E (V)	LED power (mW/cm 2 )
	9.0	10.6	9.53E-08	4.67E-05 0.46	-1.30	294.13
	8.6	10.2	9.42E-08	4.63E-05 0.46	-1.30	393.52
	8.0	9.9	9.22E-08	4.66E-05 0.45	-1.30	485.34
	7.2	9.5	8.84E-08	4.62E-05 0.43	-1.30	529.03
	6.4	11.2	8.47E-08	4.19E-05 0.36	-1.25	67.39
	5.5	10.6	8.24E-08	4.10E-05 0.34	-1.25	185.92
	5.8	10.8	8.06E-08	4.12E-05 0.35	-1.25	294.13
	5.5	10.3	7.75E-08	4.23E-05 0.35	-1.25	393.52
	5.6	10.2	7.59E-08	4.15E-05 0.35	-1.25	485.34
	5.3	10.0	7.34E-08	4.09E-05 0.35	-1.25	529.03
	4.0	11.4	6.95E-08	3.74E-05 0.26	-1.20	67.39
	3.9	11.9	6.72E-08	3.76E-05 0.25	-1.20	185.92
	4.1	11.6	6.61E-08	3.80E-05 0.26	-1.20	294.13
	4.0	11.7	6.49E-08	3.77E-05 0.26	-1.20	393.52
	4.1	11.4	6.43E-08	3.79E-05 0.26	-1.20	485.34
	4.0	11.4	6.25E-08	3.80E-05 0.26	-1.20	529.03
	3.0	12.9	6.17E-08	3.48E-05 0.19	-1.15	67.39
	2.7	12.6	6.01E-08	3.39E-05 0.18	-1.15	185.92
	2.8	12.8	6.02E-08	3.43E-05 0.18	-1.15	294.13
	2.9	12.4	6.02E-08	3.46E-05 0.19	-1.15	393.52
	2.9	12.4	6.02E-08	3.46E-05 0.19	-1.15	485.34
	2.9	12.5	6.00E-08	3.48E-05 0.19	-1.15	529.03
	2.0	13.7	5.81E-08	3.24E-05 0.13	-1.10	67.39
	1.8	13.2	5.94E-08	3.24E-05 0.12	-1.10	185.92
	1.9	13.3	5.91E-08	3.24E-05 0.12	-1.10	294.13
	1.9	12.9	5.87E-08	3.20E-05 0.13	-1.10	393.52
	2.0	13.4	5.90E-08	3.26E-05 0.13	-1.10	485.34
	1.9	12.9	5.84E-08	3.24E-05 0.13	-1.10	529.03
	1.2	13.7	5.73E-08	3.13E-05 0.08	-1.05	67.39
	1.1	13.5	5.67E-08	3.12E-05 0.08	-1.05	185.92
	1.2	13.1	5.80E-08	3.11E-05 0.08	-1.05	294.13

Table A8 .

 A8 Kinetic parameters of the OER at the surface of Rh:SrTiO3 -Pt photoelectrodes.

	kt (s -1 ) kr (s -1 ) Csc (F)	I0 (A)	η	E (V)	LED power (mW/cm 2 )
	0.013	0.009	2.35E-05 3.90E-05 0.59	1.50	529.03
	0.010	0.003	2.26E-05 8.71E-06 0.77	1.40	129.57
	0.010	0.005	2.24E-05 1.07E-05 0.67	1.40	529.03
	0.010	0.003	2.29E-05 3.62E-06 0.77	1.30	129.57
	0.007	0.003	2.27E-05 3.88E-06 0.70	1.30	529.03
	0.010	0.003	2.66E-05 1.51E-06 0.76	1.20	129.57
	0.019	0.007	2.43E-05 1.49E-06 0.72	1.20	529.03
	0.012	0.004	3.30E-05 9.20E-07 0.75	1.10	129.57
	0.020	0.009	2.97E-05 7.95E-07 0.69	1.10	529.03

Table A10 .

 A10 Total energies and relevant thermodynamic quantities (B3LYP/LANL2DZ, ECP for Co and Cl) B3LYP/LANL2DZ (ECP for Co and Cl)

	ANNEX IV. Geometric coordinates from the DFT optimization N 4.84052 3.09036 1.45707 C 6.58463 6.33826 2.73263 O 11.33404 5.62576 0.46735 C 9.25691 4.84050 7.84479 O 10.08660 3.46534 0.51586 C 11.89840 6.16104 3.96501 H 9.27345 5.87798 8.20044 O 9.02838 3.36232 5.59871
	N C [ 1 Co] -1 O C [ 1 Co(C)H] 0 3.07844 3.62291 8.81354 7.68476 O 11.26124 C 7.52896 H 6.93194 O 10.35115	4.48117 3.00485 5.78106 6.67934 5.68010 6.72026 4.85587 5.39903		2.59845 0.85852 0.43080 2.22781 0.48746 3.62925 4.28326 5.43107
	N C Co N C Co O C O	5.02936 2.24386 4.59968 9.51721 10.03015 9.41835 8.74063 9.33279 7.87310	2.43034 7.86138 4.05763 3.23083 4.83937 4.74397 5.61372 4.83695 5.50383		4.03259 4.29555 3.22213 4.39197 -1.61414 3.00387 0.42153 7.83520 5.70529
	[ 5 Co] 1 N C Cl N C Cl N C [ 1 Co(CoN)HH] 1 4.43702 4.98395 9.13533 10.92610 12.20812 10.27411 9.61867 7.79181 O 10.22459	4.73489 2.52191 5.65763 5.58945 6.16032 0.68873 3.17091 6.70517 3.69742		4.87616 5.49257 1.57443 4.46219 2.56010 4.79724 4.39831 2.28103 0.74810
	Co B C Cl N C Cl N C Co O	4.87620 3.19234 2.75074 7.09491 8.14267 10.19984 13.25068 10.87533 10.03089 9.29330 11.54229	4.10438 6.59462 4.09477 7.92683 5.70405 2.14833 7.39832 5.55875 4.78745 4.67626 5.71299		3.14823 3.85687 1.25017 2.79755 4.29599 2.43261 5.00194 4.47770 -1.60231 3.22077 0.17823
	Species Cl B C Cl N H Cl N C Cl O Cl O C Cl N H Cl N C Cl N	E (Hartree) 9.14696 6.63621 7.52911 3.42387 8.47608 10.07159 7.60288 8.12944 12.12644 10.07037 9.12151 7.32511 7.51748 4.26294 1.42937 10.01957 9.11805 6.28903 8.44814 10.17421 12.60960 9.29890	Gcorr (kJ/mol) 5.40776 1.66079 0.33698 2.04778 5.77513 5.84447 8.23044 5.55961 6.35602 1.06118 5.85153 8.03457 2.83099 3.72108 4.68721 3.39807 4.34736 7.31103 5.69494 2.12042 6.39673 3.59180	Ezpe (kJ/mol) 1.82804 2.34332 1.96507 -0.61157 1.77196 -2.05537 4.27198 4.26811 2.52125 4.93845 0.70341 Ethermal (J/mol) 2.73002 2.86093 5.86311 0.15179 1.90865 -1.97669 1.13372 1.76942 2.46184 5.16861 4.22725	E + Gcorr (kJ/mol)	E + Gcorr + ZPE (kJ/mol)	E + Gcorr + ZPE + Ethermal (kJ/mol)
	Cl O H Cl N H Cl N H Cl N		3.10143 4.31601 8.38719 5.60772 11.22974 10.89459 13.47511 9.98373 10.03484 6.49375 10.45739	1.86451 6.97564 0.20770 1.36378 5.97362 4.27371 6.79114 3.28059 5.78981 7.41563 5.37385		-0.50390 2.85611 2.63826 6.67162 1.81208 -1.98662 1.78638 1.87818 -2.05160 4.48320 3.87649
	[ 5 Co] 1 Cl O H Cl B H Cl N H Cl N		-1371.51642 1.21966 4.46091 472.201 317.482 0.33214 67689.549 5.83187 2.18927 1.12463 2.12147 8.56107 3.45844 3.60077 3.94557 7.56292 9.38490 4.85491 6.26188 8.31651 4.36432 8.15357 10.47003 0.65677 1.45054 11.17494 5.80460 1.86814 9.11536 4.27442 -1.92486 7.52396 7.73725 1.21687 8.26402 5.36603 4.24487	-3600444	-3600126.677 -3600058.987
	[ 1 Co] 1 Cl O H N B H O B H Cl N	-1371.536781 338.831 484.980567 64064.939 5.22586 1.14723 6.66751 2.33959 5.48205 3.19603 6.91545 -0.57205 2.01914 7.11359 3.97912 2.48555 10.04111 4.94868 -0.03005 10.08347 4.28522 8.30814 9.79073 3.47636 5.70192 9.39152 4.76608 6.27734 10.89054 4.23557 -2.00692 13.81108 6.92312 2.18075 8.92807 5.57461 2.09301	-3600631	-3600146.007 -3600081.942
	Cl O H N C H O B H Cl N	3.52940 5.61497 7.91508 5.37608 10.08568 9.26885 10.75737 10.04675 8.42569 11.05866 9.88592	3.86727 1.31905 0.42524 5.86017 2.13840 5.86258 5.75010 4.92321 4.34474 1.35785 3.78860		7.54958 3.45857 0.94037 3.12864 3.86955 8.24571 6.07872 -0.03446 8.21078 1.69507 2.12023
	[ 4 Co] 0 N O H N C H O C H O N [ 2 Co] 0 N C H N C O C H O B N C N C [ 3 Co(Co)H] 0 -1371.699747 313.751 471.23843 68467.571 6.87032 4.07418 2.53409 3.88094 5.97700 5.10199 1.24510 7.54045 4.61926 4.64477 2.90453 1.71108 12.01053 6.13887 4.02190 7.95619 3.89928 2.89143 8.30161 5.46952 5.53992 10.09659 2.07357 3.88286 10.20263 4.30864 8.24795 8.93446 3.31744 5.66451 11.33044 5.72907 1.64065 -1371.47263 323.803 478.782055 67634.384 5.43066 6.10627 3.10585 7.45344 5.15902 2.67997 2.70938 8.40895 5.12572 3.04462 4.65816 2.37511 7.37349 6.56929 3.67855 9.76542 3.39355 0.42442 11.89947 6.22697 4.05410 9.34431 5.86517 8.22034 10.36983 5.32921 5.45881 9.14224 4.81803 6.18640 4.60744 2.74721 1.58435 6.54390 6.31827 2.62754 5.42476 2.67420 4.25072 9.28158 4.89182 7.84362 O 11.18264 5.41999 0.70756 C 7.27322 6.55922 3.67442 H 7.17400 4.80735 4.25353 O 7.90262 5.52301 5.71327 B 10.13504 5.01633 -0.04873	-3601084 -3600478	-3600612.696 -3600544.228 -3599998.804 -3599931.169
	N C [ 4 Co] 0 N C Co O C O C		3.16812 3.67672 3.78990 7.57485 9.14086 8.70810 9.21066 10.31603 9.85696	4.79879 3.05286 4.41503 6.61812 4.58395 5.66591 4.76379 3.66701 2.36725		2.20808 0.86436 4.86540 2.22867 3.12017 0.34368 7.84106 0.78202 3.91365
	[ 3 Co] -1 N C Co B C Cl N C [ 3 Co(N)H] 0 5.47035 -1371.901656 308.466 467.114069 69713.71 2.51180 4.32536 2.31057 7.82941 4.24126 4.91191 4.17984 2.94836 3.04002 6.52376 3.92837 10.03090 4.91147 -1.61659 10.45010 0.68407 4.87939 9.85682 3.34553 4.33316 7.49463 6.47556 2.18222 O 11.50168 5.79272 0.17943 C 11.66069 6.02278 3.80757	-3601619	-3601152.218 -3601082.504
	[ 1 Co] -1 N C Cl B C Cl N C Co O C	-1371.612991 325.426 477.253622 66768.634 4.02651 4.56393 4.96540 4.82759 2.48685 5.32194 9.18794 5.31194 2.06153 6.72169 1.65562 2.35797 12.26408 6.06578 2.56884 13.22186 6.85187 5.10978 11.08454 5.69155 4.73990 10.05751 4.85726 -1.61149 9.15815 4.50475 3.14566 9.10438 5.76710 0.74241 7.60187 6.51758 3.65506	-3600844	-3600367.227 -3600300.459
	B C Cl O C Cl N C Cl N C	3.11688 2.67781 7.41660 7.74175 10.27736 6.38145 8.33188 12.13818 10.44091 9.28070 9.37504	6.61793 3.94083 7.99495 2.81905 2.19717 7.77084 5.54390 6.25285 0.61556 3.58182 4.83941		3.90607 1.47848 3.06572 2.10294 2.45140 4.54277 4.16285 2.58706 4.88023 4.28210 7.78617
	[ 3 Co(Co)H] 0 B 6.65815 -1372.257779 339.613 495.155695 68406.668 1.58361 2.35086 C 7.51458 0.42509 1.95438 Cl 3.15428 1.90921 -0.55096 O 4.51300 6.88198 3.54897 H 10.04513 5.92914 -2.03193 Cl 6.75197 7.81820 1.20418 N 8.44075 5.74651 1.69419 C 10.26125 2.12106 2.41277 Cl 13.14537 6.77873 5.09876 N 10.48521 5.31596 3.90583 C 8.05375 6.63422 2.34337 [ 1 Co(Co)H] 0 -1372.317662 350.023 501.391676 67016.977 O 7.49763 2.91956 2.20409 C 4.37474 3.80468 5.79108 Cl 1.00000 4.21810 0.73257 O 5.51917 1.84072 1.45938 H 9.13196 4.40280 -1.99110 Cl 13.93147 6.18855 1.93115 N 9.72744 3.25114 1.79897 H 9.99818 5.86536 -2.04381 Cl 6.61772 7.94311 4.52852 N 8.28722 5.37097 4.26567 C 9.82662 4.76473 -1.61238 O 4.56775 7.08513 3.47479 H 8.23150 0.18376 2.75043 Cl 5.51237 1.36194 6.67809 O 2.37801 5.83568 2.75255 H 10.91074 4.37602 -2.00040 Cl 10.94129 0.81979 1.50382 N 11.10644 5.51954 2.10551 H 9.20674 4.27477 -1.98926 Cl 7.50679 8.22851 1.30024 N 8.92406 5.54949 2.11187 C 12.30145 6.25674 2.46271 [ 2 Co(Co)H] -1 -1372.465417 330.997 488.708503 69747.172 O 5.47109 1.69203 1.37746 H 1.96965 8.36397 3.34436 Cl 3.37265 3.84586 7.36170 O 6.28732 1.66794 3.80866 H 8.34688 4.42911 8.18850 O 9.49882 3.41315 5.73245 B 9.51761 4.87475 6.29059 H 10.98062 4.38725 -1.97707 Cl 13.20195 7.60688 1.87114 N 9.94025 3.77081 2.16544 C 10.24799 2.49976 2.55762	-3602523 -3602670 -3603076.9 -3602588.245 -3602518.498 -3602028.029 -3601959.622 -3602168.607 -3602101.590
	[ 3 Co(N)H] 0 O H N O H 10.11851 -1372.32564 2.49074 5.89824 352.25 6.89408 -0.46304 6.86688 4.05898 3.05208 5.58083 4.34540 O 10.63196 5.62115 B 9.97092 4.85355 H 8.29450 4.23337 Cl 10.85816 0.69569 N 11.32641 5.74278 H 9.77615 5.78701 O 6.20812 1.46406 H 8.08608 0.62556 N 5.40074 6.15440 C 7.53665 5.17671 H 9.30874 5.92511 O 8.13143 5.56086 C 10.04672 2.15557 H 10.05855 4.26781 O 9.35801 3.32186 B 9.14985 4.74364 H 8.81679 4.18685 [ 1 Co(N)H] 0 -1372.305906 358.809 506.866816 65606.023 507.030175 67852.574 2.69406 1.77692 2.74525 5.11687 8.29942 5.82054 -0.02604 8.13299 1.55047 1.65497 -2.20124 3.81332 1.03821 2.90125 2.32644 8.21541 5.66123 3.82466 8.33194 5.77522 6.21211 -1.80136 O 3.27172 5.70761 5.13669 H 1.42034 7.51341 4.80234 N 4.78065 2.99318 1.42738 C 6.58186 6.21233 2.76379 O 10.06777 3.52607 0.58215 C 12.04941 6.31160 4.17511 H 9.14835 5.78826 8.23107 O 10.64209 5.46271 5.76236 B 10.18048 4.96004 -0.01780 H 10.69547 4.13923 -2.11151	-3602689 -3602630	-3602181.687 -3602113.834 -3602123.48 -3602057.874
	C H N C [ 1 Co(Co)H] 0 7.48656 2.86944 3.11399 3.65519 O 11.28797 C 7.30234 H 6.22794 O 8.13646 C 9.86938 H 8.43205	5.23901 8.53837 4.55299 3.08153 5.67023 6.43862 6.53061 5.57097 2.40377 4.36389		2.39412 4.86639 2.50028 0.82420 0.45960 3.64861 3.99274 5.70582 3.97827 8.32194
	[ 3 Co(C)H] 0 C N C Co O C O C 11.69877 -1372.348853 348.379 507.291709 68798.526 6.67742 6.39711 2.76350 5.20542 2.38853 4.15713 2.28969 7.86810 4.28922 9.20646 4.59185 3.12605 8.76454 5.71676 0.43813 9.17966 4.75156 7.82542 10.05711 3.42295 0.54193 5.92404 3.83278 H 10.32291 4.24231 8.14699	-3602754	-3602246.242 -3602177.443
	[ 1 Co(C)H] 0 C [ 2 Co] 0 N C Cl 10.46290 -1372.334165 358.139 508.980663 67104.276 3.55346 2.92448 0.83646 4.24812 4.69648 4.91477 5.07110 2.63277 5.53879 0.69466 4.86087 N 9.56466 3.26551 4.38608 C 7.44277 6.43140 2.14869 [ 1 Co(N)H] 0 O 11.37554 5.56525 0.40441 C 7.58702 6.47383 3.65722 H 9.47219 5.94617 8.18168	-3602705	-3602196.23	-3602129.126
	C Co B C Cl N C Co O C H	2.26115 4.78073 3.20977 2.76953 13.16394 10.88288 10.19130 9.33748 8.91396 9.38691 7.31882	7.87998 4.02980 6.66841 4.12719 6.94577 5.59447 4.91387 4.64766 5.72877 4.85276 4.81258		4.27523 3.18284 3.88166 1.18412 5.11780 4.44280 -1.58537 3.18709 0.49300 7.80799 3.99974
	[ 3 Co(NN)HH] 1 C 2.71707 Cl 7.23596 O 7.51902 C 4.16790 Cl 6.80485 N 8.49490 C 10.02998 Cl 13.12971 N 10.76910 C 9.78850 Converged to [ 3 Co(CoN)HH] 1 4.09933 7.99279 2.87509 3.66762 7.81749 5.80277 2.11428 6.75036 5.63493 4.74509 C 4.98830 2.48495 Cl 9.11609 5.36575 B 6.66080 1.60811 C 7.44045 0.28481 Cl 6.44233 7.78578 N 8.14579 5.71289 C 12.09101 6.13277 Cl 10.12905 0.58496 N 9.54234 3.14400 C 8.01850 6.61924 H 8.02276 3.95099	1.20405 2.67028 2.42898 5.89877 1.19640 1.78688 2.35977 5.12341 4.37899 -1.56854 5.53652 1.90292 2.35981 2.01862 4.53470 4.28812 2.70453 4.85755 4.42105 2.33736 2.73582
	[ 1 Co(NN)HH] 1 C 7.56312 -1372.712519 419.851 562.630564 63641.474 0.36148 1.96562 Cl 3.28409 1.96577 -0.53026 O 4.51353 7.16197 3.25346 H 8.31193 0.12982 2.67013 Cl 13.77206 6.78057 1.89261 N 9.97242 3.39016 1.92768 H 10.33308 5.94982 -1.92064 Cl 6.69691 7.99918 4.51157 N 7.79756 5.43049 4.27696 C 12.31259 6.21420 2.47943 [	-3603637	-3603074.237 -3603010.595
	C Cl O H Cl N H Cl N C	4.19541 1.33603 5.51707 2.26852 10.71042 11.18885 9.32709 7.16721 8.67105 10.29957	3.69282 4.58004 1.84556 8.54817 0.72693 5.89776 4.49911 7.91545 5.79509 2.52762		5.92123 0.30469 1.30475 3.42719 1.50807 1.83082 -2.12170 1.14031 1.83752 2.61582
	[ 3 Co(NC)HH] 1 H 8.43970 -1239.098958 503.63 0.29504 Cl 5.41095 1.25693 O 2.49369 5.72293 H 6.75579 -0.56257 O 9.42307 3.38572 B 9.38009 4.90155 H 11.07906 4.33855 Cl 13.22891 7.67853 N 9.94377 3.24079 H 9.67330 5.77599	635.070362 49814.392 2.62319 6.64922 2.83457 2.15556 5.76107 6.26831 -1.87936 1.93763 1.90541 -2.13080	-3252751	-3252115.613 -3252065.799
	[ 1 Co(NC)HH] 1 H 2.18040 -1239.092152 505.103 631.123561 47953.443 8.56518 3.42147 Cl 3.63175 4.00042 7.48803 O 6.00118 1.33843 3.70567 H 7.79271 0.27539 0.97771 O 10.67282 5.55193 5.84107 B 10.02817 4.99751 -0.03777 H 8.27987 4.14366 7.98675 Cl 10.66021 0.68259 1.53979 N 11.42784 5.48868 1.79299 H 8.78832 4.13896 -1.71586	-3252731	-3252100.219 -3252052.266
	H N O H O C H O B H	7.00413 6.85705 3.47760 1.25207 8.18191 10.10420 10.00904 9.23054 9.34062 10.64544	-0.57946 4.02162 5.83830 7.66632 5.58876 2.08230 4.28305 3.34548 4.82972 4.15568		2.05656 2.62723 5.13071 4.58967 5.65915 3.85382 8.37255 5.76117 6.23992 -2.12933
	[ 3 Co(CoN)HH] 1 -1239.063473 516.192 647.179458 48356.425 H 7.92098 0.44047 0.93088 N 5.35065 6.06171 3.03434 C 7.49957 5.19287 2.59827 H 2.78902 8.38799 5.11830 O 9.98901 3.47332 0.52901 C 11.98859 6.12189 4.01850 H 9.00369 5.74162 8.26713 O 10.71133 5.33871 5.74853 B 10.11052 4.84670 -0.03745 H 8.46676 4.39608 8.39540 H 1.24404 7.59012 4.57094 N 4.66609 2.84948 1.64242 C 6.67820 6.39350 2.82365 O 11.31073 5.59918 0.46774 C 7.44064 6.63487 3.69395 H 6.29881 6.19225 4.01094 O 8.24021 5.68924 5.71551 C 10.02182 2.04140 3.91626 H 10.35195 4.28183 8.17145	-3252645	-3251997.777 -3251949.42
	[ 1 Co(CoN)HH] 1 -1239.101762 524.833 653.039086 47957.061 H 2.70895 8.43194 5.11179 N 3.13195 4.69507 2.35219 C 3.50664 2.98559 0.81283 [ 3 Co] -1 O 8.80757 5.71440 0.43517 C 9.25754 4.86662 7.83689 O 10.17456 3.46378 0.57208 C 11.87004 6.19206 3.96828 H 9.49121 5.97500 8.15517	-3252737	-3252083.805 -3252035.848
	N C Co N C [ 3 Co(C)H] 0 5.31736 2.26821 9.17254 9.59164 7.62700 O 11.34728 C 7.53079 H 8.07795	2.49161 7.88891 4.59357 3.23103 6.67214 5.67947 6.71186 3.93246		4.22063 4.20102 3.12278 4.40381 2.23067 0.40221 3.64488 2.74319
	[ 1 Co] 1 N C Cl N C Co O C H B3LYP/LANL2DZ (ECP for Fe) for Ferrocene 4.09782 4.56369 4.86409 4.96028 2.51571 5.42371 10.64204 0.75294 4.86601 10.90710 5.55911 4.45947 10.00275 4.86496 -1.60654 9.21047 4.54926 3.13029 8.86478 5.62122 0.50544 9.29750 4.84694 7.82304 7.34767 4.79672 3.94756 Species E (Hartree) Gccorr (kJ/mol) Ezpe (kJ/mol) Ethermal (J/mol) Co 4.92452 4.12938 3.09132 B 3.12795 6.62889 3.87343 C 2.62347 3.88136 1.35812 Cl 13.22008 6.98593 5.09205 N 8.20660 5.73018 4.29033 C 12.23069 6.09827 2.55741 Cl 10.57593 0.65725 4.83178 N 9.49267 3.19490 4.41082 C 7.93126 6.83325 2.32311 Cl 9.17511 5.29703 2.36271 B 6.68964 1.60951 2.35939 C 7.53141 0.37339 1.91622 Cl 6.19985 7.62703 4.51307 N 8.54650 5.80419 1.78196 C 10.30602 2.14007 2.49232 Cl 13.01492 7.12472 5.14633 N 10.81800 5.54554 4.36865 C 9.99412 4.76458 -1.60827 [ 3 Co(CoN)HH] 1 Cl 7.13571 7.97138 2.59249 O 7.56673 2.86281 2.34637 C 4.24575 3.75043 5.80445 Cl 6.71552 7.79849 1.19919 N 9.91528 3.30421 1.89284 H 9.97391 5.85547 -2.08095 Cl 7.85363 8.32707 4.25141 N 7.94205 5.51300 4.30016 C 12.10528 6.30407 2.51326 Co 9.27319 4.65907 3.20911	E + Gcorr (kJ/mol)	E + Gcorr + ZPE (kJ/mol)	E + Gcorr + ZPE + Ethermal (kJ/mol)
	[ 1 Fe(Cp)2] 0 Cl O H Cl N H Cl N C 10.21899 -510.1348768 353.698 3.30909 2.01139 4.48133 7.10168 8.30483 0.14936 13.99968 5.85229 11.24644 5.69620 9.12150 4.30371 6.50289 7.47969 8.62229 5.66903 2.08503 Cl 10.04327 1.04279	442.354273 15886.585 -0.49805 3.33358 2.66271 2.00018 1.85093 -1.94478 1.10569 1.86209 2.44724 4.89734	-1339359.12 -1339005.42	-1338989.54
	[ 2 Fe(Cp)2] 1 Cl O H Cl B H Cl N H Cl	-509.9728737 352.142 1.12592 4.28500 5.54097 1.81329 2.01349 8.43884 10.74927 0.76572 9.39920 4.85034 10.89827 4.34416 13.73409 6.82816 10.00335 3.30641 10.04615 5.76471 12.52031 6.58453	444.529323 16663.683 0.73146 1.36459 3.28529 1.47612 6.27480 -1.97120 1.93813 1.93113 -2.05909 5.14458	-1338933.78 -1338581.64	-1338564.97
	Cl O H O B H Cl N H Cl	5.11329 2.42232 6.90451 9.47709 10.04699 8.32679 10.79846 11.43210 9.04378 6.55155	1.14690 5.80045 -0.52155 3.41527 4.91774 4.37560 0.70824 5.57784 4.30433 7.50497		6.41560 2.79576 1.80252 5.78935 -0.03880 8.15133 1.48649 1.77832 -1.91070 4.49024
	Cl O H O C H O B H Cl	3.74440 6.08390 8.02956 10.62913 10.04209 10.09760 9.45816 9.36535 10.81036 7.58241	4.06177 1.43792 0.56131 5.65456 2.11634 4.31749 3.31774 4.82240 4.16186 7.78849		7.40753 3.75500 0.95602 5.82392 3.89702 8.28249 5.76342 6.25582 -2.02963 1.23636
	N O H O C H O B H Cl	6.84931 3.38455 1.33223 8.12648 11.97667 9.26030 10.60805 10.11643 8.40819 13.79069	4.03324 5.72626 7.55402 5.56285 6.14550 5.88310 5.55272 4.87774 4.32489 6.97817		2.94464 5.08796 4.66681 5.67563 4.02729 8.25231 5.85683 -0.02949 8.20025 2.15432
	N C H O C H O C H Cl		5.27827 7.43511 2.75847 9.97628 7.50295 7.92354 8.12628 9.90398 10.18657 10.96166	5.99810 5.17336 8.59049 3.52853 6.64884 3.85609 5.47965 2.06361 4.35509 1.33603		2.69554 2.46010 4.88934 0.50384 3.68842 2.84463 5.61857 3.90604 8.24083 1.59669

1 Co(NN)HH] 1

	N C TRANSITION STATE 10.78094 6.04737 10.00611 2.38133 C 1.34047 1.02894	2.07834 2.70334 1.36691
	B H Co H	9.43877 9.97833 4.36331 0.45047	4.83896 5.58460 3.70341 -2.74718	6.24153 -2.08194 3.26209 0.52575
	B H Cl H	9.96914 9.24850 8.97869 -1.18989	4.96290 3.86530 5.31449 -1.38326	0.05286 -1.71845 1.82326 2.20808
	C H Cl H	9.72089 11.13716 7.18544 -2.78205	2.16396 4.11436 7.89485 0.22652	3.85774 -1.83098 2.75704 0.70810
	C H Cl H	11.98627 8.76607 3.85629 -2.12443	6.05411 4.23854 2.54583 -0.13853	4.06763 8.09301 -1.00767 -1.90463
	C H Cl H	7.79563 10.60785 1.88508 -0.12787	6.82016 3.77892 5.11737 -1.97833	3.42920 7.85432 -0.15502 -2.01216
	C H Cl H	9.34391 10.11736 6.22737 1.96015	4.78563 5.59628 1.79814 0.85530	7.80294 8.11516 6.84135 -1.95140
	C H Cl H	7.62018 7.78355 4.38259 0.00034	6.42118 4.97343 4.46249 2.62056	2.15090 4.81913 7.66142 -1.30212
	C H N H	10.17469 6.49874 6.74453 2.86152	4.96545 5.66935 3.93106 -0.28785	-1.50593 3.36898 2.53338 0.34389
	C N H	11.87714 5.26695 -0.30963	6.45936 6.00826 2.57048	2.66087 3.14213 1.39497
	C N H	10.23770 4.57069 1.45605	2.20830 2.74722 0.77585	2.47386 1.59699 2.41301
	H [ 3 Co(NC)HH] 1 9.95762 N 3.15429	5.95886 4.78219	-1.92205 2.21609
	H Co N [ 2 Fe(Cp)2] 1 9.50523 9.42518 5.44355	4.24495 4.80463 2.51440	-1.99296 3.22917 4.35033
	H Cl N	11.20757 8.72967 4.02498	4.70528 1.11678 4.54428	-1.77147 4.80661 4.97603
	H Cl B Fe	8.32621 12.68609 3.06002 0.01346	4.53591 6.46564 6.60779 0.05931	8.13228 5.24155 3.93541 0.02088
	H Cl B C	10.02919 6.77765 6.62656 -0.33448	4.03016 8.11262 1.52779 -2.04338	8.21164 4.19329 2.37041 0.24435
	H Cl O C	9.61239 7.09660 7.44318 -1.25495	5.75554 7.07129 2.78150 -1.35389	8.24562 0.79016 2.19152 1.11534
	H Cl O C	7.56282 13.20765 4.43851 -2.09875	5.05680 7.96968 7.05740 -0.51739	4.41134 2.32251 3.52139 0.30496
	H Cl O C	7.38203 10.71631 5.36707 -1.70466	4.34006 1.10257 1.64377 -0.67772	1.82926 1.92763 1.44670 -1.07077
	O O C	8.34871 2.43306 -0.61332	3.84887 5.81976 -1.62487	5.31577 2.73616 -1.11210
	O O C	10.75730 6.14201 1.60352	4.49286 1.44913 1.07350	5.15497 3.84919 -0.95450
	[ 1 Co(NC)HH] 1 O 9.16783 O 3.20695 C 0.57717	6.29590 5.62979 2.02831	5.59402 5.14093 -0.59249
	Co O C C	9.39771 10.74534 7.30781 2.12787	4.77393 3.73487 5.08440 0.49844	3.21927 1.03310 2.40950 0.26267
	Cl O C C	8.80058 11.27598 6.48586 0.47026	1.09835 6.16909 6.25407 2.03177	4.86085 0.28217 2.79711 0.84632
	Cl O C C	12.49517 8.89848 3.83711 1.42464	6.61492 5.34771 3.20954 1.09105	5.32303 0.73210 0.61970 1.36967
	Cl N C H	6.63450 8.99496 2.11082 0.42638	7.97883 3.71469 7.79086 -2.74982	4.27232 4.01536 4.33222 0.54918
	Cl N C H	7.21505 10.60171 5.38986 -1.29081	7.21526 5.42019 2.75775 -1.43260	0.81932 3.80841 5.63208 2.19434
	Cl N C H	13.27011 8.51553 2.99202 -2.87673	7.90603 5.88874 4.36591 0.14052	2.32408 4.29383 0.98876 0.67139
	Cl N C H	10.66349 8.75026 7.42120 -2.15105	1.08639 5.41650 0.22339 -0.18058	1.88751 2.15794 2.01340 -1.92157
	O N C H	8.42367 10.12246 4.57227 -0.10464	3.77861 3.77511 3.93509 -1.97055	5.37710 2.28824 5.99291 -2.00144
	O N H H	10.80292 11.23835 8.29907 1.93896	4.45451 6.05698 0.11306 0.84786	5.11545 1.76392 2.66409 -1.95860
	O B H H	9.15155 9.52735 1.99598 0.00249	6.22633 4.81417 8.49645 2.63959	5.51678 5.99563 3.49911 -1.27585
	Co O B H H	9.65881 10.55666 10.26125 6.79695 2.89999	4.81725 3.66876 4.98410 -0.67159 -0.25615	3.15315 0.96687 0.14626 2.13469 0.33146
	Cl O C H H	9.74530 11.44008 9.22629 7.77530 -0.22280	0.70117 5.98470 2.37945 0.25161 2.62359	4.82971 0.32800 3.88120 0.97436 1.43004
	Cl O C H H	13.24444 8.97141 11.68192 1.11254 1.56726	6.65022 5.48891 6.13587 7.42383 0.84799	5.13731 0.71847 3.96636 4.60486 2.41451
	Cl N C H	7.28601 8.99761 7.38188 2.51326	8.34273 3.70317 6.63407 8.34478	4.14942 4.04697 3.57369 5.19028
	Cl N C H	6.78363 10.54640 9.71396 2.78772	7.35019 5.42812 4.47949 2.98087	0.90585 3.79542 7.58224 3.65633
	Cl N C H	13.15859 8.40307 7.84126 3.24330	7.32504 5.77951 6.45715 2.35212	1.82779 4.28672 2.14265 3.53850
	Cl N C	10.50345 8.76356 10.13495	0.75108 5.47104 4.52080	1.52540 2.15337 -1.40483
	O N C [ 1 Fe(Cp)2] 0 8.83661 10.03552 12.04005	3.52317 3.75448 6.78711	5.58477 2.26371 2.62432
	O N C Fe	10.91591 11.36191 10.03643 0.01481	4.88985 5.90786 2.41143 0.05574	5.77527 1.78448 2.70565 0.02141
	O B H C	8.73888 9.60397 9.79636 -0.31006	6.06221 4.78147 5.43644 -2.03397	5.62142 5.99578 -2.07221 0.23540
	O B H C	10.62803 10.23693 9.35848 -1.18019	3.65767 4.95889 3.65464 -1.30592	0.67228 0.12593 -1.58960 1.12844
	O C H C	10.67020 9.24620 11.18224 -2.02369	6.17103 2.35722 4.17153 -0.44696	0.70943 3.90027 -1.82401 0.33026
	O C H C	8.51530 11.63066 8.70399 -1.67440	4.97835 6.17295 4.11795 -0.63989	0.40002 3.97036 8.07341 -1.05794
	N C H C	9.27173 7.28645 10.53155 -0.61493	3.31353 6.55669 3.64565 -1.62110	4.28206 3.56776 7.76246 -1.11434
	N C H C	11.04456 9.78199 10.08840 1.60190	5.23369 4.58585 5.45274 1.06709	4.44637 7.59976 8.14163 -0.95220
	N C H C	8.32069 7.86236 7.84517 0.56334	5.74811 6.48905 5.10453 2.01041	4.27107 2.16768 4.77848 -0.60787
	N C H C	8.11814 10.12943 6.55760 2.08628	5.06348 4.59830 5.75293 0.46309	1.81299 -1.44921 3.46771 0.26737
	N C C	10.34369 12.11257 0.40160	3.42164 6.72255 1.98402	1.99297 2.64120 0.82685

ACKNOWLEDGEMENTS

There are many people who contributed to the conclusion of this thesis and I have multiple reasons to be thankful. I would want to thank my Ph.D. supervisor Prof. Dr. Pierre Millet for his efforts and comprehension that allowed my research in France.

𝑀 + 1/2𝑂 2 , with 𝜃 𝑂 ≈ 0 and 𝜃 𝑂𝐻 ≈ 1, while for the HER the observed Tafel slopes did not allow us to differentiate between the Volmer step or the Heyrovsky step as rds in the potential region of high surface density of adsorbed H atoms. In particular, there were two Tafel behaviors (the system Rh:SrTiO3 -Cu towards the HER and the system Rh:SrTiO3 -Pt towards the OER) that could not be explained with current kinetic models.

Subsequently, photoelectrochemical kinetic determinations under anodic and cathodic polarizations were performed by Photoelectrochemical Impedance Spectroscopy (PEIS) analysis. In most cases (excepting Rh:SrTiO3 -Ch photoelectrodes at strong illumination of 529.03 mW/cm 2 ), the experimental PEIS spectra displayed the two characteristic relaxations associated to the space charge capacitance (at HF) and to the interplay between charge transfer and recombination kinetics (at LF).

At positive overpotentials, no photocurrents were detected, indicating that the measurements were performed beyond the flat-band potential and under accumulation of majority carriers at the interface (holes for p-type semiconductors), thus, minority carriers (electrons) originated from visible-light photoexcitation moved towards the bulk of the semiconductor, hence the independence of current density on light intensity.

All photoelectrodes displayed very slow charge transfer kinetics with kt in the order of 10 -2 s -1 which were independent of the electrode potential (in the range of +1.5 V to +1.3 V vs. SCE) and light intensity (in the range of 0.4 to 529.03 mW/cm 2 ), as determined by PEIS analysis. Likewise, all photoelectrodes displayed huge overpotentials in LSV, which is due to the slow charge transfer kinetics. Nevertheless, the overpotentials observed in LSV were not the same for all photoelectrodes, and we speculate that this could be due to differences in proton affinities at the surfaces.

Conversely, the behavior of the four photoelectrodes under cathodic bias can be Thus, in the Nyquist representation, such sign inversion affects the sense of rotation of the light modulation because the real component (plotted in the abscissa) remains unchanged, while the imaginary component (plotted in the ordinates) is reflected through the abscissa axis because of the change in sign. The consequence of the sign of the imaginary exponent is therefore the sense of rotation of the light modulation.

The calculated IMVS response with both positive (𝑒 𝑖𝜔𝑡 ) and negative (𝑒 -𝑖𝜔𝑡 ) light modulation are shown in Fig. 5-6 a to d. In addition, the simulated LED modulation is represented in Fig. 5-6 e to h. Certainly, Fig. 56demonstrates that the sense of rotation of the spirals is the same as the sense of light modulation. Fig. 56shows that, when the sign of the imaginary exponent was changed, the real component of both 𝐻 and 𝐴 was unaffected while the imaginary component of 𝐻 and 𝐴 presented inverted signs. Additionally, the phase angle (Fig. 56) has the same shape as the experimental one (Fig. 5-2 d). Such odd shape is a consequence of the alternative pass from one quadrant to the other of the complex plane (Nyquist plot), due to the periodic modulation of light.

In conclusion, the direction of spirals' rotation is not due to inherent kinetic characteristics of the photoelectrochemical system, but caused by the sense of light modulation, which is controlled by the optical bench coupled to the potentiostat. -------------------------------------------------------------------------% selecting the photopotential evolution when the light is ON time_on =

ANNEXES ANNEX I. Example of Matlab program to treat OCPD measurements