Noham Lucia Laurent

Fabien

La présence croissante de diverses substances dans notre environnement, conséquence des activités anthropiques de ces dernières décennies, a entraîné un besoin grandissant et urgent de nouveaux matériaux et dispositifs dans la quête de senseurs chimiques efficaces et fiables. D'énormes progrès technologiques ont permis de mettre à disposition toute une gamme d'outils techniques pour leur développement, en prenant en compte les exigences à respecter en terme de sélectivité ou de rapidité de réponse, entre autres. Dans ce contexte, les méthodes de chimie quantique permettent une compréhension fondamentale des processus en jeu dans la détection des espèces chimiques, et par extension, l'élaboration de manière rationnelle de nouveaux matériaux sensibles. Certaines molécules organiques pouvant être largement fonctionnalisées, elles constituent un point de départ idéal en raison des importantes modulations possibles de leurs propriétés par des modifications structurales appropriées.

Cette étude vise à développer de manière rationnelle des chromoionophores pour la complexation de cations par une approche combinant méthodes de chimie computationnelles et caractérisation par spectroscopie optique. Deux points principaux ont été traités à l'aide de la Théorie de la Fonctionnelle de la Densité (DFT) et son extension dépendante du temps (TD-DFT): d'une part les relations structure moléculaire-propriétés optiques de chromophores, d'autre part le phénomène de complexation. En particulier, la détection de l'ion Zn 2+ , démontrée de manière théorique et expérimentale, est finalement réalisée après intégration du senseur moléculaire dans un dispositif à fibre optique. Il me semble impossible de débuter ces remerciements autrement que par toi, Frédéric, sans qui rien de tout ceci ne serait arrivé. Sache que je ne regrette pas une seconde de t'avoir croisé sur le chemin de mon indécision chronique, je n'aurais pas pu mieux tomber. Merci pour tout. Beaucoup de reconnaissance aussi envers tes deux "complices" dans cette affaire, Roberto et David, que je remercie avant tout pour leur confiance. Roberto, merci pour ta bienveillance tout au long de ce travail de thèse, mais aussi pour ta rigueur (celle qui m'a parfois fait défaut), et ta disponibilité. Au delà de l'aspect scientifique, je voudrais aussi te remercier pour ta grande générosité et l'atmosphère vivante et humaine que tu privilégies au sein du groupe, et sans laquelle les choses ne seraient à mon sens pas tout à fait les mêmes. David, merci pour ton enthousiasme et ton optimisme débordants, ton humanité, ainsi que ta disponibilité sans limites -ou presque. Malgré les quelques incompatibilités de nos langages respectifs, tes précieux conseils et ta patience m'auront plus d'une fois permis d'avancer et de m'enrichir. Tu as été pour moi un peu plus qu'un directeur de thèse, ça valait bien des pommes pour la vie. Besides my supervisors, I would like to thank the other members of my thesis committee, the professors Jean-Luc Brédas, Toussaint Robert, Luisa de Cola and Mark Van der Auweraer, for accepting to be part of my jury and evaluate my work.

Agnès, un grand merci pour ton aide (incommensurable) bien avant que j'arrive et tout au long de ces 4 années, du logement aux méandres de l'administration, en passant par le sauvetage d'une petite boule de poil.

Naturally, I would like to thank my two first friends in Mons, without who things would not have been the same. Lucas, thank you for knocking at my door the very first evening I was facing my new life alone, and for all that followed. Mike, thank you for all that we shared, and the things you made me discover, from Praha to Abingdon, with a hint of garlic and ginger, awful mouthwash smell not included. I also would like to thank the other people of the small group that welcomed me. Juan, Cris and Sara, I share with you great memories of moments together, chatting around a beer or stuck in endless darts games, and sincerely hope it was just a beginning. Sergey, I'm sure you understand what I just meant, you were part of it. Place enfin à ces belges, qui m'ont permis de me sentir chez moi. Bro, merci pour tous ces moments que l'on a partagé, ces carnavals et ces festivals de Dour, et ta générosité de chaque instant. Finalement, pour un type qui se la raconte dans Chemical Reviews, t'es quand même plutôt chouette. Merci aussi à ta Paupiette. Mathieu, merci pour ces longues heures à refaire le monde, d'une façon ou d'une autre, sous les oranges ou sous la lune, je n'oublierai pas. Patrick, merci de t'être suffisamment ouvert pour tolérer le petit dinosaure qui est en moi. Et plus sérieusement, Papinou, merci pour ton soutien, ta gentillesse, et tout simplement, ton amitié. Je tiens aussi à remercier toutes les autres personnes que j'ai eu la chance de côtoyer au sein du groupe. Olivier, "crouch, touch, pause, engaged" (à l'ancienne), merci pour ça et tout le reste. Colin, pour m'avoir fait découvrir les chemins de ton enfance, à bicyclette. Max, merci pour ta patience dans ma relation tumultueuse avec la DFT, entre autres. Vincent, pour tes précieux conseils et tous les moments partagés. Séb K., pour tes sauvetages informatiques. Merci aussi à mon grand maquereau Stefan, à Ahmadou, Séb M

Abstract

The increasing presence of various substances in our environment has brought about a growing need for rapid emergence of new materials and devices in the quest for efficient and reliable chemical sensors. Massive technological progress have made available an extensive range of technical tools to serve their development, accounting for the requirements to be fulfilled (selectivity, quick response..). In this context, quantum chemistry methods provide a fundamental understanding of the processes at stake in the detection of chemical species and allow for rational design of sensing materials. Certain organic molecules can be extensively functionalised and thus constitute an evident starting point owing to the tunability of their properties provided by appropriate choice of structural modifications. The versatility of some chromophores associated to the selectivity offered by receptor units constitute the research playground for the development of ever better chemosensors.

The present research aims at the rational development of chromoionophores for the complexation of cations, combining computational chemistry methods with basic spectroscopic characterisation. Using Density Functional Theory (DFT) and its timedependent extension (TD-DFT), two main aspects were treated, namely the relationship between molecular structure and optical properties of organic chromophores featuring valuable characteristics, and the complexation phenomenon.

Photophysics of Zn 2+ ion detection were more specifically studied, and recognition was demonstrated with both quantum-chemical calculations and experiments, accounting for the future integration of the chemical sensor in an optical fibre device.

Modélisation des

propriétés photophysiques de capteurs chimiques pour des applications de détection de cations par fibre optique.

Bien que naturellement présents dans notre environnement, la quantité d'ions métalliques a fortement augmenté durant les dernières décennies en raison d'intensives activités humaines, telles que les exploitations minières ou le rejet croissant de déchets industriels et agricoles, engendrant un intérêt grandissant pour la détection de ces espèces au sein des communautés industrielle et scientifique. Les méthodes analytiques à ce jour disponibles présentent pour la plupart des limitations techniques et/ou des coûts excessifs. Une alternative réside dans l'élaboration de senseurs chimiques abiotiques en se basant sur les principes de la chimie moléculaire et supra-moléculaire. Ainsi, un senseur chimique moléculaire peut être défini comme étant composé de 2 éléments: l'unité de reconnaissance de l'ion métallique, ou ionophore, responsable de la liaison spécifique avec un analyte donné, et l'unité chromophore qui permet de traduire la complexation en un signal optique, la détection étant généralement basée sur des modifications d'absorption ou d'émission de la lumière. Ces deux entités, dont les modifications permettent d'obtenir des propriétés et fonctionnalités désirées, peuvent être liées de façon covalente par un éventuel groupe espaceur, et constituent le senseur moléculaire chimique, aussi appelé chromoionophore. Ce travail de recherche vise à développer de tels systèmes de manière rationnelle en utilisant les outils de la chimie computationelle, principalement la Théorie de la Fonctionnelle de la Densité (DFT, pour Density Functional Theory) et son extension dépendante du temps (TD-DFT, pour Time-Dependent DFT), combinés à une caractérisation basique par spectroscopique optique.

Pour cela, deux aspects principaux ont été abordés, à savoir les relations structurepropriétés optiques du chromophore, ainsi que les aspects photophysiques associés au phénomène de complexation. Nous nous sommes plus particulièrement focalisés à la détection de l'ion Zn 2+ , intéressant dans le cadre du suivi de la corrosion de l'acier galvanisé, considérant l'intégration du senseur chimique dans un futur dispositif à fibre optique.

Modulation des propriétés optiques et électroniques de colorants BODIPY.

L'étude des relations structure-propriétés optiques du chromophore a été menée sur la famille des BODIPYs, un colorant très populaire et largement utilisé dans diverses applications, telles que les dispositifs photovoltaïques luminescents, en raison de ses remarquables propriétés thermiques et photochimiques, entre autres, ainsi que sa grande versatilité résultant des multiples fonctionnalisations possibles du BODIPY non-substitué (Figure 1). Alors que les valeurs des longueurs d'onde d'absorption et d'émission se révèlent quasi-insensibles à l'introduction d'un groupement aryle en position meso, une telle substitution peut en revanche conduire à un important changement du rendement quantique de fluorescence puisqu'elle offre une voie de désexcitation non-radiative efficace via la rotation permise de ce substituant. La restriction de ce degré de liberté par l'introduction de groupes stériquement encombrés permet alors de restaurer la fluorescence. Fonctionnaliser le BODIPY en position meso de manière appropriée est l'une des stratégies employées par exemple dans l'élaboration de senseurs chimiques basés sur des processus d'oxydation ou de réduction (ou senseurs PET -Photoinduced Electron Transfer). Cette position 8 présente aussi un grand intérêt en terme de modulation des longueurs d'onde d'absorption et d'émission: ces dernières peuvent en effet être déplacées vers le bleu par l'introduction de groupements amino. L'autre partie du spectre peut être explorée par des modifications structurales aux positions de substitution présentes sur les cycles pyrroles. Ainsi, en fonction de la nature des substituants, de la symétrie de la substitution, ou encore de la possible rigidification de la molécule, nous avons montré que d'importants déplacements spectraux vers les grandes longueurs d'onde peuvent être obtenus, accompagnés d'une augmentation de la force d'oscillateur.

Étude conjointe expérimentale et théorique de chromoionophores pour la détection de cations Zn 2+ .

Parmi les multiples chromophores disponibles, les pérylènes sont d'intéressantes plateformes de départ pour l'élaboration de nouveaux senseurs moléculaires de part leurs remarquables propriétés photochimiques pouvant être largement modulées grâce aux multiples fonctionnalisations possibles. Le senseur d'ions zinc objet de notre étude, constitué d'un pérylène monoimide (PMI) couplé à une unité dipicolylamine (DPA), possède une architecture de type donneur-accepteur. Nous avons montré par nos calculs que le déplacement spectral du maximum d'absorption vers le bleu, mesuré en solution lors d'ajout d'ion Zn 2+ , s'expliquait par l'impact du cation sur le transfert de charge intramoléculaire ayant lieu dans le composé libre après photo-excitation. La formation du complexe s'accompagne d'une stabilisation asymétrique des orbitales frontières principalement impliquées dans la transition électronique d'intérêt. Plus spécifiquement, cet effet est dû à une diminution du caractère donneur de l'azote de l'unité DPA, sa paire libre étant impliquée dans la complexation du cation, contribuant à l'altération du transfert de charge intramoléculaire (Figure 2). En d'autres termes, la réponse optique du PMI-DPA à l'ion Zn 2+ est reliée au degré de couplage électronique entre l'unité ionophore et l'unité chromophore qui le constituent.

Conclusions and perspectives

List of publications

1

General introduction

lthough metal ions occur naturally in our environment, intensive human activities have severely modified the original balance and the past decades have seen an increased interest among the scientific and industrial communities for the detection and the quantification of those species i . In spite of the essential role some of them can play in various biological processes of living organisms (e.g. the zinc ion for protein synthesis, activity of many enzymes, regulation of the cell production in the immune system of the human body or genetic expression [1] ), excessive amounts of most metal ions in water, air and soil represent serious environmental and public health issues due to their potential (eco-)toxicity [2,3] , which depends on their chemical form. Diverse anthropogenic sources may be identified, as corrosion, industrial effluents or gold mining wastes, and dramatic concentrations can be reached as a consequence of their accumulation over the years. A wide number of analytical approaches are currently available for the detection of cations, such as atomic absorption spectrometry [4] , but most of them entail excessive costs and/or present technical limitations (impossibility of use for on-site detection). Precise understanding of complex processes established in nature, such as the efficient detoxification mechanisms for i in this context, they are generally incorrectly referred to as "heavy metals", see IUPAC Technical Report, J. H. Duffus, Pure Appl. Chem. 74, 793 (2002).

A the regulation of metal ions, provides a rich source of inspiration for the elaboration of abiotic chemical sensors, or chemosensors. Rational design of systems fulfilling accurate metal ion detection requirements via the achievement of desired properties and functions, from molecular and supramolecular chemistry principles, however still proves to be a challenging task.

Defined as the "chemistry beyond the molecule" [5] or "chemistry of molecular assemblies and of the intermolecular bond" by one of its main instigators J.-M. Lehn ii , supramolecular chemistry is fundamentally based on the concepts of receptor [6] , i.e. that molecules do not act if they do not bind, recognition [7] (lock and key), and coordination [8] . Molecular recognition, which has emerged as an highly active domain of chemical research, relies on the specific binding of a guest (analyte) by a given host (receptor), the event being characterised by the associated amount of energy and information brought into play [9] . Optimal recognition can then be regarded as being achieved when the free energy difference for binding of a given guest largely differs as compared to other guests.

In a molecular chemical sensor, the recognition unit, responsible for the selective binding of the metal ion, can be covalently linked, via a spacer or not, to a chromophore to build a so-called chromoionophore (figure below, adapted from ref 10). When designing such sensing compounds, one has to account for both moieties to achieve the expected functionalities and properties, and for the possible spacer for interactions and geometry modulations. While the ionophore binds the analyte, "storing" the information that for instance a metal ion is present, the ii J.-M. Lehn was awarded the Nobel Prize in Chemistry 1987 jointly with D.J.

Cram and C.J. Petersen "for their development and use of molecules with structure-specific interactions of high selectivity".

chromophore translates the complexation event into an optical signal, the detection being generally based on modifications of light absorption or fluorescence.

An efficient chromoionophore sensor can thus be defined as a molecule that selectively, and ideally reversibly, binds a given ion, inducing changes in the photophysical properties of the system (spectral displacement, change of quantum yields..). Such systems are inherently attractive given the multiple advantages they provide, from both their selectivity and sensitivity, to the ability of performing continuous monitoring or in situ remote sensing when combined with optical fibres [11] .

The present research aims at the rational development of chromoionophores for the complexation of cations, using computational chemistry methods in combination with basic spectroscopic characterisation. Two main aspects are treated, namely the molecular structure-optical properties relationships of the chromophore and the complexation phenomenon. More specifically, we focus on the detection of Zn 2+ , which is the ion of interest when monitoring the corrosion of galvanised steel, and account for the future integration of the chemical sensor in an optical fibre device.

In the first chapter, a detailed introduction to the major photophysical processes that take place upon interaction of light with an organic molecule is given. In a second step, we recall the cation sensing principles on which chromoionophore design is based, and present the main photophysical changes associated to the cation complexation event. Basic concepts of quantum chemistry and computational methods employed in this work are reviewed in Chapter 2. The next chapter is dedicated to the chromophore unit, which constitutes the signalling element of our molecular chemical sensor. Four series of BODIPY dyes are studied to get insight into how their optical properties can be modulated by substitution and appropriate structural modifications. Chapter 4 reports the comprehensive study of a zinc ion molecular sensor. The perylene monoimide derivative we investigated is decorated by an appropriate ionophore and the complexation of Zn 2+ is characterised in terms of signalling optical response by quantum chemical methods and experimental measurements. In order to demonstrate the detection of the zinc ion with optical fibre sensor technology, a series of experiments have been performed. Starting from deposition of pure films on glass substrates and the spectroscopic characterisation of the Zn 2+ detection, the chromoionophore is then encapsulated in a sol-gel that constitute the active layer on a modified optical fibre.

Chapter 1

Photophysics of cation detection

o ensure that complexation of a metal ion yields the desired optical response, one has to efficiently tailor the optical properties of the chromophore moiety. A chromophore is defined by the IUPAC as "the part (atom or group of atoms) of a molecular entity (...) responsible for the dye's colour", this colour arising from the ability of the molecule to interact with light. To define how and to what extent optical properties can be modulated, it is of utmost importance to understand the interaction of light with a molecule and its consequences on the optical properties.

Absorption

Light is a transverse electromagnetic radiation that can be characterised by its frequency  or wavelength  but is also quantised in discrete packets of energy E called photons (wave-particle duality).

T hc E h hc (1.1) with h the Planck constant, c the speed of light and the wavenumber.

Depending on the wavelength of the radiation interacting with matter (Figure 1.1), different phenomena can be observed. Our work deals with the optical spectral range comprising the UV, visible and NIR regions.

Electronic structure of molecules and the role of

-conjugation

The electronic structure of a molecule is described within the quantum theory by probability density functions involving eigenstates associated with discrete eigenvalues (see chapter 2). Absorption of a photon will bring the molecule from its electronic ground state to an electronic excited state higher in energy (while light emission consists in the inverted process).

In

Transition probability

As mentioned above, there are conditions for a transition to occur and the ability of a photon of specific energy to modify the electronic structure of the molecule will govern the probability of the transition. The changes in charge distribution and electronic structure consequent to the interaction, i.e. the transitory moment relative to the field induced oscillation of the electron cloud, is described by the so-called transition dipole moment:

îj i j (1.3)
with i and j the electronic wavefunctions of the molecule in the initial and final states, respectively, and ˆ the electric dipole moment operator.

For a transition to be allowed, the transition dipole moment, the magnitude of which directly determines the intensity of spectroscopic absorption/emission, should be nonzero, and symmetry selection rules can be derived (e.g. Laporte's rule for centrosymmetric molecules). The second important selection rule concerns the spin multiplicities of the initial and final states, which should be equal for the transition to be allowed. The probability of an allowed transition is proportional to the squares of ij and electric field intensity and is thus the highest when the transition dipole moment is parallel to the polarisation vector of the oscillating electric field.

The transition dipole moment can be related to the oscillator strength f :

2 8² 3² ij m f he (1.4)
It is a dimensionless quantity which links the quantum and classical approaches and can be interestingly expressed as a function of an experimental quantity, namely the molar extinction coefficient () : proportional to the square of the overlap integral between the vibrational wavefunctions of the two states that are involved in the transition. [1] In other words, one can invoke the Franck-Condon principle to separate the transition dipole moment in equation 1.3 into electronic and nuclear terms:

ˆ,, tot

tot ij i j el el i i j j el el i j i j (1.6)
The probability of any transition thus depends on the electronic transition dipole moment times the square of the vibrational overlap integral (or Franck-Condon integral) that determines the relative intensity of each peak, known as the Franck-Condon factor:

2 ij ij FC (1.7)
Franck-Condon factors are governed by the relative positions of the ground-state and excited-state potential energy surfaces. This is illustrated in Figure 1.3 where two particular cases are depicted: namely, when equilibrium nuclear coordinates are the same in both S 0 and S 1 states, as opposite to the situation in which there is an offset in position of the excited state equilibrium geometry relative to the ground state.

S v = 0→ 1 S v = 2 one,
as it corresponds to the transition for which the overlap between i and j is maximal (largest Franck-Condon factor), giving rise to a very different shape for the absorption spectrum.

Dynamics of the excited state 1.2.1 De-excitation pathways

Excitation from the ground state to an excited singlet state by absorption of a photon is a very fast process, occurring on the order of 10 is the lowest excited level of that multiplicity". [2] A corollary, known as the Kasha-Vavilov rule, says that the quantum yield of luminescence is independent of the wavelength of the exciting radiation. Both rules have exceptions. [3] i When there is a small gap, i.e. no overlap, a tunnelling process takes place, with a probability governed by the difference in energy between the lower and upper vibrational levels of the initial and final electronic states, respectively. Phosphorescence is the second radiative de-excitation that can take place, initiated via a radiationless process known as intersystem crossing (Figure 1.4 c). The crucial difference with all pathways already described is that it involves the formation of a triplet state and hence concerns states of different multiplicities, i.e. transitions of the S n →T n or T n →S n types. The probability for such S n -T n transition increases with the overlap of vibrational levels of the singlet and triplet excited states (for instance 1 S v = 0 and higher vibrational levels of T 1 ). However, unlike internal conversion, intersystem crossing requires a spin conversion, which is in principle forbidden, but can nevertheless take place due to spin-orbit coupling giving rise to weakly allowed transition. A quick vibrational relaxation follows and leaves the molecule in a vibrationally-relaxed triplet state. Although intersystem crossing is a slow process compared to the similar internal conversion, it is able to compete with and dominate fluorescence in some cases, like in molecules containing heavy atoms, because of a more efficient spin-orbit coupling.

From the lowest vibrational level of the triplet state T 1 , the molecule can end up in the ground state S 0 by a second intersystem crossing but it can also, depending on the conditions, lose its energy via phosphorescence emission, both processes involving a change in the spin multiplicity and thus exhibiting low probability. Similarly to fluorescence, phosphorescence consists of transitions to vibrational levels of the ground state by emission of a photon and the spectrum is often a mirror image of the ground state absorption. However, as it is characterised by a forbidden spin conversion, it occurs on such long time-scale (10 -3 -10 2 seconds) that it is not so commonly observed, as other deactivation processes might compete and become dominant. Finally, due to the lower energy of the zero th vibrational level of the triplet state compared to that of S 1 , the phosphorescence spectrum is shifted from the fluorescence spectrum towards longer wavelengths.

Note that when the energy gap between S 1 and a long-lifetime T 1 is small, delayed fluorescence can also occur, which consists in a reverse intersystem crossing to S 1 followed by fluorescence emission (thermal activation or triplet-triplet annihilation).

A very convenient way to summarise all the different excitation/deexcitation pathways is provided by the Perrin-Jablonski diagram (Figure 1.5). By convention, the various optical processes that can occur are depicted by arrows between electronic states and their respective vibrational levels, wavy arrows being associated with non-radiative events.

Decay characteristics

While the molar extinction coefficient  reflects the ability of a molecule to absorb light at a certain wavelength, the efficiency of a given deactivation process can be estimated by its quantum yield Φ process , which is the ratio of quanta absorbed to the number of quanta that undergo that process. It can also be expressed as a function of the relative excited state decay rates:

process process process deact k kk (1.8)
where deact k is the sum of the rate constants for all the deactivation processes that compete with the process of interest, to which k process is the associated rate constant.

Clearly, the fluorescence quantum yield decreases as the number of possible efficient deactivation pathways increases. For instance, the fluorescence quantum yield, given by the ratio of photons emitted to photons absorbed, can be calculated by:

fluo fluo fluo IC ISC k k k k (1.9)
As already mentioned, the extent of conjugation, reflected in the electronic structure of the molecule, constitutes a key parameter defining the absorption and emission spectra properties: the longer the πconjugated system, the longer the wavelength of the absorption maximum.

As for the geometrical constraints, fluorescence emission is favoured in molecules that exhibit a rather rigid structure, as they are less likely to undergo radiationless deactivation due to vibrational and rotational dynamics. However, not only the chemical and molecular structures are determining the nature and efficiency of the various de-excitation processes, many environmental parameters also come into play, such as the temperature, as the efficiency of thermal agitation-related nonradiative processes increases with it, or what usually receives the most attention, the solvent effects, known to greatly condition the photophysical properties of a molecule.

Solvent effects

Responsible for the inhomogeneous broadening of spectral bands, solvents can strongly affect the intensity and position of absorption and emission bands and thus constitute one origin of the Stokes shift. [4] Following the absorption of a photon, vibrational relaxation towards the zero th vibrational level of the excited state is accompanied by solvent relaxation.

The excitation of the molecule brings about changes in the ground state charge density and results in a different dipole moment in the excited state, 01 SS , inducing a rearrangement of the surrounding solvent molecules that reorient to stabilise S 1 , then known as thermally-relaxed excited state (the dynamical aspects of solvation are described in section 2.9.2 of Chapter 2). The extent of this stabilisation depends on the polarity of the solvent (Figure 1.6): assuming 01 SS , an increasing solvent polarity causes larger stabilisation of the excited state, so that the transition band experiences an increasing bathochromic shift (or red-shift).

Conversely, when going from a more polar solvent to a less polar one, the band undergoes an hypsochromic shift (or blue-shift) ; this spectral dependence on the solvent polarity for a given molecule is called solvatochromism. Opposite behaviour is observed when 01 SS , or in the case of n- transitions. Note that the intensity can also be affected and one talks about hyperor hypochromic shifts for an increase or a decrease in the molar extinction coefficient, respectively. These spectral changes are evidently also determined by the polarity of the solute: while polar molecules are logically very sensitive to solvent polarity, apolar molecules exhibit a modest dependency. The absorption phenomenon happening on a very short timescale (~10 -15 s), it is not much affected by the solvent polarity. For the excited state, solvent relaxation can occur (timescale 10 -10 s), before fluorescence takes place. Solvents are roughly classified as polar or non-polar, the former being further subdivided into protic or aprotic. However, solvent polarity with related spectral shifts is a tricky concept encompassing nonspecific and specific solute-solvent interactions (inter-and intramolecular processes such as hydrogen bonding or charge-transfer..), and many alternatives to its primary expression in terms of dielectric constant have been proposed, leading to a large variety of "solvent polarity scales". [5] Among polar solvents, one can find water but also methanol or acetonitrile, while chloroform and toluene are considered as apolar. A protic solvent, or protogenic solvent, as preferentially defined by the IUPAC, is "capable of acting as a proton donor", as well as making specific hydrogen bonding.

Cation sensing principles

Chemical sensors have been developed to detect and monitor an extensive set of species and properties, ranging from ions to biochemical molecules and gases, as well as temperature or conductivity. Following the "recognition event", a sensor returns information by means of various transduction mechanisms, such as for instance, a modification of the optical properties (spectroscopic features, refractive index..) or the redox potential. The ever-growing interest that sensors have raised over the past decades has led to a jungle of compounds and devices based on various operative principles, and we refer the interested reader to several books and reviews that can provide a clear and detailed understanding of a given related issue. [6][7][8][9] One has to be cautious while employing the term "chemical sensors", which according to the so-called "Cambridge definition" [10] are miniaturized analytical devices that can deliver real-time and on-line information on the presence of specific compounds or ions in complex samples. Clearly, we are not addressing fully the wide topic of chemical sensors which is beyond the scope of this manuscript but restrict our attention to optical chemical sensors, and more particularly chromogenic and fluorescent molecular sensor elements that allow for cation detection based on absorbance or luminescence of chromoionophores, respectively.

Although from now on, we might use the term "sensor" in this manuscript to refer to the systems we are dealing with, it is however important to realise and keep in mind that there is a long way to go from the molecular design of an active compound to a functional final device.

Architecture of the chromoionophore

The classical design of a chromoionophore relies on the coupling of a receptor, achieving the recognition of the analyte with ideally the highest possible selectivity, to a chromophore acting as a transducer, whose changes in optical properties constitute the signalling of the recognition event. A spacer may provide further possibilities for modulation of the processes inherent to the detection of a given analyte (Figure 1.7). Great care has to be taken regarding each of these elements and their association, according to the principles of supramolecular chemistry. that in the integrated system, some atoms or the chromophore may participate into the complexation event.

Ionophore -Stability and selectivity

The ionophore moiety constitutes the key component of the sensor, governing its selective response to a particular analyte without interferences with other species. The preferential complexation of a given cation can be discussed in terms of thermodynamic stability constants of the complex, also known as the binding constant K b , or its inverse, the dissociation constant K d . These equilibrium constants can depend on various environmental factors such as the temperature, the pH or the nature of the solvent. Considering a 1:1 complex formation, one can write the complexation equation and associated equilibrium constants as: The larger the binding constant, the larger the concentration of complexed cation. However, if high values for K b (or small for K d )

reflecting more stable complexes are usually sought, selectivity, i.e. the relative affinity of a given ligand with one metal cation among other analytes, is defined as the ratio between the associated binding constants, not their absolute magnitude.

Many examples can be found in nature, which elegantly manages optimal complexation of metal ions for diverse purposes, such as biological ion transport and regulation. [11,12] However, to achieve with synthetic ionophores strong selectivity towards a given cation is a complicated task, as the interactions involved are ruled by the physical and electronic complementarity between ligand and cation: the ionophore structure (size, pre-organisation..) and the number and nature of the binding atom(s) should fit the cation characteristics (diameter, charge density, coordination number). The ionophore can be a simple chelator or possess a more complex architecture from macrocycles like crown ethers [13] , to macrobicycles (cryptands) [14] , or calixarene derivatives [15] , to provide for example three-dimensional encapsulation, thus allowing more stable complexation. Crown ethers are particularly suitable for complexation of alkali metal cations, with selectivity depending on the size of the cavity relative to the cation radius. Typical examples are the 18-crown-6 and dibenzo-18-crown-6, the first crown ethers synthesized by Pedersen [16] ,

which present the strongest affinity for potassium cations among alkali metal cations (Figure 1.8). Ionophores have also been developed for the complexation of transition metal cations such as the bis(2-pyridylmethyl)amine chelator presented in Figure 1.9, or more commonly dipicolylamine (DPA), first reported by Kabzinska in 1964 [17] . It contains three nitrogen atoms that can strongly bind Zn 2+ and has become very popular in the field of chemical sensors.

Moreover, the availability of the nitrogen lone pair in the guest-free DPA allows for electronic processes with an appended chromophore and thus makes it a very appealing receptor subunit for the design of a zinc ion sensor. Denticity is defined by the number of binding atoms and a complex is referred to as monodentate when only one atom intervenes in the complexation, or multidentate when two or more atoms coordinate the ion (bidentate, tridentate, and so on). Note that for integrated-like architectures, the selectivity will not only depend on the ionophore but might involve the whole system. Finally, solvent effects are of major importance regarding both selectivity and stability. The rational design and development of ionophores are out of the scope of this work and the reader may find more information in the reviews, publications or textbooks that cover the topic. [18][19][20]

Chromophore and spacer

The properties of the signalling unit are ruled by the type of detection process selected and the kind of final device desired, so that the choice of the chromophore depends on many parameters. It is generally of utmost interest to work with tuneable compounds to obtain high molar extinction coefficients and quantum yields of fluorescence as a function of the nature and position of the substituent groups, and by extension a modulation of all properties to achieve a given photoinduced process upon complexation.

Ideally, the change in photophysical properties should be the largest possible to facilitate the detection. Moreover, the ease for substitution can allow the addition of anchoring groups, when for instance the chromoionophore has to be grafted directly on a substrate, and is also the key to modify the compound solubility. Finally, certain families of chromophores, like the rylene and BODIPY derivatives presented in section 1.4.3, allow for spanning a wide portion of the UV-Vis-NIR region and one can extensively change the wavelength working range of the sensor according to the needs; for instance, implementation on an optic fibre requires the ability for the chromoionophore to work at wavelengths for which the losses of transmitted signal are minimised (see chapter 4). [21] Further modulation can also be achieved with the inclusion of a spacer, which depending on its nature and its length [22] , can greatly affect the electronic processes at stake in the detection event.

From the optimised selectivity of the ionophore moiety to the adapted photophysical properties of the chromophore, each part plays a crucial role in the detection process and rather than strictly being concerned by the design of one or more of them, we mainly focused our attention on their rational combination and the description of the cation-induced processes associated with the photophysical changes, in particular the photoinduced intramolecular charge transfer and photoinduced electron transfer.

Photophysical processes involved in cation

detection [23][24][25][26] 1.

Photoinduced intramolecular charge transfer (ICT)

ICT systems typically possess an integrated-like architecture, in which the receptor is conjugatively coupled to the chromophore without inclusion of any spacer, and exhibit push-pull character arising from the nature of the terminal parts, one end being electron-donating (often an amino group), the other end being electron-withdrawing. Upon photoexcitation, the electron density is redistributed as the compound experiences an intramolecular charge transfer from the donor to the acceptor, which results in a significant change of the molecular dipole moment. It is expected that the presence and interaction of a metal cation with either the donor or acceptor site will modify the photophysical properties of the When the donor moiety of the chromoionophore interacts with a cation, its electro-donating character is reduced (since its electrons are involved in the binding), so that a blue-shift of the absorption spectrum relative to that of the cation-free compound is observed, accompanied by a lower molar extinction coefficient. The opposite behaviour, i.e. a bathochromic shift and an increase of () , is expected following the interaction with the acceptor, as its electro-withdrawing capacity will be enhanced and the push-pull effect strengthened. These effects can be illustrated by the evolution of the frontier orbitals, usually preponderantly involved in the transition of interest, as a function of the strength of the donor and acceptor parts of the system. [27] Another rationalisation of the spectral displacements aforementioned is given by considering the state dipoles in the presence and absence of the cation. As previously noted, the initial electronic polarisation in the donor-acceptor system becomes larger upon photoexcitation: the electron density reorganisation leads to a substantial increase of the molecular dipole moment on going from S 0 to S 1 . The interaction of a cation with the donor group causes an asymmetric destabilisation of the two states, with a stronger effect in the excited state due to the repulsive interaction with the positively charged donor in the charge transfer excited state, resulting in an hypsochromic shift. An inverse spectral behaviour is observed when the interaction takes place on the acceptor moiety as the excited state is more stabilised with respect to the ground state (Figure 1.10). Emission spectra generally experience the same kind of spectral displacements. However, not only the transition wavelengths are affected by the cation complexation, but also the quantum yield and lifetimes may change.

Finally, the ICT process is by nature clearly very sensitive to the solvent polarity (see section 1.3), and solvent effects may even favor the appearance of a twisted intramolecular charge transfer (TICT), in which the donor and acceptor components of the push-pull system are rotated in the excited state, leading to the observation of extra-emission bands. [28] The concept of photoinduced intramolecular charge transfer has been widely used in the design of cation sensors and numerous examples are reported in the literature. [29][30][31][32][33] For instance, the aza-crown based sensor from W. Qin and al. has proven to be sensitive to several metal cations, displaying large spectroscopic changes upon complexation as a result of an altered intramolecular charge transfer in the complexed form (Figure 1.11). [34] [35,36] Photoinduced electron transfer requires an electron donor and an electron acceptor components and is based on the enhancement of the redox properties of a molecule upon absorption of light, which may result in an electron transfer. The photon absorption activates a donor or an acceptor for an electron transfer process that occurs only if the excitation energy is sufficient for the molecule to undergo a redox reaction. [37,38] Whenever the oxidation potential of the chromophore is larger than that of the receptor, i.e. its HOMO is lower in energy, the PET process can occur and puts the chromophore in "off" state ; the opposite behaviour applies in the "on" state. Together with the choice of the right selective receptor for a given analyte as well as the choice of an appropriate spacer, this criterion on molecular orbitals energies and associated redox potentials guides the design of PET sensors for cations. The PET process in the framework of cation detection has been extensively studied over the last decades and numerous cation PET sensors have been developed. [39][40][41][42] 1.4.3 Chromophores studied in this work

Photoinduced electron transfer (PET)

Rylene derivatives

The rylene family of dyes is based on the highly functionalisable perylene core, which provides an ideal platform for further modulation. [43] Perylene Functionalised rylenes have been extensively studied since their discovery and owing to their exceptional chemical, thermal and photophysical properties (high molar extinction coefficient and fluorescence quantum yields among others) they are nowadays used in a broad range of domains, from industrial paints to electronic and optical applications such as organic photovoltaic solar cells (OPVs), organic field-effect transistors (OFETs) or organic light-emitting diodes (OLEDs). [44][45][46] The photophysical properties of perylene (di)imides can be modulated by expanding the aromatic system along the long molecular axis to obtain the higher order homologues terrylene (TDI), quaterrylene (QDI) and so on. The Absorption and emission spectra of these dyes are increasingly bathochromically shifted with the extension of the conjugated system, spanning a broad range of wavelengths in the Vis-NIR spectrum up to 950 nm in absorption for the hexarylenebis(dicarboximide)s. Substitution at the available bay positions (and peri position in the case of PMI) provides large possibilities for further improvement, for instance in terms of solubility or aggregation prevention as well as fine tuning of the optical properties. [47] In the framework of chromoionophore design, PMI constitutes an advantageous platform with the electron-acceptor imide group to generate push-pull systems able to exhibit strong intramolecular charge transfer when coupled to electron-donor ionophores at the bottom peri position.

BODIPY derivatives

Discovered in 1968 by Treibs and Kreuzer [48] , BODIPY dyes have ever since been the subject of numerous comprehensive investigations and are nowadays, owing to their remarkable properties, very popular in many different applications including photovoltaic and luminescent devices [49,50] ,

fluorescent switches [51] , laser dyes [52] , and chemosensors, among others. More generally, spectral displacements towards longer wavelengths could be induced not only by the extension of the pi-conjugated system via substitution in all possible positions, but also by the rigidification of the structure, as it is presented in chapter 3, as well as the exchange of the carbon atom at the meso-position by a nitrogen atom (aza-BODIPYs).

Chapter 2

Quantum chemistry methods t the end of the 19th century, electromagnetism and classical mechanics were successful in rationalising all physical phenomena.

However, it became soon clear that the behaviour of elementary particles was not governed by classical laws. The Planck "quantisation" (1900) [1] being the first crack of the classical edifice, it was not long before Newton's old suggestion of light consisting in particles revived through Einstein's key experiment of the photoelectric effect (1905) [2] and subsequent avant-garde light quantum hypothesis. Unravelling the schizophrenic behaviour of light paved the way for the ground breaking proposition of De Broglie who postulated that matter was also subject to the so-called wave-particle duality (1924) [3] . The need for a wave equation to support a wave theory of matter was fulfilled two years later when Schrödinger came up with the most fundamental equation of quantum mechanics.

A

The Schrödinger equation and the wavefunction

As a consequence of the probabilistic aspect of the quantum theory, a new mathematical tool is introduced to treat the possible positions of the particles, the wavefunction ψ(x,y,z,t). Having no physical meaning itself, its square represents the probability density for the particle to be in a given point of space (x,y,z) at a time t. Moreover, it allows the calculation of all the electronic properties of the system.

To characterise the time evolution of a quantum state, the timedependent Schrödinger equation has to be solved:

( ) ( ) ( ) i t H t t t (2.1)
with (t) the wavefunction of the system, the reduced Planck constant, and ˆ() Ht the Hamiltonian of the system. However, one is usually dealing with stationary states so that the Ĥ operator does not explicitly depend on time, but simply on the coordinates of the particles (r, R). The Schrödinger equation reduces then to its time-independent formulation [4] :

ˆ( , ) ( , ) tot tot H R E R rr (2.2)
where (r,R) is the wavefunction of the system that depends on r and R, the electrons and nuclei spatial coordinates, respectively, tot E is the total energy of the system, and ˆtot H the total Hamiltonian of a system of m nuclei and n electrons. The latter can be written as the sum of the kinetic and potential energies of the nuclei and electrons:

ˆtot n e ne ee nn H T T V V V (2.3)
with T n and T e , the nuclear and electronic kinetic energy, V ne the attractive interaction between nuclei and electrons, V ee the repulsive electron-electron interactions, and V nn the repulsive interaction between nuclei. It is defined in atomic units (m e =  = 4 0 = e = 1) as:

    22 1 1 1 1 11 1 ˆ2 1 m n n m a tot a i a i i a a ia n n m m ab i j i a b a ij ab Z H mr ZZ rr (2.4)
where m a is the mass of the atom a, Z a and Z b the nuclei charge of atom a and b respectively, r ab the distance between the nuclei a and b, r ia the distance between the nucleus a and electron i, and r ij the distance between electrons i and j.

Because of the complexity associated with interdependency in the motion of the particles, exact solutions of the Schrödinger equation only exist for a small set of simple quantum systems such as the hydrogen atom or hydrogenoïd systems. Therefore, several approximations are typically used, as described below.

The Born-Oppenheimer approximation

Considering that the nuclei are moving much more slowly than the electrons (they are more than 1800 times lighter in mass than neutrons and protons), one can assume that the electronic cloud somehow instantaneously adapts to the molecular geometry. Born and Oppenheimer proposed in 1927 to decouple the electronic and nuclear motions [5] . This approximation, referred to as the Born-Oppenheimer approximation (or adiabatic approximation), results in neglecting the kinetic energy of the nuclei (T n ) and considering the interactions between nuclei (V nn ) to be a constant for a given geometry. The electronic Hamiltonian depends explicitly on the electron coordinates (only parametrically on the nuclear positions) and is defined as:

ˆel e ne ee H T V V (2.5)
It is then reasonable to factorise the total molecular wavefunction as follows:

( , ) ( , ) ( )

BO elec nuc R R R rr (2.6)
with  elec the electronic wavefunction and  nuc the nuclear wavefunction, and solve the Schrödinger equation for the electrons alone in the field of the fixed nuclei. In this picture, nuclei are moving on a potential energy surface (PES) that is solution of the electronic Schrödinger equation.

In the framework of the Born Oppenheimer approximation, one still cannot find solutions to the electronic Schrödinger equation for polyatomic systems containing more than one electron and further approximations have to be introduced.

The independent model

Within this model, electrons of the system are supposed to be noninteracting. Neglecting the electron-electron interactions allows to "split" the electronic Hamiltonian for N independent electrons into a sum of oneelectron Hamiltonians, each describing the motion of the ith electron in the average field due the other electrons (and the potential of the nuclei).

The electronic Schrödinger equation can be written as a set of N monoelectronic equations that can be solved independently:

( ) ( ) i i i i h r r (2.7)
with h i the one electron Hamiltonian of the ith electron, containing its kinetic energy term T e and the attractive interaction with the nuclei V ne , and  i the energy of the one-electron state  i (r). Eigenfunctions of ˆi h are known : the hydrogenoïd spin-orbitals, product of one-electron orbital and a spin function  are the building blocks of the total electronic wavefunction. The total energy is then simply the sum of the individual energies and the total wavefunction the product of the spin-orbitals (or Hartree product). Thus, one just has to choose a set of spin-orbitals to describe the electrons and obtain the total electronic energy of the system. However, this model should be considered as a minimal description only and leads to mediocre results.

Moreover, one has to take into account the fact that electrons are indistinguishable to build a correct wavefunction. This property imposes that electrons must be described by wavefunctions that are antisymmetric with respect to particle exchange (spatial and spin coordinates). Such a many-electron wavefunction, satisfying the antisymmetry principle, can be, in the simplest case of a closed-shell system, written as a Slater Determinant [6] (SD) of the one-electron wavefunctions, antisymmetric by construction. In the general case of N electrons and N spin-orbitals, the SD is expressed as:

1 1 2 2 1 1 2 2 1 1 2 2 (1) (1) (1) (1) ... (1) (1) (2) (2) (2) (2) ... ( 2
) (2) 1 (1, 2,..., ) ... ... ... ... ! ( ) ( ) ( ) (1) ... ( ) ( ) NN NN NN N N N N N N N (2.8)
Note that, any two of the spin-orbitals cannot be identical to avoid the determinant being equal to zero, in agreement with the Pauli principle which states that two electrons cannot have all the same quantum numbers.

2.4

The Hartree-Fock formalism

The Hartree-Fock method

Based on the variational principle [7] , which states that the energy of an approximate wavefunction is always an upper bound of the true energy, the Hartree-Fock model [8,9] allows the determination of the "best" electronic wavefunction , considering that it can be approximated by an antisymmetrised product of N one-electron wavefunctions, i.e., a unique Slater Determinant. In the HF framework, each electron is moving in the average electrostatic field created by all the other electrons.

From a trial SD, the variational principle can be applied to generate the "best" one that minimises the electronic energy, the expected energy being calculated as:

0 trial trial approx trial trial H EE (2.9)
The HF energy is the expectation value of the electronic Hamiltonian operator on a Slater Determinant and is, for a closed shell system of N electrons, given by:

1 1 1 2 (2 ) N N N ii ij ij i i j E H J K (2.10)
where:

51 ( ) ( ) ii i i i i H r h
r , is the average energy of an electron in the field of the nuclei (i.e., the sum of the kinetic energy of the electron and the attractive interaction)

1 ( ) ( ) ( ) ( ) ij i i j j i i j j ij J r r r r r
, the Coulomb integral, is the electrostatic repulsion between two electrons with electronic density of 2 () ii r and 2 () jj r , respectively,

1 ( ) ( ) ( ) ( ) ij i i j i j j i j ij K r r r r r
, the exchange integral, arises from the antisymmetry condition imposed on the wavefunction and has no classical equivalent.

Minimising the expectation value of the energy via the variational method, one can show that the optimal spin-orbitals are eigenfunctions of the effective one-electron Fock operator ˆi f and satisfies the Hartree-Fock equations:

î i i i f (2.11)
where  i is the energy of the spin orbital  i and the Fock operator is expressed as:

1 ˆˆˆ2 N i j j j f h J K (2.12) with  2 1 1 ˆ2 m a i a ia Z h r
, the one-electron Hamiltonian from the independent model, 1 ˆ( ) ( )

j j j j j ij J r r r
, the Coulomb operator, which accounts for the interaction between an electron at position r i and the average charge distribution of another electron in the spin orbital  j , 1 ˆ( ) ( ) ( ) ( )

j i i j j i j j i ij K r r r r r
, the exchange operator defined with respect to the spin orbital upon which it is applied, and where occupied orbitals are considered.

Considering the HF energy equation, one can notice that the term i=j is allowed in the double summation, meaning that in this case, the Coulomb interaction of an electron with its own charge distribution will be taken into account. As a consequence, the Coulomb integral will not be equal to zero even if one computes the energy of a one-electron system (where there is obviously strictly no electron-electron repulsion). This physical nonsense, known as the self-interaction error, is well handled in the HF formalism as for i=j, Coulomb and exchange terms are equal and therefore exactly cancel. We will see that the treatment of exchange and correlation becomes a major issue in the Density Functional Theory (DFT) approach (see section 2.6).

As the Fock operator depends on the orbitals that themselves enter the expression of the Coulomb and exchange operators, the problem has to be solved by an iterative procedure referred to as the Hartree-Fock Self-Consistent Field (SCF). Starting from a set of N trial orbitals () trial i , the energy () trial E is calculated. In a second step, the Fock operator (1) F is formed and the Hartree-Fock equations solved, giving a new set of orbitals (1) i that is used in the next iteration and a new energy (1) E is calculated, as well as a new Fock operator (2) F . This cycle continues until the new set of orbitals differs by less than a predefined threshold from the orbitals used to build the Fock operator, i.e., until the energy (or the electronic density) converges.

The Roothaan-Hall approximation

If the method briefly described above is sufficient in the case of atoms and some diatomic molecules, one has to rely on the Roothaan-Hall approximation [10,11] to solve the Hartree-Fock equations for non linear molecules. In this formalism, the molecular orbitals  i are expressed as a linear combination of a finite set (or basis set) of predefined basis functions  p , called atomic orbitals (Linear Combination of Atomic Orbitals, LCAO):

K i pi p p C (2.13)
where C pi , the LCAO coefficients, gives the weight of the p-th atomic orbital  p in the i-th molecular orbital i , and K the dimension of the basis set (number of basis functions).

Note that the use of a complete basis set (i.e.K=) leads to the wavefunction corresponding to the lowest possible Hartree-Fock energy, the Hartree-Fock limit.

Substituting the LCAO expansion in the Hartree-Fock equations yields:

ˆKK i pi p i pi p pp f C C (2.14)
Multiplying by  q on both side and integrating leads to the Roothaan-Hall equations:

54 KK pi p q i pi p q pp C f C (2.15)
or, in matrix form:

ε FC = SC (2.16)
where S is the overlap matrix with elements

pq p q S
, and F is the Fock matrix with elements F pq given by :

2 1 ˆ2 2 mN a pq p q p j q p j q aj ia Z F J K r (2.17)
Recalling the expressions of the Coulomb and exchange operator and using the LCAO expansion of  j (r j ), where the first term accounts for the one electron part while the ( | ) pq rs and ( | ) pr qs terms corresponds to the two electrons Coulomb and exchange integrals, respectively, that can be written as:

1 1 2 2 12 1 ( | ) ( ) ( ) ( ) ( ) p q r s pq rs r r r r r (2.19)
The orbitals  p and  q associated to the electron n°1 are centered on the atoms p and q, and equivalently, the orbitals  r and  s associated to the electron n°2 are centered on the atoms r and s.

The LCAO coefficients obtained by solving the Roothaan-Hall equations also appear in the definition of the Fock operator, so that a SCF procedure is adopted. Given a defined basis set, an initial guess is made for the C pi coefficients and the F pq elements are calculated. By Fock operator, and so on. The procedure stops when a predefined convergence criterion is reached (generally comparing the difference in the "new" and "old" energies).

Semi-empirical methods

In an ab initio Hartree-Fock calculation, all the one-and two-electrons integrals are explicitly calculated in the Roothaan-Hall SCF procedure with a specified basis set. One can easily foresee the main practical limitations of such an approach : as the number of atoms increases, the number of atomic functions used to build the Fock matrix rapidly grows as well as the number of bi-electronic integrals (N 4 , with N basis functions) and the computational cost quickly becomes prohibitive. To tackle this issue, semi-empirical methods have been developed, which rely on several approximations to make the calculation more tractable without sacrificing the accuracy of the results.

First, usually only valence (sometimes only ) electrons are considered, and it is assumed that they are affected by a constant electrostatic potential due to the core electrons. The molecular orbitals are thus developed in the LCAO approximation using only the valence atomic orbitals. Secondly, some of the two-electron integrals and other

Hamiltonian matrix elements are neglected or parameterised against experimental data. The different levels of approximation lead to a large variety of methods, among which we have used in our work the AM1 model [12] , as implemented in the AMPAC software [13] .

Based on the NDDO approximation [14] (Neglect of Diatomic Differential Overlap) that mainly consists in neglecting the overlap matrix S (approximated as a unit matrix) and the two-electrons integrals ( | ) pq rs containing a product of two orbitals centred on two different atoms, the Austin Model 1 method includes a modified nuclear repulsion term to account for hydrogen bonds and mimic van der Waals interactions via non-physical attractive forces. It has been parameterised to reproduce several physical quantities such as heats of formation, dipole moments, geometries and ionisation potentials of molecules in their ground-state.

The electron correlation and post Hartree-Fock methods

By considering that each electron is moving in the average electrostatic field created by all the other electrons, the Hartree-Fock method improperly treats the correlation between the motion of the electrons, as the instantaneous repulsion between them is neglected. Consequently, electrons virtually get "too close" to one another and the electron-electron repulsion energy is overestimated, so is the electronic energy. The difference between the HF limit E HF and the exact energy E exact is the socalled electron correlation energy:

corr exact HF E E E (2.20)
Two contributions to the correlation are generally distinguished: the Fermi correlation, that deals with same spin electrons, and the Coulomb correlation, that accounts for interactions between electrons with opposite spins. While the HF approximation accounts exactly for exchange interactions (inherent to the antisymmetric nature of the wavefunction, i.e.

the SD), electrons with opposite spins are not correlated.

Provided one is using an extended basis set to solve the HF equations, 99% of the total energy can be accounted for. However, the missing ~1% may turn out to be determining in the description of certain chemical phenomena (dissociation of molecules, H 2 for example). Using HF method as starting point, several post Hartree-Fock methods [15] have been developed to improve E corr to various extents and, among these, the Configuration Interaction (CI) used in this thesis is reviewed in detail in the following section. Note that other approaches are also available such as Møller-Plesset Perturbation Theory (MPx), Multi-Configuration Selfconsistent Field (MCSCF), and Coupled-Cluster Theory (CC). [15,16]

Configuration interaction

If the Hartree-Fock method can account for the stability of a molecule, it is unable to describe properly the formation or dissociation of a bond.

This limitation is inherent to the mono-determinantal expression of the wavefunction that does not provide enough flexibility: electrons are assigned to a given set of orbitals and the resulting constraints on the wavefunction restrict their spatial correlations.

The obvious solution to tackle this problem is to express the trial wavefunction as a linear combination of multiple determinants, each one corresponding to a given electronic configuration, so that the drawback inherent to "residential electrons" unable to move from one orbital to the other can be overcome. The aim of the configuration interaction is then to determine the best approximate N-electron wavefunction  CI as a linear combination of SD associated to all possible occupations possible of the HF orbitals that are held fixed:

58 0 1 CI HF i i i aa (2.21)
As already mentioned, the HF solution account for ~99% of the energy and the HF wavefunction  HF can thus reasonably be taken as the reference determinant and starting point. The a i are the configuration interaction coefficients that have to be optimised so that the energy is minimum and  i all the possible electronic configurations resulting from the promotion of electrons from occupied to virtual orbitals.

The CI wavefunction can be conveniently rewritten according to the order of excitations considered: A full CI corresponds to a calculation where all the possible excitations are allowed, and is generally way too demanding to be achieved. Thus, one has to select the excitations that have to be considered (single and double -CISD-generally allow to recover a significant part of the correlation energy) as well as the molecular orbitals that will constitute the active space.

           0 ...
The variational principle is applied to find the best wavefunction that minimises the energy of the system with respect to the configuration interaction coefficients i a and one has to solve the following matrix eigenvalue equation:

( ) 0 E  Ha (2.23)
Note that in the MCSCF method, not only the i a are optimised but also the molecular orbitals, allowing to account for a larger fraction of the correlation energy compared to the CI technique.

Although post Hartree-Fock correlated methods give more accurate results owing to the inclusion of electron correlation, they are computationally expensive and not very practical once the system studied becomes large and complex. Density Functional Theory provides an interesting alternative that includes electron correlation at a relatively low computational cost, so that larger systems can be treated.

Density Functional Theory

Although the wavefunction  is the key to all information one would like to obtain about a particular system, this rather unintuitive quantity that depends on three spatial and one spin coordinates for each electron quickly becomes very complicated to treat. Recalling that the Hamiltonian only depends on the positions and charges of the nuclei and the number of electrons in the system, the electron density of the system, which is not a function of the number of electrons, appears to be a good candidate among the various physical observables of a system, since its integration over all space gives the total number of electrons N of the system:

() r dr N (2.24)
The position of the nuclei corresponds to local maxima of (r) while the atomic charges can be obtained from the electronic density at the position of the nuclei. Intuitively, the electron density could thus in principle be used to form an Hamiltonian operator and solve the Schrödinger equation.

The year 1927 marks the very first step of electron density based approaches (rather than wave-function based theories) with the work of Thomas [17] and Fermi [18] . In their model, a classical expression is used for the nuclear-electron and electron-electron potentials while the kinetic energy of electrons, based on an uniform electron gas (i.e. constant electron density), is derived from a quantum statistical model; the Thomas-Fermi expression of the energy is given by: Improvement was attempted by Dirac [19] who included an exchange term in the expression (first derived by Bloch [20] ), yielding the Thomas-Fermi-Dirac model, which proved to be still not satisfactory [21] . Although these models are not showing themselves to be reliable and practically useful, as they predict molecules to be unstable relative to their separated constituents (no chemical bonds !), they constituted the first attempts to express the energy solely from the electron density of the system.

Decades later, Hohenberg and Kohn were to lay the foundations of modern density functional theory [22] .

The Hohenberg-Kohn theorems

The first Hohenberg-Kohn theorem, often referred to as the "proof of existence", states that, considering a system of electrons moving in an external field  ext (r), "the external potential  ext (r) is (to within a constant) a unique functional of (r); since, in turn  ext (r) fixes Ĥ we see that the full many particle ground state is a unique functional of (r)". In other terms, a given electron density (r) uniquely determines the Hamiltonian operator and consequently the wavefunction and all electronic properties of the system.

In this framework, the electronic energy is expressed as a functional of

(r): [] [ ] [ ] [ ] [ ] HK e

The Kohn-Sham formalism

The main reason for the failure of Thomas-Fermi like approaches lies in the expression of the kinetic energy T e () within the homogeneous gas model as well as in the classical treatment of electron interactions (correlation, self-interaction error). On the basis of the cornerstone's theorems of DFT, Kohn and Sham [23] proposed in 1965 an approach to recast the equations into a solvable and practical form.

Considering a fictitious system of N non-interacting electrons moving in an external potential  ext (r i ), that can be exactly represented by a Slater Determinant of N spin-orbitals  i , the Kohn-Sham orbitals, one can express the kinetic energy:

2 1 2 N ni i i i i T (2.27)
and define its electronic density as:

Exchange-correlation functionals

If [] xc E
was exactly known, one would be able to calculate the true energy of a system, electron correlation included. It can be defined by making equivalent the energies of the real and fictitious system as:

[ ] ( [ ] [ ]) ( [ ] [ ]) xc e ni ee E T T E J (2.34)
Its name might be a bit misleading as it does not only account for the non classical portion of the electron-electron interaction, but also includes the correction for the self-interaction error, and the missing part of the true kinetic energy arising from the non-interacting electrons approximation.

Up to now, its exact expression remains the holy grail of DFT and one has to rely on approximations, the quality of the resulting energy thus depending on the accuracy of the functional form chosen. There exists no systematic strategy to improve a functional, and even more dramatic, violation of required physical conditions in its expression does not necessarily lead to less accurate results. A set of precise reference data is used to estimate the accuracy of a given functional, the G2 thermochemical database [24] being the most common.

Several improvements have been achieved since exchange-correlation functionals started being developed, and each new level of approximation has been associated by John P. Perdew to the mythical Jacob's Ladder rungs [25] , each one allowing to recover the results of lower rungs while adding capabilities.

The assumption is generally made that exchange and correlation contributions are separable and the exchange-correlation energy functional can conveniently be expressed as:

[ ] ( ) [ ( )] [ ] [ ] ( ) [ ( )] ( ) [ ( )] xc xc x c xc E r r dr E E r r dr r r dr (2.35)
where [ ( )]

x r and [ ( )] c r are the exchange and correlation energy densities (per particle).

The Local (Spin) Density Approximation (L(S)DA)

The local density approximation is based on the model that gave birth to DFT, the uniform electron gas, where the density is considered to be locally constant, and it is assumed that the exchange and correlation potentials at a certain position depend only on the local value of this density, so that the exchange-correlation energy functional can be written as:

[ ] ( )[ ( )] LDA LDA xc xc E r dr (2.36)
where the exchange part (of a uniform electron gas) is exactly known and given by the Dirac formula [18] :

13 43 33 [] 4 x E dr (2.37)
while there is no explicit form known for the correlation energy. Monte Carlo simulations of the homogenous electron gas have been performed by Ceperley and Alder [26] to numerically determine the correlation energy at very high accruracy. From this work, correlation functionals have been developed by Vosko, Wilk, and Nusair [27] (VWN) or Perdew and Wang (PW) [28] .

Explicit introduction of the spin is achieved by defining  xc respective to a sum of  and  densities:

[ , ] ( )[ ( ( ), ( ))] LSDA LSDA xc xc E r r r dr (2.38)
Being based on the crude approximation of the uniform electron gas, which might be reasonable for metals, L(S)DA does not perform so well for molecules, notably overestimating the bond energies and describing very poorly breaking or forming of bonds.

The Generalized gradient Approximation (GGA)

In molecular system, the electronic density is far from being uniform and improvements over the L(S)D Approximation have to account for the non-homogeneity of the true density. This is done within the Generalized Gradient Approximation by considering a dependency for  xc not only on the density, but also on the gradient of the density, i.e. allowing the density to locally change.

[ , ] ( )[ ( , )]

GGA GGA xc xc E r dr (2.39)
The majority of the GGA exchange-correlation functionals are constructed by adding a correction term to the L(S)DA functional, treating separately exchange and correlation parts. Note that these functionals have a rather complicated mathematical form that is chosen upon the quality and accuracy of the results, not the physics behind. Two approaches for their development have to be distinguished: a semiempirical one, with parameters fitted to reproduce experimental data, among which the popular BLYP functional (Becke exchange functional [29] and Lee, Yang, Parr correlation functional [30] ), and the non-empirical like PW91 [31] (Perdew and Wang) and PBE [32] (Perdew-Becke-Ernzenhof).

A step further is achieved with the meta-GGA functionals that include a dependency over the second-order derivatives of the density, though the associated computational cost and numerical stability problems do not necessarily translate into improved results.

Although all these functionals constitute a great improvement over the L(S)DA method, some efforts are still to be made to reach better accuracy and this motivated the development of hybrid functionals.

Hybrid functionals

The first attempt for improvement was based upon the idea that, the exchange energy being exactly given by the Hartree-Fock method, one could directly include it, even partially, in the functional expression, the correlation energy being purely calculated by DFT. In the framework of the Adiabatic Correction Method, one can make an exact connection between the non-interacting reference system and the fully interacting one, and using the Hellmann-Feynman theorem, compute the exchangecorrelation energy as:

υ 1 0 ( ) ( ) xc xc Ed (2.40)
where  describes the range of the electronic interactions. When =0, the electrons are totally uncorrelated and, a single Slater Determinant of Kohn-Sham orbitals being the exact wavefunction of the system, the exchange energy that remains is given exactly by the HF theory. For =1, the fully interacting system can be approximated by L(S)DA or GGA functionals. Finally, when  01 , the exchange-correlation functional is not known and the integral has thus to be approximated as a sum: Several attempts have been made where additional parameters weighting the contributions of L(S)DA and GGA exchange and correlation are determined together with the parameter a. Among the wide panel of hybrid functionals available, the most famous and widely used B3LYP [33] functional has the following expression:

( ) (1
(1 ) (1 ) As compared with the G2 database, the average absolute error on atomisation energies (using a large basis set) of the B3LYP functional is only of about 2 kcal.mol -1 . [34] Note the parameter-free hybrid functional PBE1PBE [35] (or PBE0) that shows very promising results for many important molecular properties. However, in practice, one always has to chose the functional as carefully as possible accordingly to the system treated and the properties investigated.

LSDA HF B LSDA LYP xc x x x c c E a E aE b E c E cE (2.

Long-range corrected functionals

Certain failures of the aforementioned functionals, such as the inability to deal with charge-transfer excitations, are understood to arise from the incorrect long-range behaviour of the exchange potential. One way to with a value of =0.33 a 0 -1 . [36]

Time-Dependent Density Functional Theory

While limited to the ground state and thus not strictly applicable to excitation energies calculations, static DFT can be extended to investigate properties of a given system subject to an external time-dependent potential, i.e. an electric field. At the origin of TD-DFT, the Runge-Gross theorem [37] is the analogous of the first HK theorem and states that there is a one-to-one mapping between the time-dependent external potential  ext (r,t) and the time-dependent density (r,t), the later allowing to determine all the observables of the system. Following the philosophy employed in the DFT approach, a reference system of N non-interacting electrons moving in an effective time-dependent potential  eff (r,t) is described by a Slater Determinant (r,t) of mono-electronic orbitals  i (r,t) yielding the same charge density as the interacting system:

2 1 ( , ) ( , )
N i i r t r t (2.45)
and satisfies the time-dependent Kohn-Sham (TDKS) equations: xc A r t is the time-dependent counterpart of the energy in static DFT and the exact density of the system is given at its stationary point.

υ 2 1 ( , ) ( , ) ( , ) 2 i
As in DFT, the determination of the xc functional requires to introduce approximations, the first and simplest being the adiabatic approximation in which the ground-state exchange-correlation functional is evaluated at time-dependent densities.

() () [ ( )] [ ( , )] [ ( )] () xc xc xc t t Er r t r r (2.49)
It is thus a local approximation in time expected to be valid provided that the perturbation on the system varies slowly in time, i.e. when the time dependence is small.

Within the TD-DFT approach, a second approximation based on the linear response theory is introduced for the calculation of excitation energies. If the time-dependent external perturbation of the system in its stationary ground state is considered to be small, one can retain only the linear response of the density of the system, referred to as LR-TD-DFT [38] .

Considering a system in its ground-state ( (0) (r)) subject to a small perturbation υ (1) ( , ) rt at a time t 0 , so the total external potential reads υ υ υ ) ext r t r r t , the concomitant linear change of the density with time as

(0) (1) ( , ) ( ) ( ,
(0) (1)
( , ) ( ) ( , ) r t r r t will be described by the response function . It is however easier to calculate the response function of a Kohn-Sham system (that gives the density of the interacting system from a fictitious non-interacting one) than a fully interacting one.

The linear change  (1) (r,t) of such a system can be expressed in the frequency domain as: The KS effective potential reads: where f xc is the exchange-correlation kernel that depends on the unperturbed ground-state density and explicitly relates the response function of the interacting system  to the KS one  KS (as a consequence of the requirement that the change of the density for both description is the same).

υ (1) (1)
υ υ υ (1) (1) (1) (1)
Combining the results with some mathematics, the relationship between  and  KS is given by a Dyson-like equation: From this equation, one can find the excitation energies of the interacting system by searching for the poles of the response function ( KS has poles at the Kohn-Sham orbital energy differences). One must keep in mind that an accurate TD-DFT calculation relies on a good description of the ground-state density (exchange-correlation functional, basis set..).

Basis sets and pseudopotentials

Basis sets

As presented in section 4.4.2. and 4.6.2., the LCAO expansion of molecular orbitals yields the best result within a given method when an infinite basis set is used. However, achieving this optimal description of the system is beyond the computational capacities available and various basis sets have been developed, constituted by a limited number of mathematical functions, Slater-type orbitals [39] (STOs) or Gaussian-type orbitals [40] (GTOs), to reach accurate results as efficiently as possible. The STOs, although physically more attractive (directly deduced from the hydrogenoïd orbitals), suffer from calculatory complexity when dealing with poly-atomic molecules as multi-center integrals cannot be efficiently treated. To circumvent this issue, Boys proposed to use GTOs instead. [40] Computationally convenient as they ensure analytical solutions for all integrals, they are, however, not so well adapted to the description of the shape of the orbital : no discontinuity for r = 0 (i.e. at the nucleus) and too fast decay for r  . For these reasons, GTOs are used in a linear combination to reproduce as close as possible a STO. As an example, the STO-nG minimal basis sets combine n primitive GTOs into a contracted GTO to fit an STO, the most used and optimal being for n=3. Clearly, the more primitives combined, the better will be the fit with the STO, but the larger the computational effort associated. However, one can reasonable assume that from a chemical point of view, a correct description of the valence orbital is more determining than of the core ones. As a consequence, more flexibility to assess properly for different molecular environment was achieved by Pople and coworkers [41,42] with the so-called split-valence basis sets of the type 12 C-v v G . The core orbitals are described by one contracted GTO from C primitives, while two contracted functions are used for the valence orbitals, developed over v 1 and v 2 primitives respectively, for instance as in the 6-31G basis set. One can add diffuse or polarisation functions for better flexibility and reach a more accurate description. [43]

Pseudopotentials

The fundamental concept of distinguishing core and valence electrons, illustrated by the structure of the periodic table, becomes even more crucial when dealing with heavy elements. The number of electrons increasing with the atomic number, systems containing one or more heavy atoms turn to be rather complex and computationally costly to treat, as a large number of basis functions are needed to describe properly the electron-electron interactions. Simplification of this problem is achieved by the introduction of pseudopotentials, in which only the valence electrons are explicitly treated, while the core electrons (and the nucleus), considered chemically inert but still influencing the reactivity of an atom, are modelled by a suitable effective (core) potential (ECP). Not only do they reduce the number of electrons, rendering the calculation computationally more feasible, but they also allow accounting for the relativistic effects arising from the high velocities of core electrons. Among the currently available pseudopotentials, the LANL2DZ combination of ECP from Hay and Wadt [44] and valence basis set (double zeta) have been used in this thesis.

Solvent effects: the polarizable continuum model

The vast majority of chemical reactions as well as experimental measurements take place in solutions. Molecular properties may be greatly affected by the surrounding condensed phase and it is therefore of utmost importance to take properly into account these effects. The most straightforward approach to mimic a solution is to simply add explicitly the solvent molecules around the system investigated. However, as a single solvation shell would clearly be insufficient (absence of long-range effects), it is evident that the system constituted of the solute surrounded by explicit solvent molecules will quickly become enormous and computationally impossible to treat. To cope with this problem, one usually resorts to the use of implicit solvent models in which the solute is treated explicitly, while the solvent molecules are replaced by a continuous medium characterised by the properties of the solvent and surrounding the cavity occupied by the solute. Specific solute-solvent interactions can be accounted for by introducing solvent molecules in the explicit system to give a more reliable and accurate picture. Two types of continuum approaches are commonly used : dielectric PCM or conductorlike PCM. Implicit solvation has been extensively reviewed and further details are to be found in references 45 and 46. In this work, we have used the Polarizable Continuum Model in its integral equation formulation (IEFPCM) developed by Tomasi and co-workers [47] , which falls into the category of dielectric continuum methods.

Basic considerations on the polarizable continuum solvation model

Within a continuum approach of solvation, the total Hamiltonian can be written as:

ˆˆê ff solute int H H V (2.55)
with ˆsolute H the Hamiltonian of the isolated solute and ˆint V , the interaction term describing the solute-solvent interactions, which is a sum of different operators each accounting for a physical contribution. Solvation is the process by which solvent molecules interact with the solute they surround and is characterised by the free energy of solvation G sol that corresponds to the change in free energy associated with the transfer of a molecule from the gas phase to the solvent environment. This free energy is partitioned into different contributions as follows:

sol cav rep disp elec G G G G G (2.56)
and the interaction potential is equivalently a sum of operators each corresponding to a term of this partition.

Here, G cav is the cavitation free energy necessary to create a cavity for the solute in the continuous dielectric medium with an appropriate shape for the solute, which should reproduce as well as possible its molecular shape while excluding the solvent. Many definitions have been proposed

for the cavity, reflecting compromises between accuracy and computational cost, as well as the diverse physical requirements for a given system. In the PCM model, it is defined as a superposition of interlocked spheres centred on the solute nuclei assigned with suitable radii. The formation energy is not related to the electronic properties of the solute but only depends on its geometry (which does not change in the BO approximation) and is evaluated independently according to Pierotti's modified formula (details can be found in ref. 48 and 49).

G rep is associated to solute-solvent repulsion interactions arising from electron exchange contributions while G disp accounts for the dispersion contribution owing to the interactions between instantaneous multipoles due to electrons correlated motion. These quantities are computed in the PCM model according to expressions from Amovilli and Mennucci [50] .

Finally, the last contribution G elec is the free energy associated to the solute-solvent electrostatic interactions and is at the heart of the selfconsistent reaction field (SCRF) procedure. Bringing in solution a solute characterised by a given charge distribution in the gas phase will cause a polarisation of the charges in the surrounding (dielectric) medium, inducing in turn an extra electric field, the so-called reaction field [51] , in the vicinity of the solute, that will affect its electronic structure Several approaches are available to solve this electrostatic problem such as the apparent surface charge (ASC) method used in the PCM model.

Here, the second contribution to the total electrostatic potential aforementioned is the interaction potential of the solute electrons with an apparent surface charge due to the polarisation of the dielectric medium spread on the cavity surface. In practice, this surface is divided into a number of finite triangular non-overlapping elements of known area, called tesserae, at the centre of which is placed a punctual charge. By definition, there is a mutual polarisation between the solute and surrounding solvent, as the solvent reaction field acting upon the solute results from the polarisation it induces in the solvent, and the problem has to be solved iteratively (Poisson equation coupled to Schrödinger equation for the solute). Basically, starting from 0 sol the charge density of the solute without solvent, one can obtain a set of apparent charges by solving the electrostatic problem at the cavity surface. These charges are used to define the interaction potential in ˆeff H and solve the corresponding Schrödinger equation, leading to a new 1 sol for the solute that will be used to solve the new electrostatic problem, and so on, until self-consistency.

Dynamical aspects of solvation

When the solvated system is experiencing brutal changes such as the ones accompanying the vertical electronic transitions associated with UV-Vis optical absorption, it is necessary to extend the basic PCM model to account for the dynamics of solvation and properly describe timedependent processes in solution.

Absorption is a very fast event that occurs on a time-scale of 10 -15 seconds (see chapter 1), shorter than the associated solvent polarisation response, so that the dynamic effects commonly fall into two distinct time regimes known as the equilibrium (Eq) and non-equilibrium (NEq) solvation regime, in a picture analogous to the Franck-Condon principle presented in section 1.3 (Figure 2.1). The dielectric continuum response is generally approximated by a decomposition into a fast electronic component instantaneously in equilibrium with the excited state charge distribution of the solute, and a slow one, known as the inertial component, that remains in equilibrium with the ground state. In the non-equilibrium regime, only the solvent electronic polarisation, i.e. the fast component, is in equilibrium with the solute excited state electron density while the inertial component remains equilibrated with the ground state; the equilibrium regime is reached provided a complete solvent relaxation is achieved (fast and slow components). The description of excited states in solution can be done combining TD-DFT with PCM via two different approaches, the state-specific method [52] (SS) or the linear-response (LR). The latter consists in adding directly to the TD-DFT equations an additional PCM contribution and assessing the excitation energies without any explicit calculation of the excited state electron density which, even if it allows to compute reasonably the solvent effect on the excited state energy, has to be compensated by a PCM correction. Although LR-PCM is the most widely used method to compute vertical energy excitations, one has to remember that in this approach, the solvent degrees of freedom are always equilibrated with the ground state density, preventing a proper treatment of the timedependence of solvent effects and making it particularly not suitable for the description of light-emission (luminescence) processes. In contrast, the state-specific method gives the possibility of computing the solvent contribution to excitation energy according explicitly to the density of the state of interest considered in the relevant time regime involved in a given transition. For instance, in the absorption process, for which only the fast component is in equilibrium with the excited state density, the transition energy corresponds to the energy difference between the solute ground state equilibrium and excited state non equilibrium energies. For emission, the excited state equilibrium and ground state non equilibrium are considered instead. The determination of these quantities is basically achieved in a two-step procedure that starts with the calculation of the initial electronic state considering equilibrium solvation, after which slow and fast components of solvation charges are stored to be used in the second phase, i.e. the non-equilibrium solvation of the final state. SS-PCM approach obviously leads to more accurate energies regarding the emission process as it considers for the initial state the solvent reaction field relative to the excited state density. [53] The partition function is the key to determine the thermodynamical properties of a system. In the following, we expose how these thermodynamic quantities are calculated, assuming a set of noninteracting particles, along with other approximations mentioned when introduced.

Thermodynamic properties

Given that the energy of a molecule can be to a good approximation expressed as a sum of independent contributions from translational, rotational, vibration, and electronic motions, the partition function can be, in turn, written as a product of these contributions : t r v e q q q q q (2.57)

The evaluation of each of these contributions allows to determine their respective entropy contributions, and thus the total entropy S of the system: ( , ) ln ln

B B B V q V T q S Nk Nk Nk T NT (2.

58)

The expression used in the calculations is given in molar values and reads: ln ln( ) t r v e V q S R q q q q e T T

(2.59)

The internal thermal energy E and the heat capacity C V are also obtained from the partition function:

, ln ² B V V NV q E Nk T T E C T (2.

60)

Several approximations are done in the calculation of the components of the partition function:

-the translation contribution q t is calculated according to the following expression (ideal gas):

32 2 ² BB t mk T k T q hP
(2.61)

-the following rotational partition function for nonlinear polyatomic molecules is used: -the energy of the ground state is set to be zero, while the first and higher excited states are assumed to be inaccessible, reducing the electronic partition function to the electronic multiplicity of the molecule: BODIPY shows absorption and emission around 500 nm [1,2,3] , and attaching suitably chosen substituents at the pyrrole ring and/or central meso-position and/or the boron atom can lead to large changes in the spectra. Moreover, they tend to be relatively insensitive to the environment properties (solvent, pH) and are stable in physiological conditions. All these very attractive features explain the intensive investigations on the tuning of their optical properties to develop new better-performing derivatives for given applications. In the quest for NIR absorbing and fluorescent dyes with high performance, BODIPY derivatives constitute attractive potential candidates and much effort has been devoted to the modulation of their D spectroscopic properties, notably in shifting their absorption and emission maxima. Extension of the -conjugated system is the most straightforward and commonly used method to obtain BODIPY dyes with bathochromically shifted absorption and emission spectra. In particular, appropriate functionalisation by aryl groups at the 3,5-positions has been shown to significantly shift both the absorption and emission maxima to longer wavelengths (Figure 3.2) [4,5,6] . Electron-donating groups (e.g., methoxy groups) provide an extra red-shift, as can be seen comparing 2a and 2c.

 max abs.

(nm) However, although bathochromic shifts of more than 100 nm can be achieved, these derivatives suffer from low to moderate fluorescence quantum yields due the possible rotation of the substituents, which results in efficient non-radiative decay pathways. The strategy employed to circumvent this drawback and enhance the fluorescence consists in rigidifying the structure of the system, as described by Burgess et al. [7] .


The more rigid BODIPY derivatives they reported (Figure 3.3), in which the free rotation of 3,5 substituents is prevented, exhibit absorption and emission at longer wavelengths as well as generally higher quantum yields (except for 3b). In this context, we investigated a series of BODIPY dyes with increasing rigidity caused by benzofuran ring formation, as well as related ring-fused BODIPY dyes (section 3.1).

 max abs.

(nm) Aromatic ring-fusion has proven to be an efficient strategy in the search for improvement as it allows an extension of the conjugation leaving open the possibility for further functionalisation at the meso and 3,5-positions [8] .


Further steric constraints for improved fluorescence can be achieved via methyl substitution at the 1,7-positions to lock the meso-substituent.

Apart from the possible modulation of the quantum yield, the mesosubstitution actually does not directly affect the absorption and emission maxima and can thus be performed to impart another function to the molecule. It has given rise to a large variety of compounds from redox active molecules to pH probes as well as metal chelators [9] .

Another route towards NIR dyes consists in replacing the carbon atom in mesoposition by a nitrogen atom to obtain the aza-BODIPY analogues, which can exhibit very large bathochromic shifts compared to their BODIPY counterparts. Their remarkable spectral properties can be successfully tuned by the same kind of modifications used on the BODIPY core, with a very strong dependence of the absorption and emission maxima on the nature of the substitution [10,11,12,13] .

Conformational restrictions

Together with extended -conjugation, the rigidification of the BODIPY structure, via for instance annulation, i.e., the building of homo-of heterocyclic rings onto the aromatic rings attached to the BODIPY core, allows for further expansion of the conjugated ring system and constitutes an efficient strategy to obtain spectral displacements towards longer wavelengths together with an enhancement of the fluorescence.

Heterocyclic ring annulation

Many rigid BODIPY dyes, decorated by various substituents, have already been reported in the literature [7,8,14,15,16,17,18,19] . An alternative

Experimental characterisation

Crystallographic structure

As shown in Figure 3.5, the BODIPY ring system of 2 is remarkably planar, and the benzofuran fragment also lies in the BODIPY plane. The tolyl group at the meso-position makes an angle of 62.1° with the BODIPY plane, which is in the range of most BODIPY derivatives (40°-90°), while the 2-bromophenoxy substituent is tilted relative to the same plane, with a dihedral angle of 58.8°. In dye 3, the entire aromatic system is flat: the deviation from planarity for the boron atom, when considering the entire aromatic system is 0.2 Å. The p-tolyl group makes an angle of 55.4° with the BODIPY core. The main absorption band of 1 is hardly affected by solvent polarity: the maximum being slightly blue-shifted when the solvent is changed from toluene (518 nm) to acetonitrile or diethyl ether (511 nm), which is consistent with the general behaviour of BODIPY chromophores. [9] The same behaviour is observed for 2 and 3 and the fact that the absorption band positions of 1-3 do not show any particular trend as a function of solvent polarity suggests that the absorbing state of the dyes is weakly dipolar. The emission spectra also show the typical features of BODIPY:

i.e., a narrow, slightly Stokes-shifted band that is a mirror image of the absorption and blue-shifts with decreasing solvent polarisability (from 537 nm in CCl 4 to 528 nm in methanol). The observation that the emission band positions of 1-3 do not exhibit any distinct trend as a function of solvent polarity implies that emission occurs from the weakly dipolar, relaxed Franck-Condon excited state of the dyes. The properties of these dyes can be compared to those of conformationally restricted BODIPY derivatives published in the literature (Figure 3.8 and Table 3.3) [4,7,16,17] .  max abs.

(nm)

 max em. (nm) (cm -1 )
 max (L.mol -1 .cm -1 )  f solvent [7] 637 647 243 151 000 0.34 CHCl 3 [4] 630 642 297 138 000 0.96 cyclohexan e [16] 579 583 118 202 000 0.96 CHCl 3 [17] 652 661 209 314 000 0.96 Experimentally, 4 has been found to absorb and emit light ~50 nm more to the red relative to dye 3 (Table 3.3), reflecting its improved conjugation. Theoretical transition wavelengths were simulated and frontier orbitals as well as transition densities analyzed to confirm this observation. An absorption maximum located at 562 nm is computed for 3, which is 25 nm less than the experimental result (587 nm). in the case of 4, the difference with the experimental transition is even bigger with a transition calculated at 599 nm, 38 nm less than the measured one. We compare the frontier orbitals of these compounds, as well as the transitions densities, in Figure 3.10, in order to evaluate the impact of the nature of the substituent on the furan rings (6 and 7) and disentangle the influence of the presence of O-linked bridges (5 against 6 and 7).

There are no obvious differences between the HOMO and LUMO orbitals of 5 and 6. It thus appears that extending the conjugation from 6 to 5 through substitutions at the 3,5 positions of the BODIPY core is not in this case very effective in raising the oscillator strength and/or in lowering the excitation energy. We attribute this to the fact that the extension of the -system then occurs along a direction that is almost perpendicular to the polarisation of the lowest electronic excitation. By far, a much more dramatic improvement is seen in 7. Although the frontier molecular orbitals of 6 and 7 look very similar and are in both cases mostly confined on the central BODIPY core, the transition densities extend significantly over the external phenyl rings in 7 (Figure 3.10), which explains the largest oscillator strength computed for that compound. This effect arises from multi-configurational mixing of the HOMO-LUMO excitation with electronic configurations involving deeper molecular orbitals with large weights on the outer phenyl rings.

Homocyclic ring annulation

Just as annulation with an hetero atom has been shown to give BODIPY derivatives with bathochromically shifted absorption and emission maxima, fusing the BODIPY core to rigid -conjugated carbocycles can also lead to NIR emitting dyes. Both symmetrically [5] and asymmetrically [24] ring-fused systems have been reported. To understand the spectral behaviour and associated photophysical properties of such dyes depending on the symmetry of the substitution as well as on the presence or absence of conformational constraints, we investigated the series of BODIPY derivatives presented in

Experimental observations

Compounds 8 and 9 display the typical absorption features of classic BODIPY dyes, with a narrow first absorption band assigned to S 0 S 1 , transition which is red-shifted with increasing solvent polarity, and an additional, considerably weaker, broad absorption band around 350 nm, attributed to the S 0 S 2 transition. The two systems also show the characteristic emission features of BODIPY, i.e., a narrow slightly Stokesshifted band with a mirror image shape. Data for 8-11 measured in acetonitrile are compiled in Table 3.4.

Computational method

All calculations were performed with the Gaussian (G09) program package [28] . Density functional theory (DFT) was used with the CAM-B3LYP [29] hybrid functional and 6-31G* basis set for geometry optimisations. From these equilibrium structures, UV-Vis absorption and emission spectra were computed in the framework of time-dependent density functional theory (TD-DFT), with the same functional and the same basis set. To take the solvent effect into account (acetonitrile), the polarised continuum model (IEFPCM formalism [30] ) was adopted using linear response [31] (LR) or state-specific [32,33] (SS) approaches available in G09.

Optical properties computed with the LR and SS aproaches

Absorption and emission wavelengths/energies of systems 8, 9, 10 and 11

and their unconstrained counterparts, calculated with the LR-PCM and SS-PCM approaches, are compiled in Table 3.5 and Table 3.6, respectively. Inner-and outer-sphere relaxations occur upon electronic transition from the ground state to the singlet excited state of the dye (in absorption)

and vice versa (in emission). The intramolecular relaxation is substantial, it involves high-frequency vibrations and largely contributes to the energy difference between vertical transitions. It manifests itself as a vibrational progression in the experimental spectra and has not been modelled further here. We have rather focused on the Stokes shift between the 0-0 energy transitions in absorption and emission that mostly originates from solvent relaxation. Thus, we have computed the vertical transition energies in absorption and emission successively based on the solvent reaction fields produced in the ground state and the lowest singlet excited state (and using the ground-or excited-state optimised geometry).

Symmetry of the substitution

The computed electronic absorption spectra of 8 and 9 both present a low-lying HOMOLUMO transition band, at 430 and 487 nm, respectively (Table 3.6). Although these values are underestimated with respect to the experimental results (Table 3.4 and Figure 3.12), the redshift measured upon disubstitution of the BODIPY core, namely, when going from 8 to 9, is properly reproduced with a calculated value of ~57 nm (compared to a measured value of ~67 nm). The origin of the bathochromic shift can be better appreciated by looking at the frontier orbitals involved in the transitions (Figure 3.12). The rigidisation of two 3,5-phenyl groups in 9 is accompanied by a more extended conjugation, illustrated by the clear delocalisation of both HOMO and LUMO over the two phenyl rings, which accounts for the observed spectral displacements. Molar absorption coefficients  max of 8 and 9 have been measured in methanol and the corresponding oscillator strengths f calculated [20] . In agreement with the measurements that give  max and f values of 71600 L.mol -1 .cm -1 and 0.52, respectively, for 9 (versus 48600 L.mol -1 .cm -1 and 0.34, respectively, for 8), the computed oscillator strengths are higher in the disubstituted compounds 9 and 11 (0.85 and 0.71, respectively, versus 0.78 and 0.63 in compounds 8 and 10).

Effects of the conformational restriction

The effect of conformational restriction on the optical properties of 8-11

has been investigated by studying the corresponding unrestricted dyes, 8u-11u. As expected, the absence of conformational restriction in 8u and 9u, in which the phenyl group substituents are free to rotate, leads to an hypsochromic shift of the absorption band by ~21 nm and ~51 nm, respectively (Table 3.6 and Figure 3.13). These spectral changes arise from an increased planarity of the system together with the extended delocalisation of the HOMO orbital over the ethylene bridge linker in 8 (Figure 3.13). Constriction leads to a more rigid compound and partly prevents the rotation of the phenyl group at the 3-position: the value of the dihedral angle between the BODIPY core and the substituent decreases from ~40° to ~23° when passing from 8u to 8. Consistently with the conclusions of section 3.1.2.1., the same behaviour is observed for 9, at higher wavelengths. The calculated spectral displacements of the absorption and emission maxima upon conformation restriction as well as the oscillator strengths are in good agreement with the only experimental data available, which report a clear bathochromic effect in both absorption and emission (in CH 2 Cl 2 , 77 and 53 nm, respectively). Moreover, the increase in the oscillator strength value upon constriction is consistent with the hyperchromic shift observed when going from 9u to 9 ( max (544 nm) = 57000 L.mol -1 .cm -1 for 9u vs  max (621 nm) = 134000 L.mol -1 .cm -1 for 9). However, this effect may also arise from a decreased bandwidth due to the conformational restriction, resulting in an increase in the maximum extinction coefficient without changes in the oscillator strength.

Although no change in the absorption spectra is expected when passing from 10u to 10, it is most likely that the very small increase in transition wavelength (3 nm) predicted upon going from the unconstrained to the restricted form arises from enhanced hyperconjugation effects associated with the methyl groups in 10u (see Figure 3.13, where small weights are circled). Likewise, there is no significant spectral displacement upon conformational restriction of 11u. The computed absorption wavelengths for 11u and 11, ~417 nm and ~422 nm, respectively, present only a small red shift (~5 nm), expectedly slightly larger than for 10(u) as the BODIPY core is disubstituted. The same features are observed for the emission wavelengths.

Influence of the substituent nature and position

The variety of (hetero)atomic groups that can be grafted on the BODIPY core provides an outstanding opportunity to investigate the spectroscopic and photophysical characteristics of these dyes as a function of the substituents. Moreover, functionalisation at the  and  positions may result in distinct effects on the spectroscopic properties. To assess how these two effects (nature of the substituent and position of the substitution) affect the optical and electronic properties, we studied a series of 3-aryl-BODIPY derivatives with various substituent groups (13a-15a) and their 2-isomers (13b-15b) together with a reference compound 12

(

Computational method

Ground-state geometries were optimised in the framework of the density functional theory (DFT) at the CAM-B3LYP/6-31G(d) level [29] . The equilibrium structures were subsequently used as input for the timedependent DFT (TD-DFT) calculations of the vertical transition energies and oscillator strengths. Solvent effects were accounted for by using the polarizable continuum model (IEFPCM formalism [30] ). The Gaussian G09 package [28] was used for all calculations.

Influence of the substituent nature

The effect of the nature of the substituent on the optical properties is investigated through the 13a-14a-15a series in which the electro-donating strength of the 3-aryl group is varying (Phenyl, 4-MeOPhenyl, and Thiophene, respectively). As the reference compound 12, all three asymmetrically substituted systems display the typical absorption and emission features of BODIPY already encountered in the previous sections of this chapter (narrow bands, small Stokes shifts, weak solvent dependence). Their theoretical absorption wavelengths are compared to the experimental values in acetonitrile in Table 3.7. with the presence of Cl atoms at the 2,6 positions of the meso-aryl group.

We investigated the consequences of changing the meso-substituent nature of 13a on its structural, optical and electronic properties, namely by studying 16 and 17 in which the 2,6-dichlorophenyl group is replaced by a phenyl and a p-nitrophenyl substituent, respectively (Figure 3.18).

The absence of Cl atoms in 16 and 17 gives rise to smaller dihedral angles between the planes of the 8-aryl group and the BODIPY core, namely ~54° and ~57°, respectively, instead of 90° in the chlorinated derivatives in which rotation of the meso-substituent is locked. The first absorption transition of 17 is computed at 447 nm and involves mainly the frontier molecular orbitals (~93 %) but a higher charge-transfer (HOMOLUMO+1) excitation is also found to weakly contribute. While the HOMO orbital is strictly centred on the BODIPY core, the LUMO extends over the whole -system whereas the LUMO+1 is localised mostly on the meso-substituent bearing the nitro group (Figure 3.18). The nature of the meso-substitution only has a small effect on the spectral position of absorption and emission maxima ( abs (max) of 13a at ~446 nm), consistent with the absence of coupling between the two parts of the -system, due to the twisting of the meso-aryl group out of the BODIPY plane. However, the removal of the chlorine atoms drastically reduces the quantum yield of fluorescence, with a measured value of 0.005 (against 0.884 for 13a). This lowering is a consequence of the free rotation of the 8-aryl group that allows the molecule to lose its excited state energy via non-radiative molecular motions, while the rotation of the 8-(2,6-dichlorophenyl) group in the other dyes is obstructed by steric hindrance between the Cl atoms and the 1,7hydrogen atoms of the BODIPY core.

Fluorescence quenching via photo-induced electron transfer has already been demonstrated for sterically hindered 8-substituted BODIPY derivatives bearing a nitro aromatic moiety [35,36] . Although the partial charge transfer character of the lowest excited state might have an impact

Towards the blue side of the spectrum

In the search for dyes with absorption and emission maxima shifted towards ever longer wavelengths, many strategies have been developed to tune the optical properties of BODIPY and a substantial number of NIRemitting derivatives were synthesised over the past decade. However, despite their outstanding thermal, photochemical and photophysical properties, only few BODIPY dyes optically active in the blue spectral region have been reported so far [37,38] .

In this context, we investigated the electronic and optical properties of a series of 8-amino-BODIPY derivatives substituted with electron donating groups of various electro-active strengths (Figure 3.20). Meso-substitution of the BODIPY core can either result in a coplanar conformation in which the BODIPY core and the meso-substituent are in the same plane, or in a geometry with the two moieties in a perpendicular conformation (Figure As expected from the relative positions of the frontier orbitals, almost exclusively involved in the S 0 S 1 electronic transition, and the energy gaps between them, the largest wavelength is computed for 18c at 377 nm while similar lower values are obtained for 18a and 18b with transitions at 363 nm and 361 nm, respectively (Table 3.8). The first absorption band being in all cases dominated by the HOMOLUMO transition, it is sufficient to follow the evolution of these two orbitals to get insight into how the photophysical properties might be affected by the nature of the amino-substituent and its orientation relative to the BODIPY plane. We computed the potential energy surfaces (PES) of the three compounds in their ground state as a function of the dihedral angle between the chromophoric core and amino- For each geometry considered, the S 0 S 1 transition was thus computed and the corresponding transition energy plotted against the dihedral angle (Figure 3.24): its evolution is in very good agreement with the trends already noticed in the HOMO/LUMO gap. Upon twisting of the mesosubstituent away from coplanarity, the absorption maximum is red-shifted. The optimised geometries of 19 and 20 reveal a coplanar-like conformation of the meso-substituent with respect to the BODIPY core, with dihedral angles of -177° and -166°, respectively. In these two systems, the substituent is not directly linked to the nitrogen in meso-position so that delocalisation in the LUMO does not extend over the phenyl ring as in 18c. However, vanishingly small weights are noticeable over the -CH2 and, additionally in 20, over the carbon atom of the phenyl to which it is linked. This is consistent with the overall frontier orbital delocalisation 19

and 20 experience compared to 18c. While methylation of the nitrogen is expected to bring about a destabilisation of the LUMO, rather similar energies are computed for this orbital in 19 and 20, most likely due to the larger delocalisation of the LUMO in 20 (contribution on the methyl group). However, it also increases the donor character of the mesosubstituent, which is illustrated by the HOMO destabilisation when going from 19 to 20.

Conclusions

In this chapter, we reviewed different approaches to modulate the optical properties of BODIPY derivatives through the study of several series of compounds. Our theoretical results support the experimental observation that conformational restrictions via homo-or heterocyclic annulation constitute an efficient strategy to obtain large spectral displacements towards longer wavelengths. More specifically, we evidenced that symmetrical di-substitution (position 3 and 5) combined with annulation allows for an expansion of the conjugated system, and leads to very large bathochromic shifts of both the absorption and emission maxima, by up to ~50 nm. Regarding the consequences of a substitution at the 2-position, the same trends are reported, with lower oscillator strengths. Contrary to what is observed for the and -substitution, the introduction of a substituent at the meso-position, while providing another way to functionalise the BODIPY core, does not affect the absorption and emission wavelengths. However, it can greatly modify the fluorescence quantum yields: when steric hindrance prevents the rotation of the mesogroup, the fluorescence can be enhanced. The opposite trend is observed for molecules where free rotation of the substituent is allowed, which results in a quenching of the fluorescence. Finally, we showed that the optical properties can also be tuned towards shorter wavelengths via the introduction of amino groups on the meso-position of BODIPY core. In summary, our theoretical results allowed us to reach a deeper insight into the changes of the spectroscopic properties of BODIPY derivatives, illustrating the relationships between their structure and conformation and their optical properties, with either hypso-or bathochromic shifts and modulation of the fluorescence. espite its biological benefits, zinc is also known as a contributing factor in several psychiatric and neurological diseases. [1][2][3] Moreover, it is an environmental pollutant that may for instance be found in agricultural wastes and cause phytotoxicity. [4] Nowadays, zinc is one of the most heavily consumed metals in industry, with numerous applications such as in alloys, in particular for the corrosion protection of steel, oxide fillers and batteries. Its widespread use has raised the need for Zn 2+ chemosensors and the development of probes for the zinc ion in water has retained much interest in the past decade. [5] In this context, our work aims at the development of a zinc ion sensor for monitoring the corrosion of galvanised steel.

The possibility to efficiently custom-design the molecular structure of organic dyes according to needs provides a cheap and straightforward platform for the creation of efficient optical sensors. Most organic-based optical probes rely either on inter/intramolecular photo-induced electron transfer (PET) or on charge transfer (see chapter 1). In short, the former usually consists of a chromophore-spacer-receptor system that undergoes fluorescence quenching or enhancement in the presence of the analyte, while the latter involves a conjugated chromophore-receptor pair and relies on ratiometric sensing using either light absorption or emission.

Among all the available chromophores, perylene dyes are widely used in commercial applications due to their outstanding chemical, thermal and photochemical stability, their low toxicity, and low cost. [6][7][8][9][10][11][12][13][14] These features make them attractive building blocks for the design of novel zinc ion chemosensors. More specifically, appropriate functionalisation of perylene monoimide (PMI) at the 9 and/or 10 peri-positions allows for the generation of push-pull type molecules that can act as intramolecular charge transfer-based sensors, using the imide group as the acceptor and a zinc ionophore as the donor. In this work, PMI has been substituted with D coupled perturbed Hartree-Fock equations. All the calculations were carried out using the Gaussian (G09) program package [18] .

Geometries of [1•Zn 2+ ]

Optimisation of the PMI-DPA-Zn 2+ system yields two different local minima with relatively close energy (~0.39 eV). In the first conformation (noted 1a hereafter), one pyridine rotates around the CH 2 -pyridine bond so that the zinc ion interacts with the two pyridinic nitrogen atoms (Figure 4.2, Table 4.1). In the absence of Zn 2+ , the calculated absorption spectrum from the optimised ground state geometry of 1 presents an absorption band at 555 nm associated with an excited state largely dominated by the HOMO/LUMO transition. Though slightly underestimated (0.1 eV), the computed transition energy can be considered in good agreement with the experimental value of 534 nm measured in acetone (Figure 4.4). In the presence of one equivalent of ZnCl 2 , an hypsochromically shifted peak at 501 nm is observed, with a clear isosbestic point at 515 nm (Figure 4.4), consistently with a transition from purple (i.e., the colour of 1) to red (a colour similar to PMI without substitution in 9-position). We simulated the absorption spectra for the two conformations of the complex, with the different coordination numbers possible for the zinc ion.

Optical properties

Conformation n°1: 1a •Zn 2+

Two acetone molecules were included to the system in 1a to obtain the (distorted) tetrahedral geometry of the tetra-coordinated complex (see this effect, we have computed the absorption spectrum of the complex in its equilibrium geometry, after removal of the zinc ion and acetone molecules, to isolate the conformational rearrangement. It is found to provide only a 3 nm contribution to the hypsochromic shift, which is thus dominated by electronic effects (discussed hereafter). Note that the same conclusions can be drawn for the complexes with CN=5 and CN=6 (Table 4.2).

Conformation n°2: 1b •Zn 2+

Complex 1b is characterised by a larger torsion angle around the perylene-ionophore C-N bond, together with a shorter distance between Zn 2+ and N9, suggesting a stronger electronic interaction and, as a result, a stronger impact on the absorption spectrum compared to 1a. In line with these expectations, the simulated absorption spectrum of 1b

Response to other ions

In order to investigate the response of 1 to other cations, namely Ca 2+ , Ag + , Hg 2+ , Fe 2+ , Cu 2+ , Ni others [20] .

The simulation of the emission spectra associated to all these cation complexes is a computationally very demanding task. Thus, we decided to focus on the thermodynamic aspects of the complexation of 1 with the copper ion, which results in a quenching of the fluorescence. To this end, we proceeded as for the complexation of the zinc ion presented in the previous section.

The most common coordination number of Cu 2+ being 4, we calculated the thermal corrections to the enthalpy and Gibbs free energy for [Cu(acetone) 4 ] 2+ as well as for the 1a•Cu 2+ (CN4) complex. Single-point calculations on these two systems at the B3LYP/6-311g(d) level were performed to compute the H and G of complexation and values of -18.63 kcal.mol -1 and -32.53 kcal.mol -1 , respectively, were obtained. These values are more negative than those determined for the Zn 2+ complexation. This indicates that the unwanted presence of Cu 2+ in the environment where the detection of the zinc ion is intended to be done could lead to interference and diminish the efficiency of the sensor. However, in the framework of the corrosion detection of galvanised steel, the key aspect does not lie in the interference from other ions but rather in the sensitivity of the sensor response in the presence of Zn 2+ .

Detection of Zn 2+ by PMI-DPA within an optical fibre sensor

Among the possible platforms that can serve for the development of sensing devices, the optical fibres display many attractive features, such as their flexibility, small dimensions and light weight, but also the possibility to perform distributed measurements over potentially long distances. Optical fibres can be decorated with a Bragg grating, which is a periodic and permanent modulation of the core refractive index of a section of the optical fibre along the propagation axis that acts as a wavelength-selective filter around the so-called Bragg wavelength. [21] When the Bragg grating is tilted by a few degrees relative to the perpendicular to the fibre axis (TFBG), the fibre becomes sensitive to the environment as the TFBG couples light from the core to the cladding. As a result, it presents a comb-like transmission amplitude spectrum comprising several tens of resonances, each one characterised by its own sensitivity to the surrounding refractive index. The resulting TFBG spectrum is directly influenced by the refractive index of the surrounding medium and naturally act as a refractometer accurate to 10 -4 RIU (refractive index unit). [22][23][24] Specific chemical sensors can be built by using TFBGs covered with a dedicated coating that changes its refractive index when in contact with the target chemical species. [25,26] The sensor envisioned in this work consists in a standard silica fibre with a tilted fibre Bragg grating covered by a sensitive layer of 1 whose refractive index (real and imaginary part) changes after the formation of a complex with Zn 2+ .

Estimation of the refractive index change upon complexation

The refractive index modification accompanying the complexation of Zn 2+ has to be large enough to enter the range of detection of the fibre aforementioned. We thus performed quantum-chemical calculations to estimate the change in refractive index upon complexation, n, as a function of the number density. n was computed from the calculated molecular polarisabilities of 1 and 1a•Zn 2+ [CN4] . The molecular polarisability α, i.e., the linear response to an electric field of the electronic charge distribution of a molecule, is a microscopic quantity that can be related to the macroscopic refractive index n through the following expression according to the Lorentz-Lorenz equation:

149 0 0 23 ² 3 NV n NV (4.1)
where N is the number of molecules in a volume V and ε 0 is the vacuum permittivity.

We considered the case of a single molecule in a varying volume comprised between two limit cases, the van der Waals density and a large dilution. In order to approach the experimental conditions, where the dye concentration amounts to ~1.5% in weight of the final dry film, we estimated a volume of V~150000 ų for a single molecule and computed the corresponding n for V and V±33%, both in the gas phase and considering the solvent effects of water (Table 4.4). Chloride ions are added to complete the coordination of Zn 2+ in the gas phase, and kept when accounting for the water, for better comparison. The n values found are all above the detection limit of the fibre sensors considered in this work (*10 -4 ), indicating that 1 may successfully be used in such devices for Zn 2+ sensing.

Detection of zinc ions by 1 in the solid state

On glass substrates

Prior to depositing 1 on optical fibres, experiments were first performed on simple glass substrates. Films of about 100 nm thickness were prepared by drop casting THF solutions of 1 and they were dipped in aqueous Zn 2+ solutions of various concentrations (1 is not soluble in water). We followed the evolution of the optical properties of 1 upon complexation with the zinc ion by recording absorption spectra every 2 minutes over a 30 minutes immersion period. As a control experiment, a film was dipped into pure water. When dipped in water (and at t=0 in the Zn 2+ solution), the absorption spectrum is similar to that observed in acetone solutions, with a slight (~0.1 eV) shift most probably associated to the difference in dielectric environment, and it does not evolve with time. In the presence of Zn 2+ , the absorption peak gradually shifts hypsochromically from 559 nm to 521 nm, as a result of the complexation of the zinc ions (as no spectral change is observed in the control experiment). This shift of 38 nm is very similar to that measured in solution (33 nm). However, it appears more clearly only after 15 mins and one can clearly note the persistence of a shoulder around 560 nm in the spectrum at t=30mins. This long response time and spectral behaviour is most likely due to the slow diffusion of the ions in the rather thick, hydrophobic organic layer.

To improve the diffusion of Zn 2+ , the dye was then encapsulated in a silica sol-gel and deposited on a glass substrate to perform a similar experiment previously described. Incorporating 1 in the sol-gel permits to deposit even thicker, more uniform films i for a better optical signal, while allowing the easy diffusion of the ions.

i The interrogation length of the TFBG is of the order of the wavelength, typically 1µm. To obtain maximum response of the TFBG to the refractive index changes of the sensitive coating, its thickness should thus be more than 1µm. Considering the increasing size of the systems, the study of the complexation becomes computationally very heavy and the calculations were thus performed in the gas phase, with chloride ions added in the complexes to complete the coordination of the zinc ion, instead of two solvent molecules. To assess for the potential spectral displacement associated to the complexation event, calculations on the free systems were performed at the same level of theory employed in the study of PMI-DPA, i.e., using DFT at the B3LYP/6-31G(d) level, with the LanL2DZ pseudopotential and basis set to describe Zn 2+ . We only considered the conformation noted a earlier (with CN4 for the metal cation) and simulated the absorption spectra of the free and complexed systems for the two aforementioned higher rylene derivatives, 2a and 3a, respectively (Table 4.5). Upon extension of the -conjugated system (PMI-DPATMI-DPAQMI-DPA), the first absorption band is substantially shifted towards longer wavelengths, compared to 1a, by 116 nm and 227 nm for 2a and 3a, respectively. As the transitions computed are all characterised by a HOMOLUMO excitation, we focused our attention on these orbitals and how they evolve with the length of the system (Figure 4.12).

Both frontier orbitals, delocalised over the whole rylene conjugated system, are strongly affected by the increasing -conjugation of the system and, as the HOMO is destabilised and LUMO stabilised along the series 1a2a3a, the π-conjugation extension is accompanied by a narrowing of the HOMO-LUMO gap (total decrease of 0.93 eV from 1a to 3a). We also observe a strengthening of the transition intensity with higher oscillator strength along the series, as a longer conjugation causes an enhancement of the transition dipole moment. This behaviour is in agreement with the reported dependence between the number of naphtalene units in rylene derivatives and their extinction coefficient. [30] The spectral displacement originating from the complexation of Zn 2+ by 1a amounts to 19 nm, as calculated in the gas phase. A similar hypsochromic shift (17 nm) is computed when going from 2a to 2a•Zn 2+ [CN4] and from 3a to 3a•Zn 2+ [CN4] . The change in the conformation of 2a and 3a upon complexation is similar to that observed in 1a and the origin for the blue-shift is very likely to arise from electronic effects. To confirm this, the evolution of the frontier orbitals upon complexation was investigated and an asymmetrical stabilisation is observed, with a larger effect on the HOMO, which leads to a wider HOMO-LUMO gap and a blue-shift of the absorption spectrum. Moreover, as in the perylene compound, the electron density in the HOMO for the nitrogen atom bearing the DPA group decreases for the two higher rylene derivatives upon complexation of the cation, resulting in the alteration of the intramolecular charge transfer from the nitrogen lone pair to the imide group. Considering that the zinc ion detection is achieved with higher rylenes, QMI-DPA is a very interesting compound for optical fibre technology as it is optically active in a range of wavelengths close to the first transmission window.

Exploiting the aza-BODIPY structure for zinc ion detection

BODIPY derivatives can feature the required characteristics for the design of chromoionophores active at wavelengths of ~800 nm and above, taking advantage of the multiple possible modifications of the BODIPY core. More specifically, combining the replacement of the carbon atom in the 8-position by a nitrogen atom with extended conjugation and electron donating group substitution within a rigid structure is expected to result in NIR absorbing and emitting dyes. Gresser et al. reported a series of benzannulated aza-BODIPY dyes, with absorption and fluorescence maxima ranging from 681 to 793 nm and 723 to 841 nm, respectively. [31] Grafting the DPA unit on the longest-wavelength active compound among the series described by Gresser et al. (dye BDP-1) is expected to result in a chromoionophore for zinc ion sensing based on intramolecular charge transfer. This is a consequence of the donor-π-acceptor nature of the system, in which the aza-BODIPY unit acts as the acceptor and the DPA group acts as the donor, operating in a range of wavelengths fitting the first transmission window aforementioned. Increasing the number of thiophene units between the aza-BODIPY and the ionophore is a reasonable approach to allow for further expansion of the -conjugated system and possible tuning of the sensor response to Zn 2+ .

Calculations were performed to get insight into the complexation phenomenon and its consequences on the optical properties of BDP-1-DPA. We also investigated the influence of the conjugated spacer length by adding one and two thiophene groups, to yield compounds BDP-2-DPA and BDP-3-DPA, respectively (Figure 4.13). To conserve a reasonable computational time, no solvent effects were considered and the B3LYP/6-31G(d) level of theory was employed.

Complexation of Zn 2+ by BDP-1-DPA

We first investigated the impact of grafting the DPA unit on the thiophene group at the 3-position of BDP-1. For this purpose, the geometry optimisations of BDP-1 and BDP-1-DPA were performed and the optical properties were simulated. In a second step, the influence of the presence of Zn 2+ was studied.

The geometry of BDP-1 is in very good agreement with reported data, as the benzoannulated groups are in the plane of the aza-BODIPY core, and a dihedral angle of ~30° between this rigid plane and the methylthiophene substituents is found (31° reported). The computed absorption maximum is located at 657 nm and corresponds to a HOMOLUMO excitation (in line with reported calculations at the B3LYP/6-31G(d,p) level).

The grafting of the DPA moiety on BDP-1-DPA introduces a further planarisation of the system as, while the dihedral angle between the core and the thiophene at the 5-position remains unchanged (~31°), it decreases to ~25° for the 3-thiophene-DPA substituent. Just as a bathochromic shift is expected to accompany the planarisation of BODIPY derivatives (see chapter 3), more planar aza-BODIPY dyes present a spectral displacement towards longer wavelengths. [32] BDP-1-DPA exhibits a maximum absorption band, arising from a HOMOLUMO transition, at 696 nm, red-shifted by 39 nm compared to BDP-1. The evolution of the frontier orbitals illustrates this trend as upon substitution, both levels are substantially destabilised, with a larger effect on the HOMO, in line with the donor character of the DPA unit, yielding a smaller HOMO-LUMO gap. Considering the interesting behaviour expected from the presence of the terthiophene spacer, we focused on compound BDP-3-DPA and investigated the potential optical response of the system upon complexation of the zinc ion. Interestingly, in the presence of Zn 2+ , the absorption maximum is computed at 763 nm, yielding upon complexation an hypsochromic shift of 38 nm, in the range of what is calculated for the PMI-DPA system. The S 0 S 1 transition corresponds to a HOMO→LUMO excitation. In BDP-3-DPA, the HOMO orbital is delocalised over the whole -conjugated system, whereas the LUMO is more centered on the aza-BODIPY unit, with however small weights remaining on the terthiophene (Figure 4.15), indicating that an intramolecular charge transfer occurs between the latter and the aza-BODIPY core. The frontier orbitals of BDP-3-DPA•Zn 2+ [CN4] follow the same trend in terms of delocalisation, with however a HOMO that computed for the copper ion suggest a lower detection efficiency for Zn 2+ in the case where interfering Cu 2+ ions would be present.

As we envision the use of PMI-DPA within optical fibre sensor devices, we investigated the possible extension of the wavelength working range of the sensitive compound to fit the "first window" of the transmission spectrum of an optical fibre and thus reduce signal losses. It is shown that by incorporating naphtalene units to yield higher rylene derivatives (terrylene and quaterrylene), the absorption maximum can be bathochromically shifted by up to 227 nm, without altering the process of cation detection. We finally simulated the refractive index change of PMI-DPA upon complexation and showed it is in the range of detection of a tilted fibre Bragg grating (TFBG). In order to demonstrate the feasibility of zinc ion detection in the solid state with fibre sensor technology, we performed a series of experiments in which the optical response upon complexation was measured. We first considered pristine films of PMI-DPA on glass as the active layer, and then we focused on the encapsulation of the dye in a silica sol-gel, improving the response time by an order of magnitude. The very same sensitive sol-gel has been deposited on the TFBG of optical fibres and a significant modification of its transmission spectrum was recorded in the presence of zinc ions. PMI-DPA and the higher rylene compounds can thus be considered as promising systems for the detection of Zn 2+ ions, both in organic solutions and in thin film sensors.

The inclusion of the DPA unit onto an aza-BODIPY derivative with an oligothiophene spacer of increasing length has been shown to provide interesting optical features with absorption in the NIR region of the spectrum (~800 nm, for the terthiophene-containing compound). As in the perylene derivatives, a significant blue-shift is expected upon complexation of Zn 2+ .

Conclusions and perspectives

his work is devoted to the rational development of chromoionophores from a comprehensive understanding of the photophysics underlying the detection process. Using quantum chemical methods in combination with basic spectroscopic experiments, we addressed two aspects of designing molecular sensors for cations, namely, the relationships between the structure and optical properties of the organic chromophore building blocks, and the photophysical processes involved in the cation detection.

As a first step, we focused in chapter 3 on studying series of compounds from the versatile family of BODIPY dyes, to assess the consequences of structural modifications on their optical properties.

T

We show that large bathochromic shifts together with higher oscillator strength values can be achieved by imposing conformational constraints via homo-or heterocyclic annulation, as a result of the more rigid structure. More generally, extension of the -conjugation leads to spectral displacements towards longer wavelengths and can be efficiently obtained by substitution of the BODIPY core, more specifically with electron donating groups. On the one hand, 3,5-symmetrical di-substitution provides further bathochromic shift of the absorption and emission maxima. On the other hand, substitution at the meso-position can have very different effects on the optical properties. The introduction of an aryl group at the 8-position does not particularly affect absorption and emission features but allows for a modulation of the fluorescence quantum yield, depending on the possible rotation of the group with respect to the BODIPY core. In constrast, the 8-amino-BODIPY derivatives we studied do not exhibit fluorescence quenching, but provide a way to modulate the optical properties towards shorter wavelengths, owing to the evolution of the absorption maximum with the twist angle between the BODIPY core and the meso-substituent.

In chapter 4, we presented a joint experimental/theoretical study of molecular chromoionophores for the detection of the zinc ion. First, we investigated extensively a perylene monoimide (PMI) derivative functionalised with a dipicolylamine (DPA) complexing unit. Based on the experimental observation of a blue-shift of the absorption maximum in the presence of the zinc ion, we performed a theoretical study to unravel the electronic processes responsible for the spectral displacement associated with the Zn 2+ complexation by PMI-DPA. It turns out that the system, which exhibits an intrinsic push-pull character owing to the acceptor nature of the imide group and the donor nature of DPA, undergoes an intramolecular charge transfer (ICT) upon photoexcitation. already reported for the design of chromophores with large two-photon absorption cross sections, the elaboration of chromoionophores with specific dependence on cation binding of their two-photon spectroscopic properties is of great interest for operating in the range of the 1310 nm transmission window of the optical fibre. The detailed exploration of the non-linear optical properties of PMI-DPA and aza-BODIPY-DPA, as well as the effect of Zn 2+ complexation on these features, would be an important first step, before devoting efforts to their improvement and, more generally, the optimisation of two-photon-active molecular cation sensors.

Owing to its very attractive properties (lightness, resistance, electrical and thermal conductivity, strength, ductility..), aluminium is one of the most widely used metals in technological applications, for instance in the aeronautic industry and construction. Aluminium is covered by a thin layer of aluminium oxide in the presence of oxygen, which gives it remarkable corrosion resistance. However, once the oxide layer is damaged, aluminium is prone to severe corrosion, with possibly dramatic consequences. The design of chromoionophores for Al 3+ detection, in possible combination with optical fiber technology, is thus of high interest as an extension of the present work. The high affinity of the Al 3+ ion for ionophores bearing negatively-charged oxygen atoms leads us to propose the catechol unit as a ligand to be coupled with appropriate chromophores.

In the study of those new compounds, particular attention will have to be paid to the pH range in which the sensor has to perform.

Beyond the development of organic molecules for metal ion detection, a very different aspect of cation complexation can also be envisioned, with the theoretical study of the important biological process of metal-induced oxidation of polyphenols and the redox processes related to the

Figure 1 .

 1 Figure 1. Structure et nomenclature IUPAC du BODIPY et principaux résultats.

Figure 2 . 4 . 4 . 2 4 . 5 4 . 6 4 . 6 . 1 4 . 6 . 2 4 . 7

 2442454646146247 Figure 2. Structure du dérivé de pérylène monoimide senseur d'ions zinc et principe de détection par fibre optique.

Figure 1 . 1

 11 Figure 1.1 Spectrum of electromagnetic radiation. [0]

  a molecular orbital picture, atomic orbitals (AO) are combined to obtain molecular orbitals (MO), electronic wavefunctions describing the probability of finding an electron in any given region of the molecule in a certain electronic state. The electronic ground state thus corresponds to the case in which all the electrons are filling the molecular orbitals of lowest possible energy while respecting the Pauli principle. Excited states are described by a combination of transitions from occupied to unoccupied molecular orbitals, generally involving mainly the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Depending on the type of AOs combined, the resulting MOs can be of , n or  nature and different energies are associated with the possible electronic transitions between them. Contrary to the -MOs, which are oriented along the internuclear axis, the -MOs lie above and below the latter, and -electrons are consequently only loosely bound by atoms. When several atomic p-orbitals are combined along a sequence of adjacent atoms in sp 2 -hybridisation, in such a way that a pattern of alternating single and multiple bonds is formed, a so-called -conjugated system is formed in which the electrons are delocalised over the atoms of the molecule. The molecular energy levels are affected by -conjugation: the larger the extent of conjugation, the smaller the energy gap between the frontier orbitals (Figure 1.2).

Figure 1 . 2

 12 Figure 1.2 Schematic evolution of the HOMO/LUMO energy gap as a function of increased conjugation in a series of linear polyenes.

  the area under the curve of the extinction coefficient plotted against wavenumber. A value of f of ~0 represents a forbidden transition, while a value close to unity indicates a strong transition.Having discussed the types, probability and intensity of transitions, we can finally consider the shape of an absorption spectrum, which will depend both on the vibrational sublevels of the molecular states and on the interaction with the surrounding medium (see section 1.3), causing homogeneous and inhomogeneous broadening.Absorption of a photon not only results in a 'pure' electronic transition since the molecule also acquires some extra vibrational energy giving rise to a vibrational structure in the absorption band. The intensities of the vibronic transitions (simultaneous electronic and vibrational excitation) are described by the Franck-Condon principle, based on the premise that electrons are so much lighter than the nuclei that they respond to the excitation instantaneously compared to the time scale of nuclear motion (in analogy to the Born-Oppenheimer approximation, presented section 2.2). It states that an electronic transition is most likely to occur without changes in the positions of the nuclei in the molecular entity and its environment. The resulting state is called a Franck-Condon state, and the transition achieved, a vertical transition. The quantum chemical formulation of this principle is that the intensity of a vibronic transition is

Figure 1 . 3 Sv = 0 and 1 Sv

 131 Figure 1.3 (a) and (c) depict the potential energy surfaces of two different molecules in the ground (S 0 ) and excited (S 1 ) states. (b) and (d) present the associated vibrational transitions probabilities and possible resulting shape of the absorption spectra, broadened by solvent effects (dashed curves).

Figure 1 . 4

 14 Figure 1.4 (a) fluorescence, (b) non-radiative deactivation via S 1 -S 0 internal conversion, (c) intersystem crossing (triplet state formation) and subsequent phosphorescence emission.

Figure 1 . 5

 15 Figure 1.5 Perrin-Jablonski diagram of an organic molecule and characteristic lifetimes.

Figure 1 . 6

 16 Figure 1.6 Perrin-Jablonski diagram of an organic molecule including the effect of solvent relaxation.

Figure 1 . 7

 17 Figure 1.7 Schematic representations of the spaced and integrated architectures of a molecular sensor for cations. Note

Figure 1 . 8

 18 Figure 1.8 Structures of 18-crown-6 and dibenzo-18-crown-6.

Figure 1 . 9

 19 Figure 1.9 Structures of the guest-free DPA ligand and its complex with the zinc ion.

  sensor, and thus by extension alter the intramolecular charge transfer subsequent to photoexcitation, inducing a displacement in both absorption and fluorescence spectra that constitutes the cation recognition transducer signal. One can modulate the strength of the ICT by substitution with more or less strong donor and acceptor groups, and thus the expected spectral shifts in the presence and absence of the analyte.

Figure 1 . 10

 110 Figure 1.10 Spectral shifts arising from photoinduced charge transfer for cation interaction either with the donor or acceptor moiety of the sensor.

Figure 1 . 11

 111 Figure 1.11 Working principle of the aza-crown ether based sensor from ref. 34.

Figure 1 . 12 presents

 112 the molecular orbital representations of oxidative and reductive electron transfers, where the chromophore either plays the role of the donor or the role of the acceptor.

Figure 1 . 12

 112 Figure 1.12 Molecular orbitals diagrams for oxidative (left) and reductive (right) PET between an excited chromophore and a ground state quencher.

Figure 1 . 13

 113 Figure 1.13 Principles of cation detection by PET sensor and associated frontier orbitals energy diagrams illustrating the electron transfer mechanism in the "on" and "off" states.

(

  mono-and di-) imides are formed on the 3, 4, and/or 9, 10 positions and it is nowadays possible to introduce substituents at the bay and ortho positions (Figure 1.14).

Figure 1 . 14

 114 Figure 1.14 Chemical structures of the perylene core (with substitution positions) and perylenes mono-and diimide (PMI and PDI respectively).

  photochemical stability, high quantum yield and extinction coefficient, as well as quasi insensitivity to solvent polarity and pH. Their versatility

Figure 1 . 15

 115 Figure 1.15 Structure and IUPAC numbering of the BODIPY core.

Figure 1 . 16 Figure 1 . 17

 116117 Figure 1.16 Illustration of the meso-substituent effect on spectroscopic properties (pictures taken from ref. 53).

  diagonalisation of the pq i pq FS matrix, one can determine the  i and generate a new set of LCAO coefficients, used in turn to define a new

  42) where the parameters a, b and c, set respectively to 0.2, 0.72 and 0.81, have not been optimised as they are simply taken from the B3PW91 functional without further fitting of experimental data.

  υυ

  -interacting density response  KS expressed as:

  . The electrostatic problem relative to a charge distribution inside a cavity surrounded by a dielectric continuum can be solved by considering the Poisson equation and associated boundary conditions: electrostatic potential V, sum of the electrostatic potential generated by the solute's charge distribution ρ sol and the solvent reaction potential, ε the dielectric constant of the solvent, n the unit vector perpendicular to the cavity surface and pointing outwards, and the subscript in and out to indicate the regions inside and outside the cavity.

Figure 2 . 1

 21 Figure 2.1 Solvation dynamics: schematic representation of the equilibrium and non-equilibrium regimes.

,

  mode provides a contribution to the vibrational partition function, except those with imaginary frequency: vK the characteristic vibrational temperature of each mode. Zero point vibrational energy is also computed and included in the internal energy E.

  Photochemistry and Spectroscopy of the Katholieke Universiteit Leuven.Our contribution consists in a quantum-chemical study performed to unravel the relationships between the molecular structure and the optical properties for series of BODIPY derivatives.

Figure 3 . 1

 31 Figure 3.1 Structure and IUPAC numbering of the BODIPY core.

Figure 3 .

 3 Figure 3.2 3,5-disubstituted BODIPY derivatives, with Ar : a.Ph, b.1-Naph, c.4-MeOC 6 H 4 , d.4-FC 6 H 4 , e.2-MeOC 6 H 4 (in CHCl 3 ).  f is the fluorescence quantum yield.

Figure 3 . 3

 33 Figure 3.3 Rigidified BODIPY derivatives, with X : a.O, b.S, c.Y=R=H, d.R=H;Y=OMe, e.R=Me;Y=H (in CHCl 3 ).

  synthetic strategy, proposed by V. Leen et al., has proven to be a powerful and facile method for the formation of ring-annulated BODIPY dyes with bathochromically-shifted visible absorption and fluorescence spectra with considerably higher molar absorption coefficients (()), and fluorescence quantum yields ( f ) values. We investigated three BODIPY derivatives prepared according to the aforementioned synthetic route and characterised by increasing conformational restrictions along the 1  2  3 series (Figure 3.4).

Figure 3 . 4

 34 Figure 3.4 Structures of the BODIPY dyes series with reaction conditions of transition metal catalyzed annulation.

Figure 3 . 5 Dyes 1 - 3

 3513 Figure 3.5 Stick representation of compound 2 (top) and compound 3 (bottom). To illustrate the planarity of the ring systems, a side view is placed at the right. Created with PyMol, (DeLano, W.L. The PyMOL Molecular Graphics System (2002) on http://www.pymol.org).

Figure 3 . 6

 36 Figure 3.6 Normalised absorption (dashed lines) and fluorescence emission (full lines) profiles of 1 (blue), 2 (green) and 3 (orange) in diethyl ether. Absorption (upper row) and fluorescence (lower row) emission colours of 1-3 (from left to right) in diethyl ether.

  bromophenoxy group is replaced by a benzofuran ring (in 2). When a second benzofuran ring is introduced (in 3), the bathochromic shift reaches ~24 nm (~0.10 eV) in comparison to 2. The calculations thus reproduce well the observed spectral shifts, even though the AM1/SCI transition energies are systematically overestimated. The computed transitions are of HOMOLUMO nature and the spectral displacement when going from 1 to 3 can be traced back to the changes in the shape of these orbitals with the geometrical constraints (Figure 3.7).

Figure 3 . 7 - 3 .

 373 Figure 3.7 Graphical representations of the frontier orbitals of 1-3.

Figure 3 . 8

 38 Figure 3.8 Chemical structures of (ring-fused) BODIPY dyes from the literature discussed here.

CHCl 3 993 and 4

 34 CompoundIt is instructive to compare 3 with the symmetrically constrained dye 4 of Burgess and co-workers, which only differs by the position of the benzofuran rings: compound 3 presents 3,5-dioxy benzofuran rings whereas 4 features 2,6-dioxy benzofuran rings (Figure3.8).

  Again, although the theoretical values of the absorption maxima and of the spectral shifts are underestimated for both compounds, the qualitative trend is nicely reproduced by the calculations, with 4 showing a calculated bathochromic shift of ~37 nm (~0.14 eV) compared to 3 (against the experimental value of ~50 nm).

Figure 3 . 9 - 7 .

 397 Figure 3.9 Graphical representations of the frontier orbitals of 4-7.

Figure 3 . 10 4 , 6 and 7 (C

 31047 Figure 3.10 Transition densities of compounds 3, 4, 6 and 7 (electron density is shifting from the red to the blue region). Atomic transition densities are given as: ab m K m m K q C C C

Figure 3 . 11 .

 311 The 8-11"u" derivatives are the equivalent of compounds 8-11 with no rotational restriction around the single bond at position 3.

Figure 3 . 11

 311 Figure 3.11 Chemical structures of the BODIPY derivatives studied.

Figure 3 . 8 and 9 ,

 389 Figure 3.12 Experimental (solid lines) and theoretical (dashed lines) vertical transition energies for absorption and emission of 8-11 (left). Graphical representations of the frontier orbitals of 8 and 9 (right).

Figure 3 .

 3 Figure 3.13 Experimental (solid lines) and theoretical (dashed lines) vertical transition energies for absorption and emission of 8(u)-11(u) (left). Graphical representations of the HOMO of 8 and 10 and their unconstrained counterparts (right).

Figure 3 . 14

 314 Figure 3.14 Scanned dihedral angle and associated groundstate PES of 8u (left) and computed absorption spectra (right) -equilibrium geometry (black curve) and Boltzmannweighted (green crosses).

Figure 3 .

 3 15).

Figure 3 . 15

 315 Figure 3.15 Structure of the 3-aryl and 2-aryl substituted BODIPY derivatives (and reference compound 12).

  compounds is well reproduced by the calculations. More specifically, the introduction of one phenyl group at the 3-position (13a) is characterised by an expected bathochromic shift in absorption of 34 nm compared to the reference 12, in very good agreement with experimental measurement (28 nm), as a result of the extended conjugation. Replacing the 3-phenyl substituent in 13a by electron donating groups (p-anisyl in 14a and 3thienyl in 15a) results in red-shifted absorption of about ~10 nm (against ~15 nm experimentally). Globally, the overall spectral displacements towards longer wavelengths of the absorption maximum going from 12 to 13a, 14a and 15a (of 34, 46 and 42 nm, respectively) are in very good agreement with the experimental findings.

Figure 3 . 16

 316 Figure 3.16 Graphical representation of the frontier orbitals of 12-15a and evolution of their energies.

Figure 3 . 18

 318 Figure 3.18 Structure of 16 and 17 and graphical representation of their respective HOMO, LUMO and LUMO+1.

  on the overall emission efficiency, we think the main reason for the much lower values measured for 17 in comparison to 13a has a conformational origin. Indeed, we expect that the conformational restriction brought by the bulky 2,6-dichlorophenyl substituent in 13a slows down considerably nonadiabatic internal conversion to the ground state, thus favouring the radiative over non-radiative decay mechanisms. This is confirmed by the first excited state potential energy surface of compounds 13a and 17 and their relative Boltzmann populations (as a function of the dihedral angle) presented in Figure 3.19. From this figure, the much narrower distribution for 13a compared to 17 is clear.

Figure 3 . 19

 319 Figure 3.19 Potential energy surfaces of the first excited state (in black) and Boltzmann population histograms (in red), as a function of the dihedral angle between the BODIPY core plane and the meso-substituent, of 13a (left) and 17 (right).

3. 21 )

 21 , depending on steric repulsion effects. These two possible arrangements lead to very different photophysical properties.

Figure 3 . 20

 320 Figure 3.20 Structure of the 8-amino-substituted BODIPY derivatives investigated.

Figure 3 . 22

 322 Figure 3.22 Graphical representation of the frontier orbitals of 18a-c, 19 and 20, with their associated energy.

  substituent planes. According to these PES and associated Boltzmann population histograms (Figure 3.23 -left), we restrain our investigations to ±50° around the fully planar position. In this range of dihedral angles, we plotted the evolution of the frontier orbitals together with the corresponding HOMO/LUMO gap (Figure 3.23 -right).

Figure 3 .

 3 Figure 3.23 Individual PES with Boltzmann population histograms (in red) for 18a, 18b and 18c and associated HOMO-LUMO evolution and energy gap (in grey), as a function of the dihedral angle between the BODIPY core and meso-substituent planes.

Figure 3 . 24

 324 Figure 3.24 Evolution of the transition energy as a function of the dihedral angle between the BODIPY core and mesosubstituent.

  The perylene monoimide derivative investigated in this chapter has been synthesised in the group of Prof. Dr. Klaus Müllen at the Synthetic Chemistry Department of the Max Planck Institute for Polymer Research in Mainz, Germany. The formation of the complex and the associated optical response were characterised with several spectroscopic techniques (FD-MS, 1 H-NMR, UV-Vis) as well as isothermal titration microcalorimetry (ITC). We performed quantum-chemical calculations to get insight into the detection mechanism and the consequences of Zn 2+ binding on the optical properties of the PMI-DPA compound. Finally, we conducted further experiments to demonstrate the successful detection of Zn 2+ with thin films on glass and, ultimately, the incorporation of the sensitive molecule in a sol-gel deposited as the active layer within an optical fibre sensor (in collaboration with the 'Materials Science' and 'Electromagnetism and Telecommunication' departments of the UMONS-Faculté Polytechnique).

Figure 4 . 2 Figure 4 . 3 ,

 4243 Figure 4.2 Optimised geometries of 1 and 1a•Zn 2+ .

Figure 4 . 3

 43 Figure 4.3 Optimised geometries of 1 and 1b•Zn 2+ .

Figure 4 . 4

 44 Figure 4.4 Absorption spectra of the complexes of 1 (4.42 × 10 -5 M) with increasing amounts of ZnCl 2 in acetone solution. The black and blue vertical bars are the oscillator strengths associated to the computed transition for 1 and 1a•Zn 2+ , respectively.

Figure 4 . 2 )

 42 Figure 4.2). The simulated absorption spectrum of 1a•Zn 2+ presents a strong absorption band at 527 nm corresponding to the S 0 S 1 transition, essentially characterised by a HOMOLUMO excitation, as found in the free molecule. The computed blue shift of the first absorption band upon complexation amounts to 28 nm, in very good agreement with the experimental shift (33 nm), and comprises two different contributions: a conformational reorganisation and a change in the electronic structure. As already mentioned, the main structural modification in the presence of the ion involves the rotation of one pyridine unit in the ionophore. To assess

  2+ and Co 2+ (where the metal salts were CaCl 2 , AgNO 3 , HgCl 2 , FeCl 2 , CuCl 2 , NiCl 2 , respectively), fluorescence experiment were conducted. None of the equimolar complexes of 1 with the abovementioned cations results in a fluorescence enhancement at 600 nm upon irradiation at 515 nm (Figure 4.6), in contrast to the results for the Zn 2+ ion. The Hg 2+ ion generated a negligible two-fold increase of compound 1 fluorescence, as compared to the fluorescence enhancement induced by Zn 2+ (20-fold increase).

Figure 4 . 6

 46 Figure 4.6 Fluorescence intensity at 600 nm of a 1:1 mixture of metal salts and compound 1 at 600 nm upon excitation at 515 nm. The control measurement is labelled with the asterisk. Cu 2+ quantitatively quenches the fluorescence, due to the photo-induced electron transfer already demonstrated by

Figure 4 . 7 Figure 4 . 7 ,

 4747 Figure 4.7 Evolution of the absorption maximum with time of exposure to the Zn 2+ solution (full dots) and pure water (open dots) of 100 nm thick films of 1 on glass (left) and absorption spectra of a film of 1 dipped in an aqueous solution of Zn 2+ (2.0M) at t=0min and t=30mins (right).

Figure 4 . 8

 48 Figure 4.8 (left) Evolution of the absorption maximum with time of exposure to a 1M Zn 2+ solution of a 5 µm-thick sensitive sol-gel coating on glass and (right) absorption spectra of the coating in pure water (black line), after 5 mins exposure to the Zn 2+ solution (blue line), and after addition of EDTA at the end of the Zn 2+ exposure (orange line).

Figure 4 . 10

 410 Figure 4.10 Attenuation of the optical signal as a function of the wavelength of the light beam and transmission windows of a glass optical fibre.

Figure 4 . 11

 411 Figure 4.11 Structure of the PMI-DPA sensor and associated higher rylene derivatives, TMI-DPA and QMI-DPA.

Figure 4 . 12

 412 Figure 4.12 Graphical representation of the HOMO and LUMO of perylene derivatives of increasing length and evolution of their energies, with HOMO/LUMO gap values.

Figure 4 . 13

 413 Figure 4.13 Structure of the chromoionophore BDP-1-DPA resulting from the combination of the aza-BODIPY derivative reported by Gresser et al. (noted BDP-1) with the dipicolylamine unit. Compounds BDP-2-DPA and BDP-3-DPA are obtained for n=2 and n=3, respectively.

Figure 4 . 14 1 -Figure 4 . 15

 4141415 Figure 4.14 Graphical representation and evolution in energy of the frontier orbitals of BDP-1, BDP-1-DPA and BDP-1-DPA•Zn 2+ [CN4] .

  -14 -10 -11 seconds) down to the lowest vibrational level of the electronic state it reached, called a vibrationally-relaxed state. If initially a higher excited state (S 2 , S 3 ... S n ) is reached, a fast internal conversion (timescale of vibrational relaxation) into the lowest excited state S 1 takes place owing to the overlap existing between vibrational levels of excited states, also called horizontal transition i . Note that molecules with a high degree of rigidity are less likely to undergo internal conversion. From S 1 to the ground state, it is however an inefficient and very slow process due to large energy gap between the two states and other competing events

-15

seconds, which brings the molecule in one of the upper vibrational levels of the latter state. Once excited, the deactivation, either radiative or nonradiative, can take 10 -14 to some seconds, and several pathways with varying probabilities are available for the molecule to dissipate the excitation energy and return to the ground state, such as fluorescence emission, internal conversion (IC), intersystem crossing (ISC) or phosphorescence.

Prior to any of the aforementioned processes, the excited molecule finds itself in a nonequilibrium state and undergoes quick vibrational relaxation (10 might happen first. These vibrational relaxation and internal conversion processes are non-radiative (the excess energy is dissipated as heat) and when combined, they result in the molecule being in the lowest vibrational level of the first excited singlet state S 1 . This is the basis of Kasha's rule, which states that "the emitting level of a given multiplicity

  It is nothing but a statement of the variational principle, already used in the wavefunction models, for the density. It implies that any trial electron density  trial will always give an energy larger than the

	E	T			ee E	E	ne	(2.26)
			F
	While the nuclear-electron attractive potential	E	[]	is system dependent,
							ne
	the Hohenberg-Kohn functional	F	[]	, constituted by the kinetic energy
			HK
	term and the repulsion between electrons, is a universal functional.
	According to the second theorem, "	E	[]	assumes its minimum value for
	the correct (r), if the admissible functions are restricted by the condition
	() r dr ". true ground-state energy. Assuming that the N	[]

HK F

functional is exact, it delivers the ground-state energy minimum of the system if and only if the input electron density is the true ground-state density.

  The KS potential depends explicitly on the density via the coulomb term and just like in HF, the problem has to be solved iteratively. Given a trial density, one can calculate the effective potential and solve the Kohn-Sham equations. The resulting orbitals  i give a new electron density (equation 2.28) that can be used to calculate a new effective potential and so on until a predefined threshold is reached. However, the exact

	where	E	xc	[]	is the so-called exchange-correlation term, that exists (HK
	theorem) but which exact expression remains unknown.
	Assuming that	E	[]	is known, the problem can then be solved in a
										xc
	similar way as done for the HF model. The Kohn-Sham orbitals  i (linear
	combination of the basis functions) that minimise the energy satisfy the
	pseudo-eigenvalue equations:
												ˆKS f	(2.31)
												i	i	i i
	2 where the Kohn-Sham one-electron operator ˆKS ( ) ( ) N rr i f is defined as:	(2.28)
												i
												i	1
	2 Even if, as already mentioned, the universal functional i i eff i υ 2 1 ˆ() KS fr	[]	(2.32)
	and  eff (r i ), the effective external potential,
												nuclei
	be written as:			2 rr 2 a i ia υυ 2 eff i xc () ( ) a rZ r dr	( ) r	(2.33)
										E	[ ]	T	[ ]	E	[ ]	E	[ ]	T	[ ]	(2.29)
												ni	ee	ne
	with	T	[]	the kinetic energy of the non-interacting system,
			ni
	E	[ ]	J	[ ]	E	[ ]	,	J	[]	the classical electron-electron repulsion and
	ee								nc
	E	[]	all the non-classical part of electron-electron repulsion (exchange,
	nc
	electrons correlation effects, self-interaction error),	E	[]	, the nuclear-
												ne
	electron potential, and expression []	T	[]	the correction to the kinetic energy,
	necessary to account for the interacting nature of the electrons.
	One can rewrite the DFT energy as:
										E	[ ]	T	[ ]	J	[ ]	E	[ ]	E	[ ]	(2.30)
												ni	ne	xc

HK

F is unknown, one can define the effective potential  eff (r i ) that will render the density and energy of the fictitious non-interacting reference system identical to the one of the real interacting system such that the energy functional can xc E is unfortunately not known and its approximate determination constitutes the key issue to DFT improvement.

  )

	hybrid xc E	HF x E	DFT xc k E	HF x E	a E	DFT xc	aE	HF x	(2.41)

Table 3 .

 3

		 max abs. (nm)	 max em. (nm)	(cm -1 )	 max (L.mol -1 .cm -1 )	f	 f
	1	518	536	648	35 000	0.248	0.47
	2	553	569	508	42 000	0.390	0.48
	3	587	602	424	155 000	0.802	0.58
	Introduction of the benzofuran ring in 2 causes a large bathochromic shift
	in both the absorption and emission maxima, by 35 and 33 nm,
	respectively, compared to 1 (Table 3.1). The absorption and emission
	maxima of the most rigid structure 3 are further red-shifted by
	approximately 30 nm compared with 2. The progressively more extended
	planarity of the chromophore in the series 1  2  3 accounts for the
	increasing bathochromic shifts of 

1 Spectroscopic and photophysical properties of 1-3 in toluene. abs (max) and  em (max). The conformational restriction that results in locking the bond rotation in the

Table 3 .

 3

	n	n	2	3	2	2	. [23]
	theoretical values (in the gas phase)	experimental values
	transition energy (eV)	transition wavelength (nm)	oscillator strength f	transition energy (eV)	transition wavelength (nm)	oscillator strength f
		2.382		521	0.7515	2.396 a	518 a	0.248 a
		2.303		538	0.8525	2.245 a	553 a	0.390 a
		2.206		562	1.0182	2.114 a	587 a	0.802 a
		2.069		599	0.7912	1.949 b	637 b	/
		2.090		593	0.8995	1.933 c	642 c	/
		2.152		576	0.8544	2.144 b	579 b	/
		2.023		613	1.2316	1.904 b	652 b	/
	a) Data in toluene. b) Data in chloroform. c) Data in cyclohexane.

2 Calculated (AM1/SCI) (left) and measured (right) photophysical properties of compounds 1-7. To convert the theoretical value of the oscillator strength f (for the gas phase) to values in a solvent with refractive index n, one has to multiply the theoretical f value by

Table 3 .3 Spectroscopic

 3

and photophysical properties of 4-7 in toluene.

Table 3 . 4

 34 Spectroscopic and photophysical properties of 8-11 in acetonitrile.

		 max abs. (nm)	 max em. (nm)	(cm -1 )	 f
	8	546	560	458	0.72
	9	613	625	313	0.91
	10	508	520	454	0.83
	11	534	543	310	0.76

Table 3 . 5

 35 Computed wavelengths/energies of the first absorption and emission vertical transitions with the LR-PCM approach and associated vertical transition energy differences for 8-11 and their corresponding unrestricted forms.

		absorption			emission			E abs/em
		transition energy (eV)	transition wavelength (nm)	oscillator strength f	transition energy (eV)	transition wavelength (nm)	oscillator strength f	energy (eV)
	8	2.74	452	0.7786	2.34	530	0.96	0.40
	8u	2.88	430	0.7002	2.45	505	0.89	0.43
	9	2.42	511	0.8509	2.07	599	1.03	0.35
	9u	2.71	457	0.7600	2.25	552	0.96	0.46
	10	2.98	415	0.6320	2.62	473	0.76	0.36
	10u 3.01	412	0.5859	2.64	469	0.74	0.37
	11	2.81	440	0.7084	2.52	493	0.84	0.29
	11u 2.85	435	0.6226	2.54	488	0.76	0.31

Table 3 . 6

 36 Computed wavelengths/energies of the first absorption and emission vertical transitions with the SS-PCM approach and associated vertical transition energy differences E abs/em for 8-11 and their corresponding unrestricted forms a .

		absorption		emission		E abs/em		Stokes shift
		transition	transition	transition	transition
		energy	wavelength	energy	wavelength	(eV)	(cm -1 )	(cm -1 )
		(eV)	(nm)	(eV)	(nm)
	8	2.89	430	2.70	459	0.19	1465	169
	8u	3.03	409	2.83	438	0.20	1638	181
	9	2.55	487	2.40	517	0.15	1199	138
	9u	2.85	436	2.59	479	0.26	2068	128
	10	3.12	397	2.97	418	0.15	1245	209
	10u 3.15	394	2.99	415	0.16	1245	226
	11	2.94	422	2.83	438	0.11	836	151
	11u 2.97	417	2.86	433	0.11	879	155

a The Stokes shifts are based on solvent relaxation (see below).

Table 3 . 7

 37 Computed wavelengths/energies of the first absorption vertical transition and associated oscillator strengths. Experimental absorption maximum is measured in acetonitrile.

						experimental values in
		theoretical values			MeCN
		trans. energy (eV)	 abs (nm)	oscillator strength f	shift vs 12 (eV / nm)	 abs max (nm)	shift vs 12 (eV / nm)
		3.01	412	0.5363	-	508	-
		2.78	446	0.7046	0.23 / 34	536	0.13 / 28
	a	2.71	458	0.7998	0.30 / 46	552	0.19 / 44
	a	2.73	454	0.6938	0.28 / 42	549	0.18 / 41
	a	2.79	444	0.6546	0.22 / 32	-	-
	b	2.70	460	0.6295	0.31 / 48	-	-
	b	2.74	452	0.6063	0.27 / 40	-	-
	b
		As is typically the case for BODIPY derivatives, the TD-DFT  max are
		underestimated, but the overall trend across the whole series of

Table 3 . 8

 38 Computed wavelengths/energies of the first absorption vertical transition of 18a-c, 19 and 20 compounds and their associated oscillator strengths, with the nature of the transition.

		transition energy (eV)	transition wavelength (nm)	oscillator strength f	nature of the transition
	18a	3.42	363	0.4420	HOMO HOMO-2	 	LUMO LUMO	96.9% 3.0%
	18b	3.43	361	0.4055	HOMO HOMO-2	 	LUMO LUMO	96.8% 2.7%
	18c	3.29	377	0.3925	HOMO HOMO-2	 	LUMO LUMO	96.7% 2.8%
	19	3.42	363	0.3939	HOMO HOMO-2	 	LUMO LUMO	96.8% 2.7%
	20	3.30	375	0.3287	HOMO HOMO-2	 	LUMO LUMO	96.5% 2.8%

Table 4 .1 Zn

 4

-N and Zn-O bond lengths in 1a

•Zn 2+ and 1b•Zn 2+ .

	bond	1a•Zn 2+ 1b•Zn 2+
	lengths (Å)
	Zn-N9	3.90	2.24
	Zn-Npyr1	2.15	2.01
	Zn-Npyr2	2.13	2.02
	Zn-O1	2.08	2.01
	Zn-O2	2.09	-

Table 4 . 2

 42 Calculated spectroscopic properties of the free dye and the complexes investigated.

	•Zn 2+ +

Table 4 . 3

 43 Single-point electronic energy and thermal corrections to enthalpy and Gibbs free energy (at 298.15K) for the reactants and products involved in the complexation reaction of Zn 2+ (in atomic units).

		1	acetone	Zn 2+	1a•Zn 2+ (CN4)
	E elec (from single point)	-1346510.70	-121241.19	(acetone) 6 -768489.85	-1630025.77
	H corr	487.55	56.70	350.06	608.45
	G corr	409.44	35.21	275.59	512.74
	E elec + H corr	-1346023.15	-121184.48	-768139.78	-1629417.32
	E elec + G corr	-1346101.26	-121205.98	-768214.26	-1629513.03
	Calculating H° (G°) by simply taking the difference of individual
	enthalpy (Gibbs free energy) values for the reactants and the products
	requires to pay particular attention to the proper equilibration of the
	complexation reaction ; thus, the following equation is considered: 1 +
	[Zn((CH 3 ) 2 CO) 6 ] 2+ → 1a•Zn 2+ [CN4] + 4(CH 3 ) 2 CO. From the values collected
	in

Table 4 .

 4 3, we calculated a negative Gibbs free energy of -21.41 kcal.mol -1 , in line with the exergonic character already measured in the ITC experiment. A positive enthalpy of complexation of 7.67 kcal.mol -1 is computed, again in line with the endothermic character measured.

Table 4 . 4

 44 Computed n upon complexation of Zn 2+ by 1, in the gas phase and in water.

	volume (ų)	n (1) gas phase	n (1) pcm	n (1a•Zn 2+ + 2 Cl -) gas phase	n (1a•Zn 2+ + 2 Cl -) water	n gas phase	n water
	100000	1.00623	1.00903	1.00660	1.00952	0.00037	0.00049
	150000	1.00415	1.00601	1.00440	1.00634	0.00024	0.00033
	200000	1.00311	1.00451	1.00330	1.00476	0.00018	0.00025

Table 4 . 5

 45 Computed wavelengths/energies of the first absorption vertical transition, associated oscillator strengths and shift upon complexation of the zinc ion.

		transition energy (eV)	transition wavelength (nm)	oscillator strength f	shift upon complexation (eV / nm)
	1a	2.37	522	0.7286	-
	2a	1.94	638	1.2411	-
	3a	1.66	749	1.8715	-
	1a•Zn 2+ [CN4]	2.47	503	0.7713	0.10 / 19
	2a•Zn 2+ [CN4]	2.00	621	1.2598	0.06 / 17
	3a•Zn 2+ [CN4]	1.69	732	1.7861	0.03 / 17

Acknowledgements

achieve correct asymptotic behaviour, is to introduce a partitioning of the Coulomb operator, in the exchange interaction, into short-and long-range components: 12 12

erf r erf r r r r (2.43) The first term accounts for the short-range part of the Coulomb operator by DFT exchange while the second term describes long-range interactions with the exact HF exchange.

Various LC functionals are available, and among them, we used the CAM-B3LYP functional, which combines the widely used B3LYP

functional with a Coulomb-attenuating method (CAM) potential. Within the CAM approach, two parameters are introduced in equation 2. 43, to control the degree of mixing of DFT and exact HF exchange:

12 12 12 12 12 ring-fused systems explains the noticeably higher quantum yields  f of 3.

Progressive reduction of the flexibility of the chromophore is also reflected by the considerably higher  max and corresponding f values. The oscillator strength f is calculated according to the following equation [20] : where n is the solvent index of refraction and is the wavenumber (in cm -1 ).

Quantum chemical calculations

For all compounds investigated, the ground-state geometry optimisation was first performed at the AM1 [21] semi-empirical level, using the commercial package AMPAC 8.15.9 [22] . These geometries were subsequently used as input for calculations at the AM1/SCI level (in the gas phase) to compute excited-state properties, including transition energies (Table 3.2), dipole moments and densities, with an active space of 60 molecular orbitals.

Compounds 1-3

To understand the effect of conformational constraints on the optical properties of BODIPY dyes, we performed calculations on molecules 1-3.

Starting from 1, the structure of the system has been increasingly constrained by the introduction of benzofuran rings instead of bromophenoxy groups (1  2  3, see Figure 3.4), leading to a completely planar structure in compound 3. This increase in rigidity results in an overall bathochromic shift of the absorption and emission maxima. A red shift of ~18 nm (~0.08 eV) is computed when one

Compound 5-7

The Keio Fluors (KFL) 6 and 7 of Suzuki et al. [16] have, like 4, 2,6-dioxy furan rings, but differ from each other in that a single methyl is added on the furan rings of 6 where phenyl rings are present in 7. The latter can be regarded as a 3,5-distyryl substituted BODIPY such as 5, but with oxygen atom bridge linkers that preclude free rotation of the ethenyl fragments. Note that the absence of a meso-substituent and hence limited conformational flexibility in 6 and 7, which exhibit extremely high  max and very small Stokes Shift , leads to very high quantum yields  f . Except for 6, for which the computed absorption maximum is in very good agreement with the experimental value as only underestimated by ~3 nm, the computed transition wavelengths for 5 and 7 are underestimated by a larger amount, of about 40 nm, compared to the experimental results (652 and 630 nm, respectively). However, the increase in the oscillator strength associated to the presence of O-linked bridges to prevent rotation of the 3,5-distyryl substituents is in agreement with the observed experimental trend.

The lowest optical transition in all molecules is dominated by a HOMOto-LUMO transition, so it suffices to discuss the shape and changes in the energetic position of the frontier orbitals upon substitution (Figure 3.16).

The reference compound 12 possesses frontier orbitals that are strictly localised on the BODIPY core, with only vanishingly small contributions on the meso-substituent in the LUMO. The measured and computed bathochromic shift of the first absorption band upon adding a substituent at the 3-position is well illustrated by the frontier orbital representation of 13a, 14a and 15a, which present the same bonding-antibonding pattern as 12 but spread out substantially over the conjugated arm (phenyl, p-anisyl and 3-thienyl, respectively). Compared to 12, the larger spectral displacements obtained for 14a and 15a with respect to the 3-phenyl analogue 13a can be rationalised by the shift in energy of the HOMO and LUMO orbitals upon substitution. The presence of electron-donating groups leads to an overall destabilisation of the frontier levels, which is larger for the HOMO as a consequence of the donor character of the substituents, and this translates into a reduced HOMO/LUMO energy gap, and thus a spectral shift towards the red.

Influence of the position of the functionalisation

The isomers resulting from the same substitutions of 12 in the 2-position (instead of the 3-position) were also studied (compounds 13b, 14b, 15b, Table 3.7). The absorption maximum computed for 13b is very close to the value calculated for the corresponding compound 13a, suggesting that the conjugation extends equally over the phenyl side arm in 2-and 3positions. This is borne out by the shape of the frontier orbitals involved in the transition, which reveal a similar delocalisation over the HOMO for the two systems, yet a more confined (over the BODIPY core) character of the LUMO in 13b (Figure 3.17 experimental observations reported by V. Leen et al [34] .

meso-substitution of the BODIPY core

All the chlorinated derivatives investigated so far present a 90° dihedral angle between the meso-substituent and the mean plane of the BODIPY core, which can be attributed to the strong steric hindrance associated

Computational method

In the framework of Density Functional Theory (DFT), all geometries were optimised at the B3LYP/6-31G(d,p) level [39] , applying the Polarizable Continuum Model (in its IEFPCM formulation [30] ) to account for solvent effects. On the basis of these structures, Time-Dependent Density Functional Theory (TD-DFT) has been applied to compute the vertical transition energies.

Impact of the meso-substituent donor character and orientation

To evaluate how the donating strength of the meso-substituent can affect both conformational and electronic properties, we investigated 18a

(regarded as the reference compound), 18b and 18c, which differ by the donor character of the -NHR meso-substituent (-NH 2 < -NHCH 3 < -NHPh). All optimised geometries present a coplanar-like arrangement, with dihedral angles close to 180° for 18a and 18b, and a slight distortion in 18c which exhibits a -167° angle between the two moieties, most likely as a result of the steric hindrance generated by the larger substituent size.

123 Substitution by a donor group is known to bring about an asymmetric destabilisation of the frontier orbitals, with a larger effect on the HOMO.

Computational method

The ground-state geometry of 1 in the absence/presence of Zn 2+ was optimised at the density functional theory B3LYP/6-31G* level [15] . Those equilibrium geometries were subsequently used as input for the calculation of the electronic excited states and the simulation of the optical absorption spectra in the framework of time-dependent density functional theory (TD-DFT). We used the LanL2DZ [16] effective core potential and a valence basis set to describe the zinc ion. Solvent effects were taken into account by combining a dielectric continuum model (IEFPCM [17] ) with an This effect is due to a reduced electronic density over the nitrogen atom in the 9-position (thereby reducing its electron-donating strength) and a concomitant smaller intramolecular charge transfer character of the amino-substituted PMI dye in the presence of Zn 2+ . This is confirmed by the analysis of the electronic density distribution over N9 in the HOMO level (Table 4.2): in the presence of the zinc ion, the donating strength of the nitrogen drastically decreases, in particular for 1b, as does the intramolecular charge transfer (ICT) character.

Thermodynamics of Zn 2+ complexation 4.3.1 Stability of the complex

Isothermal Titration Microcalorimetry (ITC) represents a valuable experimental method in the determination of the thermodynamic parameters characterizing recognition processes. [19] ITC measurements The enthalpy and Gibbs free energy changes associated to the complexation of Zn 2+ were quantum-chemically evaluated according to the following equation:

The individual free energy terms comprised in these equations were calculated by summing thermal corrections to enthalpy and Gibbs free energy, H corr and G corr , respectively, extracted from the vibration frequency analysis (performed on each isolated energy minimum structure) to the

On optical fibres

The same sensitive sol-gel encapsulating 1 was deposited on an optical fibre and the TFBG transmitted amplitude spectra recorded in pure water and in the presence of Zn 2+ ions (1M solution) are presented in

Higher rylene derivatives

Among all the very attractive features of perylene derivatives, the DPA, which led us to the conclusion that BDP-1-DPA is not a suitable compound for use into zinc ion detection applications.

Influence of the π-conjugated spacer length

A bathochromic shift of the absorption maximum being expected as a consequence of the introduction of more repeating unit in donor--bridgeacceptor dyes, one and two thiophene units were added to determine the effect of increasing the conjugated spacer length of BDP-1-DPA.

Expectedly, the supplementary thiophene units allow for an extension of

Conclusions

In this chapter, we present an in-depth study of chromoionophores for zinc ion detection, combining experimental and theoretical approaches. As the first stage in the study, a perylene monoimide chromophore was combined with a dipicolylamine complexing unit (PMI-DPA).

Characterised Once the lone pair of the DPA unit gets involved in the complexation of the zinc ion, the ICT is altered and a hypsochromic shift is observed. The thermodynamic characterisation of the complex reveals that the presence of interfering copper ions might result in a lower detection efficiency for Zn 2+ .

Our research takes place in the framework of optical fibre sensor technology, more specifically for the distributed monitoring of corrosion of galvanised steel. In this context, it is highly desirable to make use of chromoionophores that are optically active in certain ranges of wavelengths, namely, in the transmission windows of the optical fibre, where the signal loss is reduced. For this purpose, we modelled higher rylene derivatives (terrylene and quaterrylene) and showed that the zinc ion detection ability is maintained, while the optical signalling of the complexation event is transposed to longer wavelengths.