Introduction to the Special Section on

Induction Heating Systems I NDUCTION heating (IH) systems are a faster, cleaner, and more efficient alternative to conventional heating systems. Its contactless nature provides superior heating performance that has been successfully applied in industrial, domestic, and medical applications. Since the early IH developments in the late 19th century, technology has evolved to provide high-performance and reliable equipment with a wider application spectrum. Nowadays, the number of applications and installed power makes IH of great interest not only from an industrial and economic point of view but also considering its social and environmental impact.

Following this interest, the Annual Conference of the IEEE Industrial Electronics Society (IECON) has organized since 2011 a special session devoted to IH technology. During these years, the main achievements and research lines in the fields of power electronics and semiconductor technology, magnetic component design, and control of power converters for IH have been presented and discussed in these sessions. After these experiences, it is now a pleasure for us to introduce this "Special Section on Induction Heating Systems" of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. This Special Section aims at bringing some of the most recent and interesting ideas in this area by the worldwide research community and at presenting some of the latest advancements and developments in the field of IH technology.

The first paper of this Special Section is a review paper written by the Special Section Guest Editors Lucia et al. [START_REF] Lucía | Induction heating technology and its applications: Past developments, current technology, and future challenges[END_REF], which covers some of the most relevant IH research papers published in recent years, details the current state of the art of IH systems, and identifies some future design trends for such systems. This paper categorizes the main enabling technologies that have made possible the advancement and spread of IH systems and its main applications. Following this classification, the remaining papers of this Special Section can be classified according to the enabling technology focused upon and its main application (see Table I). From this point of view, IH systems can be subdivided into the power electronic system, which generates the required medium frequency currents; the inductor system, which creates the alternating magnetic field to heat up the IH target; and the control system. Papers [START_REF] Sarnago | A class-e direct ac-ac converter with multi-cycle modulation for induction heating systems[END_REF]- [START_REF] Esteve | Improving the reliability of series resonant inverters induction heating applications[END_REF] are focused on the power electronic systems, papers [START_REF] Kennedy | Empirical verification of a short-coil correction factor[END_REF]- [START_REF] Chen | Thermotherapy induction heating apparatus with new magnetic-wrapped coil design[END_REF] are focused on the inductor system, and papers [START_REF] Jimenez | Design and evaluation of a low-cost high-performance Σ-Δ ADC for embedded control systems in induction heating appliances[END_REF]- [START_REF] Imaz | Infrared thermometry system for temperature measurement in induction heating appliances[END_REF] are focused on the control system. From the application point of view, papers [START_REF] Sarnago | A class-e direct ac-ac converter with multi-cycle modulation for induction heating systems[END_REF] and [START_REF] Namadmalan | Tunable self-oscillating switching technique for current source induction heating systems[END_REF]- [START_REF] Mach | Finite-element 2-D model of induction heating of rotating billets in system of permanent magnets and its experimental verification[END_REF] are intended for industrial applications, papers [START_REF] Sarnago | A class-e direct ac-ac converter with multi-cycle modulation for induction heating systems[END_REF]- [START_REF] Sarnago | A class-E direct ac-ac converter with multicycle modulation for induction heating systems[END_REF] and [START_REF] Jimenez | Design and evaluation of a low-cost high-performance Σ-Δ ADC for embedded control systems in induction heating appliances[END_REF]- [START_REF] Imaz | Infrared thermometry system for temperature measurement in induction heating appliances[END_REF] detail domestic applications, and finally, in [START_REF] Chen | Thermotherapy induction heating apparatus with new magnetic-wrapped coil design[END_REF], a medical application is discussed.

The first part of this Special Section is focused on the power electronic system. It is usually composed of a resonant inverter to generate the required alternating magnetic field with high efficiency and power density. Depending on the power range and/or applications, different topologies are applied, as explained in [START_REF] Lucía | Induction heating technology and its applications: Past developments, current technology, and future challenges[END_REF]. The first paper of this part is written by Sarnago et al. [START_REF] Sarnago | A class-e direct ac-ac converter with multi-cycle modulation for induction heating systems[END_REF], and it proposes a single-switch resonant inverter applied to IH appliances. The proposed converter combines the benefits of direct ac-ac conversion [START_REF] Saha | Commercial frequency AC to high frequency AC converter with boostactive clamp bridge single stage ZVS-PWM inverter[END_REF] with the cost-effective implementation of single-switch quasi-resonant inverters. Moreover, a multicycle modulation is proposed to improve the output power control. This allows alleviating control limitations of other previous class-E proposals such as [START_REF] Leisten | Single ended resonant power supply for induction heating[END_REF] and [START_REF] Omori | New single-ended resonant inverter circuit and system for induction-heating apparatus[END_REF]. This converter takes advantage of wide band-gap power devices [START_REF] Sarnago | Design and implementation of a high-efficiency multiple-output resonant converter for induction heating applications featuring wide bandgap devices[END_REF], [START_REF] Millan | A survey of wide band gap power semiconductor devices[END_REF] to improve the converter efficiency and hightemperature performance.

It is important to note that one key design point when dealing with resonant converters for IH systems is to ensure softswitching conditions and high efficiency in the complete operation range [START_REF] Lucía | Load-adaptive control algorithm of half-bridge series resonant inverter for domestic induction heating[END_REF]. This can be difficult in some applications, such as domestic ones, due to the highly variable load and output power range. In order to address these issues, Mishima et al. [START_REF] Mishima | A new current phasorcontrolled ZVS twin half-bridge high-frequency resonant inverter for induction heating[END_REF] propose a current phasor-controlled resonant converter. This converter is based on a dual half-bridge structure, and it uses the phase shift between converters, in a similar way in [START_REF] Pham | Phase angle control of high-frequency resonant currents in a multiple inverter system for zonecontrol induction heating[END_REF] and [START_REF] Burdío | Asymmetrical voltage-cancelation control for full-bridge series resonant inverters[END_REF], to perform the power control. This converter achieves a wider soft-switching operation area and improved output power control, being particularly suitable for variable load IH applications.

Following the same goals of the previous paper, Sarnago et al. propose in [START_REF] Sarnago | A class-E direct ac-ac converter with multicycle modulation for induction heating systems[END_REF] a full zero current switching (ZCS) quasi-resonant inverter. This converter is based on a half-bridge structure and achieves ZCS during both turn-on and turn-off transitions, regardless of the required switching frequency and output power. As a consequence, a significant reduction on switching losses is obtained, leading to higher efficiency in the complete operation range. In addition, the output power control is simplified, allowing the implementation of efficient and reliable systems.

In [START_REF] Namadmalan | Tunable self-oscillating switching technique for current source induction heating systems[END_REF], Namadmalan and Moghani propose a tunable selfoscillating inverter [START_REF] Sarnago | Design and implementation of a class-E self-oscillating inverter for cost-effective induction heating systems[END_REF] that features an improved start-up operation. Unlike the previous converters, this approach features a current-source inverter with parallel resonance, which is suitable for industrial IH applications. Compared with classical solutions, the converter proposed in this paper achieves faster dynamics with reduced component stress, improving its reliability.

The last paper of this part is devoted to the power converter reliability [START_REF] Huai | Toward reliable power electronics: Challenges, design tools, and opportunities[END_REF], which is a general concern among power electronic designers. Esteve et al. present in [START_REF] Esteve | Improving the reliability of series resonant inverters induction heating applications[END_REF] a comprehensive study of a high-power (100 kW) resonant converter. The authors analyze the operation of a full-bridge inverter operating with a modified phase-shift modulation strategy. The efficiency and power cycling capability is deeply studied using a calorimetric method, and as a conclusion, the authors prove that a significant lifetime extension can be obtained.

The second part of this Special Section is devoted to the inductor system, which is the most important magnetic component of an IH system. It is responsible for creating the required alternating magnetic field and, as a consequence, heating up the induction target. Moreover, it is usually a part of the powerconverter resonant tank, determining the power-converter operation and performance. Consequently, significant attention has been paid to the design and modeling of the inductor system. In this Special Section, papers [START_REF] Kennedy | Empirical verification of a short-coil correction factor[END_REF]- [START_REF] Chen | Thermotherapy induction heating apparatus with new magnetic-wrapped coil design[END_REF] present some models and designs aimed at different IH applications.

Usually, one of the main challenges when designing an IH system is to provide an accurate model of the inductorload system, particularly when complex and/or variable geometries are present. An example of this is shown in [START_REF] Kennedy | Empirical verification of a short-coil correction factor[END_REF], where Kennedy et al. present an accurate model for short-coil geometries. This geometry present complex dependence of the coil and IH target geometries, and the prediction of the heating rate becomes difficult. The authors propose an analyticalempirical model that provides good accuracy in a wide frequency operating range. This proposal is thoroughly validated with finite-element method (FEM) simulations and a complete set of experimental measurements.

The design of IH systems intended to heat nonmagnetic elements is particularly challenging. Heating such elements usually entails high current levels, significantly degrading the power converter, the efficiency of the inductor, and the reliability of the nonmagnetic elements, as shown in [START_REF] Millán | Series resonant inverter with selective harmonic operation applied to all-metal domestic induction heating[END_REF]. In order to address this issue, Mach et al. propose in [START_REF] Mach | Finite-element 2-D model of induction heating of rotating billets in system of permanent magnets and its experimental verification[END_REF] an alternative method for heating such nonmagnetic elements. Instead of generating an alternating magnetic field, the authors propose to use a static magnetic field plus the rotation of the IH target. The proposed system is modeled and numerically solved, and the accuracy of the results is experimentally verified. The most remarkable achievements are the simplicity and robustness of the proposed system, and the efficiency improvement obtained when heating nonmagnetic elements.

Finally, Chen et al. detail in [START_REF] Chen | Thermotherapy induction heating apparatus with new magnetic-wrapped coil design[END_REF] a specific inductor design for tumor thermotherapy. This treatment requires the precise and deep generation of a magnetic field to heat up a needle in order to cauterize the targeted tumor tissues [START_REF] Stauffer | Magnetic induction heating of ferromagnetic implants for inducing localized hyperthermia in deep-seated tumors[END_REF]. The authors propose in this paper a high-permeability inductor coating to precisely focus the magnetic field, increasing the magnetic flux density. The proposed IH apparatus is modeled and analyzed through FEM simulation and experimentation, showing a significant performance improvement.

The third and last part of this Special Section is focused on the control system. Modern IH systems highly rely on advanced control systems to optimize the power control and heating quality [START_REF] Souley | Optimization of the settings of multiphase induction heating system[END_REF], [START_REF] Pham | Estimating method of heat distribution using 3-D resistance matrix for zone-control induction heating systems[END_REF], to guarantee the proper converter operation [START_REF] Sarnago | Modulation scheme for improved operation of a RB-IGBT based resonant inverter applied to domestic induction heating[END_REF], and to ensure the process safety [START_REF] Esteve | Improving the efficiency of IGBT seriesresonant inverters using pulse density modulation[END_REF], [START_REF] Jiménez | FPGA-based gain-scheduled controller for resonant converters applied to induction cooktops[END_REF]. This part of the Special Section contains three papers [START_REF] Jimenez | Design and evaluation of a low-cost high-performance Σ-Δ ADC for embedded control systems in induction heating appliances[END_REF]- [START_REF] Imaz | Infrared thermometry system for temperature measurement in induction heating appliances[END_REF] that show some of the current research lines being followed to improve IH systems.

In order to ensure the proper converter operation and measure important parameters, such as the current through the coil and the output power, several currents/voltages need to be measured. Jimenez et al. propose in [START_REF] Jimenez | Design and evaluation of a low-cost high-performance Σ-Δ ADC for embedded control systems in induction heating appliances[END_REF] an accurate and cost-effective sigma-delta analog-to-digital (ADC) converter applied to induction appliances. The proposed design is a second-order single-bit sigma-delta ADC that takes advantage of field-programmable gate array (FPGA) technology [START_REF] Lucía | A versatile power electronics test-bench architecture applied to domestic induction heating[END_REF]- [START_REF] Buccella | Digital control of power converters: A survey[END_REF] for its implementation. A design procedure is fully explained, and in order to assess the accuracy of the ADC, a calibration process with a complete set of experimental measurements is performed. As a conclusion, the proposed ADC is a costeffective and accurate solution, particularly indicated for consumer goods such as IH appliances.

One of the main difficulties when dealing with IH control systems is the highly variable load [START_REF] Pham | Dynamic analysis and control for resonant currents in a zone-control induction heating system[END_REF], [START_REF] Jiménez | FPGA-based test-bench for resonant inverter load characterization[END_REF], which makes the output power control complicated and potentially unstable. In order to address this challenge, Dominguez et al. propose in [START_REF] Dominguez | Inverse-based power control in domestic induction-heating applications[END_REF] an inverse-based control strategy. The proposed strategy combines different modulation strategies, as in [START_REF] Ahmed | High-frequency soft-switching ac conversion circuit with dual-mode PWM/PDM control strategy for high-power IH applications[END_REF], to deal with the load uncertainty and to optimize the response time while ensuring stability. As a consequence, more reliable and higher performance IH systems can be achieved.

Finally, modern control techniques of IH systems includes the control of not only the output power but also of the temperature of the IH target [START_REF] Pham | Estimating method of heat distribution using 3-D resistance matrix for zone-control induction heating systems[END_REF], [START_REF] Egalon | Multiphase system for metal disc induction heating: Modeling and RMS current control[END_REF]. For instance, advanced control scheme of IH cookers [START_REF] Lucía | Induction heating appliances: Towards more flexible cooking surfaces[END_REF] include the control of the pan temperature to provide superior user performance. To implement such feature, Imaz et al. propose in [START_REF] Imaz | Infrared thermometry system for temperature measurement in induction heating appliances[END_REF] an infrared thermometry system based on an InGaAs p-i-n photodiode to detect the pan temperature. To achieve this, a radiation model of the complete system is proposed, including the pan and the vitroceramic glass effects. The accuracy of the proposed sensor has been tested in a domestic IH system, obtaining adequate accuracy for the application with a cost-effective implementation.

ACKNOWLEDGMENT

The Guest Editors would like to thank all the authors that have submitted their valuable contributions and to the numerous and highly qualified anonymous reviewers. They think that the selected contributions, which represent the current state of the art in the field, will be of great interest to the industrial electronics community. They would like to thank Prof. C. Cecati, Editor-in-Chief of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS (TIE), for giving them the opportunity to organize this Special Section and for all the encouragement, help, and support given throughout the process, and S. McLain and A. Ul-Haq, TIE staff, for their professional support and assistance during the entire preparation of this Special Section. ÓSCAR LUCÍA, Guest Editor Group of Power Electronics and Microelectronics (GEPM) University of Zaragoza 50018 Zaragoza, Spain

TABLE I SPECIAL

 I SECTION PAPERS ACCORDING TO THEIR FOCUS ON APPLICATIONS AND ENABLING TECHNOLOGIES

PASCAL MAUSSION, Guest Editor LAboratory for PLAsma and Conversion of Energy (LAPLACE) University of Toulouse 31062 Toulouse cedex 9, France ENRIQUE J. DEDE, Guest Editor GH Electrotermia S.A. 46184 Valencia, Spain JOSÉ M. BURDÍO, Guest Editor Group of Power Electronics and Microelectronics (GEPM) University of Zaragoza 50018 Zaragoza, Spain

Óscar Lucía (S'04-M'11) received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Zaragoza, Zaragoza, Spain, in 2006 and 2010, respectively.

Since 2010, he has been a member of the Power Electronics and Microelectronics Group and an Assistant Professor with the Department of Electronic Engineering and Communications, University of Zaragoza. In 2009 and in 2012, he was a Visiting Scholar with the Center for Power Electronics Systems, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA. He is the author of more than 80 technical papers published in international journals and conference proceedings and the holder of 12 international patents and patent applications. His main research interests include resonant power converters and digital control for induction heating applications.

Dr. Lucía is an active member of the IEEE Industrial Electronics, IEEE Industry Applications, and IEEE Power Electronics Societies, participating in several conferences and committees. He is also a member of the Aragon Institute for Engineering Research. Since 2011, he has coorganized the IEEE Annual Conference of the IEEE Industrial Electronics Society Special Session on Induction Heating. Since 1991, he has been a Full Professor of power electronics with the University of Valencia and a Research and Development Director with GH Electrotermia S.A., Valencia. He is a holder of several international patents on high-frequency inverters for induction heating and the author of more than 200 papers in the field of power electronics. He has more than 30 years experience in the field of power electronics, particularly in the design of high-frequency inverters for induction heating, telecom power, and recently, in the conception and design of fast chargers for electric vehicles.

Pascal Maussion

Dr. Dede is a former member of the European Working Group of the IEEE Industry Applications Society and was the President of the joint Spanish IEEE Chapter of the Power Electronics and Industrial Electronics Societies. He is a member of the International Advisory Board of the Power Conversion Intelligent Motion Europe and Asia, and is the Vice-President of the European Power Electronics Association (EPE). He was the General Chair of the EPE European Power Electronics Conference in 2009, which was held in Barcelona, Spain.

José M. Burdío (M'97-SM'12) received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Zaragoza, Zaragoza, Spain, in 1991 and 1995, respectively.

He has been with the Department of Electronic Engineering and Communications, University of Zaragoza, where he is currently a Professor, and the Head of the Group of Power Electronics and Microelectronics. He is the author of more than 60 international journal papers and over 100 papers in international conference proceedings and the holder of more than 50 international patents. His main research interests include modeling of switching converters and resonant power conversion for induction heating applications.

Dr. Burdío is a member of the IEEE Industrial Electronics and IEEE Power Electronics Societies. He is also a member of the Aragon Institute for Engineering Research.


Martial Boggio-Pasqua
email: martial.boggio@irsamc.ups-tlse.fr

Marta López Vidal

Marco Garavelli

Theoretical mechanistic study of self-sensitized photooxygenation and singlet oxygen thermal release in a dimethyldihydropyrene derivative

Keywords:

The self-sensitized photo-oxygenation and singlet oxygen thermal release mechanisms in a pyridinium-substituted dimethyldihydropyrene (DHP) derivative have been investigated using quantum chemical calculations. First, the main photophysical pathway for intersystem crossing was identified, allowing the production of a DHP triplet state. Second, the energy transfer pathway between this triplet state and the oxygen triplet ground state was computed revealing a very efficient route for the photosensitized generation of singlet oxygen. Finally, the thermal pathway for the formation of a metacyclophanediene endoperoxide and the singlet oxygen release was characterized. A concerted and a stepwise mechanism were identified, the first one being lower in energy. All these results are consistent with recent experimental results and confirm that this type of system could be attractive oxygen carriers and singlet oxygen delivery agents.

Introduction

Singlet oxygen ( 1 O2) is one of the most important reactive oxygen species. Due to its remarkable reactivity and oxidizing property, it can be exploited in various applications ranging from chemical synthesis, waste water treatment, atmospheric chemistry, materials science, optical imaging and therapy [START_REF] Prein | The Schenck ene reaction: Diastereoselective oxyfunctionalization with singlet oxygen in synthetic applications[END_REF][START_REF] Esser | The photochemical synthesis of fine chemicals with sunlight[END_REF][START_REF] Derosa | Photosensitized singlet oxygen and its applications[END_REF][START_REF] Schweitzer | Physical mechanisms of generation and deactivation of singlet oxygen[END_REF]5,[START_REF] Fudickar | Reversible light and air-driven lithography by singlet oxygen[END_REF][START_REF] Fudickar | Imaging by sensitized oxygenations of photochromic anthracene films: Examination of effects that improve performance and reversibility[END_REF][START_REF] Zehm | Molecular switches flipped by oxygen[END_REF][START_REF] Zehm | 9,10-Diarylanthracenes as molecular switches. Syntheses, properties, isomerisations and their reactions with singlet oxygen[END_REF][START_REF] Fudickar | Photoimaging with singlet oxygen at the solid-air interface[END_REF][START_REF] Park | Photochromic metal-organic frameworks: Reversible control of singlet oxygen generation[END_REF][START_REF] Dewilde | Virucidal activity of pure singlet oxygen generated by thermolysis of a water-soluble naphthalene endoperoxide[END_REF][START_REF] Castano | Photodynamic therapy and anti-tumour immunity[END_REF][START_REF] Agnez-Lima | DNA damage by singlet oxygen and cellular protective mechanisms[END_REF]. Not surprisingly then, the control of trapping and releasing 1 O2 has become a very important topic of research in the past decades. 1 O2 is the first electronic excited state of molecular oxygen and the direct transition from its triplet ground state 3 O2 is spin forbidden. To facilitate this transition, an indirect mechanism can be achieved using photosensitizers, which are light-absorbing molecules capable of transferring a part of the photonic energy to another molecule (e.g., 3 O2) to induce an electronic transition (e.g., 3 O2→ 1 O2). As schematized in Fig. 1, in the present context, the photosensitizer in its ground electronic state S0 absorbs light to produce a singlet excited state S1, which can decay non-radiatively by intersystem crossing (ISC) to a triplet state T1. Provided that this triplet state is sufficiently high in energy and that the photosensitizer is physically close enough to 3 O2, an energy transfer process can occur producing 1 O2 and regenerating the photosensitizer in its original ground state. One way to control the release of 1 O2 is to produce chemical species incorporating molecular oxygen and capable of releasing 1 O2 in a controlled way. This aim can be achieved by the use of specific aromatic organic compounds [START_REF] Zehm | Molecular switches flipped by oxygen[END_REF][START_REF] Zehm | 9,10-Diarylanthracenes as molecular switches. Syntheses, properties, isomerisations and their reactions with singlet oxygen[END_REF][START_REF] Aubry | Kinetic studies of singlet oxygen [4+2]-cycloadditions with cyclic 1,3-dienes in 28 solvents[END_REF][START_REF] Nardello | Synthesis and properties of a new cationic water-soluble trap of singlet molecular oxygen[END_REF][START_REF] Pierlot | First evidence of the formation of 5,8-endoperoxide from the oxidation of 1,4-disubstituted naphthalene by singlet oxygen[END_REF][START_REF] Aubry | Reversible binding of oxygen to aromatic compounds[END_REF][START_REF] Fudickar | Remote substituent effects on the photooxygenation of 9,10-diarylanthracenes: Strong evidence for polar intermediates[END_REF][START_REF] Fudickar | Novel anthracene materials for applications in lithography and reversible photoswitching by light and air[END_REF][START_REF] Fudickar | Reversible photooxygenation of alkynylanthracenes: Chemical generation of singlet oxygen under very mild conditions[END_REF][START_REF] Fudickar | Why triple bonds protect acenes from oxidation and decomposition[END_REF][START_REF] Klaper | Evidence for an oxygen anthracene sandwich complex[END_REF][START_REF] Zhang | Electronic effects of ring fusion and alkyne substitution on acene properties and reactivity[END_REF] that can chemically trap 1 O2 in the form of endoperoxides (EPO) following a cycloaddition reaction. These EPOs exhibit the exceptional feature of releasing oxygen, often in its singlet excited state 1 O2, under heating or UV irradiation.

The properties of molecular switches can also be used to regulate the production of 1 O2 [START_REF] Balzani | Molecular devices and machines[END_REF][START_REF] Feringa | Molecular switches: Second, completely revised and enlarged edition[END_REF]. Supramolecular species and solid materials based on spiropyran [START_REF] Silvi | Photochemical switching of luminescence and singlet oxygen generation by chemical signal communication[END_REF] and dithienylethene [START_REF] Park | Photochromic metal-organic frameworks: Reversible control of singlet oxygen generation[END_REF][START_REF] Hou | Reversible photochemical control of singlet oxygen generation using diarylethene photochromic switches[END_REF][START_REF] Liu | A highly efficient supramolecular photoswitch for singlet oxygen generation in water[END_REF] photochromic compounds associated with an external 1 O2 photosensitizer (e.g., a metal complex or a porphyrin) were used for the reversible control of 1 O2 generation. In these systems, the production of 1 O2 is governed by the state ("on" or "off") of the photochromic unit. Very recently, photochromic dimethyldihydropyrene [START_REF] Blattmann | Photoisomerization of trans-15,16-dimethyldihydropyrene[END_REF][START_REF] Mitchell | The metacyclophanediene-dihydropyrene photochromic π switch[END_REF][START_REF] Murphy | Photophysical studies on the photochromism of trans-10b,10c-dimethyldihydropyrene[END_REF][START_REF] Sheepwash | Mechanistic insights into the photochromism of trans-10b,10c-dimethyl-10b,10c-dihydropyrene derivatives[END_REF][START_REF] Sheepwash | Mechanistic studies on the photochromism of [e]-annelated dimethyldihydropyrenes[END_REF][START_REF] Bohne | Characterization of the photochromism of dihydropyrenes with photophysical techniques[END_REF] (DHP) derivatives were also found to be efficient singlet oxygen carriers and releasing agents [START_REF] Cobo | Reactivity of a pyridinium-substituted dimethyldihydropyrene switch under aerobic conditions: self-sensitized photo-oxygenation and thermal release of singlet oxygen[END_REF][START_REF] Bakkar | A new surface-bound molecular switch based on the photochromic dimethyldihydropyrene with light-driven release of singlet oxygen properties[END_REF]. The main advantages of these DHPs over the spiropyran and dithienylethene compounds is that they do not need an external 1 O2 photosensitizer, as they photosensitize oxygen themselves, and they work using low energy (red) light. As illustrated in Scheme 1, a pyridinium-appended DHP 1 can be switched to its open-ring cyclophanediene (CPD) isomer 2 by irradiation at λ ≥ 630 nm [START_REF] Roldan | A multi-addressable switch based on the dimethyldihydropyrene photochrome with remarkable proton-triggered photo-opening efficiency[END_REF]. The reverse conversion can be achieved either by irradiation in the UV range or thermally. A solution of 1 in the absence or presence of air and exposed to such an irradiation produces compounds 2 and 2-O2 quantitatively. Upon heating at 35 °C the thermal release of 1 O2 was observed from 2-O2. Δ Scheme 1. Conversion processes between 1, 2 and 2-O2. Adapted from ref. [START_REF] Cobo | Reactivity of a pyridinium-substituted dimethyldihydropyrene switch under aerobic conditions: self-sensitized photo-oxygenation and thermal release of singlet oxygen[END_REF].

These experimental observations were interpreted with the mechanism proposed in Eqs.

(1)-( 4). Red visible irradiation of the closed isomer 1 in its ground state S0 produces its singlet excited state 1(S1), which isomerizes to 2 (Eq. ( 1)). However, the excited state 1(S1) can also non-radiatively decay by ISC to produce the triplet 1(T1) (Eq. ( 2)). The DHP in its lowest triplet state can then undergo an energy transfer process with molecular oxygen O2(T0) producing singlet oxygen O2(S1). Thus, 1 also plays the role of O2 photosensitizer (Eq. ( 3)). The photogenerated 1 O2 rapidly reacts with 2 to form the corresponding EPO 2-O2, which can release singlet oxygen upon warming (Eq. ( 4)).

1(S0) + hν → 1(S1) → 2

(1)

1(S1) → 1(T1) (2)
1(T1) + O2(T0) → 1(S0) + O2(S1) (3) O2(S1) + 2 2-O2 (4)
The purpose of the present study is to bring some mechanistic information on this mechanism using theoretical chemistry. While the photoswitching mechanism between the closed-ring DHP and the open-ring CPD isomers (Eq. ( 1)) has been investigated from a computational point of view for a number of DHP derivatives [START_REF] Williams | A DFT study of the thermal, orbital symmetry forbidden, cyclophanediene to dihydropyrene electrocyclic reaction. Predictions to improve the dimethyldihydropyrene photoswitches[END_REF][START_REF] Boggio-Pasqua | Toward a mechanistic understanding of the photochromism of dimethyldihydropyrenes[END_REF][START_REF] Boggio-Pasqua | Rationalization and design of enhanced photoinduced cycloreversion in photochromic dimethyldihydropyrenes by theoretical calculations[END_REF], including the pyridinium-appended DHP shown in Scheme 1 [START_REF] Roldan | A multi-addressable switch based on the dimethyldihydropyrene photochrome with remarkable proton-triggered photo-opening efficiency[END_REF], no theoretical study has focused on the self-sensitized photo-oxygenation and singlet oxygen thermal release of dimethyldihydropyrene derivatives (Eqs. [START_REF] Esser | The photochemical synthesis of fine chemicals with sunlight[END_REF][START_REF] Derosa | Photosensitized singlet oxygen and its applications[END_REF][START_REF] Schweitzer | Physical mechanisms of generation and deactivation of singlet oxygen[END_REF]). In this article, we report a theoretical study based on density functional theory (DFT) of the singlet to triplet intersystem crossing pathway of compound 1 (Eq. ( 2)), the subsequent energy transfer process occurring with oxygen (Eq. ( 3)), and the thermal pathway for the corresponding EPO formation (Eq. ( 4)).

Computational details

DFT and time-dependent DFT (TD-DFT) have been used to perform calculations on the ground and first excited singlet and triplet states of the isolated system 1. A model system was used by simply replacing the bulky tert-butyl groups by hydrogen atoms in order to reduce the computational cost. The B3LYP functional [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF] was used throughout along with the 6-311G(d,p) basis set [START_REF] Krishnan | Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions[END_REF], unless otherwise specified. Open-shell singlet biradical structures were computed at the broken-symmetry unrestricted B3LYP level. To account for the spin contamination, spin-projected energies have been calculated with the approximate spin-correction procedure proposed by Yamaguchi and coworkers [START_REF] Yamaguchi | A spin correction procedure for unrestricted Hartree-Fock and Møller-Plesset wavefunctions for singlet diradicals and polyradicals[END_REF][START_REF] Yamanaka | Effective exchange integrals for open-shell species by density functional methods[END_REF]. Broken-symmetry DFT calculations combined with such a spin-correction procedure was successfully used to describe the 1 O2 thermal release pathway in a model EPO [START_REF] Boggio-Pasqua | Thermolysis biradical mechanisms in endoperoxides: A challenge for density functional theory?[END_REF]. The spin-orbit coupling (SOC) between a pair of intersecting singlet and triplet states was computed at the complete active space self-consistent field (CASSCF) level using the four most relevant orbitals involved in the main electronic transitions (Fig. S1 in Supplementary material). All the optimized Cartesian coordinates and energies are collected in Table S1 in Supplementary material. All calculations were performed with Gaussian 09 [START_REF] Frisch | Gaussian 09, Revision D.01[END_REF].

Results and discussion

Electronic transitions to singlet and triplet excited states

The nature and vertical transition energies of the lowest singlet and triplet excited states of compound 1 are first described in this subsection. The optimized structure of compound 1, which belongs to the Ci symmetry point group, is presented in Fig. 2 along with the molecular orbitals involved in the main electronic transitions describing these excited states. Table 1, which collects the TD-DFT results, shows that the first two singlet excited states S1 and S2 correspond mainly to a HOMO→LUMO and a HOMO-1→LUMO transition, respectively. These states display substantial charge transfer character due to the electron withdrawing character of the pyridinium substituents and are located respectively at 1.720 and 2.122 eV vertically above the ground state S0. The corresponding absorption wavelengths are 721 nm for S1 and 584 nm for S2, in good agreement (error < 0.3 eV) with the experimental first absorption bands centered at 680 and 528 nm [START_REF] Roldan | A multi-addressable switch based on the dimethyldihydropyrene photochrome with remarkable proton-triggered photo-opening efficiency[END_REF]. These results are also in good agreement with previous TD-DFT results performed with a range-separated CAM-B3LYP functional [START_REF] Yanai | A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP)[END_REF], for which absorptions at 657 and 548 nm were computed for these two singlet states [START_REF] Roldan | A multi-addressable switch based on the dimethyldihydropyrene photochrome with remarkable proton-triggered photo-opening efficiency[END_REF]. Two triplet states were located below S1. T1 corresponds to a HOMO→LUMO transition like S1, whereas T2 is mainly described by a HOMO-1→LUMO transition like S2. The next two triplet states T3 and T4 are intercalated between S1 and S2 and correspond respectively to HOMO→LUMO+2 and HOMO→LUMO+1 transitions. ) a H and L represent the HOMO and LUMO, respectively. Amplitudes > 0.5 are given.

Singlet to triplet intersystem crossing pathway

Upon visible irradiation, DHPs are excited to singlet excited states, which decay either by fluorescence or internal conversion, formation of the corresponding CPD, and ISC to the triplet state [START_REF] Sheepwash | Mechanistic insights into the photochromism of trans-10b,10c-dimethyl-10b,10c-dihydropyrene derivatives[END_REF]. The formation of a triplet excited state is necessary for the photosensitization of oxygen. Thus, we have investigated the main photophysical pathway for ISC in compound 1.

In Fig. 3a, we report the potential energy profiles of the first three singlet and four triplet electronic states computed at the TD-DFT level along the main relaxation coordinate of the S1 state initially populated. This coordinate mainly involves a stretching of the transannular central C-C bond along with a loss of the planarity of the DHP core. The minimum on the S1 potential energy surface (PES) corresponds to a CPD precursor for CPD formation, thus associated with the initial part of the photoisomerization mechanism [START_REF] Roldan | A multi-addressable switch based on the dimethyldihydropyrene photochrome with remarkable proton-triggered photo-opening efficiency[END_REF]. Because the ISC probability will mainly depend on the energy gap between this singlet state and the triplet states, and the associated SOCs, the search for singlet/triplet crossings is interesting as they provide efficient ISC funnels provided that the SOC is non negligible. In Fig. 3a, it is clear that the T1 state remains energetically well below the S1 state at all relaxation geometries. However, the T2 state increases slightly in energy to become close to the S1 state (~0.1 eV) at the S1 minimum. As a consequence, the T2-S1 energy gap is reduced along the S1 relaxation coordinate and this behavior opens the opportunity to find a T2/S1 crossing in the vicinity of the S1 minimum. Indeed, following the T2 gradient, the T2 state crosses the S1 state only 0.04 eV above the S1 minimum, as shown in Fig. 3b, making this funnel for ISC easily accessible energetically. CASSCF calculations of the SOC between the S1 and T2 states at the T2/S1 crossing geometry reveals that it is small (2 cm -1 ) but sufficient to induce the expected ISC between S1 and T2. Thus, upon irradiation of 1(S0) at λ ≥ 630 nm, the system is excited to its first singlet excited state 1(S1), which can undergo an ISC to 1(T2). Further relaxation by internal conversion to the lowest T1 state will then proceed efficiently, as this non-radiative transition is not spin-forbidden. Thus, the photophysical pathway for triplet DHP formation can be summarized as follows:

1(S0) + hν → 1(S1) → 1(T2) → 1(T1)
(5)

Photosensitized generation of singlet oxygen

As observed experimentally, 1(T1) can be quenched by molecular oxygen to produce singlet oxygen (Eq. ( 3)). This quenching process requires an energy transfer between the triplet excited state of DHP and the triplet ground state of molecular oxygen so that DHP is deactivated back to its singlet ground state and oxygen is excited to its singlet state. To be efficient, this energy transfer step will need to be favorable both thermodynamically and kinetically. Moreover, the two reactants (i.e., 1(T1) and O2(T0)) will need to approach each other close enough, as the energy transfer efficiency decreases upon increasing the distance between the two partners.

Our DFT study provides information only on the energetics of a possible physical quenching pathway (Eq. ( 3)), its potential energy profile and the activation energy involved. Other factors governing the energy transfer such as vibronic couplings are not considered here. Thus, our study gives an indication of the feasibility of the process based on the existence of an energetically favorable route connecting the triplet-triplet (1(T1) and O2(T0)) starting reactants to the singlet-singlet (1(S0) and O2(S1)) products.

To determine a possible energy transfer path, we have performed a linear interpolation between two optimized electrostatic complexes, the relaxed triplet-triplet complex [ 3 O2 ••• 1(T1)], which represents the starting reactant, and the relaxed singlet-singlet complex [ 1 O2 ••• 1(S0)], which represents the final product. These optimized electrostatic complexes are shown in Fig. 4 and provide stable structures allowing the two partners (i.e., DHP and molecular oxygen) to be in close contact to proceed with the energy transfer. The initial position of the oxygen molecule in the two electrostatic complexes has been chosen to be consistent with the observed EPO 2-O2 where the oxygen is only observed on one exo side of the cyclophane for steric reasons [START_REF] Cobo | Reactivity of a pyridinium-substituted dimethyldihydropyrene switch under aerobic conditions: self-sensitized photo-oxygenation and thermal release of singlet oxygen[END_REF]. The structure of the DHP core in the triplettriplet [ 3 O2 ••• 1(T1)] complex is consistent with the optimized structure of 1(T1) (compare with Fig. S2 in Supplementary material), where the transannular bond length is increased by 0.035 Å compared to the ground-state structure. On the other hand, the transannular bond length in the singlet-singlet [ 1 O2 ••• 1(S0)] complex is similar to the one in 1(S0), as expected (compare with Fig. 1). Note that the relaxed structures of 3 O2 and 1 O2 remain almost identical, reflecting the fact that the interatomic distance in both states is very similar, but the distance and orientation between the oxygen molecule and the DHP core is very different in both complexes. Single-point energy calculations have been performed along the interpolated energy transfer pathway. Spin-projection on the singlet-singlet 1 (1(S0) + 1 O2) wavefunction is required to obtain a correct energy profile but for the triplet-triplet coupling (globally a singlet state wavefunction), no decontamination is needed. Due to the abrupt change in the singlet state wavefunction passing from a triplet-triplet coupling 1 (1(T1) + 3 O2) to a singletsinglet 1 (1(S0) + 1 O2) coupling description, it was possible to follow each coupling situation all along the linearly interpolated pathway. In this way, we have determined the diabatic components of the path as well as the singlet ground-state and the singlet excited-state potential energy profiles along the energy transfer path. The results are collected in Fig. 5 and suggest that the energy transfer process (physical quenching) is energetically favorable, as the product complex is located 0.091 eV below the reactant complex. In addition, the energy transfer occurs along an almost barrierless pathway with an upper limit to the barrier of only about 0.03 eV (a simple linear interpolation provides an upper boundary to the energy). Along the linear interpolation path, going from a triplet-triplet to a singlet-singlet coupling through the diabatic state crossing point, a change in the spin densities of the system occurs (see Fig. 5). Of course, our linear interpolation provides only an approximate pathway that connects reactants to products. However, the fact that we have obtained a very small barrier is a demonstration of the efficiency of such a process (at least from an energetic point of view). Thus, we can expect a very fast process for the singlet oxygen production. • 1(S0)] product complex. The blue and red curves correspond to the triplet-triplet coupling 1 (1(T1) + 3 O2) and to the singlet-singlet coupling 1 (1(S0) + 1 O2) diabatic states, respectively. The spin densities are given for each diabatic state (positive spin density in blue and negative spin density in cyan).

Thermal pathway for endoperoxide formation and singlet oxygen release

Experimentally, the DHP compound 1 irradiated with red light (λ ≥ 630 nm) under aerobic conditions is quantitatively converted into an EPO derivative, which can then thermally release singlet oxygen to regenerate the starting compound (Scheme 1) [START_REF] Cobo | Reactivity of a pyridinium-substituted dimethyldihydropyrene switch under aerobic conditions: self-sensitized photo-oxygenation and thermal release of singlet oxygen[END_REF]. In this subsection, we investigate the thermal pathway for EPO formation between the photoproduced CPD isomer 2 and singlet oxygen (Eq. ( 4)). It is important to note that 2 does not absorb the irradiation red light and thus can only react in its ground electronic state with 1 O2. This is confirmed by our TD-DFT calculation of the electronic transitions in 2, as the lowest energy π→π* bright transition is computed at 438 nm with CAM-B3LYP (Table S2 in Supplementary material) [START_REF]The TD-DFT calculation of the lowest π→π* electronic transition in 2 at the B3LYP level is inaccurate with a corresponding absorption wavelength computed at 576 nm[END_REF], in good agreement with the experimental data [START_REF] Roldan | A multi-addressable switch based on the dimethyldihydropyrene photochrome with remarkable proton-triggered photo-opening efficiency[END_REF].

To investigate the cycloaddition reaction of 1 O2 with CPD, an electrostatic complex [ 1 O2 ••• 2] was first optimized (Fig. 6 and Table S1 in Supplementary material). This complex represents the starting reactant and provides a stable structure allowing the two partners (i.e., CPD and singlet oxygen) to be in close contact to proceed with the EPO formation. The CO bond lengths are ca. 3.7 Å and the OO bond length is 1.2 Å corresponding to that of 1 O2. The 2-O2 EPO product has also been optimized (Fig. 6 and Table S1 in Supplementary material). The two CO bond lengths are 1.46 and 1.49 Å. The X-ray structure gives bond lengths of 1.51 and 1.79 Å, respectively [START_REF] Cobo | Reactivity of a pyridinium-substituted dimethyldihydropyrene switch under aerobic conditions: self-sensitized photo-oxygenation and thermal release of singlet oxygen[END_REF]. The much longer distance for the CO bond adjacent to the methyl group is not reproduced by the DFT calculation. The OO bond length is shortened to 1.46 Å in fairly good agreement with the 1.50 Å distance found experimentally.

As shown in Fig. 6, two pathways that connect [ 1 O2 ••• 2] with 2-O2 were identified corresponding to a stepwise and to a concerted mechanism. This is similar to what was found on a simple benzene EPO model system [START_REF] Boggio-Pasqua | Thermolysis biradical mechanisms in endoperoxides: A challenge for density functional theory?[END_REF]. The lowest energy path involves the concerted mechanism in which the transition state (TSconc) displays two simultaneously elongated CO bonds (~2 Å). The energy barrier of this synchronous activated process amounts to 0.61 eV, and the 2-O2 EPO product generated is lower in energy (by 0.32 eV) than the reactant [ 1 O2 ••• 2] complex. The second mechanism involving a stepwise process lies slightly higher in energy. In this case, the two CO bonds are broken sequentially. In a first step, one CO bond is formed (1.61 Å), leading to a biradical intermediate denoted Mi lying 0.73 eV above the reactant. The transition state involved along this step (TS1) lies close in energy to the Mi intermediate and corresponds to an energy barrier of 0.74 eV. In the second step, the other CO bond is being formed (2.5 Å at TS2). Note however that upon applying the spin-correction procedure, the energy barrier along this step disappears indicating that the second CO bond could be formed in a barrierless manner. Considering the lowest energy concerted mechanism, the cycloreversion process from the 2-O2 EPO will require an energy barrier of 0.93 eV, which accounts for the thermal release of singlet oxygen upon heating. The further addition of singlet oxygen on the endoperoxyde 2-O2 could potentially form a bis-endoperoxyde 2-(O2)2. Experimentally, no such bis-endoperoxyde was identified. The cycloaddition reaction of 1 O2 with 2-O2 was investigated considering the lowest energy concerted pathway, as shown in Fig. 7. First, an electrostatic complex [ 1 O2 ••• 2-O2] was optimized (Fig. 7 and Table S1 in Supplementary material) to provide the starting reactant. The CO bond lengths are ca. 3.8 Å and the OO bond length is 1.2 Å corresponding to that of 1 O2. The transition state found along the concerted path (TS'conc) displays two simultaneously elongated CO bonds (~2 Å). The energy barrier of this synchronous activated process amounts to 0.79 eV, which is 0.18 eV higher than the cycloaddition barrier of 1 O2 with 2 (compare with Fig. 6). In addition, the 2-(O2)2 bis-EPO product generated is almost isoenergetic with the reactant [ • 2-O2] complex. Thus, the calculations show that the cycloaddition of a second singlet oxygen molecule is energetically less favorable than the first one. However, when it is compared with the thermally activated 1 O2 release pathway from 2-O2, this second cycloaddition is a competitive process from an energetic point of view. The fact that the 2-(O2)2 bis-EPO product is not observed is certainly due to kinetic reasons, as the 1 O2 thermal release is a unimolecular process, while the bis-EPO formation results from a bimolecular reaction. Note also that to undergo the cycloaddition 1 O2 has only one reactive site left in 2-O2, while two sites were present in 2.

Conclusions

In this contribution, we have investigated theoretically the mechanisms of the selfsensitized photo-oxygenation and singlet oxygen thermal release in a dimethyldihydropyrene derivative following the recent experimental work of Royal and coworkers [START_REF] Cobo | Reactivity of a pyridinium-substituted dimethyldihydropyrene switch under aerobic conditions: self-sensitized photo-oxygenation and thermal release of singlet oxygen[END_REF]. These authors reported that red light irradiation (λ ≥ 630 nm) of a colored pyridinium-substituted DHP photochromic compound readily leads to the quantitative formation of the thermodynamically less stable colorless CPD form following the opening of the central C-C bond [START_REF] Roldan | A multi-addressable switch based on the dimethyldihydropyrene photochrome with remarkable proton-triggered photo-opening efficiency[END_REF]. In the presence of molecular oxygen, this DHP derivative also plays the role of an O2 sensitizer. The photogenerated 1 O2 reacts with the CPD isomer to afford the corresponding EPO-CPD species. The EPO-CPD then releases 1 O2 thermally with a high yield of ca. 85% [START_REF] Cobo | Reactivity of a pyridinium-substituted dimethyldihydropyrene switch under aerobic conditions: self-sensitized photo-oxygenation and thermal release of singlet oxygen[END_REF].

Our study is based on the computation of the relevant photophysical and chemical pathways using DFT-based methods. The first step involves the formation of a DHP triplet excited state (Eq. ( 2)), which is required for the photo-sensitization of oxygen. The main photophysical pathway for ISC was identified and involves the non-radiative decay at an easily accessible crossing between the initially excited S1 state with the T2 state. This state can then rapidly decay to the lowest T1 state by efficient internal conversion. The resulting T1 state can then be quenched by molecular oxygen to produce singlet oxygen. This second step requires an energy transfer between the triplet excited state of DHP and the triplet ground state of molecular oxygen so that DHP is deactivated back to its singlet ground state and oxygen is excited to its singlet state (Eq. ( 3)). The potential energy profile computed for this process shows that it is energetically favorable, as it involves a quasi-barrierless energy transfer. Finally, the thermal pathway for the EPO-CPD formation between the photoproduced CPD isomer 2 and singlet oxygen (Eq. ( 4)) has been computed. Two different pathways were identified, one corresponding to a concerted mechanism, while the other involves a stepwise process. The lowest energy synchronous pathway involves a barrier of 0.61 eV for the EPO formation, while a 0.93 eV barrier needs to be overcome for the thermal release of singlet oxygen by this EPO. These results are consistent with an efficient EPO-CPD formation at low radiant energies and singlet oxygen production upon warming [START_REF] Cobo | Reactivity of a pyridinium-substituted dimethyldihydropyrene switch under aerobic conditions: self-sensitized photo-oxygenation and thermal release of singlet oxygen[END_REF] and they confirm that this type of system could be attractive oxygen carriers and singlet oxygen delivery agents.

Fig. 1 .

 1 Fig. 1. Schematic diagram depicting the photosensitized excitation of oxygen in its ground triplet state ( 3 O2) to its lowest singlet excited state ( 1 O2).

Fig. 2 .

 2 Fig. 2. Optimized structure of model compound 1 and relevant molecular orbitals. Bond lengths are in Å.

Fig. 3 .

 3 Fig. 3. Potential energy profiles for (a) the first three singlet (S0, S1 and S2) and four triplet (T1, T2, T3, T4) electronic states along the S1 relaxation coordinate, and for (b) the first two singlet (S0 and S1) and second triplet (T2) electronic states along the S1 relaxation coordinate and along the T2 gradient (beyond the vertical dotted line).

Fig. 4 .

 4 Fig. 4. DFT optimized structures for (a) the triplet-triplet [ 3 O2 ••• 1(T1)] complex and (b) the singlet-singlet [1O2••• 1(S0)] complex. Bond lengths are in Å.

Fig. 5 .

 5 Fig. 5. Potential energy profiles along the energy transfer process. The energy transfer coordinate has been approximated by linear interpolation between the optimized structures of the triplet-triplet [3O2••• 1(T1)] reactant complex and the singlet-singlet [ 1O2••• 1(S0)] product complex. The blue and red curves correspond to the triplet-triplet coupling1 (1(T1) + 3 O2) and to the singlet-singlet coupling1 (1(S0) + 1 O2) diabatic states, respectively. The spin densities are given for each diabatic state (positive spin density in blue and negative spin density in cyan).

Fig. 6 .

 6 Fig. 6. DFT energies (eV) for stepwise (black) and concerted (red) thermal pathways of endoperoxide 2-O2 formation. Spin-corrected energies in normal font and non-corrected energies in parentheses. Energies given relative to the starting [1O2••• 2] complex. CO and OO bond lengths (in Å) are in red and black font, respectively.

Fig. 7 .

 7 Fig. 7. DFT energies (eV) for the concerted thermal pathway of bis-endoperoxide 2-(O2)2 formation. Spin-corrected energies in normal font and non-corrected energies in parentheses. Energies given relative to the starting [1O2••• 2-O2] complex. CO and OO bond lengths (in Å) are in red and black font, respectively.

Table 1 TD

 1

	State	Nature	Excitation	λabs /nm	Oscillator	Main transitions
			energy /eV		strength (f)	and amplitudes a
	T1(Au)	(π,π*)	1.039	n.r.	0.000	0.60(H→L)
	T2(Au)	(π,π*)	1.474	n.r.	0.000	0.55(H-1→L)
	S1(Au)	(π,π*)	1.720	721	0.101	0.66(H→L)
	T3(Au)	(π,π*)	1.831	n.r.	0.000	0.56(H→L+2)
	T4(Ag)	(π,π*)	1.919	n.r.	0.000	0.70(H→L+1)
	S2(Au)	(π,π*)	2.122	584	0.344	0.62(H-1→L

-DFT lowest energy electronic transitions in model compound 1.

  3

  1

  •• 2] complex. CO and OO bond lengths (in Å) are in red and black font, respectively.

  1

  1

Acknowledgements

This work was granted access to the HPC resources of CALMIP under the allocation 2016-[12158]. The corresponding author thanks G. Royal for fruitful discussions on this topic.

Supplementary material

Fig. S1 for a comparison between TD-DFT and CASSCF electronic structures at the T2/S1 crossing. Table S1 for Cartesian coordinates and energies of all the optimized structures. Fig. S2 for the DFT geometry of 1(T1). Table S2 for the TD-DFT lowest energy singlet electronic transitions in 2 using CAM-B3LYP.