Adrien Soupart

Fabienne Alary

Jean-Louis Heully

Paul I P Elliott

Isabelle M Dixon

Exploration of uncharted 3 PES territory for [Ru(bpy) 3 ] 2+ : a new 3 MC minimum prone to ligand loss photochemistry

We have identified a new 3 MC state bearing two elongated Ru-N bonds to the same ligand in [Ru(bpy) 3 ] 2+ . This DFT-optimized structure is a local minimum on the 3 PES. This distal MC state ( 3 MC cis ) is destabilized by less than 2 kcal/mol with respect to the classical MC state ( 3 MC trans ), and energy barriers to populate 3 MC cis and 3 MC trans from the 3 MLCT state are similar according to nudged elastic band minimum energy path calculations. Distortions in the classical 3 MC trans , i.e. elongation of two Ru-N bonds towards two different bpy ligands, are not expected to favour the formation of ligandloss photoproducts. On the contrary, the new 3 MC cis could be particularly relevant in the photodegradation of Ru(II) polypyridine complexes.

For the last four decades, [Ru(bpy) 3 ] 2+ has been at the heart of inorganic photochemistry and has been thoroughly studied for its intrinsic photophysical properties, which arise from the interplay of two excited states of different electronic nature. [START_REF] Thompson | Ru(bpy) 3 ] 2+ * and Other Remarkable Metal-to-Ligand Charge Transfer (MLCT) Excited States[END_REF] Irradiation in the visible region populates a singlet metalto-ligand charge transfer state ( 1 MLCT), which populates a [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MLCT state following quantitative intersystem crossing. This charge transfer state can deactivate radiatively (the complex is phosphorescent at room temperature), non radiatively, [START_REF] Englman | The Energy Gap Law for Radiationless Transitions in Large Molecules[END_REF] or via the population of a metal-centred state ( 3 MC). This [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC state is by nature highly distorted with respect to the ground state geometry, which is thought to be related to its capacity to quench the [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MLCT luminescence through direct crossing with the reactant's ground state surface or through photoreactivity. [START_REF] Thompson | Ru(bpy) 3 ] 2+ * and Other Remarkable Metal-to-Ligand Charge Transfer (MLCT) Excited States[END_REF] But this photoreactivity, resulting in the loss of bpy, seems unlikely to be due to classical axially-elongated [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC states repelling two pyridines from two distinct bpy ligands. The recent computational identification of several [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC minima displaying various modes of elongations in heteroleptic tris(bidentate) Ru(II) complexes evidenced the existence of novel [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC states, in which bond elongations are focused towards a single bidentate ligand (hence involving elongation of two Ru-N bonds cis to one another. This class of MC state is called 3 MC cis hereafter). This type of 3 MC minimum, only once previously reported in a photochromic Ru sulfoxide complex, [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] has been shown to be particularly prone to eject a bidentate ligand. [START_REF] Dixon | Theoretical Illumination of Highly Original Photoreactive 3 MC States and the Mechanism of the Photochemistry of Ru(II) Tris(bidentate) Complexes[END_REF] Very recently this type of geometry has also been reported to be involved in Δ/Λ isomerism, and its involvement in ligand loss was suggested. [START_REF] Feng | Triplet Ground-State-Bridged Photochemical Process: Understanding the Photoinduced Chiral Inversion at the Metal Center of [Ru(phen) 2 (L-Ser)] + and Its Bipy Analogues[END_REF] In relation with the reported (relative) photoinstability of the archetypical [Ru(bpy) 3 ] 2+ , [START_REF] Van Houten | Temperature Dependence of the Photophysical and Photochemical Properties of the tris(2,2'-bipyridyl) Ruthenium(II) Ion in Aqueous Solution[END_REF][START_REF] Durham | Photochemistry of Ru(bpy) 3 2+[END_REF][START_REF] Hoggard | Photoanation of the tris(2,2'-bipyridine) Ruthenium(II) Cation by Thiocyanate[END_REF]9,[START_REF] Gleria | Photochemistry of Tris(2,2'-bipyridine)ruthenium(II) in Chlorinated Solvents[END_REF] we were interested in testing the hypothesis that such MC states had a more general existence and could also be found in homoleptic tris(bidentate) complexes. The aim of this work was therefore to search for such a 3 MC cis minimum on the triplet excited potential energy surface of [Ru(bpy) 3 ] 2+ and we report its successful characterization here. We show that this new 3 MC cis state is only marginally higher in energy than the classical axiallyelongated [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC state, and that both 3 MC states have a similar barrier to their population from the 3 MLCT state. Thus, these novel [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC cis states are likely to have significant involvement in the photophysics and photochemistry of [Ru(bpy) 3 ] 2+ -type complexes. We may therefore need to fundamentally reassess our presumptions of how photorelease of bpy and other ligands occurs in this class of complexes, in search for a better photoreactive 3 MC candidate.

Experimental background. In the 1970s, [Ru(bpy) 3 ] 2+ was reported to undergo photolysis in the presence of coordinating solvents (e.g. water or acetonitrile) [START_REF] Van Houten | Temperature Dependence of the Photophysical and Photochemical Properties of the tris(2,2'-bipyridyl) Ruthenium(II) Ion in Aqueous Solution[END_REF] or ions (e.g. chloride [START_REF] Durham | Photochemistry of Ru(bpy) 3 2+[END_REF][START_REF] Gleria | Photochemistry of Tris(2,2'-bipyridine)ruthenium(II) in Chlorinated Solvents[END_REF] or thiocyanato [START_REF] Hoggard | Photoanation of the tris(2,2'-bipyridine) Ruthenium(II) Cation by Thiocyanate[END_REF] ). This photodegradation phenomenon was specifically studied in particularly unfavourable conditions (0.1 M HCl at 95°C) in order to allow the complete characterization and quantification of photoproducts. [START_REF] Van Houten | Temperature Dependence of the Photophysical and Photochemical Properties of the tris(2,2'-bipyridyl) Ruthenium(II) Ion in Aqueous Solution[END_REF][START_REF] Van Houten | Photochemistry of tris(2,2'-bipyridyl) Ruthenium(II) in Aqueous Solutions[END_REF] In terms of mechanism, to our knowledge, no structural data is available on [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC states of Ru(II) complexes, which are short-lived species. The population of such [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC states has been recently evidenced through characteristic signatures obtained in transient absorption spectroscopy [START_REF] Sun | Experimental Evidence of Ultrafast Quenching of the 3 MLCT Luminescence in Ruthenium(II) Tris-Bipyridyl Complexes via a 3 dd State[END_REF][START_REF] Cadranel | Spectroscopic Signatures of Ligand Field States in {Ru II (imine)} Complexes[END_REF] and time-resolved infrared spectroscopy. 14,[START_REF] Mukuta | Direct Observation of the Triplet Metal-Centered State in [Ru(bpy) 3 ] 2+ Using Time-Resolved Infrared Spectroscopy[END_REF][START_REF] Sun | Ultrafast Transient IR Spectroscopy and DFT Calculations of Ruthenium(II) Polypyridyl Complexes[END_REF] But the fact that κ 1 -bpy intermediates bearing a monodentate bpy ligand are obtained [START_REF] Gleria | Photochemistry of Tris(2,2'-bipyridine)ruthenium(II) in Chlorinated Solvents[END_REF][START_REF] Van Houten | Photochemistry of tris(2,2'-bipyridyl) Ruthenium(II) in Aqueous Solutions[END_REF][START_REF] Durham | Synthetic Applications of Photosubstitution Reactions of Poly(pyridyl) Complexes of Ruthenium(II)[END_REF] leads us to think that a specific 3 MC state is distorted in such a way as to allow for this, in line with the postulated dissociative mechanism. [START_REF] Durham | Synthetic Applications of Photosubstitution Reactions of Poly(pyridyl) Complexes of Ruthenium(II)[END_REF][START_REF] Va Nquickenborne | Ligand-Field Models and the Photochemistry of Coordination Compounds[END_REF] Methodology. In order to rationalize the photoreactivity of ruthenium complexes, one needs to map the topology of their lowest triplet potential energy surface ( 3 PES). Once the minima are localized and identified, the quantification of the energy barrier that is encountered by the system along the minimum energy path (MEP) is highly informative as it is related to the ease with which one triplet state populates another. In addition, the localization of singlet/triplet minimum energy crossing points (MECPs) is crucial because these points lead the system to closed-shell species that will either repopulate reactant GS or, according to Wigner rules, react with solvent and form the photoproduct (the latter being out of the scope of this work). [START_REF] Va Nquickenborne | Ligand-Field Models and the Photochemistry of Coordination Compounds[END_REF] This work therefore reports minima, MEPs and MECPs for [Ru(bpy) 3 ] 2+ in MeCN solution, following the same computational procedure as the one recently used to establish the 3 MLCT-3 MC energy barrier. [START_REF] Soupart | DFT Rationalization of the Room Temperature Luminescence Properties of Ru(bpy) 3 2+ and Ru(tpy) 2 2+ : 3 MLCT-3 MC Minimum Energy Path from NEB Calculations and Emission Spectra from VRES Calculations[END_REF] Only a limited number of mechanistic theoretical studies have highlighted the crucial role of distorted [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC states in photoreactive Ru(II) complexes, [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF][START_REF] Dixon | Theoretical Illumination of Highly Original Photoreactive 3 MC States and the Mechanism of the Photochemistry of Ru(II) Tris(bidentate) Complexes[END_REF][START_REF] Feng | Triplet Ground-State-Bridged Photochemical Process: Understanding the Photoinduced Chiral Inversion at the Metal Center of [Ru(phen) 2 (L-Ser)] + and Its Bipy Analogues[END_REF][START_REF] G̈ttle | Unravelling the S → O Linkage Photoisomerization Mechanisms in Cisand Trans-[Ru(bpy) 2 (DMSO) 2 ] 2+ Using Density Functional Theory[END_REF][START_REF] G̈ttle | Pivotal Role of a Pentacoordinate 3 MC State on the Photocleavage Efficiency of a Thioether Ligand in Ruthenium(II) Complexes: A Theoretical Mechanistic Study[END_REF][START_REF] Greenough | Ultrafast Photo-Induced Ligand Solvolysis of Cis-[Ru(bipyridine) 2 (nicotinamide) 2 ] 2+ : Experimental and Theoretical Insight into Its Photoactivation Mechanism[END_REF][START_REF] Ding | Excited-State Proton Transfer Controls Irreversibility of Photoisomerization in Mononuclear Ruthenium(II) Monoaquo Complexes: A DFT Study[END_REF][START_REF] Camilo | Photosolvolysis of Cis-[Ru(α-diimine) 2 (4aminopyridine) 2 2+ Complexes: Photophysical, Spectroscopic, and Density Functional Theory Analysis[END_REF][START_REF] Hirahara | Photoisomerization of Ruthenium(II) Aquo Complexes: Mechanistic Insights and Application Development[END_REF][START_REF] Tu | Selective Photodissociation of Acetonitrile Ligands in Ruthenium Polypyridyl Complexes Studied by Density Functional Theory[END_REF][START_REF] Arora | Effects of Methyl Substitution in Ruthenium Tris(2-Pyridylmethyl)amine Photocaging Groups for Nitriles[END_REF][START_REF] Nisbett | DFT Investigation of Ligand Photodissociation in [Ru II (tpy)(bpy)(py)] 2+ and [Ru II (tpy)(Me 2 bpy)(py)] 2+ Complexes[END_REF][START_REF] Salassa | Mechanism of Ligand Photodissociation in Photoactivable [Ru(bpy) 2 L 2 ] 2+ Complexes: A Density Functional Theory Study[END_REF][START_REF] Salassa | Ligand-Selective Photodissociation from [Ru(bpy)(4AP) 4 ] 2+ : A Spectroscopic and Computational Study[END_REF][START_REF] Borfecchia | Monitoring Excited State Dynamics in Cis-[Ru(bpy) 2 (py) 2 ] 2+ by Ultrafast Synchrotron Techniques[END_REF] but only three of these describe 3 MC states displaying elongations towards both bonds to the same bidentate ligand. [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF][START_REF] Dixon | Theoretical Illumination of Highly Original Photoreactive 3 MC States and the Mechanism of the Photochemistry of Ru(II) Tris(bidentate) Complexes[END_REF][START_REF] Feng | Triplet Ground-State-Bridged Photochemical Process: Understanding the Photoinduced Chiral Inversion at the Metal Center of [Ru(phen) 2 (L-Ser)] + and Its Bipy Analogues[END_REF] Computational methods. This study was performed in solvent (MeCN, as modelled by SMD) [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] since solvent significantly stabilizes [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MLCT states. [START_REF] Soupart | DFT Rationalization of the Room Temperature Luminescence Properties of Ru(bpy) 3 2+ and Ru(tpy) 2 2+ : 3 MLCT-3 MC Minimum Energy Path from NEB Calculations and Emission Spectra from VRES Calculations[END_REF] Geometry optimizations were performed with Orca 3 [START_REF] Neese | The ORCA Program System[END_REF] using the B3LYP functional, [START_REF] Lee | Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density[END_REF][START_REF] Becke | A New Mixing of Hartree-Fock and Local Density-Functional Theories[END_REF] a relativistic small-core pseudopotential on Ru (SD28), [START_REF] Andrae | Energy-Adjusted Ab Initio Pseudopotentials for the Second and Third Row Transition Elements[END_REF] the def2-TZVP(-f) basis set, [START_REF] Weigend | Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy[END_REF] and the empirical D3 dispersion correction. [START_REF] Grimme | A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu[END_REF][START_REF] Grimme | Effect of the Damping Function in Dispersion Corrected Density Functional Theory[END_REF] The restricted Kohn-Sham formalism was used for ground states, while its unrestricted analogue was used for triplet states. SCF convergence was achieved using the DIIS algorithm followed by a semi-quadratic SOSCF converger. Geometries of the minima in solvent were optimized starting from the gas phase ones. Geometries of the MECPs were optimized starting from the geometries of the corresponding 3 MC states in MeCN. Frequency calculations were run at the same level of theory and the absence of imaginary frequencies ascertained the nature of these points as minima. Mulliken spin densities on Ru were used as a straightforward descriptor of the electronic nature of the triplet excited state (~1 for a [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MLCT state, ~1.8 for a [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC state) and a full orbital analysis was conducted using Gabedit [START_REF] Allouche | Gabedit-A Graphical User Interface for Computational Chemistry Softwares[END_REF] to confirm the localization of the unpaired electrons. MEPs were optimized in SMD-MeCN with the nudged elastic band (NEB) method [START_REF] Jonsson | Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions[END_REF][START_REF] Henkelman | Methods for Finding Saddle Points and Minimum Energy Paths[END_REF] using a python module developed in the Clancy group that is interfaced with Orca. [START_REF] Herbol | Computational Implementation of Nudged Elastic Band, Rigid Rotation, and Corresponding Force Optimization[END_REF] A 10frame initial path was prepared by interpolating start and end geometries using the IDPP method. [START_REF] Smidstrup | Improved Initial Guess for Minimum Energy Path Calculations[END_REF] Minima. Up to now, the lowest triplet excited potential energy surface of [Ru(bpy) 3 ] 2+ was known to display two minima: a minimum of MLCT nature in the region of the GS equilibrium geometry, and a minimum of MC nature obtained after manual elongation of two trans Ru-N bonds (hereafter called [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC trans to highlight the elongation of two trans Ru-N bonds). [START_REF] Alary | Is the 3 MLCT the Only Photoreactive State of Polypyridyl Complexes?[END_REF][START_REF] Heully | Spin-Orbit Effects on the Photophysical Properties of Ru(bpy) 3 2+[END_REF] The rationale behind this strategy of manual distortion was guided by the ground state molecular orbitals, which indicated that the lowest of the two e g -type orbitals was of the d z2 -type (the terminology d z2 -like and d x2-y2 -like is employed for the sake of clarity, although it is not related to the actual axis systems of the states). The population of this d z2 -like orbital in the triplet excited state would thus result in the aforementioned bond elongations. The resulting trans-elongated minimum is considered to be the classical 3 MC state. Initially optimized under C 2 symmetry constraints in vacuum to reduce the computational cost, [START_REF] Alary | Is the 3 MLCT the Only Photoreactive State of Polypyridyl Complexes?[END_REF] this MC minimum is here more distorted but the characteristic elongation of two trans Ru-N bonds is maintained (2.42 and 2.53 Å, Figure 1 & Table S1). In MeCN solvent (SMD), the GS-3 MC trans gap is 2.21 eV (51.0 kcal/mol) while the [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MLCT-3 MC trans gap is 0.18 eV (4.2 kcal/mol). [START_REF] Soupart | DFT Rationalization of the Room Temperature Luminescence Properties of Ru(bpy) 3 2+ and Ru(tpy) 2 2+ : 3 MLCT-3 MC Minimum Energy Path from NEB Calculations and Emission Spectra from VRES Calculations[END_REF] These gaps are in good agreement with previous reports. [START_REF] Sun | Experimental Evidence of Ultrafast Quenching of the 3 MLCT Luminescence in Ruthenium(II) Tris-Bipyridyl Complexes via a 3 dd State[END_REF] A possible distal cis-elongated 3 MC state was searched for by building a starting geometry with two elongated Ru-N distances of ca. 2.5 Å involving a single bpy ligand, while keeping the other two bpy ligands at more classical Ru-N distances (2.08-2.18 Å). The angle between the mean planes of these two ligands was also increased to ca. 130° to mimic the flattened geometry observed in a related series of bi(triazolyl) (btz) complexes. [START_REF] Dixon | Theoretical Illumination of Highly Original Photoreactive 3 MC States and the Mechanism of the Photochemistry of Ru(II) Tris(bidentate) Complexes[END_REF] This geometry gently optimized to a minimum, as testified by the absence of imaginary frequencies in the calculation. Due to the steric clash between α-hydrogen atoms in bpy ligands, the equilibrium geometry of the [Ru(bpy) 3 ] 2+ distal 3 MC ( 3 MC cis ) is not as flat as with btz (which does not induce such a steric clash), and a final interligand angle of 121° is observed in the opposite quadrant with respect to the distal ligand (Figure 1). The distal bpy displays final Ru-N distances of 2.38 and 2.53 Å. The other two bpy ligands display final Ru-N distances of 2.09 and 2.17 Å. Note that Ru-N1 and Ru-N5 are necessarily elongated in [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC trans as a consequence of the major elongations observed on the two attached pyridines (Ru-N4 and Ru-N3). On the other hand, Ru-N4 (and to a lesser extent Ru-N2) are elongated in [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC cis as a result of direct antibonding interactions with two lobes of the d x2-y2 -like dσ* orbital. Remarkably, the distal 3 MC cis state is only 0.08 eV destabilized (1.9 kcal/mol) with respect to the classical 3 MC trans state. Overall the 3 MC cis state displays four elongated Ru-N bonds (two elongations of which are more pronounced) with respect to the GS geometry, and results from the occupation of a d x2-y2 -like antibonding orbital (Figure 2). As shown on Figure 3, the singly occupied natural orbitals of these two 3 MC minima, [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC trans and 3 MC cis , display clear d z2 -like and d x2-y2 -like features that are responsible for the observed geometric distortions in these excited states. These d-orbital contributions match those for singly occupied natural orbitals for 3 MC states for [Ru(N^N)(btz) 2 ] 2+ complexes reported recently (N^N = bpy, 4-(pyrid-2-yl)-1,2,3-triazole). [START_REF] Dixon | Theoretical Illumination of Highly Original Photoreactive 3 MC States and the Mechanism of the Photochemistry of Ru(II) Tris(bidentate) Complexes[END_REF] Figure 2. Schematic antibonding interactions in the classical [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC trans (d z2 -like, left) and in the new [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC cis (d x2-y2 -like, right) minima (Ru atom not shown). The dashed lines signify the approximate planes of the two other bpy ligands for 3 MC cis . Remarkable Ru-N distances and N-Ru-N angles with B3LYP-D3 in SMD-MeCN.

Minimum energy paths (MEPs).

We have previously shown that the nudged elastic band (NEB) method, [START_REF] Jonsson | Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions[END_REF][START_REF] Henkelman | Methods for Finding Saddle Points and Minimum Energy Paths[END_REF] which derives from a chain-of-states approach, [START_REF] Liotard | Critical Paths and Passes: Application to Quantum Chemistry[END_REF][START_REF] Liotard | Algorithmic Tools in the Study of Semiempirical Potential Surfaces[END_REF] is a powerful method to probe the topology of the 3 PES. [START_REF] Soupart | DFT Rationalization of the Room Temperature Luminescence Properties of Ru(bpy) 3 2+ and Ru(tpy) 2 2+ : 3 MLCT-3 MC Minimum Energy Path from NEB Calculations and Emission Spectra from VRES Calculations[END_REF][START_REF] G̈ttle | Pivotal Role of a Pentacoordinate 3 MC State on the Photocleavage Efficiency of a Thioether Ligand in Ruthenium(II) Complexes: A Theoretical Mechanistic Study[END_REF] This type of method determines the minimum energy path and provides the activation barrier encountered along this MEP, with no apriorism regarding the geometry of a transition state (explicit searching for which is not required). Further confirmation of the quality of the 3 MEP computed using the NEB method came from transition state optimization starting from the NEB crests, which converged smoothly at similar energies and geometries. [START_REF] Soupart | DFT Rationalization of the Room Temperature Luminescence Properties of Ru(bpy) 3 2+ and Ru(tpy) 2 2+ : 3 MLCT-3 MC Minimum Energy Path from NEB Calculations and Emission Spectra from VRES Calculations[END_REF] In this work, MEPs have been computed in solvent between the three triplet excited state minima (Table S2). As schematized in Figure 4, the 3 MLCT-3 MC trans and 3 MLCT-3 MC cis barriers are similar at 9 and 10 kcal/mol respectively, whilst the 3 MC trans -3 MC cis barrier only amounts to 2 kcal/mol. Figure 4. Energy profiles for the 3 MLCT-3 MC trans (blue) and 3 MLCT-3 MC cis (red) conversions following two distinct reaction coordinates. The green dashed line schematizes the direct 3 MC trans -3 MC cis conversion with a 2 kcal/mol barrier.

Minimum energy crossing points (MECPs).

The existence of singlet/triplet MECPs in the vicinity of a 3 MC minimum is well established and provides an efficient nonradiative deactivation funnel. In [Ru(bpy) 3 ] 2+ , the MECP between the classical 3 MC trans state and the ground state PES was described in 2009 in vacuum, 46 lying 7 kcal/mol (0.3 eV) above the 3 MC minimum after further geometrical distortions along the GS  3 MC reaction coordinate. This MECP is called MECP trans hereafter. At the current level of theory, MECP trans is found 6.2 kcal/mol above the 3 MC trans minimum. Having now characterized another [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC state, we also searched for the MECP between this 3 MC cis state and the ground state PES. This crossing point, called MECP cis , was found to lie only 1.3 kcal/mol above 3 MC cis . The two MECPs are distinct and MECP cis is lower in energy than MECP trans by 3 kcal/mol. Table S1 displays selected geometrical parameters and Table S3 displays the singly occupied natural orbitals (SONOs) of the cis and trans 3 MECPs, showing the orbital parentage between each 3 MC minimum and its corresponding MECP. These two MECPs connect the 3 PES to the reactant GS PES, but others would bring the system further towards photoreactivity, once the system has entered the region where pentacoordinate species are accessible. This was hypothesized in ref. [START_REF] G̈ttle | Pivotal Role of a Pentacoordinate 3 MC State on the Photocleavage Efficiency of a Thioether Ligand in Ruthenium(II) Complexes: A Theoretical Mechanistic Study[END_REF] and further developed in ref. [START_REF] Dixon | Theoretical Illumination of Highly Original Photoreactive 3 MC States and the Mechanism of the Photochemistry of Ru(II) Tris(bidentate) Complexes[END_REF] Impact on the photoreactivity of [Ru(bpy) 3 ] 2+ . The formation of bis(bipyridine) ligand-loss photoproducts from the reaction of [Ru(bpy) 3 ] 2+ in the presence of coordinating solvents or anions indicates that the complex is able to lose one bpy ligand after photoexcitation, albeit in very low yield under normal experimental conditions. Photoinduced ligand loss is triggered by the population of dissociative excited states. As shown in Figure 1, the classical 3 MC trans state displays two elongated trans Ru-N bonds. As such, it does not seem to be prone to lose one bpy ligand, although we may not completely exclude it from all possible photoreactivity mechanisms. On the other hand, the newly identified distal [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC cis excited state displaying major bond elongations towards a single bpy ligand may be expected to evolve towards photoproducts involving loss of bpy. Mechanistically, the new 3 MC cis is equivalent to previously described flattened [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MC states, [START_REF] Dixon | Theoretical Illumination of Highly Original Photoreactive 3 MC States and the Mechanism of the Photochemistry of Ru(II) Tris(bidentate) Complexes[END_REF] in that it could be the last step before ligand decoordination and diffusion. In any case, the comparative ease with which both 3 MC trans and 3 MC cis states will be populated from the [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MLCT state, and the highly accessible MECP for the latter, mean that hitherto unrecognised 3 MC cis states will undoubtedly play a major role in the photophysics and excited state deactivation dynamics of [Ru(bpy) 3 ] 2+ and related complexes.

Conclusion.

A 3 MC state displaying one distal bpy ligand was identified and optimized to a minimum for [Ru(bpy) 3 ] 2+ . This distal MC state ( 3 MC cis ) is destabilized by less than 2 kcal/mol with respect to the classical MC state ( 3 MC trans ). The 3 MLCT-3 MC trans and 3 MLCT-3 MC cis barriers are both ~10 kcal/mol in acetonitrile solution, and the 3 MC trans -3 MC cis barrier is as low as 2 kcal/mol. These figures are larger than those recently reported for photoreactive Ru bi(triazolyl) derivatives, [START_REF] Dixon | Theoretical Illumination of Highly Original Photoreactive 3 MC States and the Mechanism of the Photochemistry of Ru(II) Tris(bidentate) Complexes[END_REF] in line with the much greater photostability of [Ru(bpy) 3 ] 2+ . Nevertheless the very existence of the distal 3 MC cis state as a local minimum, and its accessibility, may have broad implications in our understanding of the photochemistry and photophysics of [Ru(bpy) 3 ] 2+ and related complexes. The lowest 3 PES is clearly far more complex than previously appreciated and previous presumptions regarding excited state processes involved in photoreactivity may therefore require some reassessment. At this moment the existence of other 3 MC minima cannot be excluded, and we are currently exploring photoreactivity mechanisms in relation with the observed photochemistry of [Ru(bpy) 3 ] 2+ . Supporting Information. Computational details regarding NEB calculations; selected geometrical parameters and total energies; NEB minimum energy paths (MEPs) and Mulliken spin population on Ru along the MEPs; singly occupied natural orbitals for 3 MC states and associated MECPs (PDF). Cartesian coordinates (xyz).

TOC graphic

A new 3 MC minimum displaying bond elongations towards a single ligand is described ( 3 MCcis). According to NEB calculations of the minimum energy paths, this new state is equally accessible from the [START_REF] G̈ttle | Adiabatic Versus Nonadiabatic Photoisomerization in Photochromic Ruthenium Sulfoxide Complexes: A Mechanistic Picture from Density Functional Theory Calculations[END_REF] MLCT state than the well-known dz 2 -like 3 MC state ( 3 MCtrans). This new electronic excited state should be relevant in the photodecomposition of Ru(bpy) 3 2+ .

Figure 1 :

 1 Figure 1: Structures of optimized 3 MC trans and 3 MC cis (B3LYP-D3, SMD-MeCN; Ru label not shown). Ru-N distances in angstroms.

Figure 3 . 3

 33 Figure 3. 3 MC singly occupied natural orbitals.

ACKNOWLEDGMENT

We thank the French Ministry for Higher Education and Research for a Ph. D. fellowship to AS. This work was performed using HPC resources from CALMIP (Grant 2017-[p1112]). PE also acknowledges the University of Huddersfield for supporting this work.

AUTHOR INFORMATION

Corresponding Authors * P.I.Elliott@hud.ac.uk * isabelle.dixon@irsamc.ups-tlse.fr

Author Contributions

The manuscript was written through contributions of all authors.

Funding Sources

No competing financial interests have been declared.


Isabelle M Dixon
email: isabelle.dixon@irsamc.ups-tlse.fr

Jean-Louis Heully

Fabienne Alary

Paul I P Elliott
email: p.i.elliott@hud.ac.uk

Theoretical illumination of highly original photoreactive 3 MC states and the mechanism of the photochemistry of Ru(II) tris(bidentate) complexes

)) have been optimised by density functional theory (DFT) and characterised. There is a gradual and significant destabilisation of the 3 MLCT states as the triazole content of the complexes increases, which occurs with a slight stabilisation of the 3 MC states. Whilst consistent with the promotion of photochemical reactivity in the heteroleptic complexes of the series relative to 1, these classical 3 MC states fail to account for the extraordinary ligand rearrangement processes that accompany ligand ejection.

Thorough theoretical exploration of the lowest excited triplet potential energy surface ( 3 PES) here reveals the 2 existence of a new type of 3 MC state and the role it plays in the photochemical reactivity of the complexes. This newly discovered state, called MC(F), displays a flattened geometry (indicated by the 'F' in the parentheses) which makes it clearly on the path to achieving the coplanarity of the bidentate ligands in the experimentally observed trans-photoproduct. Further novel 'pentacoodinate' 3 MC states with coplanar bidentate ligands, called MC(P) (where the 'P' in the parentheses denotes the pentacoordinate character), were then identified and optimised. The energy barriers between the different triplet states were confirmed to be small which makes all triplet states accessible. Solvent trapping, which occurs on the singlet PES according to Wigner's rules, is finally achieved by a singlet pentacoordinate species to yield the monosolvento photoproduct. Thus, our calculations not only reveal highly novel 3 MC states but more significantly demonstrate their crucial role in the formation of the experimentally observed photoproducts.

Introduction

The photophysics and photochemistry of oligopyridyl complexes of kinetically inert d 6 metals has been the subject of intense investigation over the past four decades. 1,[START_REF] Balzani | Photochemistry and Photophysics: Concepts, Research, Applications[END_REF] Of renewed interest in systems of this type is the interplay between the initial photoexcited metal-to-ligand-charge transfer (MLCT) states responsible for their characteristic singlet absorption ( 1 MLCT) and luminescent triplet emission [START_REF] Brown | [END_REF][4][5] ( 3 MLCT) and their triplet metalcentred ( 3 MC) states [6][7][8][9][10][11][12][13][14][15][16][17] that are responsible for deactivating said emission by nonradiative quenching. These [START_REF] Brown | [END_REF] MC states can also be intimately involved in photochromic rearrangement and ligand dissociation reactions, a subject that we are particularly interested in.

As an example of a typical luminescent complex the occupied frontier orbitals of [Ru(bpy) 3 ] 2+ -type complexes 42 are predominantly metal-based while the LUMO is bpy * in character with the LUMO+1 and LUMO+2 orbitals having d-bpy* character. Thus the lowest energy features of the optical absorption spectra of these complexes are typically of 1 MLCT character through promotion of an electron from these metal-based orbitals to an unoccupied ligand dominated orbital (process a in Figure 1a and1b). Rapid intersystem crossing due to the presence of the heavy metal centre results in efficient conversion to the triplet [START_REF] Brown | [END_REF] MLCT state (process b). It is then radiative decay from the [START_REF] Brown | [END_REF] MLCT state that leads to the characteristic phosphorescent emission (process c). Being in close proximity, [START_REF] Brown | [END_REF] MC states can be thermally populated from the [START_REF] Brown | [END_REF] MLCT state (process d), resulting in quenching of emission and even photochemical reactivity through the weakening and elongation of metal-ligand bonds. This can therefore result in isomerisation or ligand loss reactions.

These excited states and transitions between them are often depicted using a Jablonski diagram (Figure 1a) familiar from undergraduate lectures. However, the traditional Jablonski diagram is often inadequate to satisfactorily convey the true energetics of the processes occurring as it disregards the structural distortions between ground and excited states. Indeed the [START_REF] Brown | [END_REF] MC states are depicted as being higher in energy than the [START_REF] Brown | [END_REF] MLCT states in a traditional Jablonski diagram (i.e. the 3 MC state at the 3 MLCT geometry), however geometry relaxation through Ru-N bond elongation can lead to the relaxed [START_REF] Brown | [END_REF] MC state being at lower energy than the relaxed [START_REF] Brown | [END_REF] MLCT state. 6,[42][43][44] Instead, potential energy curve descriptions (Figure 1b) are more intuitively informative. Here the reaction coordinate (r.c.) may be defined by the Ru-N bond lengths for example, and thus takes into account geometrical rearrangement after excitation. Over the last few years theoretical work has illuminated what can now be considered classical [START_REF] Brown | [END_REF] MC states in which the population of a d* orbital leads to a Jahn-Teller type distortion in which two mutually trans Ru-N bonds become elongated to yield a [Ru( 2 -N^N)( 1 -N^N) 2 ] 2+ -like structure. The efficiency of [START_REF] Brown | [END_REF] MC population is determined by the magnitude of the activation barrier following the [START_REF] Brown | [END_REF] MLCT  3 MC minimum energy path (MEP), as well as by the overall topology of the [START_REF] Brown | [END_REF] PES and the vibrational energy within the system. Chart 1. Structures of the complexes computationally investigated in this study (in our experimental studies R = benzyl, but to limit computational expense in the calculations R is simplified to methyl).

Complexes of 1,2,3-triazole-based ligands 45,46 have revealed an extraordinary diversity in photophysical and photochemical properties, ranging from highly tunable phosphors [47][48][49][50][51][52][53][54] for light-emitting devices to efficient sensitisers for dye solar cell applications. 55 We have demonstrated that the inclusion of bitriazolyl (btz) ligands 56- 59 leads to photochemical ejection of btz for ruthenium(II) complexes, [60][61][62][63][64] and far more extraordinarily, for osmium(II) which one would expect to be photochemically inert. 65 In the series of complexes [Ru(bpy) 3- n (btz) n ] 2+ (n = 0, 1; n = 1, 2; n = 2, 3; n = 3, 5; Chart 1) 66 and the pyridyltriazole (pytz) analogue 4, 60 absorption bands are observed to progressively blue-shift from 1 to 3 as the bpy-centred LUMO becomes destabilised. The absorption profile then undergoes a dramatic blue-shift for 4 and then 5, reflecting the much higher energies of the LUMO of the pytz and btz ligands relative to that of bpy. Timedependent DFT (TD-DFT) calculations at the ground state geometry reproduce this experimental data and confirm the bpy-localisation of the S 1 1 MLCT states for 2 and 3. It is noteworthy that the nature of the S 1 state switches from 1 MLCT to 1 MC in character for complex 5. Thus the destabilisation of the LUMO occurs to such an extent in this complex that the ordering of the lowest energy excited states is reversed. When optimised the lowest lying triplet states of 4 and 5 are indeed of MC nature and adopt a classical [Ru( 2 -N^N)( 1 -btz) 2 ] 2+ structure (N^N = pytz and btz respectively) in which two trans Ru-N bonds elongate by ca. 0.4 Å.

[Ru(pytz)(btz) 2 ] 2+ (4),
We have recently reported the photochemical ligand ejection reactivity of 2, 3 and 4 with efficient conversion to the bis-solvento complexes and liberation of an equivalent of free btz (Scheme 1). [60][61][62][63] This is consistent with the destabilisation of the [START_REF] Brown | [END_REF] Scheme 1. Photochemical reactivity of 2, 3 and 4 in acetonitrile solutions. 60,62,63 It is noteworthy that the key actors involved in the mechanism for ligand photorelease from ruthenium complexes have been studied theoretically with monodentate departing ligands only, using a combination of unrestricted DFT and TD-DFT. 29,30,32,33,[67][68][69][70][71] This reaction proceeds along a rather intuitive reaction coordinate, i.e. Ru-L elongation, which can be probed by relaxed surface scans. 29,30,32,33,69 Mechanistic studies have emphasized the complexity and the multistep nature of ligand photolabilisation processes. 30,67,70,71 However, following an in-depth study of the 3 PES, we have identified new structural isomers of the 3 MC state and have shown that, in addition to bond elongation, the reaction may also involve an offset of the departing ligand from its initial coordination axis. 70 Despite the tremendous importance of Ru(II) complexes in sensing, solar cells or PDT to name a few of their applications, relatively little is known regarding the triplet excited state dynamic processes that result in desired (photorelease) or undesired (photoinstability) photolabilisation of bidentate ligands from Ru(II) complexes. Therefore it is still a real challenge to establish the mechanism of bidentate ligand photorelease from Ru(II) complexes.

The aim of this work was to study the mechanism of such photorelease processes by theoretical approaches. In this contribution we report theoretical characterisation of 3 MC states of these complexes, with a particular emphasis on those relevant to photochemical reactivity for 3 and 4. The topology of their [START_REF] Brown | [END_REF] PES was initially probed by series of relaxed surface scans. In addition to characterisation of classical [Ru( 2 -N^N)( 1 -N^N) 2 ] 2+ -type 3 MC states, these scans have led us to identify a new type of [START_REF] Brown | [END_REF] MC state in which two Ru-N bonds to the same btz ligand are elongated whilst the N-Ru-N angle for the Ru-N bonds trans to the 'distal' btz ligand undergoes significant enlargement, thus flattening the Ru( 2 -N^N)( 2 -btz) fragment towards coplanarity (where N^N is bpy or pytz). To probe this hypothesis, we have then accentuated the flattened geometries, which were optimized to yield pseudo-pentacoordinate square pyramidal [START_REF] Brown | [END_REF] MC local minima for complexes 3 and 4. These states, which display coplanar bidentate ligands as observed in the photoproducts, have low energy singlet/triplet minimum energy crossing points enabling access to a square-pyramidal pentacoordinate singlet ground state with a solvent accessible coordination site. Through the use of Nudged Elastic Band calculations, we then show that this new flattened [START_REF] Brown | [END_REF] MC state is readily accessible on the 3 PES with a small activation barrier to conversion from the [START_REF] Brown | [END_REF] MLCT state. Solvent capture should be facilitated by a coordinatively unsaturated complex. We therefore not only identify highly novel and as yet unrecognised class of [START_REF] Brown | [END_REF] MC states, but also elucidate the mechanism of the experimentally observed trans photochemistry for these complexes, accounting for the highly unusual novel concomitant rearrangement occurring during these photodechelation reactions in coordinating solvents.

Results & Discussion

MLCT and 'classical' MC minima

The optimised geometries of the lowest 3 MLCT states for complexes 1 to 3 (1 3 MLCT to 3 3 MLCT) were calculated starting from their optimised ground states and specifying a spin multiplicity of 3. In agreement with the observed blue-shift in the 1 MLCT band in their UV-visible absorption spectra, the [START_REF] Brown | [END_REF] MLCT states 1 3 MLCT to 3 3 MLCT are destabilised by approximately 0.1 eV for each replacement of bpy by btz (Figure 2). Plots of the spin density for 2 3 MLCT and 3 3 MLCT confirm the localisation of the photoexcited electron on the bpy ligands (Figure S1). As was stated on our original report 66 For the pyridyltriazole complex 4 the optimisation of the T 1 state yields a 3 MC state. 60 A TDDFT calculation at the ground state geometry, however, indicated a T 1 state of 3 MLCT character. This state, 4

3 MLCT, was determined by TDDFT to lie 2.97 eV above the ground state and is intermediate in energy between 3 3 MLCT and 5 3 MLCT-D 3 .

For complexes 1 to 3 3 MC state geometries were calculated (see Figure 3) through optimisations starting from initial estimate geometries; firstly, the localisation of the d z 2 -like and d x 2 -y 2 -like antibonding dσ* orbitals for the ground states were examined to identify the participating Ru-N bonds (see Figure S2). For each complex, a pair of initial estimate geometries were then prepared by elongation of the principal participating Ru-N bonds to 2.4-2.5 Å. These geometries were then allowed to optimise with a spin multiplicity of 3. In every case, classical

[Ru( 2 -N^N)( 1 -N^N) 2 ]
2+ type geometries are obtained with two mutually trans elongated Ru-N bonds. Selected structural parameters are reported on Figure 3 and in Table S1. Mulliken spin densities for these 3 MC states were also plotted and are presented in Figure S3.

For 1 both initial estimate geometries resulted in isostructural [START_REF] Brown | [END_REF] MC states with elongated Ru-N bond lengths of 2.46 Å, reproducing our previously reported calculated structures for this complex and similar to that found for [Ru(bpz) 3 ] 2+ (bpz = 2,2'-bipyrazine). 42,43 In addition to bond elongation, the 3 MC state of 1 displays a significant rotation of the decoordinated pyridine ring relative to the coordinated ring with a N-C-C-N dihedral angle of 13.2 ° (Table S1).

In the cases of the heteroleptic complexes 2 and 3, this resulted in a pair of 3 MC states for each; one of these [START_REF] Brown | [END_REF] MC states is approximately C 2 symmetric (termed 3 MC(A) in each case: 2 3 MC(A) and 3 3 MC(A))

involving dechelation of both bpy ligands in the case of 2 and both btz ligands in the case of 3. A similar elongated Ru-N bond distance and twist in the  1 -bpy ligands to that observed for 1 3 MC is found for 2 3 MC(A)

(2.46 Å and 10.9 °). This elongation occurs to a greater extent in

Relaxed 3 PES scans leading to new flattened 3 MC states

For these complexes, optimisation of3 MC minima in itself does not provide any significant mechanistic insight into the photochemical reactivity of the complexes described, but does give a clear view of the complexity of the 3 PES. In particular, classical [START_REF] Brown | [END_REF] MC states fail to account for the observed rearrangements in the photochemistry of 3 and 4, in which the remaining bidentate ligands become coplanar. Therefore, to gain a deeper understanding of the excited state dynamics in these photochemically reactive systems, we turned our attention to probing the topology of the 3 PES connecting the 3 MLCT and 3 MC states. We initially conducted relaxed [START_REF] Brown | [END_REF] PES scans starting from the [START_REF] Brown | [END_REF] MLCT geometries in an attempt to map the landscape of the triplet manifold and obtain an indication of the magnitude of energy barriers for 3 MC state population.

For complexes 2 and 3, where the T 1 state has [START_REF] Brown | [END_REF] MLCT character at the ground state geometry, relaxed

In the case of 2, relaxed 3 PES scans involving elongation of one of the Ru-N(bpy) ligands cis to btz and one of the Ru-N(btz) bonds leads to formation of the expected geometries for 2 3 MC(A) and 2 3 MC(B)

respectively with energy barriers of ~0.04 to 0.05 eV (1 kcal mol -1 ) (Figure S4). For complex 3, whilst elongation of one of the Ru-N(btz) bonds trans to bpy yields the expected 3 3 MC(B) state (Figure S5), it is highly noteworthy that the 3 PES scan involving elongation of one of the mutually trans Ru-N(btz) bonds fails to arrive at 3 3 MC(A) but instead yields an entirely new [START_REF] Brown | [END_REF] MC state (Figure 4a, blue energy profile); as bond a as defined in Figure 4a 3. These data suggest that depopulation of the [START_REF] Brown | [END_REF] MLCT state and population of the 3 MC states is irreversible and that the three 3 MC states (A, B and F-type) are connected to one another.

Similar behaviour was observed by Zhou et al. in their [START_REF] Brown | [END_REF] PES scans in triscyclometalated iridium(III) complexes. 72 After population the 3 MC states may then either undergo direct deactivation to the ground state, or may go on to yield the observed  1 -btz photochemical reaction product. For complex 4, a series of relaxed 3 PES scans were carried out for contraction of the extended Ru-N bonds a through f starting from each of the respective classical 3 MC state geometries (Figure S6). Figure 4b summarises the interconversions that are observed to occur during these calculations. Crucially we observe that contraction of bond c starting from 4 3 MC(A) and bond b starting from 4 3 MC(B) both lead to an analogous flattened [START_REF] Brown | [END_REF] MC state, 4 3 MC(F), whose geometry was then optimised to a true minimum on the basis of these scans without geometric constraints (Figure 5 right and Table S2).

Whilst no such state is observed in the course of the 3 PES scans for 2 (Figure S4) we utilised the geometric parameters for 3 3 MC(F) and 4 3 MC(F) in order to derive a suitable estimate geometry for optimisation of the analogous state 2 3 MC(F), which we were indeed able to locate (Figure 5 left and Table S2).

Attempts were made to locate a similar state for 5 but without success with optimisations resulting in a classical 5 3 MC geometry.

Geometric and electronic structure of the new flattened 3 MC states

The extended Ru-N bonds to the distal btz ligands vary from 2.39 to 2.53 Å in the three 3 MC(F) states with N-Ru-N angles  (between the Ru-N bonds that were trans to the now distal btz ligand) ranging from 124.5

 for 2 3 MC(F) to 136.1  for 3 3 MC(F) (Figure 5 and Table S2). For each 3 MC(F) state, plots of the spin density demonstrate that the unpaired electrons are primarily localised on the metal centre thereby confirming their 3 MC character (Figure S3). The observation in our calculations of these 3 MC(F)-type flattened states demands explanation. In Flattening of the M(L^L) 2 fragment where the ligands in the ground state are approximately orthogonal has been characterised in calculations on trigonal bipyramidal formally pentacoordinate 3 MC states, for example, for triscyclometalated iridium(III) complex [START_REF] Brown | [END_REF] MC states of the type [Ir( 2 -C^N) 2 ( 1 -C^N)] where the  1 -C^N ligand is indeed monodentate and dechelated with a large dihedral angle between the planes of the two rings of the dechelated ligand. 73 Flattening has also been observed in calculations on pentacoordinate ruthenium(II) species 67 but examples of this behaviour in "hexacoordinate" 3 MC states are almost unknown. This type of flattening has been observed previously in ruthenium(II) [START_REF] Brown | [END_REF] 20 In our experimental photochemistry only ejection of the btz ligands is observed, which clearly indicates the need for participating [START_REF] Brown | [END_REF] MC states to involve elongation of Ru-N bonds to the departing btz ligand. This prompted us, however, to investigate whether an analogous flattened 3 MC state could be found for 3 in which the distal ligand is now bpy. After several attempts such a geometry was optimised (3 3 MC(F)', Figure S7) and lies some 0.3 eV higher in energy than 3 3 MC(F) and is therefore unlikely to be populated. We attribute this destabilisation to the greater -acceptor character of the bpy ligand over btz, which reduces the propensity for the elongation of Ru-N(bpy) bonds (c.f. the significantly shorter Ru-N(bpy) distances compared to the Ru-N(btz) distances in the geometries of 2 3 MC(B) and 3 3 MC(B), Figure 3). With regards to the mechanism of photochemical ejection that is experimentally observed for the btz ligands detailed here, 3 MC(F)'-type states with a distal bpy or pytz ligand are thus discounted in our discussion. We should also note that an alternative 3 MC(F)-type state can be envisage in the case of 4 in which the btz lying trans rather than cis to the pyridine ring of the pytz ligand adopts the distal position. Since this alternative state is not seen in our [START_REF] Brown | [END_REF] PES scan studies described earlier this is also discounted from further discussion.

Nonradiative deactivation of classical and flattened 3 MC states via singlet-triplet ISC

To probe the propensity of the complexes for nonradiative deactivation, we then optimised the singlettriplet minimum energy crossing points ( 1,3 MECPs) 74,75 for all classical and new flattened 3 MC states of the photoreactive complexes 2, 3 and 4 (Table 1). Singlet state geometry optimisations starting from the 1,3 MECP geometries for the classical [START_REF] Brown | [END_REF] MC states for these complexes results in the full recoordination of the ligands and relaxation to the initial ground state geometry in each case. Therefore, MECPs(A/B/C) bring the system back to its initial reactant state.

The 1,3 MECP for 3 3 MC(F) (3

Pseudo-pentacoordinate triplet and pentacoordinate singlet states

Following this line of reasoning, initial guess geometries for further [START_REF] Brown | [END_REF] MC states were derived from those of 3 3 MC(F) and 4 3 MC(F) in which the Ru(N^N)( 2 -btz) fragments were set to be approximately co-planar, as in the primary photoproducts. For both 3 3 MC(F) and 4 3 MC(F) the N donor atoms of the triazole ring of the distal btz ligand with the shortest Ru-N distance was positioned in the approximate square pyramidal axial position. Triplet state optimisation then allowed us to obtain the geometries of two new 3 MC minima 3 3 MC(P) and 4 3 MC(P) (where the "P" denotes the pseudo-pentacoordinate nature of these states, Figure 7 and Table S2).

The distal btz in Geometries for the 1,[START_REF] Brown | [END_REF] MECPs associated with 3 3 MC(P) and 4 3 MC(P), i.e. 3 MECP(P) and 4 MECP(P), were optimised and are located 0.05 and 0.09 eV higher in energy than their respective 3 MC state minima (Figure 7). These highly accessible MECPs are the connection between the reactive 3 PES and a singlet PES suitable for Wigner-allowed solvent trapping. Strikingly, singlet state geometry optimisation starting at these 1,3 MECP(P)s yields formally pentacoordinate, distorted square pyramidal species 3 1 GS(P) and 4 1 GS(P) (Figure 7 and Table S2), which are the missing link to the photoproducts and were hypothesized in previous work. 70 In each case the distal btz ligand now adopts a formally monodentate coordination mode with a Ru-N bond length of approximate 2.05 Å and exhibits a significant torsion angle between the planes of the two triazole rings. Although initially discussed in the context of excitation into MC states, the importance of MECP(P) was already highlighted in 1983, as formulated by Vanquickenborne and Ceulemans for d 6 complexes: 'Nowhere in the triplet state, is a vacant orbital available to facilitate nucleophile attack. In fact, the only species able to restore the low-spin ground state of the hexacoordinated products is the singlet square pyramidal ground state, via a vacant orbital on its empty coordination site. This association therefore presupposes triplet + singlet intersystem crossing in the five-coordinated fragment.' 76 Whilst the flattened state 2 3 MC(F) is energetically accessible, the steric clash between the two bpy ligands in 2 will prevent the coplanarisation of the Ru(bpy) 2 fragment, thereby inhibiting and precluding the formation of a similar 3 MC(P)-like state. Indeed, crystallographically characterised bis(bipyridyl) complexes of the form trans-[Ru(bpy) 2 (L) 2 ] 2+ (L = NH 3 , py) are heavily distorted with a significant bending of the bpy ligands. 77,78 Several attempts were made to locate a pseudo-pentacoordinate analogue of

Triplet-triplet interconversions

Having characterised the [START_REF] Brown | [END_REF] MLCT states and various classical 3 MC, flattened 3 MC(F) and pseudopentacoordinate 3 MC(P) states of 2 to 4, we carried out nudged elastic band (NEB) [START_REF] Henkelman | Theoretical Methods in Condensed Phase Chemistry[END_REF][START_REF] Jonsson | Classical and Quantum Dynamics in Condensed Phase Simulations[END_REF] calculations to determine energy barriers for their interconversions (Table 2 and Figures S8 to S10). This method is derived from Liotard's chain of states method [START_REF] Liotard | [END_REF][START_REF] Liotard | Numerical methods in the study of critical phenomena[END_REF] and provides the minimum energy path connecting two points, without requiring optimisation of the absolute transition state. It was found that for 2 conversion of the 3 MLCT state to any of the three 3 MC states 2 3 MC(A/B/F) proceeds with extremely low energy barriers of < 0.05 eV. Similarly, for 3, all triplet-triplet interconversions involve very low energy barriers (Table 2). While these barriers are within the error expected for these calculations, what is evident is that these 3 PES are very flat and all states are readily accessible, and will be populated upon photoexcitation.

Regarding complex 4, the least photoreactive of the complexes 2 to 4, calculated interconversion barriers are larger but still relatively small, ranging from 0.10 to 0.25 eV. A shallow minimum is observed on the minimum energy NEB path from 3 3 MLCT to 3 3 MC(P) corresponding to the complex transiting through the 3 presents the appropriate singlet spin multiplicity and a free coordination site trans to the monodentate btz ligand available for rapid solvent coordination, in agreement with the observed monosolvento primary photoproduct 7. 22 In the case of 4, after initial photoexcitation to a 1 MLCT state, rapid population of 43 MC(A) is likely to occur (blue line, Figure 9). Population of 4 3 MC(F) and 4 3 MC(P) states, 0.1 and 0.2 eV higher in energy than 4

3 MC(A) and transitioning to the 1 PES through 4 1,3 MECP(P), will similarly yield the square pyramidal pentacoordinate 16-electron ground state species 4 1 GS(P) (red line, Figure 9) and precursor to the observed solvento species 8. The relative slowness of conversion of 4 into 8 observed experimentally in NMR experiments was ascribed originally to the reduced overlap of its optical absorption spectrum with the emission profile of the lamp used for photolysis. 60 The theoretical data reveal that conversion of 4 to 8 might be additionally hampered relative to conversion of 3 to 7 due to the greater energy separation and greater energy barriers between MC(A) and MECP(P). It must be pointed out that as all [START_REF] Brown | [END_REF] MC states and 1,[START_REF] Brown | [END_REF] MECPs associated with them will be energetically accessible this will result in competing pathways after photoexcitation involving either restoration of the initial ground state or generation of solvated photoproduct via 3 MC(P) states. The relatively low experimentally determined quantum yield for photolysis of 4 would seem to underline this point.

To summarise, the observed trans photochemistry can be rationalized by the successive population of 3 MC(F) and 3 MC(P) species, which gives access to 1 GS(P) 16-electron intermediates prone to solvent trapping.

On the other hand, the mechanism remains unclear regarding the formation of cis photoproducts. Classical MC states do not promote photochemistry, as indicated by the outcome of singlet state optimisation from the corresponding classical MECPs. Whilst the flattened state 2 3 MC(F) is energetically accessible and will be populated, the steric clash between the two bpy ligands in 2 will prevent the coplanarisation of the Ru(bpy) 2 fragment and inhibit the formation of a similar 3 MC(P)-like state subsequent and trans photoproduct. The inexistence of MC(P) states in bis(bpy) complexes may thus rationalize the absence of  1 -ligand loss intermediates and trans photochemistry in this family of compounds. We propose that the photochemistry may well proceed through the 3 MC(F) state for 2 just as seems evident for 3 and 4, but steric pressures or lack thereof determine the feasibility of a 3 MC(P)-like structure and hence the ultimate stereochemistry of the photoproducts.

In complexes 3 and 4 each of the two btz ligand plays a distinct role in the formation of a 1 GS(P) state and hence the final trans solvento photoproducts; the poor -acceptor properties of the ligand enable it to readily occupy the distal position in the preceding 3 MC(F) state whilst the low steric demands enable the second btz ligand to become co-planar with the third (bpy or pytz) chelate ligand in the 3 MC(P) state. Whilst in retrospect the existence of 3 MC(F) and 3 MC(P) states is thus readily apparent from the observed trans stereochemistry for the photoproducts of 3 and 4 we strongly believe that 3 MC(F)-type states are far from unique to the systems described here. Firstly, the discovery of a 3 MC(F) minimum for 2 with a low energy barrier for its population from the 3 MLCT state clearly demonstrates that such states could be highly accessible in the large number of known photochemically reactive systems in which the Ru(bpy) 2 moiety is ubiquitous. Indeed, we have noted the existence of such a 3 MC(F) state in the photorearrangement mechanism of a Ru(bpy) 2 -containing chelated sulphoxide complex. 20 In systems where the ultimate photoproduct stereochemistry exhibits retention of the cis arrangement of the reactants the involvement of such 3 MC(F) may not be immediately apparent but such states may be crucial to the mechanism of many processes. Great advances have been made in the past few years in the theoretical, and indeed experimental characterisation of (classical) [START_REF] Brown | [END_REF] MC states. However, it is possible that this very retention of stereochemistry is the main reason that the novel 3 MC(F)-type states highlighted here have been, not-so-much overlooked, but unanticipated in previous studies. Work is continuing in our groups to establish the mechanism for formation of cis photoproducts from the 3 MC state manifold and will be reported elsewhere in due course.

A common route to promote ligand ejection reactivity in ruthenium(II) tris(bidentate) complexes involves the incorporation of steric congestion to weaken Ru-N bonds and stabilise 3 MC states thereby promoting their population, provided the 3 MLCT and 3 MC PES are not nested. [START_REF] Vallett | [END_REF] The results presented here, involving the incorporation of sterically unencumbered triazole-containing ligands with poor -acceptor character displaying original 3 PES topologies, therefore offer new insights into alternative design strategies for complexes that exhibit photochemical ligand ejection or photomechanical motion. The photoejection of a btz ligand has been reported for the complex [Ir(dfptz) 2 (btz)] 2+ (dfptzH = 4-(2,4-difluorophenyl)-1,2,3-triazole). 56 Based on the results presented here for 2 and the known propensity of the [Ir(C^N) 2 ] fragments to flatten in 3 MC states of triscyclometalated iridium(III) complexes 73 it is therefore possible that a 3 MC(F)-type state is also operative in this system. As we have alluded to before, a flattened 3 MC state was shown to be a crucial intermediate state in the photoisomerisation of a [Ru(bpy) 2 ]-containing chelating sulphoxide complex. 20 It is possible that such flattened states play a crucial role in the photorelease mechanism of other ligands lacking in acceptor character including diamines and dithioether type ligands 84 investigated recently but may also be intimately involved in the formation of photodechelation products proposed previously for [Ru(bpy) 3 ] 2+ type complexes. 85 Excited state dynamics involving photomechanical ligand motion may also be involved in light induced spin crossover complexes. 86 Whilst the ligand systems reported here have facilitated the illumination of these new and original flattened 3 MC states they may have as yet unrecognised impact and relevance in a wider range of metal complex systems exhibiting light induced phenomena.

Conclusions

Tris(bidentate) ruthenium(II) complexes may undergo photochemical ligand loss yielding either cis or trans photoproducts. This work has focused on the case of two bis(btz) complexes which produce exclusively trans photoproducts. We have identified and characterised highly novel [START_REF] Brown | [END_REF] MC states (flattened and pentacoordinate), which we propose are major actors in the mechanism of formation of trans photoproducts but reveal the ease with which the flattened [START_REF] Brown | [END_REF] MC can be populated in a mono(btz) complex where only a cis photoproduct is observed. The 3 MC region is a vast basin, which is favourable to photochemistry from the point of view of entropic factors. Experimental characterisation of such a landscape is certainly an extreme challenge, however, computational approaches can offer significant insights. 'Classical' 3 MC states in these systems cannot account for the mechanism of photoreactivity. The novel states proposed here fill the gap in our knowledge and represent the missing link in the photoreactive mechanism. Having identified a pentacoordinate singlet/triplet crossing point, and describing for the first time 16-electron singlet closed shell pentacoordinate ligand dechelation intermediates, this enables us to propose a full mechanism for solvent coordination that obeys

Wigner's rules. Knowledge of the origin and nature of 3 MC states of the type described here and their corresponding MECPs is compulsory when attempting to rationalise the mechanism of photochemical ligand rearrangements and dissociation reactions for transition metal complex systems. With the mechanism forming trans photoproducts having been elucidated work is currently in progress in our laboratories to complete the mechanism for the formation of cis photoproducts and demonstrate the wider significance and impact of such flattened [START_REF] Brown | [END_REF] MC states in transition metal photochemistry.

Supporting Information

Mulliken spin density plots for triplet states, plots of frontier molecular orbitals, results from relaxed potential energy surface scans and nudged elastic band calculations, summarised structural data for triplet states and calculated atomic coordinates for optimised singlet and triplet minima and minimum energy singlet-triplet crossing points.

Figure 1 .

 1 Figure 1. Jablonski (a) and qualitative potential energy curve (b) diagrams for ground and excited states for [Ru(bpy) 3 ] 2+ .

  MLCT state reducing the activation barrier to population of the 3 MC state with respect to that for 1. In the case of 2 cis stereochemistry in the product cis-[Ru(bpy) 2 (NCMe) 2 ] 2+ (6) is observed, as for 1. On the contrary, for the bis(bitriazolyl) complexes 3 and 4, ejection of btz remarkably leads to trans bis(solvento) products trans-[Ru(N^N)(btz)(NCMe) 2 ] 2+ (9 and 10) and proceeds with the observation of ligand-loss mono(solvento) products trans-[Ru(N^N)( 2 -btz)( 1 -btz)(NCMe)] 2+ (7 and 8) (Scheme 1).

  the optimised T 1 state of 5 is found to have metalcentred character. A 3 MLCT state, 5 3 MLCT-D 3 , was optimised by imposing D 3 symmetry, which does not apply to the MC excited state. On incorporation of a third btz ligand the 5 3 MLCT-D 3 state is destabilised by 0.95 eV relative to 3 3 MLCT, reflecting the much higher energy of the btz LUMO relative to that of bpy, and lies 3.45 eV above the ground state. The calculated energies of 5 3 MC and 5 3 MLCT-D 3 clearly show that there will be a large energy separation between both triplet states.

Figure 2 .

 2 Figure 2. Plot of relative energies of the 3 MLCT and 3 MC states for complexes 1 to 4 at their respective optimised geometries relative to that of each ground state (E( 1 GS) = 0). a Energy of T 1 state from TDDFT; b constrained to D 3 symmetry; c 3 MC(A); d 3 MC(B); e 3 MC(C).

3 3

 3 MC(A) with elongated Ru-N lengths of 2.54 Å (near identical to 5 3 MC) but a much smaller N-C-C-N dihedral angle of 0.3 °. The other, asymmetric, 3 MC(B) states for 2 and 3 (2 3 MC(B) and 3 3 MC(B)) respectively) involve dechelation of one bpy and one btz ligand. For both 2 3 MC(B) and 3 3 MC(B) the lengthened Ru-N(bpy) bond is shorter than found for 1 3 MC or 2 3 MC(A) at 2.38 Å, whilst the Ru-N(btz) bond length is significantly longer than in 3 3 MC(A) at 2.71 Å. These structural effects are likely to partly stem from the greater -acceptor character of the pyridine moieties over triazole, which will result in a larger trans effect for the former.

Figure 3 .For 3 ,

 33 Figure 3. Structures of the optimised geometries of classical 3 MC states for complexes 1 to 5 annotated with distances for elongated Ru-N bonds (hydrogen atoms omitted for clarity).

  undergoes elongation, bonds b and c are observed to elongate temporarily, forming a distorted 3 3 MC(B)-like geometry before bond c contracts leaving bond b extended. Concomitantly the angle between bonds c and d is observed to widen, thus generating a new flattened 3 MC state geometry (3 3 MC(F) where the "F" denotes the flattened nature of the [Ru( 2 -bpy)( 2 -btz)] moiety) with a single distal btz ligand in which both Ru-N bonds are extended. The same state is arrived at for a 3 PES scan conducted contracting Ru-N bond distance d starting from the optimised geometry for 3 3 MC(A), whereby bond b is induced to elongate as the angle between bonds d and c widens (Figure 4a, red energy profile). The geometry of 3 3 MC(F) was allowed to optimise free of geometric constraints and converged to a true minimum (Figure 5 middle), whose key parameters are summarised in Table

Figure 4 .

 4 Figure 4. a) Relaxed 3 PES scans for 3 3 MLCT  3 3 MC(F) and 3 3 MC(A)  3 3 MC(F), b) Summarised 3 MC interconversion during 3 PES scans for 3 MC states of 4 with energy profile plots for 4 3 MC(A)  4 3 MC(F) and 4 3 MC(B)  4 3 MC(F) scans (Note: the x-axis distances refer to the Ru-N distance undergoing elongation or contraction in each case).

Figure 5 .

 5 Figure 5. Optimised geometries of 3 MC(F) states of 2, 3 and 4 with annotated elongated Ru-N distances (Å) and widened angle  between Ru-N bonds trans to elongated Ru-N bonds (hydrogen atoms omitted for clarity).

'classical' 3

 3 MC states, population of a "d z 2 -like" d* orbital results in a double Ru-N bond elongation. It is possible to derive classical-type 3 MC states with elongation along each of the three possible N-Ru-N axes (e.g. as in the case of 4). Besides, formal population of a "d x 2 -y 2 -like" d* orbital is also possible, with distortion involving all three ligands. Elongation of both Ru-N bonds of one chelate ligand, both of whose N-atoms participate in the d* orbital, will diminish metal-ligand orbital overlap thus stabilising this state. Additionally, concomitant deviation from linearity of orbital overlap of the two N atoms trans to the elongated Ru-N bonds, by flattening of the Ru(N^N) 2 -fragment towards coplanarity with enlargement of the angle , will further stabilise the d* orbital. Thus, the MC(F) states are nearly degenerate with the classical MC states. The MC(F) states calculated here (2 3 MC(F), 3 3 MC(F) and 4 3 MC(F), Figure 5) represent a novel class of 3 MC states additional to the 'classical' 3 MC states described. Since 4 exhibits the broadest range of 3 MC states Figure 6 shows the pairs of singly occupied natural orbitals of 4 3 MC(A-C) and 4 4 MC(F), which illustrate the "d z 2 " origin of their structural distortions. They are representative of all 3 MC states discussed in this work. For each of the classical states 4 3 MC(A-C) the SONO+1 is of predominantly d z 2 -like d*-orbital character with alignment along the elongated N-Ru-N axis. In contrast that of 4 4 MC(F) clearly exhibits d

Figure 6 .

 6 Figure 6. Singly occupied natural orbitals (SONO (bottom)/SONO+1 (top)) of 4 3 MC(A-C) and 4 3 MC(F) (hydrogen atoms omitted for clarity).

3 3 MC(P) and 4 3

 33 MC(P) maintain approximately coplanar triazole rings and have Ru-N distances of 2.44 and 3.20 Å for 3 3 MC(P) whereas those in 4 3 MC(P) are 2.51 and 2.77 Å. 3 3 MC(P) lies only 0.05 eV (1 kcal mol -1 ) above 3 3 MC(F) (and thus these states are effectively degenerate) whereas 4 3 MC(P) lies 0.14 eV (3 kcal mol -1 ) above 4 3 MC(F).

  2 3 MC(F) but initial guess geometries relaxed to either the 2 3 MC(F) or 2 3 MC(B) states. This signals the necessity of achieving approximate coplanarity of the Ru(N^N)( 2 -btz) fragment in 3 and 4 to enable the formation of the observed trans photoproducts via the formally 16-electron pentacoordinate intermediates 3 1 GS(P) and 4 1 GS(P).

Figure 7 .

 7 Figure 7. Relaxed geometries of 3 MC(P), 1,3 MECP(P) and 1 GS(P) states of 3 and 4 annotated with distances for elongated Ru-N bonds and the narrowest trans N-Ru-N angle  of the approximate square planar base (hydrogen atoms omitted for clarity).

3

  MC(F) region of the 3 PES as might be expected. Similar dips are observed in the NEB energy profiles for the transits from 3 3 MC(B) to 3 3 MC(P) and from 4 3 MC(C) to 4 3 MC(P), the geometries at which correspond to distorted 3 3 MC(F) and 4 3 MC(F) states respectively.

3 3

 3 MC(F)3 3 MC(P) 0.06 leading to photoproduct and is highly accessible. Optimisation of the singlet ground state starting from 3 3 MECP(P) results in formal  1 -coordination of the distal btz ligand in the axial position of the square-pyramidal 16-electron species [Ru(bpy)( 2 -btz)( 1 -btz)] 2+ (3 1 GS(P), Figure7, and red line on Figure8). 3 1 GS(P) thus

Figure 9 .

 9 Figure 9. Schematic potential energy curve describing the structural evolution for 4: Conversion of 4

  MC state calculations but its full significance perhaps not recognised at the time; in calculations on the S/O-donor linkage photoisomerisation of [Ru(bpy) 2 (O^S)] + (where O^S is a 2-carboxyphenylsulphoxide ligand) to [Ru(bpy) 2 (O^O')] + , Göttle et al. noted a flattening of the Ru(bpy) 2 -fragment in one of the key 3 MC states involved in the isomerisation mechanism.

Table 1 .

 1 Energies (eV) of1,[START_REF] Brown | [END_REF] MECPs for 3 MC states of 2, 3 and 4 quoted relative to minimum of 3 MC state in

	1,3 MECP(F)) resides 0.13 eV higher in energy than the minimum for this
	state. At the 3 1,3 MECP(F) geometry one of the Ru-N distances to the distal btz ligand shortens to 2.35 Å whilst
	the other further elongates to 2.67 Å, indicating that this btz ligand is on the path to becoming formally
	monodentate. However, when a singlet state is optimised starting from 3 1,3 MECP(F) the complex reverts to the
	fully hexacoordinate pseudo-octahedral reactant ground state. Optimisation of the singlet state from the

analogous 4 1,3 MECP(F) geometry similarly yields the ground state of 4. Thus 3/4 1,3 MECP(F) can be seen as quenchers of photochemistry rather than as a route to the observed photoproducts. However, since the Ru(N^N)( 2 -btz) fragments in 3 3 MC(F) and 4 3 MC(F) would appear to be approximately half way to the coplanarity in the photoproducts 7 and 8, rather than representing the final stages on the 3 PES en route to the photoproducts, these states are clearly possible intermediate 3 MC states to further 3 MC states responsible for formal coplanarisation.

Table 2 .

 2 Calculated energy barriers (eV) from nudged elastic band calculations for triplet-triplet

	interconversions (quoted relative to state of origin). A/B/C stand for d z	2 -type 'classical' 3 MC states; F stands for
	new d x 2 -y	2 -type flattened 3 MC states; P stands for pseudo-pentacoordinate.

PES scans were carried out through Ru-N bond elongations starting from the optimised 3 MLCT geometries. For complex

4, where previous calculations had indicated that the T 1 state is of 3 MC character, 60 relaxed 3 PES scans were conducted in which the elongated bond distances in 4 3 MC(A), 4 3 MC(B) and 4 3 MC(C) were contracted in anticipation that this might lead to a 3 MLCT state, or more likely, to a transition between the different 3 MC states as previously observed in[START_REF] Brown | [END_REF] PES scans for cyclometalated iridium complexes.72

MC(A) to

1 GS(P) via 4 3 MC(F) and 4 3 MC(P).

Acknowledgements

The authors thank the Leverhulme Trust, the University of Huddersfield and the Hartree Centre, STFC Daresbury, for supporting this research. As a member of the UK Materials Chemistry Consortium PIPE also thanks the EPRSC and the UK HPC national resources, HECToR (EP/D504872) and Archer (EP/L000202), as well as the Huddersfield High Performance Computing Research Group for other computational facilities utilised in this work. The work performed in Toulouse used HPC resources from CALMIP (Grant 2016-[p1112]).

The authors declare no competing financial interests.

Mechanistic insights and wider implications

Ruthenium tris(bidentate) complexes have been shown to undergo photochemically induced ligand loss, yielding either cis or trans photoproducts. Classical 3 MC states fail to explain the observed photoreactivity for trans photoproduct formation and we propose that this involves the new triplet and singlet states presented above. This discussion will focus on productive pathways, but given the low interconversion energy barriers, all triplet states can be populated. A depiction of the singlet and triplet excited state PES exemplified by 3 is shown in Figure 8. After initial excitation from the ground state for 3 yielding the 1 MLCT state, with subsequent intersystem crossing to the [START_REF] Brown | [END_REF] MLCT state, we propose that this undergoes direct conversion to 3 3 MC(F) (blue line on Figure . 8), which is calculated to have a low energy barrier. This then undergoes conversion to the pseudo-square pyramidal pentacoordinate 3 MC state 3 3 MC(P). 3 3 MECP(P) found to lie at only 0.05 eV above the minimum for this [START_REF] Brown | [END_REF] MC state and, which is identified here for the first time, is therefore the only MECP

Computational Details

The singlet ground state geometries of the complexes were optimised at the B3LYP level of theory (20 % Hartree-Fock) 87 in the gas phase using the NWChem 6.3 software package. 88 Molecular structures and molecular orbital plots were visualised using the ECCE software package. The Stuttgart-Dresden relativistic small-core ECP 89 and associated basis set were used for ruthenium and 6-311G* basis sets 90 were used for all other atoms.

The lowest lying [START_REF] Brown | [END_REF] MLCT states for complexes 1 to 3 were calculated starting from the singlet ground state geometries and using the constraint of a spin multiplicity of 3 (UDFT). In the case of 5 where the lowest lying triplet state is [START_REF] Brown | [END_REF] MC in character, the D 3 symmetric 3 MLCT state was optimised imposing D 3 symmetry. To calculate optimised geometries of classical Jahn-Teller type [START_REF] Brown | [END_REF] MC states the distribution of the ground state dσ* orbitals were examined and the bond lengths for each Ru-N bond participating in these orbitals was manually elongated to generate an initial estimate geometry. These were then allowed to optimise under the constraint of a spin multiplicity of 3. To confirm that minima had been obtained in geometry optimisations vibration frequency calculations were carried out. In some cases small negative vibrational modes were observed (< -50 cm -1 ) and are characterised by the rotation of the methyl groups of the btz ligands. Optimisation of the 3 3 MC(F)' minimum bearing a distal bpy ligand was achieved at the same level of theory using Orca 3.0 (Cite orca here) starting from a favourable guess geometry (Ru-bpy bonds set to 2.5 Å and θ angle set to 160°) using a reduced stepsize (maxstep 0.1). Triplet state potential energy surface scans were carried out by iteratively elongating/shortening the desired Ru-N bond distances in 0.02 Å steps. At each step the complexes were optimised with the Ru-N bond length in question held constant. Molecular orbital vectors from the previous geometry iteration were discarded at each step and reformulated afresh. The evolution of the molecular geometries during the progress of the PES scans were animated using the JMol software package.

The minimum energy paths (MEPs) on the 3 PES were optimized using the nudged elastic band (NEB) method [START_REF] Henkelman | Theoretical Methods in Condensed Phase Chemistry[END_REF][START_REF] Jonsson | Classical and Quantum Dynamics in Condensed Phase Simulations[END_REF] using NWChem 6.6. The geometries were prepared (oriented and superimposed) using labdeveloped programs to minimize the discrepancy between start and end geometries. A 10-bead initial path, created by IDPP interpolation 91 using the IDPP_ase program (https://wiki.fysik.dtu.dk/ase/tutorials/neb/idpp.html), was provided for the NEB calculation. The NEB calculation itself was performed using the same functional, pseudo potential and basis sets as for minima optimisation. The following parameters were used for the NEB calculations: algorithm 0, kbeads 0.05, stepsize 0.2, nbeads 10. Two NEB calculations were run sequentially using two different SCF convergers : for the first 10 iterations the wavefunction was converged with DIIS; then at least 20 iterations were run using the semiquadratic CGMIN converger (setting the convergence gradient to 5e 3 MC/ 1 GS minimum energy crossing points (MECPs) were optimized starting from the relevant (NWChem) 3 MC geometries using Orca 3.0 92 under similar conditions (B3LYP functional, same Stuttgart-Dresden pseudopotential on Ru, def2-TZVP basis set 93 and def2-TZVP/j auxiliary basis set 94 on Ru, and 6-311G* basis sets on all other atoms). Convergence of the wavefunction was also achieved using DIIS followed by a semiquadratic converger (here SOSCF). Frequency calculations were run on the MECP geometries using the specific SurfCrossNumFreq keyword. Triplet state singly occupied natural orbitals were plotted from Orca single point calculations with 0.04 isovalue using Gabedit. 95