From complete to selected model spaces in determinant-based multi-reference second-order perturbation treatments.

The present paper reformulates and improves a previously proposed determinant-based second-order multi-reference perturbative formalism. Through a rather simple modification of the energy denominators, this formalism takes into account the interactions between the model space determinants, which are repeated in outer space. The method has been shown to be size-consistent when the model space is a complete active space, which is a severe limit. It is shown here that the completeness of the model space is not necessary to keep this property, provided that the zero-order function satisfies some conditions. For instance, size consistency may be obtained from truncated complete active spaces. It may even be satisfied from Singles and Doubles Configuration Interactions, provided that a coupled electron pair approximation is used in the definition of the model space wave function. The physical content of the method is illustrated by a series of model problems, showing its robustness. A major benefit of the fact that the perturbers are single determinants is the possibility to revise with full flexibility the model-space component of the wave function, i.e., to treat the feedback effect of the dynamic correlation on the valence component of the wave function.

Theoretical Study of the Full Photosolvolysis Mechanism of [Ru(bpy)3]2+: Providing a General Mechanistic Roadmap for the Photochemistry of [Ru(N

A complete mechanistic picture for the photochemical release of bipyridine (bpy) from the archetypal complex [Ru(bpy)3]2+ is presented for the first time following the description of the ground and lowest triplet potential energy surfaces, as well as their key crossing points, involved in successive elementary steps along pathways toward cis- and trans-[Ru(bpy)2(NCMe)2]2+. This work accounts for two main pathways that are identified involving (a) two successive photochemical reactions for photodechelation, followed by the photorelease of a monodentate bpy ligand, and (b) a novel one-photon mechanism in which the initial photoexcitation is followed by dechelation, solvent coordination, and bpy release processes, all of which occur sequentially within the triplet excited-state manifold before the final relaxation to the singlet state and formation of the final photoproducts. For the reaction between photoexcited [Ru(bpy)3]2+ and acetonitrile, which is taken as a model reaction, pathways toward cis and trans photoproducts are uphill processes, in line with the comparative inertness of the complex in this solvent. Factors involving the nature of the departing ligand and retained "spectator" ligands are considered, and their role in the selection of mechanistic pathways involving overall two sequential photon absorptions versus one photon absorption for the formation of both cis or trans photoproducts is discussed in relation to notable examples from the literature. This study ultimately provides a generalized roadmap of accessible photoproductive pathways for light-induced reactivity mechanisms of photolabile [Ru(N^N)(N^N')(N^N″)]2+-type complexes.

Unravelling the Mechanism of Excited-State Interligand Energy Transfer and the Engineering of Dual Emission in [Ir(C∧N)2(N∧N)]+ Complexes.

Fundamental insights into the mechanism of triplet-excited-state interligand energy transfer dynamics and the origin of dual emission for phosphorescent iridium(III) complexes are presented. The complexes [Ir(C∧N)2(N∧N)]+ (HC∧N = 2-phenylpyridine (1a-c), 2-(2,4-difluorophenyl)pyridine (2a-c), 1-benzyl-4-phenyl-1,2,3-triazole (3a-c); N∧N = 1-benzyl-4-(pyrid-2-yl)-1,2,3-triazole (pytz, a), 1-benzyl-4-(pyrimidin-2-yl)-1,2,3-triazole (pymtz, b), 1-benzyl-4-(pyrazin-2-yl)-1,2,3-triazole (pyztz, c)) are phosphorescent in room-temperature fluid solutions from triplet metal-to-ligand charge transfer (3MLCT) states admixed with either ligand-centered (3LC) (1a, 2a, and 2b) or ligand-to-ligand charge transfer (3LL'CT) character (1c, 2c, and 3a-c). Particularly striking is the observation that pyrimidine-based complex 1b exhibits dual emission from both 3MLCT/3LC and 3MLCT/3LL'CT states. At 77 K, the 3MLCT/3LL'CT component is lost from the photoluminescence spectra of 1b, with emission exclusively arising from its 3MLCT/3LC state, while for 2c switching from 3MLCT/3LL'CT- to 3MLCT/3LC-based emission is observed. Femtosecond transient absorption data reveal distinct spectral signatures characteristic of the population of 3MLCT/3LC states for 1a, 2a, and 2b which persist throughout the 3 ns time frame of the experiment. These 3MLCT/3LC state signatures are apparent in the transient absorption spectra for 1c and 2c immediately following photoexcitation but rapidly evolve to yield spectral profiles characteristic of their 3MLCT/3LL'CT states. Transient data for 1b reveals intermediate behavior: the spectral features of the initially populated 3MLCT/3LC state also undergo rapid evolution, although to a lesser extent than that observed for 1c and 2c, behavior assigned to the equilibration of the 3MLCT/3LC and 3MLCT/3LL'CT states. Density functional theory (DFT) calculations enabled minima to be optimized for both 3MLCT/3LC and 3MLCT/3LL'CT states of 1a-c and 2a-c. Indeed, two distinct 3MLCT/3LC minima were optimized for 1a, 1b, 2a, and 2b distinguished by upon which of the two C∧N ligands the excited electron resides. The 3MLCT/3LC and 3MLCT/3LL'CT states for 1b are very close in energy, in excellent agreement with experimental data demonstrating dual emission. Calculated vibrationally resolved emission spectra (VRES) for the complexes are in excellent agreement with experimental data, with the overlay of spectral maxima arising from emission from the 3MLCT/3LC and 3MLCT/3LL'CT states of 1b convincingly reproducing the observed experimental spectral features. Analysis of the optimized excited-state geometries enable the key structural differences between the 3MLCT/3LC and 3MLCT/3LL'CT states of the complexes to be identified and quantified. The calculation of interconversion pathways between triplet excited states provides for the first time a through-space mechanism for a photoinduced interligand energy transfer process. Furthermore, examination of structural changes between the possible emitting triplet excited states reveals the key bond vibrations that mediate energy transfer between these states. This work therefore provides for the first time detailed mechanistic insights into the fundamental photophysical processes of this important class of complexes.

Exploration of Uncharted 3PES Territory for [Ru(bpy)3]2+: A New 3MC Minimum Prone to Ligand Loss Photochemistry.

We have identified a new 3MC 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 3PES. This distal MC state (3MCcis) is destabilized by less than 2 kcal/mol with respect to the classical MC state (3MCtrans), and energy barriers to populate 3MCcis and 3MCtrans from the 3MLCT state are similar according to nudged elastic band minimum energy path calculations. Distortions in the classical 3MCtrans, that is, elongation of two Ru-N bonds toward two different bpy ligands, are not expected to favor the formation of ligand-loss photoproducts. On the contrary, the new 3MCcis could be particularly relevant in the photodegradation of Ru(II) polypyridine complexes.

Revisiting the Vibrational and Optical Properties of P3HT: A Combined Experimental and Theoretical Study.

We demonstrate that DFT-based calculations can provide straightforward means to analyze the effect of aggregation on the optical properties of regioregular P3HT oligomers of different lengths (up to 20-mers) and of bioligomers of 8-mers in two different conformations. Our conclusions substantially differ from those obtained previously by applying the exciton model. Indeed, analysis of Huang-Rhys factors has evidenced that two vibrational modes, a collective mode and an effective mode, are combined in the vibronic structure of the absorption spectrum of oligothiophene. Computed spectra match perfectly their experimental counterparts provided we consider that the oligomer and at least the five lowest excited states of bioligomers behave as absorbers, and that both oligomer and bioligomer contribute to the emission spectra. Study of the nature of the Franck-Condon excitation and optimization of the five lowest excited singlet states indicate that high (hot) excited states of the bioligomer may play an important role in the initiation of charge separation and highlight the importance to take into account the relaxation processes in the theoretical modeling of emission properties.

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

We have identified highly novel photoreactive 3MC states of ruthenium(ii) 4,4'-bi-1,2,3-triazolyl (btz) complexes of the form [Ru(N^N)(btz)2]2+ and have elucidated the mechanism of the highly unusual experimental observations of photochemical ligand dechelation and concomitant ligand rearrangement reactivity to form unusual photoproducts trans-[Ru(N^N)(κ2-btz)(κ1-btz)(solvent)]2+. The triplet metal-to-ligand charge-transfer (3MLCT) states and classical Jahn-Teller type triplet metal-centred (3MC) states of the series of complexes [Ru(N^N)3-n(btz)n]2+ (btz = 4,4'-bi-1,2,3-triazolyl; N^N = 2,2'-bipyridyl (bpy), n = 0 (1), 1 (2), 2 (3), 3 (5); N^N = 4-(pyrid-2-yl)-1,2,3-triazole (pytz), n = 1 (4)) have been optimised by density functional theory (DFT) and characterised. There is a gradual and significant destabilisation of the 3MLCT states as the triazole content of the complexes increases, which occurs with a slight stabilisation of the 3MC states. Whilst consistent with the promotion of photochemical reactivity in the heteroleptic complexes of the series relative to 1, these classical 3MC 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 (3PES) here reveals the existence of a new type of 3MC 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 'pentacoordinate' 3MC 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 3MC states but more significantly demonstrate their crucial role in the formation of the experimentally observed photoproducts.

A Theoretical Study of the N to O Linkage Photoisomerization Efficiency in a Series of Ruthenium Mononitrosyl Complexes.

Ruthenium nitrosyl complexes are fascinating versatile photoactive molecules that can either undergo NO linkage photoisomerization or NO photorelease. The photochromic response of three ruthenium mononitrosyl complexes, trans-[RuCl(NO)(py)4]2+, trans-[RuBr(NO)(py)4]2+, and trans-(Cl,Cl)[RuCl2(NO)(tpy)]⁺, has been investigated using density functional theory and time-dependent density functional theory. The N to O photoisomerization pathways and absorption properties of the various stable and metastable species have been computed, providing a simple rationalization of the photoconversion trend in this series of complexes. The dramatic decrease of the N to O photoisomerization efficiency going from the first to the last complex is mainly attributed to an increase of the photoproduct absorption at the irradiation wavelength, rather than a change in the photoisomerization pathways.

Computational Estimate of the Photophysical Capabilities of Four Series of Organometallic Iron(II) Complexes.

In this study, we examine a large range of organometallic iron(II) complexes with the aim of computationally identifying the most promising ones in terms of photophysical properties. These complexes combine polypyridine, bis(phosphine), and carbon-bound ligands. Density functional theory has allowed us to establish a comparative Jablonski diagram displaying the lowest singlet, triplet, and quintet states. All of the proposed FeN5C or FeN3P2C complexes unfavorably possess a lowest triplet state of metal-centered (MC) nature. Among the FeN4C2 and FeN2P2C2 series, the carbene complexes display the least favorable excited-state distribution, also having a low-lying (3)MC state. Validating our design strategy, we are now able to propose seven iron(II) complexes displaying a lowest excited state of triplet metal-to-ligand charge-transfer nature.

Pivotal Role of a Pentacoordinate (3)MC State on the Photocleavage Efficiency of a Thioether Ligand in Ruthenium(II) Complexes: A Theoretical Mechanistic Study.

A mechanistic study of the photocleavage of the methylthioethanol ligand (Hmte) in the series of ruthenium complexes [Ru(tpy)(N-N)(Hmte)](2+) (tpy = 2,2':6',2″-terpyridine, N-N = bpy (2,2'-bipyridine), biq (2,2'-biquinoline), dcbpy (6,6'-dichloro-2,2'-bipyridine), dmbpy (6,6'-dimethyl-2,2'-bipyridine)) was performed using density functional theory. These studies reveal the decisive role of two quasi-degenerate triplet metal-centered states, denoted (3)MChexa and (3)MCpenta, on the lowest triplet potential energy surface. It also shows how the population of the specific pentacoordinate (3)MCpenta state, characterized by a geometry more accessible for the attack of a solvent molecule, is a key step for the efficiency of the photosubstitution reaction. The difference in the photosubstitution quantum yields experimentally observed for this series of complexes (from φ = 0.022 for N-N = bpy up to φ = 0.30 for N-N = dmbpy) is rationalized by the existence of this (3)MCpenta photoreactive state and by the different topologies of the triplet excited-state potential energy surfaces, rather than by the sole steric properties of these polypyridinyl ligands.

Establishing the Two-Photon Linkage Isomerization Mechanism in the Nitrosyl Complex trans-[RuCl(NO)(py)4](2+) by DFT and TDDFT.

The density functional theory calculations presented in this work allow the first rationalization of the full linkage photoisomerization mechanism of trans-[RuCl(NO)(py)4](2+), in both the forward and reverse directions. These mechanisms are consistent with the experimental data establishing that blue-light irradiation triggers the forward process, while red or IR photons trigger the reverse process. Characterization of the singlet and lowest triplet potential energy surfaces shows that, despite the unfavorable thermodynamic character of the forward process, the topologies of the surfaces and particularly some crucial surface crossings enable the isomerization. In the forward Ru-NO → Ru-ON direction, a sequential two-photon absorption mechanism is unraveled that involves a sideways-bonded metastable state. In contrast, in the reverse reaction, two mechanisms are proposed involving either one or two photons.

Unravelling the S → O linkage photoisomerization mechanisms in cis- and trans-[Ru(bpy)2(DMSO)2](2+) using density functional theory.

A mechanistic study of the intramolecular S → O linkage photoisomerization in the cis and trans isomers of [Ru(bpy)2(DMSO)2](2+) was performed using density functional theory. This study reveals that for the cis isomer the linkage photoisomerization of the two DMSO ligands occurs sequentially in the lowest triplet excited state and can either be achieved by a one-photon or by a two-photon mechanism. A mechanistic picture of the S → O photoisomerization of the trans isomer is also proposed. This work especially highlights that both adiabatic and nonadiabatic processes are involved in these mechanisms and that their coexistence is responsible for the rich photophysics and photochemical properties observed experimentally for the studied complexes. The different luminescent behavior experimentally observed at low temperature between the cis and trans isomers is rationalized based on the peculiarity of the topology of the triplet excited-state potential energy surfaces.

Phosphoryl group as a strong σ-donor anionic phosphine-type ligand: a combined experimental and theoretical study on long-lived room temperature luminescence of the [Ru(tpy)(bpy)(Ph2PO)]+ complex.

A phosphoryl Ru(II) polypyridyl complex was prepared in a one-pot process. Theoretical analysis suggests that the phosphoryl ligand may be viewed as a strong σ-donor anionic phosphine L-type ligand. State-of-the-art free-energy profile calculations on the excited states demonstrate that both favorable thermodynamic and kinetic factors are responsible for the remarkable room temperature luminescence properties of the phosphoryl complex.

The (N4C2)2- donor set as promising motif for bis(tridentate) iron(II) photoactive compounds.

The ground and excited states of iron(II) bis(dipyridylbenzene) were probed by means of DFT and TDDFT. In comparison to the well-known Fe(tpy)2(2+), this neutral complex should not suffer from ligand loss, and it displays a better absorption profile in the visible region. The relative energies of the spectroscopically relevant excited states ((3)MLCT, (3)MC, (5)MLCT, and (5)MC) are quite different from those of its archetypical counterpart and thus make it a promising candidate for photophysics in general.

Theoretical investigation of phosphinidene oxide polypyridine ruthenium(II) complexes: toward the design of a new class of photochromic compounds.

A DFT-based computational study performed in the gas phase and in acetonitrile on polypyridine ruthenium isomer complexes [Ru(tpy)(bpy)(POPh)](2+) and [Ru(tpy)(bpy)(OPPh)](2+) (bpy = 2,2'-bipyridine, tpy = 2,2':6',2″-terpyridine, Ph = phenyl) predicts that they constitute a prototype for a new family of inorganic photochromic systems. The two isomers are found to absorb in different spectral regions to excited states that are connected adiabatically through a thermodynamically and kinetically favorable triplet potential energy profile. Nonadiabatic routes were identified and shown to be preferable over the adiabatic mechanism. The reverse isomerization reaction is found to be achievable only thermally. The current predictive work will be of prime importance to experimentalists for the design of new inorganic phosphorus-based compounds with attractive photochromic properties.

Adiabatic versus nonadiabatic photoisomerization in photochromic ruthenium sulfoxide complexes: a mechanistic picture from density functional theory calculations.

Polypyridine ruthenium sulfoxide complexes are intriguing compounds which can display both photochromic and electrochromic properties. These properties are based on the Ru-S → Ru-O linkage isomerization capability of the sulfoxide group. The photoisomerization mechanism is of particular importance in order to understand the photophysical properties of such molecules. Density functional theory calculations demonstrate that the main photoisomerization mechanism is nonadiabatic for the system under study in agreement with the experimental observations. Indeed, funnels for efficient radiationless decay back to the ground state are shown to be easily accessible compared to transition states on the adiabatic triplet potential energy surface. However, we highlight for the first time that triplet metal-centered states play a central role in the photoisomerization mechanism of these compounds.

Theoretical investigation on the photophysical properties of model ruthenium complexes with diazabutadiene ligands [Ru(bpy)(3-x)(dab)(x)](2+) (x = 1-3).

In this study we report a theoretical comparative study of some photophysical properties in the [Ru(bpy)(3-x)(dab)(x)](2+) (x = 0-3) series. Density functional theory calculations, validated by highly correlated ab initio benchmark calculations, were used to investigate the absorption and emission properties of the complexes with x = 1-3. The presence of a 1,4-diaza-1,3-butadiene (dab) ligand dramatically changes these properties because of the strong π-acceptor character of this ligand. As a result, comparing to the reference [Ru(bpy)(3)](2+) complex previously studied, we observed (i) a strong red-shift of the maximum of the absorption band, (ii) a strong decrease of the emission energy of the lowest triplet metal-to-ligand charge transfer state, with all the [Ru(bpy)(3-x)(dab)(x)](2+) (x = 1-3) complexes luminescent in the near-infrared region, while [Ru(bpy)(3)](2+) emits in the visible region, and (iii) the triplet metal-centered states become inaccessible in all the [Ru(bpy)(3-x)(dab)(x)](2+) (x = 1-3) complexes. Consequently, these complexes could be potential candidates for infrared light-emitting diodes and probes.

Ligand selection in Ru(II) complexes for direct one-electron photooxidation of guanine: a combined computational and experimental study.

Making the right ligand selection: DFT calculations of Gibbs energies for the one-electron photooxidation of guanine by six Ru(II)-polypyridine complexes are reported. The theoretical predictions are compared with new EPR spectra. Our theoretical calculations confirm the experimental observations that the direct photooxidation of guanine by [Ru(bpz)(3)](2+), [Ru(tap)(3)](2+), and [Ru(bpz)(2)(dppz)](2+) is thermodynamically favorable, but is unfavorable with [Ru(bpy)(3)](2+), [Ru(phen)(3)](2+), and [Ru(bpy)(2)(dppz)](2+) (see figure).

Spin-orbit effects on the photophysical properties of Ru(bpy)3(2+).

We present in this article a detailed study of the photophysics of the Ru(bpy)(3)(2+) complex based on a formalism using density functional theory and an a posteriori treatment of the spin-orbit coupling. The absorption and emission spectra were computed and a very good agreement was obtained with the available experimental data. This work also reveals for the first time that the triplet metal-centered (MC) dd state cannot deactivate radiatively and corresponds to a transient structure for the nonradiative de-excitation of the triplet metal-to-ligand charge transfer (MLCT) state. Thus, a competition takes place between the luminescence of the MLCT state and nonradiative decay back to the ground state via population of the MC state. This radiationless return to the ground state occurs via a deactivation funnel which has been characterized for the first time by optimizing the minimum energy crossing point between the triplet MC and singlet ground state potential energy surfaces. Its low-lying energy position relative to the energy necessary to access the MC minimum suggests that this funnel will be readily accessible.

Direct evaluation of cyclic contributions to the pi energy of conjugated hydrocarbons from strongly localized zero-order pictures.

This paper presents a new procedure for identifying that part of the pi electronic energy of conjugated hydrocarbons which results from cyclic circulation of electrons around a ring. It first shows that one may calculate perturbatively the ground state energy of the Hückel Hamiltonian from a strongly localized Kekulé-type zero-order wave function. The contributions due to cyclic circulation of the electrons appear explicitly, in terms of the interatomic hopping integral t, at the second order in cyclobutadiene (where it is equal to -t (antiaromatic)) and at third order in benzene, where its value is 0.5t (aromatic). Conjugated isomers of benzene are also considered. The cyclic circulation contributions for an N-membered ring are shown to depend strongly on the molecular graph in which it is embedded. A general expression is found for the cyclic contribution to the pi energy of a ring, the Kekulé graph of which contains N double bonds alternating with N single bonds. It is the energy of the ring, plus the sum of the energies of the N subsystems that result from one double-bond removal, minus the sum of the energies of the N open systems that result from one single-bond cut. This new aromaticity index, ACE(MC), may be seen as the enthalpy of a hyperhomodesmotic chemical equation. In contrast to the index ACE(DC) previously defined from a double cut of the ring, the multiple-cut ACE(MC) exhibits the expected asymptotic disappearance of the cyclic energy as the ring size tends to infinity. In the multiple-cut approach, aromaticity persists in bond-alternating rings, but, in contrast to the total pi energy, the purely cyclic contribution tends to resist distortion. Extension of the approach to charged, branched and heterosubstituted rings are discussed, as well as its ab initio transcription.

Linkage Photoisomerization Mechanism in a Photochromic Ruthenium Nitrosyl Complex: New Insights from an MS-CASPT2 Study.

The N → O linkage photoisomerization mechanism in a ruthenium nitrosyl complex, [RuCl(NO)(py)4]2+, for which a quasicomplete photoconversion between the stable nitrosyl (N-bonded) and metastable isonitrosyl (O-bonded) isomers has been observed under continuous irradiation of the crystal at 473 nm ( Cormary et al. Acta Cryst. B 2009 , 65 , 612 - 623 ), is investigated using multiconfigurational second-order perturbation theory (CASPT2). The results support efficient intersystem crossing pathways from the initially excited singlet states to the lowest triplet excited state of metal-to-ligand charge transfer character (3MLCT). The topology of the involved potential energy surfaces corroborates a complex sequential two-photon photoisomerization mechanism involving nonadiabatic processes in agreement with experimental observations and previous density functional theory calculations.