Unconventional two-step spin relaxation dynamics of [Re(CO)3(im)(phen)]+ in aqueous solution

A Portrait of the Chromophore as a Young System-Quantum-Derived Force Field Unraveling Solvent Reorganization upon Optical Excitation of Cyclocurcumin Derivatives

The study of fast non-equilibrium solvent relaxation in organic chromophores is still challenging for molecular modeling and simulation approaches, and is often overlooked, even in the case of non-adiabatic dynamics simulations. Yet, especially in the case of photoswitches, the interaction with the environment can strongly modulate the photophysical outcomes. To unravel such a delicate interplay, in the present contribution we resorted to a mixed quantum-classical approach, based on quantum mechanically derived force fields. The main task is to rationalize the solvent reorganization pathways in chromophores derived from cyclocurcumin, which are suitable for light-activated chemotherapy to destabilize cellular lipid membranes. The accurate and reliable decryption delivered by the quantum-derived force fields points to important differences in the solvent's reorganization, in terms of both structure and time scale evolution.

Bifurcation of Excited-State Population Leads to Anti-Kasha Luminescence in a Disulfide-Decorated Organometallic Rhenium Photosensitizer

We report a rhenium diimine photosensitizer equipped with a peripheral disulfide unit on one of the bipyridine ligands, [Re(CO)3(bpy)(S-Sbpy4,4)]+ (1+, bpy = 2,2'-bipyridine, S-Sbpy4,4 = [1,2]dithiino[3,4-c:6,5-c']dipyridine), showing anti-Kasha luminescence. Steady-state and ultrafast time-resolved spectroscopies complemented by nonadiabatic dynamics simulations are used to disclose its excited-state dynamics. The calculations show that after intersystem crossing the complex evolves to two different triplet minima: a (S-Sbpy4,4)-ligand-centered excited state (3LC) lying at lower energy and a metal-to-(bpy)-ligand charge transfer (3MLCT) state at higher energy, with relative yields of 90% and 10%, respectively. The 3LC state involves local excitation of the disulfide group into the antibonding σ* orbital, leading to significant elongation of the S-S bond. Intriguingly, it is the higher-lying 3MLCT state, which is assigned to display luminescence with a lifetime of 270 ns: a signature of anti-Kasha behavior. This assignment is consistent with an energy barrier ≥ 0.6 eV or negligible electronic coupling, preventing reaction toward the 3LC state after the population is trapped in the 3MLCT state. This study represents a striking example on how elusive excited-state dynamics of transition-metal photosensitizers can be deciphered by synergistic experiments and state-of-the-art calculations. Disulfide functionalization lays the foundation of a new design strategy toward harnessing excess energy in a system for possible bimolecular electron or energy transfer reactivity.

Vibrational Coherences of the Photoinduced Mixed-Valent Creutz-Taube Ion Revealed by Excited State Dynamics

A recent study of photoinduced mixed-valency in the one-electron reduced form (μ-pz)[RuII(NH3)5]24+ of the Creutz-Taube ion used transient absorption spectroscopy with vis-NIR broadband detection to uncover a mixed-valent excited state with a typical intervalence charge transfer band and a nanosecond lifetime [Pieslinger et al. Angew. Chem., Int. Ed. 2022, 61, e202211747]. Herein, we use excited state dynamics simulations with implicit solvation to elucidate the electronic and vibrational evolution in the first 10 ps after the optical excitation. A manifold of excited states with weak interaction between the metal centers is populated already at time zero due to the breakdown of the Condon approximation and dominates the population of electronic states at short time scales (<0.5 ps). A long-lived vibrational wave packet mostly confined to oscillations of the metal center-bridge distances is observed. The oscillations are traced to the electronic structure properties of states with weak metal-metal coupling. The long-lived mixed-valent excited state of the Creutz-Taube ion analogue is formed vibrationally cold and has a more compact geometry. While experimentally, intersystem crossing and vibrational relaxation were deduced to be completed within 1 ps, our analysis indicates that both processes might persist at longer times.

Spin-flip dynamics in core-excited states in the basis of irreducible spherical tensor operators

Recent experimental advances in ultrafast science have put different processes occurring on the electronic timescale below a few femtoseconds in focus. In the present theoretical work, we demonstrate how the transformation and propagation of the density matrix in the basis of irreducible spherical tensors can be conveniently used to study sub-few fs spin-flip dynamics in core-excited transition metal compounds. With the help of the Wigner-Eckart theorem, such a transformation separates the essential dynamical information from the geometric factors governed by the angular momentum algebra. We show that an additional reduction can be performed by the physically motivated truncation of the spherical tensor basis. In particular, depending on the degree of coherence, the ultrafast dynamics can be considered semi-quantitative in the notably reduced spherical basis when only the total populations of the basis states of the given spin are of interest. Such truncation should be especially beneficial when the number of high-spin basis states is vast, as it reduces computational costs.

Role of Ultrafast Internal Conversion and Intersystem Crossing in the Nonadiabatic Relaxation Dynamics of ortho-Nitrobenzaldehyde

ortho-Nitrobenzaldehyde (oNBA) is a well-known photoactivated acid and a prototypical photolabile nitro-aromatic compound. Despite extensive investigations, the ultrafast relaxation dynamics of oNBA is still not properly understood, especially concerning the role of the triplet states. In this work, we provide an in-depth picture of this dynamics by combining single- and multireference electronic structure methods with potential energy surface exploration and nonadiabatic dynamics simulations using the Surface Hopping including ARbitary Couplings (SHARC) approach. Our results reveal that the initial decay from the bright ππ* state to the S₁ minimum is barrierless. It involves three changes in electronic structure from ππ* (ring) to nπ* (nitro group), to nπ* (aldehyde group), and then to another nπ* (nitro group). The decay of the ππ* takes 60-80 fs and can be tracked with time-resolved luminescence spectroscopy, where we predict for the first time a short-lived coherence of the luminescence energy with a 25 fs period. Intersystem crossing can occur already during the S₄ → S₁ deactivation cascade but also from S₁, with a time constant of about 2.4 ps and such that first a triplet ππ* state localized on the nitro group is populated. The triplet population first evolves into an nπ* and then quickly undergoes hydrogen transfer to form a biradical intermediate, from where the ketene is eventually produced. The majority of the excited population decays from S₁ through two conical intersections of equal utilization, a previously unreported one involving a scissoring motion of the nitro group that leads back to the oNBA ground state and the one involving hydrogen transfer that leads to the ketene intermediate.

Non-Phenomenological Description of the Time-Resolved Emission in Solution with Quantum-Classical Vibronic Approaches-Application to Coumarin C153 in Methanol

We report a joint experimental and theoretical work on the steady-state spectroscopy and time-resolved emission of the coumarin C153 dye in methanol. The lowest energy excited state of this molecule is characterized by an intramolecular charge transfer thus leading to remarkable shifts of the time-resolved emission spectra, dictated by the methanol reorganization dynamics. We selected this system as a prototypical test case for the first application of a novel computational protocol aimed at the prediction of transient emission spectral shapes, including both vibronic and solvent effects, without applying any phenomenological broadening. It combines a recently developed quantum-classical approach, the adiabatic molecular dynamics generalized vertical Hessian method (Ad-MD|gVH), with nonequilibrium molecular dynamics simulations. For the steady-state spectra we show that the Ad-MD|gVH approach is able to reproduce quite accurately the spectral shapes and the Stokes shift, while a ∼0.15 eV error is found on the prediction of the solvent shift going from gas phase to methanol. The spectral shape of the time-resolved emission signals is, overall, well reproduced, although the simulated spectra are slightly too broad and asymmetric at low energies with respect to experiments. As far as the spectral shift is concerned, the calculated spectra from 4 ps to 100 ps are in excellent agreement with experiments, correctly predicting the end of the solvent reorganization after about 20 ps. On the other hand, before 4 ps solvent dynamics is predicted to be too fast in the simulations and, in the sub-ps timescale, the uncertainty due to the experimental time resolution (300 fs) makes the comparison less straightforward. Finally, analysis of the reorganization of the first solvation shell surrounding the excited solute, based on atomic radial distribution functions and orientational correlations, indicates a fast solvent response (≈100 fs) characterized by the strengthening of the carbonyl-methanol hydrogen bond interactions, followed by the solvent reorientation, occurring on the ps timescale, to maximize local dipolar interactions.

Photodynamics of the Molecular Ruby [Cr(ddpd)2]3

The introduction of strong-field ligands can enable luminescence in first-row transition-metal complexes. In this way, earth-abundant near-infrared emitters can be obtained using early 3d metals. A prime example is the molecular ruby [Cr(ddpd)₂]³⁺ (ddpd = N,N'-dimethyl-N,N'-dipyridin-2-ylpyridine-2,6-diamine) that can achieve high phosphorescence quantum yields at room temperature in aqueous solution. To understand these remarkable properties, here, we simulate its photodynamics in water using trajectory surface hopping on linear vibronic coupling potentials parametrized from multiconfigurational CASSCF/CASPT2 calculations. We find that after excitation to the second absorption band, a relaxation cascade through metal-centered states occurs. After an initial back-and-forth intersystem crossing with higher-lying doublet states, the complex relaxes through a manifold of quartet metal-centered states to the low-lying doublet metal-centered states which are responsible for the experimentally observed emission. These electronic processes are driven by an elongation of the Cr-ligand bond lengths as well as the twisting motion of the trans-coordinated pyridine units in the ddpd ligands. The low-lying doublet states are reached within 1-2 ps and are close in geometry to the doublet minima, thus explaining the high phosphorescence quantum yield of the molecular ruby [Cr(ddpd)₂]³⁺.

Triplet Emitting C^N^C Cyclometalated Dibenzo[c,h]Acridine Pt(II) Complexes

In a series of Pt(II) complexes [Pt(dba)(L)] containing the very rigid, dianionic, bis-cyclometalating, tridentate C^N^C2− heterocyclic ligand dba2− (H2dba = dibenzo[c,h]acridine), the coligand (ancillary ligand) L = dmso, PPh3, CNtBu and Me2Imd (N,N’-dimethylimidazolydene) was varied in order to improve its luminescence properties. Beginning with the previously reported dmso complex, we synthesized the PPh3, CNtBu and Me2Imd derivatives and characterized them by elemental analysis, 1H (and 31P) NMR spectroscopy and MS. Cyclic voltammetry showed partially reversible reduction waves ranging between −1.89 and −2.10 V and increasing along the series Me2Imd < dmso ≈ PPh3 < CNtBu. With irreversible oxidation waves ranging between 0.55 (L = Me2Imd) and 1.00 V (dmso), the electrochemical gaps range between 2.65 and 2.91 eV while increasing along the series Me2Imd < CNtBu < PPh3 < dmso. All four complexes show in part vibrationally structured long-wavelength absorption bands peaking at around 530 nm. TD-DFT calculated spectra agree quite well with the experimental spectra, with only a slight redshift. The photoluminescence spectra of all four compounds are very similar. In fluid solution at 298 K, they show broad, only partially structured bands, with maxima at around 590 nm, while in frozen glassy matrices at 77 K, slightly blue-shifted (~580 nm) bands with clear vibronic progressions were found. The photoluminescence quantum yields ΦL ranged between 0.04 and 0.24, at 298 K, and between 0.80 and 0.90 at 77 K. The lifetimes τ at 298 K ranged between 60 and 14040 ns in Ar-purged solutions and increased from 17 to 43 µs at 77 K. The TD-DFT calculated emission spectra are in excellent agreement with the experimental findings. In terms of high ΦL and long τ, the dmso and PPh3 complexes outperform the CNtBu and Me2Imd derivatives. This is remarkable in view of the higher ligand strength of Me2Imd, compared with all other coligands, as concluded from the electrochemical data.

Nonadiabatic excited-state dynamics of ReCl(CO)3(bpy) in two different solvents

We present a study of excited-states relaxation of the complex ReCl(CO)₃(bpy) (bpy = 2,2-bipyridine) using a nonadiabatic TD-DFT dynamics on spin-mixed potential energy surfaces in explicit acetonitrile (ACN) and dimethylsulfoxide (DMSO) solutions up to 800 fs. ReCl(CO)₃(bpy) belongs to a group of important photosensitizers which show ultrafast biexponential subpicosecond fluorescence decay kinetics. The choice of solvents was motivated by the different excited-state relaxation dynamics observed in subpicosecond time-resolved IR (TRIR) experiments. Simulations of intersystem crossing (ISC) showed the development of spin-mixed states in both solvents. Transformation of time-dependent populations of spin-mixed states enabled to monitor the temporal evolution of individual singlet and triplet states, fitting of bi-exponential decay kinetics, and simulating the time-resolved fluorescence spectra that show only minor differences between the two solvents. Analysis of structural relaxation and solvent reorganization employing time-resolved proximal distribution functions pointed to the factors influencing the fluorescence decay time constants. Nonadiabatic dynamics simulations of time-evolution of electronic, molecular, and solvent structures emerge as a powerful technique to interpret time-resolved spectroscopic data and ultrafast photochemical reactivity.

Photocatalytic Reduction of CO2 to CO in Aqueous Solution under Red-Light Irradiation by a Zn-Porphyrin-Sensitized Mn(I) Catalyst

This work demonstrates photocatalytic CO₂ reduction by a noble-metal-free photosensitizer-catalyst system in aqueous solution under red-light irradiation. A water-soluble Mn(I) tricarbonyl diimine complex, [MnBr(4,4′-{Et₂O₃PCH₂}₂-2,2′-bipyridyl)(CO)₃] (1), has been fully characterized, including single-crystal X-ray crystallography, and shown to reduce CO₂ to CO following photosensitization by tetra(N-methyl-4-pyridyl)porphyrin Zn(II) tetrachloride [Zn(TMPyP)]Cl₄ (2) under 625 nm irradiation. This is the first example of 2 employed as a photosensitizer for CO₂ reduction. The incorporation of −P(O)(OEt)₂ groups, decoupled from the core of the catalyst by a −CH₂– spacer, afforded water solubility without compromising the electronic properties of the catalyst. The photostability of the active Mn(I) catalyst over prolonged periods of irradiation with red light was confirmed by ¹H and ¹³C{¹H} NMR spectroscopy. This first report on Mn(I) species as a homogeneous photocatalyst, working in water and under red light, illustrates further future prospects of intrinsically photounstable Mn(I) complexes as solar-driven catalysts in an aqueous environment.

A Mn(I) bipyridyl tricarbonyl complex, where the diimine ligand is functionalized with water-solubilizing phosphonate ester groups, has been prepared and is shown to catalytically convert CO₂ to CO in aqueous solution following photosensitization from a water-soluble Zn(II) porphyrin under red-light irradiation.

Ultrafast Intersystem Crossing Dynamics of 6-Selenoguanine in Water

Rationalizing the photochemistry of nucleobases where an oxygen is replaced by a heavier atom is essential for applications that exploit near-unity triplet quantum yields. Herein, we report on the ultrafast excited-state deactivation mechanism of 6-selenoguanine (6SeGua) in water by combining nonadiabatic trajectory surface-hopping dynamics with an electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) scheme. We find that the predominant relaxation mechanism after irradiation starts on the bright singlet S₂ state that converts internally to the dark S₁ state, from which the population is transferred to the triplet T₂ state via intersystem crossing and finally to the lowest T₁ state. This S₂ → S₁ → T₂ → T₁ deactivation pathway is similar to that observed for the lighter 6-thioguanine (6tGua) analogue, but counterintuitively, the T₁ lifetime of the heavier 6SeGua is shorter than that of 6tGua. This fact is explained by the smaller activation barrier to reach the T₁/S₀ crossing point and the larger spin-orbit couplings of 6SeGua compared to 6tGua. From the dynamical simulations, we also calculate transient absorption spectra (TAS), which provide two time constants (τ₁ = 131 fs and τ₂ = 191 fs) that are in excellent agreement with the experimentally reported value (τ_exp = 130 ± 50 fs) (Farrel et al. J. Am. Chem. Soc. 2018, 140, 11214). Intersystem crossing itself is calculated to occur with a time scale of 452 ± 38 fs, highlighting that the TAS is the result of a complex average of signals coming from different nonradiative processes and not intersystem crossing alone.

Resolving Femtosecond Solvent Reorganization Dynamics in an Iron Complex by Nonadiabatic Dynamics Simulations

The ultrafast dynamical response of solute–solvent interactions plays a key role in transition metal complexes, where charge transfer states are ubiquitous. Nonetheless, there exist very few excited-state simulations of transition metal complexes in solution. Here, we carry out a nonadiabatic dynamics study of the iron complex [Fe(CN)₄(bpy)]^2– (bpy = 2,2′-bipyridine) in explicit aqueous solution. Implicit solvation models were found inadequate for reproducing the strong solvatochromism in the absorption spectra. Instead, direct solute–solvent interactions, in the form of hydrogen bonds, are responsible for the large observed solvatochromic shift and the general dynamical behavior of the complex in water. The simulations reveal an overall intersystem crossing time scale of 0.21 ± 0.01 ps and a strong reliance of this process on nuclear motion. A charge transfer character analysis shows a branched decay mechanism from the initially excited singlet metal-to-ligand charge transfer (¹MLCT) states to triplet states of ³MLCT and metal-centered (³MC) character. We also find that solvent reorganization after excitation is ultrafast, on the order of 50 fs around the cyanides and slower around the bpy ligand. In contrast, the nuclear vibrational dynamics, in the form of Fe–ligand bond changes, takes place on slightly longer time scales. We demonstrate that the surprisingly fast solvent reorganizing should be observable in time-resolved X-ray solution scattering experiments, as simulated signals show strong contributions from the solute–solvent scattering cross term. Altogether, the simulations paint a comprehensive picture of the coupled and concurrent electronic, nuclear, and solvent dynamics and interactions in the first hundreds of femtoseconds after excitation.

Photoinduced bond oscillations in ironpentacarbonyl give delayed synchronous bursts of carbonmonoxide release

Early excited state dynamics in the photodissociation of transition metal carbonyls determines the chemical nature of short-lived catalytically active reaction intermediates. However, time-resolved experiments have not yet revealed mechanistic details in the sub-picosecond regime. Hence, in this study the photoexcitation of ironpentacarbonyl Fe(CO)₅ is simulated with semi-classical excited state molecular dynamics. We find that the bright metal-to-ligand charge-transfer (MLCT) transition induces synchronous Fe-C oscillations in the trigonal bipyramidal complex leading to periodically reoccurring release of predominantly axial CO. Metaphorically the photoactivated Fe(CO)₅ acts as a CO geyser, as a result of dynamics in the potential energy landscape of the axial Fe-C distances and non-adiabatic transitions between manifolds of bound MLCT and dissociative metal-centered (MC) excited states. The predominant release of axial CO ligands and delayed release of equatorial CO ligands are explained in a unified mechanism based on the σ^*(Fe-C) anti-bonding character of the receiving orbital in the dissociative MC states.

The photodissociation of transition metal carbonyls is involved in catalysis and synthetic processes. Here the authors, using semi-classical excited state molecular dynamics, observe details of the early stage dynamics in the photodissociation of Fe(CO)₅, including synchronous bursts of CO at periodic intervals of 90 femtoseconds.

Toward Simulation of Fe(II) Low-Spin → High-Spin Photoswitching by Synergistic Spin-Vibronic Dynamics

A new theoretical approach is presented and applied for the simulation of Fe(II) low-spin (LS, singlet, t_2g⁶e_g⁰) → high-spin (HS, quintet, t_2g⁴e_g²) photoswitching dynamics of the octahedral model complex [Fe(NCH)₆]²⁺. The utilized synergistic methodology heavily exploits the strengths of complementary electronic structure and spin-vibronic dynamics methods. Specifically, we perform 3D quantum dynamics (QD) and full-dimensional trajectory surface hopping (TSH, in conjunction with a linear vibronic coupling model), with the modes for QD selected by TSH. We follow a hybrid approach which is based on the application of time-dependent density functional theory (TD-DFT) excited-state potential energy surfaces (PESs) and multiconfigurational second-order perturbation theory (CASPT2) spin–orbit couplings (SOCs). Our method delivers accurate singlet–triplet–quintet intersystem crossing (ISC) dynamics, as assessed by comparison to our recent high-level ab initio simulations and related time-resolved experimental data. Furthermore, we investigate the capability of our simulations to identify the location of ISCs. Finally, we assess the approximation of constant SOCs (calculated at the Franck–Condon geometry), whose validity has central importance for the combination of TD-DFT PESs and CASPT2 SOCs. This efficient methodology will have a key role in simulating LS → HS dynamics for more complicated cases, involving higher density of states and varying electronic character, as well as the analysis of ultrafast experiments.

Excitation-Wavelength-Dependent Photophysics of d8d8 Di-isocyanide Complexes

Binuclear Rh(I) and Ir(I) TMB (2,5-dimethyl-2,5-diisocyanohexane) and dimen (1,8-diisocyanomenthane) complexes possess dσ*pσ and dπpσ singlet and triplet excited states that can be selectively excited in the visible and UV spectral regions. Using perturbational spin-orbit TDDFT, we unraveled the detailed character and spin mixing of these electronic transitions and found that delocalization of pσ and dπ orbitals over C≡N- groups makes C≡N stretching vibrations sensitive reporters of electron density and structural changes upon electronic excitation. Picosecond time-resolved infrared spectra measured after visible light, 375 nm, and 316 nm excitation revealed excitation-wavelength-dependent deactivation cascades. Visible light irradiation prepares the ¹dσ*pσ state that, after one or two (sub)picosecond relaxation steps, undergoes 70-1300 ps intersystem crossing to ³dσ*pσ, which is faster for the more flexible dimen complexes. UV-excited ^1,3dπpσ states decay with (sub)picosecond kinetics through a manifold of high-lying triplet and mixed-spin states to ³dσ*pσ with lifetimes in the range of 6-19 ps (316 nm) and 19-43 ps (375 nm, Ir only), bypassing ¹dσ*pσ. Most excited-state conversion and some relaxation steps are accompanied by direct decay to the ground state that is especially pronounced for the most flexible long/eclipsed Rh(dimen) conformer.

On the intersystem crossing rate in a Platinum(II) donor-bridge-acceptor triad

The rates of ultrafast intersystem crossing in acceptor-bridge-donor molecules centered on Pt(II) acetylides are investigated. Specifically, a Pt(II) trans-acetylide triad NAP--Pt--Ph-CH₂-PTZ [1], with acceptor 4-ethynyl-N-octyl-1,8-naphthalimide (NAP) and donor phenothiazine (PTZ), is examined in detail. We have previously shown that optical excitation in [1] leads to a manifold of singlet charge-transfer states, S*, which evolve via a triplet charge-transfer manifold into a triplet state ³NAP centered on the acceptor ligand and partly to a charge-separated state ³CSS (NAP^--Pt-PTZ⁺). A complex cascade of electron transfer processes was observed, but intersystem crossing (ISC) rates were not explicitly resolved due to lack of spin selectivity of most ultrafast spectroscopies. Here we revisit the question of ISC with a combination and complementary analysis of (i) transient absorption, (ii) ultrafast broadband fluorescence upconversion, FLUP, which is only sensitive to emissive states, and (iii) femtosecond stimulated Raman spectroscopy, FSR. Raman resonance conditions allow us to observe S* and ³NAP exclusively by FSR, through vibrations which are pertinent only to these two states. This combination of methods enabled us to extract the intersystem crossing rates that were not previously accessible. Multiple timescales (1.6 ps to ∼20 ps) are associated with the rise of triplet species, which can now be assigned conclusively to multiple ISC pathways from a manifold of hot charge-transfer singlet states. The analysis is consistent with previous transient infrared spectroscopy data. A similar rate of ISC, up to 20 ps, is observed in the trans-acetylide NAP--Pt--Ph [2] which maintains two acetylide groups across the platinum center but lacks a donor unit, whilst removal of one acetylide group in mono-acetylide NAP--Pt-Cl [3] leads to >10-fold deceleration of the intersystem crossing process. Our work provides insight on the intersystem crossing dynamics of the organo-metallic complexes, and identifies a general method based on complementary ultrafast spectroscopies to disentangle complex spin, electronic and vibrational processes following photoexcitation.

Photoinduced hole hopping through tryptophans in proteins

Hole hopping through tryptophan/tyrosine chains enables rapid unidirectional charge transport over long distances. We have elucidated structural and dynamical factors controlling hopping speed and efficiency in two modified azurin constructs that include a rhenium(I) sensitizer, Re(His)(CO)₃(dmp)⁺, and one or two tryptophans (W₁, W₂). Experimental kinetics investigations showed that the two closely spaced (3 to 4 Å) intervening tryptophans dramatically accelerated long-range electron transfer (ET) from Cu^I to the photoexcited sensitizer. In our theoretical work, we found that time-dependent density-functional theory (TDDFT) quantum mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) trajectories of low-lying triplet excited states of Re^I(His)(CO)₃(dmp)⁺-W₁(-W₂) exhibited crossings between sensitizer-localized (*Re) and charge-separated [Re^I(His)(CO)₃(dmp^•-)/(W₁ ^•+ or W₂ ^•+)] (CS1 or CS2) states. Our analysis revealed that the distances, angles, and mutual orientations of ET-active cofactors fluctuate in a relatively narrow range in which the cofactors are strongly coupled, enabling adiabatic ET. Water-dominated electrostatic field fluctuations bring *Re and CS1 states to a crossing where *Re(CO)₃(dmp)⁺←W₁ ET occurs, and CS1 becomes the lowest triplet state. ET is promoted by solvation dynamics around *Re(CO)₃(dmp)⁺(W₁); and CS1 is stabilized by Re(dmp^•-)/W₁ ^•+ electron/hole interaction and enhanced W₁ ^•+ solvation. The second hop, W₁ ^•+←W₂, is facilitated by water fluctuations near the W₁/W₂ unit, taking place when the electrostatic potential at W₂ drops well below that at W₁ ^•+ Insufficient solvation and reorganization around W₂ make W₁ ^•+←W₂ ET endergonic, shifting the equilibrium toward W₁ ^•+ and decreasing the charge-separation yield. We suggest that multiscale TDDFT/MM/MD is a suitable technique to model the simultaneous evolution of photogenerated excited-state manifolds.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Ultrafast and long-time excited state kinetics of an NIR-emissive vanadium(iii) complex II. Elucidating triplet-to-singlet excited-state dynamics

We report the non-adiabatic dynamics of VIIICl3(ddpd), a complex based on the Earth-abundant first-row transition metal vanadium with a d2 electronic configuration which is able to emit phosphorescence in solution in the near-infrared spectral region. Trajectory surface-hopping dynamics based on linear vibronic coupling potentials obtained with CASSCF provide molecular-level insights into the intersystem crossing from triplet to singlet metal-centered states. While the majority of the singlet population undergoes back-intersystem crossing to the triplet manifold, 1-2% remains stable during the 10 ps simulation time, enabling the phosphorescence described in Dorn et al. Chem. Sci., 2021, DOI: 10.1039/D1SC02137K. Competing with intersystem crossing, two different relaxation channels via internal conversion through the triplet manifold occur. The nuclear motion that drives the dynamics through the different electronic states corresponds mainly to the increase of all metal-ligand bond distances as well as the decrease of the angles of trans-coordinated ligand atoms. Both motions lead to a decrease in the ligand-field splitting, which stabilizes the interconfigurational excited states populated during the dynamics. Analysis of the electronic character of the states reveals that increasing and stabilizing the singlet population, which in turn can result in enhanced phosphorescence, could be accomplished by further increasing the ligand-field strength.

An Ab Initio Multiple Cloning Method for Non-Adiabatic Excited-State Molecular Dynamics in NWChem

The recently developed ab initio multiple cloning (AIMC) approach based on the multiconfigurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to nonadiabatic dynamics with a particular strength in the proper description of decoherence effects because of the branching of vibrational wavepackets at a level crossing. Here, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-field theory to determine the equations of motion for classical trajectories. The multidimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based nonadiabatic coupling approach within the AIMC method, all observables are calculated on-the-fly in the nonadiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level nonadiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.

Trajectory surface-hopping photoinduced dynamics from Rydberg states of trimethylamine

We present a computational study on nonadiabatic excited-state dynamics initiated from the 3p Rydberg states of trimethylamine (TMA). We utilise a methodology based on full-dimensional (39 D) trajectory surface-hopping (TSH) simulations, in which propagation is carried out on on-the-fly density functional theory (DFT)/time-dependent DFT (TD-DFT) potentials. Both our electronic structure benchmarks to high-level ab initio methods (EOM-CCSD, CASPT2) and TSH simulations demonstrate high-accuracy of the applied CAM-B3LYP functional for the description of Rydberg excited states. Based on our excited-state simulations, we construct the following mechanistic picture: when pumped resonantly to the 3p Rydberg manifold, TMA coherently vibrates along the planarisation mode with a period of 104 fs and an exponential coherence decay time constant of 240 fs. Nonadiabatic dynamics occur on a faster (∼1 ps) and a slower (∼3 ps) timescale, along the N-C stretching mode by mixing with a dissociative σN-C* state. As a minor relaxation channel, 3p → 3s internal conversion occurs via branching at the σN-C*/3s intersection. We find that photodissociaton is hardly observable within 3 ps (1%), which is a failure of the range-separated hybrid CAM-B3LYP functional, as a consequence of its static electron correlation deficiency at long range. In contrast, pure DFT (GGA-BLYP) provides an accurate long-range description (19% dissociation yield), also supported by comparison to recent ultrafast experiments, even if the Rydberg state energies are significantly underestimated (>1 eV). Finally, we reveal the crucial role of vibrational coherence and energy transfer from the planarisation mode for N-C bond activation and resulting nonadiabatic dynamics. The present work illustrates the importance of nuclear-electronic coupling for excited-state dynamics and branching at conical intersections.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Excited-State Dynamics of [Ru(S-Sbpy)(bpy)2]2+ to Form Long-Lived Localized Triplet States

The novel photosensitizer [Ru(^S–Sbpy)(bpy)₂]²⁺ harbors two distinct sets of excited states in the UV/Vis region of the absorption spectrum located on either bpy or ^S–Sbpy ligands. Here, we address the question of whether following excitation into these two types of states could lead to the formation of different long-lived excited states from where energy transfer to a reactive species could occur. Femtosecond transient absorption spectroscopy identifies the formation of the final state within 80 fs for both excitation wavelengths. The recorded spectra hint at very similar dynamics following excitation toward either the parent or sulfur-decorated bpy ligands, indicating ultrafast interconversion into a unique excited-state species regardless of the initial state. Non-adiabatic surface hopping dynamics simulations show that ultrafast spin–orbit-mediated mixing of the states within less than 50 fs strongly increases the localization of the excited electron at the ^S–Sbpy ligand. Extensive structural relaxation within this sulfurated ligand is possible, via S–S bond cleavage that results in triplet state energies that are lower than those in the analogue [Ru(bpy)₃]²⁺. This structural relaxation upon localization of the charge on ^S–Sbpy is found to be the reason for the formation of a single long-lived species independent of the excitation wavelength.

We investigate selective excitation in two types of ligands present in [Ru(^S−Sbpy)(bpy)₂]²⁺. Femtosecond transient absorption spectroscopy identifies the formation of the same final state within 80 fs for both excitation wavelengths. Surface hopping simulations reveal ultrafast mixing of singlet and triplet states within less than 50 fs. Energy lowering due to S−S bond cleavage is identified as the driving factor for convergence to a single final state.

Ultrafast processes: coordination chemistry and quantum theory

Coordination compounds, characterized by fascinating and tunable electronic properties, are capable of binding easily to proteins, polymers, wires and DNA. Upon irradiation, these molecular systems develop functions finding applications in solar cells, photocatalysis, luminescent and conformational probes, electron transfer triggers and diagnostic or therapeutic tools. The control of these functions is activated by the light wavelength, the metal/ligand cooperation and the environment within the first picoseconds (ps). After a brief summary of the theoretical background, this perspective reviews case studies, from 1st row to 3rd row transition metal complexes, that illustrate how spin-orbit, vibronic coupling and quantum effects drive the photophysics of this class of molecules at the early stage of the photoinduced elementary processes within the fs-ps time scale range.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

Intersystem Crossing and Triplet Dynamics in an Iron(II) N-Heterocyclic Carbene Photosensitizer

The electronic excited states of the iron(II) complex [Fe^II(tpy)(pyz-NHC)]²⁺ [tpy = 2,2′:6′,2″-terpyridine; pyz-NHC = 1,1′-bis(2,6-diisopropylphenyl)pyrazinyldiimidazolium-2,2′-diylidene] and their relaxation pathways have been theoretically investigated. To this purpose, trajectory surface-hopping simulations within a linear vibronic coupling model including a 244-dimensional potential energy surface (PES) with 20 singlet and 20 triplet coupled states have been used. The simulations show that, after excitation to the lowest-energy absorption band of predominant metal-to-ligand charge-transfer character involving the tpy ligand, almost 80% of the population undergoes intersystem crossing to the triplet manifold in about 50 fs, while the remaining 20% decays through internal conversion to the electronic ground state in about 300 fs. The population transferred to the triplet states is found to deactivate into two different regions of the PESs, one where the static dipole moment is small and shows increased metal-centered character and another with a large static dipole moment, where the electron density is transferred from the tpy to pyz-NHC ligand. Coherent oscillations of 400 fs are observed between these two sets of triplet populations, until the mixture equilibrates to a ratio of 60:40. Finally, the importance of selecting suitable normal modes is highlighted—a choice that can be far from straightforward in transition-metal complexes with hundreds of degrees of freedom.

Trajectory surface-hopping simulations with a linear vibronic coupling model reveal the competition of major intersystem crossing versus minor internal conversion dynamics in an iron(II) N-heterocyclic carbene dye. The triplet population bifurcates into two regions of the potential energy surfaces, characterized by small and large static dipole moments due to different electronic character and showing coherent oscillations of 400 fs until both triplet populations coexist in a mixture of 60:40.

Competing ultrafast photoinduced electron transfer and intersystem crossing of [Re(CO) 3 (Dmp)(His124)(Trp122)] + in Pseudomonas aeruginosa azurin: a nonadiabatic dynamics study

We present a computational study of sub-picosecond nonadiabatic dynamics in a rhenium complex coupled electronically to a tryptophan (Trp) side chain of Pseudomonas aeruginosa azurin, a prototypical protein used in the study of electron transfer in proteins. To gain a comprehensive understanding of the photoinduced processes in this system, we have carried out vertical excitation calculations at the TDDFT level of theory as well as nonadiabatic dynamics simulations using the surface hopping including arbitrary couplings (SHARC) method coupled to potential energy surfaces represented with a linear vibronic coupling model. The results show that the initial photoexcitation populates both singlet metal-to-ligand charge transfer (MLCT) and singlet charge-separated (CS) states, where in the latter an electron was transferred from the Trp amino acid to the complex. Subsequently, a complex mechanism of simultaneous intersystem crossing and electron transfer leads to the sub-picosecond population of triplet MLCT and triplet CS states. These results confirm the assignment of the sub-ps time constants of previous experimental studies and constitute the first computational evidence for the ultrafast formation of the charge-separated states in Re-sensitized azurin.

TheoDORE: A toolbox for a detailed and automated analysis of electronic excited state computations

The advent of ever more powerful excited-state electronic structure methods has led to a tremendous increase in the predictive power of computation, but it has also rendered the analysis of these computations much more challenging and time-consuming. TheoDORE tackles this problem through providing tools for post-processing excited-state computations, which automate repetitive tasks and provide rigorous and reproducible descriptors. Interfaces are available for ten different quantum chemistry codes and a range of excited-state methods implemented therein. This article provides an overview of three popular functionalities within TheoDORE, a fragment-based analysis for assigning state character, the computation of exciton sizes for measuring charge transfer, and the natural transition orbitals used not only for visualization but also for quantifying multiconfigurational character. Using the examples of an organic push-pull chromophore and a transition metal complex, it is shown how these tools can be used for a rigorous and automated assignment of excited-state character. In the case of a conjugated polymer, we venture beyond the limits of the traditional molecular orbital picture to uncover spatial correlation effects using electron-hole correlation plots and conditional densities.

Time-Resolved Femtosecond Stimulated Raman Spectra and DFT Anharmonic Vibrational Analysis of an Electronically Excited Rhenium Photosensitizer

Time-resolved femtosecond stimulated Raman spectra (FSRS) of a prototypical organometallic photosensitizer/photocatalyst ReCl(CO)₃(2,2'-bipyridine) were measured in a broad spectral range ∼40-2000 (4000) cm^-1 at time delays from 40 fs to 4 ns after 400 nm excitation of the lowest allowed electronic transition. Theoretical ground- and excited-state Raman spectra were obtained by anharmonic vibrational analysis using second-order vibrational perturbation theory on vibrations calculated by harmonic approximation at density functional theory-optimized structures. A good match with anharmonically calculated vibrational frequencies allowed for assigning experimental Raman features to particular vibrations. Observed frequency shifts upon excitation (ν(ReCl) and ν(CC inter-ring) vibrations upward; ν(CC, CN) and ν(Re-C) downward) are consistent with the bonding/antibonding characters of the highest occupied molecular orbital and the lowest unoccupied molecular orbital involved in excitation and support the delocalized formulation of the lowest triplet state as ReCl(CO)₃ → bpy charge transfer. FSRS spectra show a mode-specific temporal evolution, providing insights into the intersystem crossing (ISC) mechanism and subsequent relaxation. Most of the Raman features are present at ∼40 fs and exhibit small shifts and intensity changes with time. The 1450-1600 cm^-1 group of bands due to CC, CN, and CC(inter-ring) stretching vibrations undergoes extensive restructuring between 40 and ∼150 fs, followed by frequency upshifts and a biexponential (0.38, 21 ps) area growth, indicating progressing charge separation in the course of the formation and relaxation of the lowest triplet state. Early (40-150 fs) restructuring was also observed in the low-frequency range for ν(Re-Cl) and δ(Re-C-O) vibrations that are presumably activated by ISC. FSRS experimental innovations employed to measure low- and high-energy Raman features simultaneously are described and discussed in detail.

Light-Induced Nanosecond Relaxation Dynamics of Rhenium-Labeled Pseudomonas aeruginosa Azurins

Time-resolved phosphorescence spectra of Re(CO)₃(dmp)⁺ and Re(CO)₃(phen)⁺ chromophores (dmp = 4,7-dimethyl-1,10-phenanthroline, phen = 1,10-phenanthroline) bound to surface histidines (H83, H124, and H126) of Pseudomonas aeruginosa azurin mutants exhibit dynamic band maxima shifts to lower wavenumbers following 3-exponential kinetics with 1-5 and 20-100 ns major phases and a 1.1-2.5 μs minor (5-16%) phase. Observation of slow relaxation components was made possible by using an organometallic Re chromophore as a probe whose long phosphorescence lifetime extends the observation window up to ∼3 μs. Integrated emission-band areas also decay with 2- or 3-exponential kinetics; the faster decay phase(s) is relaxation-related, whereas the slowest one [360-680 ns (dmp); 90-140 ns (phen)] arises mainly from population decay. As a result of shifting bands, the emission intensity decay kinetics depend on the detection wavelength. Detailed kinetics analyses and comparisons with band-shift dynamics are needed to disentangle relaxation and population decay kinetics if they occur on comparable timescales. The dynamic phosphorescence Stokes shift in Re-azurins is caused by relaxation motions of the solvent, the protein, and solvated amino acid side chains at the Re binding site in response to chromophore electronic excitation. Comparing relaxation and decay kinetics of Re(dmp)124K122Cu^II and Re(dmp)124W122Cu^II suggests that electron transfer (ET) and relaxation motions in the W122 mutant are coupled. It follows that nanosecond and faster photo-induced ET steps in azurins (and likely other redox proteins) occur from unrelaxed systems; importantly, these reactions can be driven (or hindered) by structural and solvational dynamics.

Sterically hindered Re- and Mn-CO2 reduction catalysts for solar energy conversion

Novel molecular Re and Mn tricarbonyl complexes bearing a bipyridyl ligand functionalised with sterically hindering substituents in the 6,6'-position, [M(HPEAB)(CO)3(X)] (M/X = Re/Cl, Mn/Br; HPEAB = 6,6'-{N-(4-hexylphenyl)-N(ethyl)-amido}-2,2'-bipyridine) have been synthesised, fully characterised including by single crystal X-ray crystallography, and their propensity to act as catalysts for the electrochemical and photochemical reduction of CO2 has been established. Controlled potential electrolysis showed that the catalysts are effective for electrochemical CO2-reduction, yielding CO as the product (in MeCN for the Re-complex, in 95 : 5 (v/v) MeCN : H2O mixture for the Mn-complex). The recyclability of the catalysts was demonstrated through replenishment of CO2 within solution. The novel catalysts had similar reduction potentials to previously reported complexes of similar structure, and results of the foot-of-the-wave analysis showed comparable maximum turnover rates, too. The tentative mechanisms for activation of the pre-catalysts were proposed on the basis of IR-spectroelectrochemical data aided by DFT calculations. It is shown that the typical dimerisation of the Mn-catalyst was prevented by incorporation of sterically hindering groups, whilst the Re-catalyst undergoes the usual mechanism following chloride ion loss. No photochemical CO2 reduction was observed for the rhenium complex in the presence of a sacrificial donor (triethylamine), which was attributed to the short triplet excited state lifetime (3.6 ns), insufficient for diffusion-controlled electron transfer. Importantly, [Mn(HPEAB)(CO)3Br] can act as a CO2 reduction catalyst when photosensitised by a zinc porphyrin under red light irradiation (λ > 600 nm) in MeCN : H2O (95 : 5); there has been only one reported example of photoactivating Mn-catalysts with porphyrins in this manner. Thus, this work demonstrates the wide utility of sterically protected Re- and Mn-diimine carbonyl catalysts, where the rate and yield of CO-production can be adjusted based on the metal centre and catalytic conditions, with the advantage of suppressing unwanted side-reactions through steric protection of the vacant coordination site.