Neural network potentials facilitating accurate complex scaling for molecular resonances: from a model to high dimensional realistic systems

Here we propose a neural network based complex scaling (NN-CS) method for computing the complex eigenvalues (Er-iΓ/2) of molecular resonances, in which the CS of the potential part in the non-Hermitian Hamiltonian is effectively achieved by NNs. Taking a two-dimensional (2D) diabatic model including two states coupled by the conical intersection for example, the NN-CS method is shown to reproduce the eigenvalues of the resonance states quite well. Subsequently, this NN-CS method with a 2D Hamiltonian model is utilized to compute the vibronic resonances in the 1nσ*-mediated photodissociation of thioanisole based on a new NN diabatic potential energy matrix. The calculated lifetimes of the vibronic resonances are found to be in good agreement with other theoretical results and available experimental data. Finally, the NN-CS method is applied to treat a much more challenging system, namely, the resonances in the six-dimensional (6D) photodissociation continuum of NH3, due to its high dimensionalities and all three dissociative coordinates needing to be scaled in the complex scaling of the potential part. Again, the calculated energy positions and widths of the 6D resonances by the NN-CS method agree well with other theoretical results. Our calculations show that the NN-CS method is able to accurately treat the vibronic resonances involving multiple coupled electronic states and resonances in high dimensional realistic systems.

Dynamic Role of the Intramolecular Hydrogen Bonding in the S1 State Relaxation Dynamics Revealed by the Direct Measurement of the Mode-Dependent Internal Conversion Rate of 2-Chlorophenol and 2-Chlorothiophenol

The dynamic role of the intramolecular hydrogen bond in the S1 relaxation of cis-2-chlorophenol (2-CP) or cis-2-chlorothiophenol (2-CTP) has been investigated in a state-specific manner. Whereas ultrafast internal conversion is dominant for 2-CP, the H-tunneling competes with internal conversion for 2-CTP even at the S1 origin. The S0-S1 internal conversion rate of 2-CTP could be directly measured from the S1 lifetimes of 2-CTP-d1 (Cl-C6H4-SD) as the D-tunneling is kinetically blocked, allowing distinct estimations of tunneling and internal conversion rates with increasing the energy. The internal conversion rate of 2-CTP increases by two times at the out-of-plane torsional mode excitation, suggesting that the internal conversion is facilitated at the nonplanar geometry. It then sharply increases at ∼600 cm-1, indicating that the S1/S0 conical intersection is readily accessible at the extended C-Cl bond length. The strength of the intramolecular hydrogen bond should be responsible for the distinct dynamic behaviors of 2-CP and 2-CTP.

Influence of Mode-Specific Excitation on the Nonadiabatic Dynamics of Methyl Nitrate (CH3ONO2)

The impact of mode-specific vibrational excitations on initial-preparation conditions was studied by examining the excited-state population decay rates in the nonadiabatic dynamics of methyl nitrate (CH₃ONO₂). In particular, exciting a few specific modes by adding a single quantum of energy clearly decelerated the nonadiabatic dynamics population decay rates. The underlying reason for this slower population decay was explained by analyzing the profiles of the excited-state potential energy surfaces in the Franck-Condon regions and the topology of the S₁/S₀ conical intersection. This study not only provides physical insights into the key mechanisms controlling nonadiabatic dynamics but also shows the possibility of controlling nonadiabatic dynamics via mode-specific vibrational excitations.

Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops

Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self-consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time-derivative CSDM (tCSDM), and with curvature-driven CSDM (κCSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in κCSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.

πσ*-Mediated Nonadiabatic Tunneling Dynamics of Thiophenols in S1: The Semiclassical Approaches

The S-H bond tunneling predissociation dynamics of thiophenol and its ortho-substituted derivatives (2-fluorothiophenol, 2-methoxythiophenol, and 2-chlorothiphenol) in S₁ (ππ*) where the H atom tunneling is mediated by the nearby S₂ (πσ*) state (which is repulsive along the S-H bond extension coordinate) have been investigated in a state-specific way using the picosecond time-resolved pump-probe spectroscopy for the jet-cooled molecules. The effects of the specific vibrational mode excitations and the SH/SD substitutions on the S-H(D) bond rupture tunneling dynamics have been interrogated, giving deep insights into the multidimensional aspects of the S₁/S₂ conical intersection, which also shapes the underlying adiabatic tunneling potential energy surfaces (PESs). The semiclassical tunneling rate calculations based on the Wentzel-Kramers-Brillouin (WKB) approximation or Zhu-Nakamura (ZN) theory have been carried out based on the ab initio PESs calculated in the (one, two, or three) reduced dimensions to be compared with the experiment. Though the quantitative experimental results could not be reproduced satisfactorily by the present calculations, the qualitative trends among different molecules in terms of the behavior of the tunneling rate versus the (adiabatic) barrier height or the number of PES dimensions could be rationalized. Most interestingly, the H/D kinetic isotope effect observed in the tunneling rate could be much better explained by the ZN theory compared to the WKB approximation, indicating that the nonadiabatic coupling matrix elements should be invoked for understanding the tunneling dynamics taking place in the proximity of the conical intersection.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

S1-State Decay Dynamics of Benzenediols (Catechol, Resorcinol, and Hydroquinone) and Their 1:1 Water Clusters

The S₁-state decaying rates of the three different benzenediols, catechol, resorcinol, and hydroquinone, and their 1:1 water clusters have been state-specifically measured using the picosecond time-resolved parent ion transients obtained by the pump (excitation) and probe (ionization) scheme. The S₁ lifetime of catechol is found to be short, giving τ ∼ 5.9 ps at the zero-point level. This is ascribed to the H-atom detachment from the free OH moiety of the molecule. Consistent with a previous report (J. Phys. Chem. Lett. 2013, 4, 3819-3823), the S₁ lifetime gets lengthened with low-frequency vibrational mode excitations, giving τ ∼ 9.0 ps for the 116 cm^-1 band. The S₁ lifetimes at the additional vibronic modes of catechol are newly measured, showing the nonnegligible mode-dependent fluctuations of the tunneling rate. When catechol is complexed with water, the S₁ lifetime is enormously increased to τ ∼ 1.80 ns at the zero-point level while it shows an unusual dip at the intermolecular stretching mode excitation (τ ∼ 1.03 ns at 146 cm^-1). Otherwise, it is shortened monotonically with increasing the internal energy, giving τ ∼ 0.67 ns for the 856 cm^-1 band. Two different asymmetric or symmetric conformers of resorcinol give the respective S₁ lifetimes of 4.5 or 6.3 ns at their zero-point levels according to the estimation from our transients taken within the temporal window of 0-2.7 ns. When resorcinol is 1:1 complexed with H₂O, the S₁ decaying rate is slightly accelerated for both conformers. The S₁ lifetimes of trans and cis forms of hydroquinone are measured to be more or less same, giving τ ∼ 2.8 ns at the zero-point level. When H₂O is complexed with hydroquinone, the S₁ decaying process is facilitated for both conformers, slightly more efficiently for the cis conformer.

Femtosecond Wavepacket Dynamics Reveals the Molecular Structures in the Excited (S1) and Cationic (D0) States

Molecular structures in the electronically excited (S₁) and cationic (D₀) states of 2-fluorothioanisole (2-FTA) have been precisely refined from the real-time dynamics of the femtosecond (fs) wavepacket prepared by the coherent excitation of the Franck-Condon active out-of-plane torsional modes in the S₁ ← S₀ transition at 285 nm. The simulation to reproduce the experiment in terms of the beating frequencies gives the nonplanar geometry of 2-FTA in S₁, where the out-of-plane dihedral angle (φ) of the S-CH₃ moiety is 51° with respect to the molecular plane. The behavior of the fs wavepacket in terms of the amplitudes and phases with the change of the probe (ionization) wavelength (λ_probe = 300-330 nm) provides the otherwise veiled structure of the cationic D₀ state. While the 2-FTA cation adopts the planar geometry (φ = 0°) at the global minimum, it is found to have a vertical minimum at φ ≈ 135° from the perspective of the D₀ ← S₁ vertical transition. Ab initio calculations support the experiment quite well although the simulation using the model potentials could improve the match with the experiment, giving the new interpretation for the previously disputed photoelectron spectroscopic results.

Diabatization by Machine Intelligence

Understanding nonadiabatic dynamics is important for chemical and physical processes involving multiple electronic states. Direct nonadiabatic dynamics simulations are often employed to observe such processes on a femtosecond time scale. One often needs to do the simulation on a longer time scale, but direct simulation based on electronic structure calculations of the surfaces and couplings is expensive due to the large number of electronic structure calculations needed for ensemble averaging or simulation of longer-time processes. An alternative approach is to construct an analytical representation of potential energy surfaces (PESs) and couplings, which allows for faster dynamics calculations. Diabatic representations are preferred for such purposes because of the smoothness of the surfaces and couplings and the scalar nature of the couplings. However, many diabatization procedures are complicated by the need to consider orbitals or vector coupling elements, and these can make the process very labor-intensive. To circumvent these difficulties, we here propose diabatization by a deep neural network (DDNN) based on a new architecture for a deep neural network that requires neither orbital input nor vector input. The DDNN method allows convenient and semiautomatic diabatization, and it is demonstrated here for a model problem and for producing diabatic potential energy matrices for thiophenol.

Multidimensional characterization of the conical intersection seam in the normal mode space

Multidimensional conical intersection seam has been characterized by utilizing the dynamic resonances in the nonadiabatic transition probability experimentally observed in the predissociation of thioanisole isotopomers.

A molecular movie of ultrafast singlet fission

The complex dynamics of ultrafast photoinduced reactions are governed by their evolution along vibronically coupled potential energy surfaces. It is now often possible to identify such processes, but a detailed depiction of the crucial nuclear degrees of freedom involved typically remains elusive. Here, combining excited-state time-domain Raman spectroscopy and tree-tensor network state simulations, we construct the full 108-atom molecular movie of ultrafast singlet fission in a pentacene dimer, explicitly treating 252 vibrational modes on 5 electronic states. We assign the tuning and coupling modes, quantifying their relative intensities and contributions, and demonstrate how these modes coherently synchronise to drive the reaction. Our combined experimental and theoretical approach reveals the atomic-scale singlet fission mechanism and can be generalized to other ultrafast photoinduced reactions in complex systems. This will enable mechanistic insight on a detailed structural level, with the ultimate aim to rationally design molecules to maximise the efficiency of photoinduced reactions.

Quantifying rival bond fission probabilities following photoexcitation: C-S bond fission in t-butylmethylsulfide

We illustrate a new, collision-free experimental strategy that allows determination of the absolute probabilities of rival bond fission processes in a photoexcited molecule - here t-butylmethylsulfide (BSM). The method combines single photon ('universal') ionization laser probe methods, simultaneous imaging of all probed fragments (multi-mass ion imaging) and the use of an appropriate internal calibrant (here dimethylsulfide). Image analysis allows quantification of the dynamics of the rival B-SM and BS-M bond fission processes following ultraviolet (UV) excitation of BSM and shows the former to be twice as probable, despite the only modest (∼2%) differences in the respective ground state equilibrium C-S bond lengths or bond strengths. Rationalising this finding should provide a stringent test of the two close-lying, coupled excited states of 1A'' symmetry accessed by UV excitation in BSM and related thioethers, of the respective transition dipole moment surfaces, and of the geometry dependent non-adiabatic couplings that enable the rival C-S bond fissions.

Experimental observation of nonadiabatic bifurcation dynamics at resonances in the continuum

The surface crossing of bound and unbound electronic states in multidimensional space often gives rise to resonances in the continuum. This situation happens in the πσ*-mediated photodissociation reaction of 2-fluorothioanisole; optically-bright bound S1 (ππ*) vibrational states of 2-fluorothioanisole are strongly coupled to the optically-dark S2 (πσ*) state, which is repulsive along the S-CH3 elongation coordinate. It is revealed here that the reactive flux prepared at such resonances in the continuum bifurcates into two distinct reaction pathways with totally different dynamics in terms of energy disposal and nonadiabatic transition probability. This indicates that the reactive flux in the Franck-Condon region may either undergo nonadiabatic transition funneling through the conical intersection from the upper adiabat, or follow a low-lying adiabatic path, along which multiple dynamic saddle points may be located. Since 2-fluorothioanisole adopts a nonplanar geometry in the S1 minimum energy, the quasi-degenerate S1/S2 crossing seam in the nonplanar geometry, which lies well below the planar S1/S2 conical intersection, is likely responsible for the efficient vibronic coupling, especially in the low S1 internal energy region. As the excitation energy increases, bound-to-continuum coupling is facilitated with the aid of intramolecular vibrational redistribution, along many degrees of freedom spanning the large structural volume. This leads to the rapid domination of the continuum character of the reactive flux. This work reports direct and robust experimental observations of the nonadiabatic bifurcation dynamics of the reactive flux occurring at resonances in the continuum of polyatomic molecules.

Ultrafast excited-state dynamics of 2,5-dimethylpyrrole

The ultrafast excited-state dynamics of 2,5-dimethylpyrrole is studied in detail following deep UV excitation.

The Role of Rydberg-Valence Coupling in the Ultrafast Relaxation Dynamics of Acetone

The electronic structure of excited states of acetone is represented by a Rydberg manifold that is coupled to valence states which provide very fast and efficient relaxation pathways. We observe and characterize the transfer of population from photoexcited Rydberg states (6p, 6d, 7s) to a whole series of lower Rydberg states (3p to 4d) and a simultaneous decay of population from these states. We obtain these results with time-resolved photoelectron–photoion coincidence (PEPICO) detection in combination with the application of Bayesian statistics for data analysis. Despite the expectedly complex relaxation behavior, we find that a simple sequential decay model is able to describe the observed PEPICO transients satisfactorily. We obtain a slower decay (∼320 fs) from photoexcited states compared to a faster decay (∼100 fs) of states that are populated by internal conversion, demonstrating that different relaxation dynamics are active. Within the series of Rydberg states populated by internal conversion, the decay dynamics seem to be similar, and a trend of slower decay from lower states indicates an increasingly higher energy barrier along the decay pathway for lower states. The presented results agree all in all with previous relaxation studies within the Rydberg manifold. The state-resolved observation of transient population ranging from 3p to 4d can serve as reference for time-dependent simulations.

Full-dimensional multi-state simulation of the photodissociation of thioanisole

The photodissociation of thioanisole is very interesting because the experiments of Lim and Kim provide evidence for mode-specific effects on the product distribution. They showed that, with a specific S-CH₃ stretching mode being excited as the reagent is excited to the S₁ electronic state, there is a sharp increase in the proportion of the ground-state product to the excited-state product. In the present work, we report 78 011 full-dimensional semiclassical multi-state trajectories of the photodissociation process using the coherent switching with decay of mixing dynamics method. The potential surfaces and couplings are based on electronic structure calculations that include dynamic correlation through second order perturbation theory. We report results for four sets of initial conditions, one corresponding roughly to 0-0 excitation and three corresponding to exciting one vibrational mode, to look for mode-specific effects. The simulations show no significant mode-specific effect on the product energy distributions, but they do show an effect on the distribution of minimum-energy gaps in the trajectories and on the lifetime for dissociation. In particular, excitation of the S-CH₃ stretching mode leads to trajectories passing closer to the S₁-S₂ conical intersection and to shorter lifetimes. This provides a possible explanation of why experimental results are different for excitation of this vibration.

Conformer specific nonadiabatic reaction dynamics in the photodissociation of partially deuterated thioanisoles (C6H5S-CH2D and C6H5S-CHD2)

In this work, we have investigated nonadiabatic dynamics in the vicinity of conical intersections for predissociation reactions of partially deuterated thioanisole molecules: C₆H₅S-CH₂D and C₆H₅S-CHD₂. Each isotopomer has two distinct rotational conformers according to the geometrical position of D or H of the methyl moiety with respect to the molecular plane for C₆H₅S-CH₂D or C₆H₅S-CHD₂, respectively, as spectroscopically characterized in our earlier report [J. Lee, S.-Y. Kim and S. K. Kim, J. Phys. Chem. A, 2014, 118, 1850]. Since identification and separation of two different rotational conformers of each isotopomer have been unambiguously done, we could interrogate nonadiabatic dynamics of thioanisole in terms of both H/D substitutional and conformational structural effects. Nonadiabatic transition probability, estimated by the experimentally measured branching ratio of the nonadiabatically produced ground-state channel giving C₆H₅S·(X[combining tilde]) versus the adiabatic excited-state channel leading to the C₆H₅S·(Ã) radical, shows resonance-like increases at symmetric (ν_s) or asymmetric (7a) S-CH₂D (or S-CHD₂) stretching mode excitation in S₁ for all conformational isomers of two isotopomers. However, absolute probabilistic value of the nonadiabatic transition is found to vary quite drastically depending on different conformers and isotopomers. The experimental finding that nonadiabatic transition dynamics are very sensitive to subtle changes in the nuclear configuration within the Franck-Condon region induced by the H/D substitution indicates that the S₁/S₂ conical intersection seam is quite narrowly defined in the multi-dimensional nuclear configurational space as far as the S-methyl predissociation reaction is concerned. In order to understand the relation between molecular structure and nonadiabaticity of reaction, potential energy surfaces near S₁/S₂ conical intersections have been theoretically calculated along ν_s and 7a normal mode coordinates for all conformational isomers. Slow-electron velocity map imaging (SEVI) spectroscopy is employed to unravel the extent of intramolecular vibrational redistribution (IVR) for particular mode excitations of S₁, providing insights into the dynamic interplay between IVR and nonadiabatic transition probability near the conical intersection seam.

Exploring the Dynamics of the Photoinduced Ring-Opening of Heterocyclic Molecules

Excited states formed by electron promotion to an antibonding σ* orbital are now recognized as key to understanding the photofragmentation dynamics of a broad range of heteroatom containing small molecules: alcohols, thiols, amines, and many of their aromatic analogues. Such excited states may be populated by direct photoexcitation, or indirectly by nonadiabatic transfer of population from some other optically excited state (e.g., a ππ* state). This Perspective explores the extent to which the fast-growing literature pertaining to such (n/π)σ*-state mediated bond fissions can inform and enhance our mechanistic understanding of photoinduced ring-opening in heterocyclic molecules.

Molecular Photofragmentation Dynamics in the Gas and Condensed Phases

Exciting a molecule with an ultraviolet photon often leads to bond fission, but the final outcome of the bond cleavage is typically both molecule and phase dependent. The photodissociation of an isolated gas-phase molecule can be viewed as a closed system: Energy and momentum are conserved, and the fragmentation is irreversible. The same is not true in a solution-phase photodissociation process. Solvent interactions may dissipate some of the photoexcitation energy prior to bond fission and will dissipate any excess energy partitioned into the dissociation products. Products that have no analog in the corresponding gas-phase study may arise by, for example, geminate recombination. Here, we illustrate the extent to which dynamical insights from gas-phase studies can inform our understanding of the corresponding solution-phase photochemistry and how, in the specific case of photoinduced ring-opening reactions, solution-phase studies can in some cases reveal dynamical insights more clearly than the corresponding gas-phase study.

The Position of the N Atom Plays a Significant Role for Excited-State Decay of Heterocycles

We have employed combined electronic structure calculations and nonadiabatic dynamics simulations to study the S₁ radiationless deactivation mechanism of pyrazole. In terms of MS-CASPT2 computed results, we propose that the ¹πσ* state-driven nonadiabatic N-N dissociation is a major relaxation path; the ring-puckering deformation path as well as the ¹πσ* state-driven N-H dissociation are less favorable. This excited-state decay mechanism is supported by MS-CASPT2 nonadiabatic dynamics simulations. The present study demonstrates that pyrazole has a different excited-state radiationless deactivation mechanism compared with its structural isomer imidazole, in which the ¹πσ* state-driven nonadiabatic N-H dissociation plays a more important role. However, such a channel is suppressed in pyrazole; instead, the ¹πσ* state-driven nonadiabatic N-N dissociation is dominant.

Ultrafast excited-state dynamics of 2,4-dimethylpyrrole

Ultrafast excited-state dynamics of 2,4-dimethylpyrrole are studied in detail following deep UV excitation.

Control of Nonadiabatic Passage through a Conical Intersection by a Dynamic Resonance

Nonadiabatic processes, dominated by dynamic passage of reactive fluxes through conical intersections (CIs), are considered to be appealing means for manipulating reaction paths, particularly via initial vibrational preparation. Nevertheless, obtaining direct experimental evidence of whether specific-mode excitation affects the passage at the CI is challenging, requiring well-resolved time- or frequency-domain experiments. Here promotion of methylamine-d2 (CH3ND2) molecules to spectral-resolved rovibronic states on the excited S1 potential energy surface, coupled to sensitive D photofragment probing, allowed us to follow the N-D bond fission dynamics. The branching ratios between slow and fast D photofragments and the internal energies of the CH3ND(X̃) photofragments confirm correlated anomalies for predissociation initiated from specific rovibronic states. These anomalies reflect the existence of a dynamic resonance that strongly depends on the energy of the initially excited rovibronic states, the evolving vibrational mode on the repulsive S1 part during N-D bond elongation, and the manipulated passage through the CI that leads to CH3ND radicals excited with C-N-D bending. This resonance plays an important role in the bifurcation dynamics at the CI and can be foreseen to exist in other photoinitiated processes and to control their outcome.

Extreme population inversion in the fragments formed by UV photoinduced S-H bond fission in 2-thiophenethiol

H atom loss following near ultraviolet photoexcitation of gas phase 2-thiophenethiol molecules has been studied experimentally, by photofragment translational spectroscopy (PTS) methods, and computationally, by ab initio electronic structure calculations. The long wavelength (277.5 ≥ λ(phot) ≥ 240 nm) PTS data are consistent with S-H bond fission after population of the first (1)πσ* state. The partner thiophenethiyl (R) radicals are formed predominantly in their first excited Ã(2)A' state, but assignment of a weak signal attributable to H + R(X˜(2)A'') products allows determination of the S-H bond strength, D0 = 27,800 ± 100 cm(-1) and the Ã-X˜ state splitting in the thiophenethiyl radical (ΔE = 3580 ± 100 cm(-1)). The deduced population inversion between the à and X˜ states of the radical reflects the non-planar ground state geometry (wherein the S-H bond is directed near orthogonal to the ring plane) which, post-photoexcitation, is unable to planarise sufficiently prior to bond fission. This dictates that the dissociating molecules follow the adiabatic fragmentation pathway to electronically excited radical products. π* ← π absorption dominates at shorter excitation wavelengths. Coupling to the same (1)πσ* potential energy surface (PES) remains the dominant dissociation route, but a minor yield of H atoms attributable to a rival fragmentation pathway is identified. These products are deduced to arise via unimolecular decay following internal conversion to the ground (S0) state PES via a conical intersection accessed by intra-ring C-S bond extension. The measured translational energy disposal shows a more striking change once λ(phot) ≤ 220 nm. Once again, however, the dominant decay pathway is deduced to be S-H bond fission following coupling to the (1)πσ* PES but, in this case, many of the evolving molecules are deduced to have sufficiently near-planar geometries to allow passage through the conical intersection at extended S-H bond lengths and dissociation to ground (X˜) state radical products. The present data provide no definitive evidence that complete ring opening can compete with fast S-H bond fission following near UV photoexcitation of 2-thiophenethiol.

Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems

A new flavor of the frozen natural orbital complete active space second-order perturbation theory method (FNO-CASPT2, Aquilante et al., J. Chem. Phys. 131, 034113) is proposed herein. In this new implementation, the virtual space in Cholesky decomposition-based CASPT2 computations (CD-CASPT2) is truncated by excluding those orbitals that contribute the least toward preserving a predefined value of the trace of an approximate density matrix, as that represents a measure of the amount of dynamic correlation retained in the model. In this way, the amount of correlation included is practically constant at all nuclear arrangements, thus allowing for the computation of smooth electronic states surfaces and energy gradients-essential requirements for theoretical studies in photochemistry. The method has been benchmarked for a series of relevant biochromophores for which large speed-ups have been recorded while retaining the accuracy achieved in the corresponding CD-CASPT2 calculations. Both vertical excitation energies and gradient calculations have been carried out to establish general guidelines as to how much correlation needs to be retained in the calculation for the results to be consistent with the CD-CASPT2 findings. Our results feature errors within a tenth of an eV for the most difficult cases and have been validated to be used for gradient computations where an up to 3-fold speed-up is observed depending on the size of the system and the basis set employed.

The role of novel Rydberg-valence behaviour in the non-adiabatic dynamics of tertiary aliphatic amines

Time-resolved photoelectron imaging was used to study non-adiabatic relaxation dynamics in N,N-dimethylisopropylamine, N,N-dimethylpropylamine and N-methylpyrrolidine following excitation at 200 nm. This series of tertiary aliphatic amines are all of similar chemical makeup, but exhibit differences in their structure - being branched, straight-chain and cyclic, respectively. Our experimental investigation, supported by extensive theoretical calculations, provides considerable new insight into the nature of the internal conversion processes that mediate dynamical evolution between electronic states of predominantly Rydberg character in this important class of model photochemical systems. In particular, the angle-resolved data afforded by the imaging approach (something not previously reported for tertiary aliphatic amines) offers novel and highly-detailed mechanistic information about the overall relaxation pathway. Strikingly, both the experimental and theoretical findings suggest that a critical factor driving the non-adiabatic dynamics is the evolution of valence character along an N-C stretching coordinate within a member of the 3p manifold. This is in stark contrast to primary and secondary amines, as well as many other small hetero-atom containing organic species, where evolution of valence character within the 3s state is now a well-established phenomenon implicated in mediating ultrafast non-adiabatic photochemistry.

Nonintuitive Diabatic Potential Energy Surfaces for Thioanisole

Diabatization of potential energy surfaces is a technique that enables convenient molecular dynamics simulations of electronically nonadiabatic processes, but diabatization itself is nonunique and can be inconvenient; the best methods to achieve diabatization are still under study. Here, we present the diabatization of two electronic states of thioanisole in the S-CH3 bond stretching and C-C-S-C torsion two-dimensional nuclear coordinate space containing a conical intersection. We use two systematic methods: the (orbital-dependent) 4-fold way and the (orbital-free) Boys localization diabatization method. These very different methods yield strikingly similar diabatic potential energy surfaces that cross at geometries where the adiabatic surfaces are well separated and do not exhibit avoided crossings, and the contours of the diabatic gap and diabatic coupling are similar for the two methods. The validity of the diabatization is supported by comparing the nonadiabatic couplings calculated from the diabatic matrix elements to those calculated by direct differentiation of the adiabatic states.

Computational simulation and interpretation of the low-lying excited electronic states and electronic spectrum of thioanisole

Three singlet states, namely a closed-shell ground state and two excited states with (1)ππ* and (1)nσ* character, have been suggested to be responsible for the radiationless decay or photochemical reaction of photoexcited thioanisole. The correct interpretation of the electronic spectrum is critical for understanding the character of these low-lying excited states, but the experimental spectrum is yet to be fully interpreted. In the work reported here, we investigated the nature of those three states and a fourth singlet state of thioanisole using electronic structure calculations by multireference perturbation theory, by completely-renormalized equation-of-motion coupled cluster theory with single and double excitations and noniterative inclusion of connected triples (CR-EOM-CCSD(T)), and by linear-response time-dependent density functional theory (TDDFT). We clarified the assignment of the electronic spectrum by simulating it using a normal-mode sampling approach combined with TDDFT in the Tamm-Dancoff approximation (TDA). The understanding of the electronic states and of the accuracy of the electronic structure methods lays the foundation of our future work of constructing potential energy surfaces.

Probing and Exploiting the Interplay between Nuclear and Electronic Motion in Charge Transfer Processes

The Born-Oppenheimer approximation refers to the assumption that the nuclear and electronic wave functions describing a molecular system evolve and can be determined independently. It is now well-known that this approximation often breaks down and that nuclear-electronic (vibronic) coupling contributes greatly to the ultrafast photophysics and photochemistry observed in many systems ranging from simple molecules to biological organisms. In order to probe vibronic coupling in a time-dependent manner, one must use spectroscopic tools capable of correlating the motions of electrons and nuclei on an ultrafast time scale. Recent developments in nonlinear multidimensional electronic and vibrational spectroscopies allow monitoring both electronic and structural factors with unprecedented time and spatial resolution. In this Account, we present recent studies from our group that make use of different variants of frequency-domain transient two-dimensional infrared (T-2DIR) spectroscopy, a pulse sequence combining electronic and vibrational excitations in the form of a UV-visible pump, a narrowband (12 cm(-1)) IR pump, and a broadband (400 cm(-1)) IR probe. In the first example, T-2DIR is used to directly compare vibrational dynamics in the ground and relaxed electronic excited states of Re(Cl)(CO)3(4,4'-diethylester-2,2'-bipyridine) and Ru(4,4'-diethylester-2,2'-bipyridine)2(NCS)2, prototypical charge transfer complexes used in photocatalytic CO2 reduction and electron injection in dye-sensitized solar cells. The experiments show that intramolecular vibrational redistribution (IVR) and vibrational energy transfer (VET) are up to an order of magnitude faster in the triplet charge transfer excited state than in the ground state. These results show the influence of electronic arrangement on vibrational coupling patterns, with direct implications for vibronic coupling mechanisms in charge transfer excited states. In the second example, we show unambiguously that electronic and vibrational movement are coupled in a donor-bridge-acceptor complex based on a Pt(II) trans-acetylide design motif. Time-resolved IR (TRIR) spectroscopy reveals that the rate of electron transfer (ET) is highly dependent on the amount of excess energy localized on the bridge following electronic excitation. Using an adaptation of T-2DIR, we are able to selectively perturb bridge-localized vibrational modes during charge separation, resulting in the donor-acceptor charge separation pathway being completely switched off, with all excess energy redirected toward the formation of a long-lived intraligand triplet state. A series of control experiments reveal that this effect is mode specific: it is only when the high-frequency bridging C≡C stretching mode is pumped that radical changes in photoproduct yields are observed. These experiments therefore suggest that one may perturb electronic movement by stimulating structural motion along the reaction coordinate using IR light. These studies add to a growing body of evidence suggesting that controlling the pathways and efficiency of charge transfer may be achieved through synthetic and perturbative approaches aiming to modulate vibronic coupling. Achieving such control would represent a breakthrough for charge transfer-based applications such as solar energy conversion and molecular electronics.

Toward control of electron transfer in donor-acceptor molecules by bond-specific infrared excitation

Electron transfer (ET) from donor to acceptor is often mediated by nuclear-electronic (vibronic) interactions in molecular bridges. Using an ultrafast electronic-vibrational-vibrational pulse-sequence, we demonstrate how the outcome of light-induced ET can be radically altered by mode-specific infrared (IR) excitation of vibrations that are coupled to the ET pathway. Picosecond narrow-band IR excitation of high-frequency bridge vibrations in an electronically excited covalent trans-acetylide platinum(II) donor-bridge-acceptor system in solution alters both the dynamics and the yields of competing ET pathways, completely switching a charge separation pathway off. These results offer a step toward quantum control of chemical reactivity by IR excitation.

Tuning photochemistry: substituent effects on πσ* state mediated bond fission in thioanisoles

The electronic branching in the thiophenoxyl radicals formed by UV photolysis of thioanisole can be tuned by placing electron withdrawing/donating substituents at the 4-position.

Evidence for quantum effects in the predissociation of methylamine isotopologues

The H product distributions obtained from the predissociation of methylamine isotopologues are extremely sensitive to the energy difference between the initially prepared vibrational states and the conical intersections and not only to the nature of the pre-excited nuclear motions.

UV-induced isomerization dynamics of N-methyl-2-pyridone in solution

The photoisomerization dynamics of N-methyl-2-pyridone (NMP) dissolved in CH3CN have been interrogated by time-resolved electronic and vibrational absorption spectroscopy. Irradiation at two different wavelengths (330 or 267 nm) prepares NMP(S1) molecules with very different levels of vibrational excitation, which rapidly relax to low vibrational levels of the S1 state. Internal conversion with an associated time constant of 110(4) ps, leading to reformation of NMP(S0) molecules, is identified as the dominant (>90%) decay pathway. Much of the remaining fraction undergoes a photoinitiated rearrangement to yield two ketenes (revealed by their characteristic antisymmetric C═C═O stretching modes at 2110 and 2120 cm(-1)), which are in equilibrium. The rate of ketene formation is found to be pump-wavelength dependent, consistent with ab initio electronic structure calculations which predict a barrier on the S1 potential energy surface en route to a prefulvenic conical intersection, by which isomerization is deduced to occur. Two kinetic models-differentiated by whether product branching occurs in the S1 or S0 electronic states-are presented and used with equal success in the analysis of the experimental data, highlighting the difficulties associated with deducing unambiguous mechanistic information from kinetic data alone.