Photodissociation Dynamics of Phenol: Multistate Trajectory Simulations including Tunneling

Fitting of Coupled Potential Energy Surfaces via Discovery of Companion Matrices by Machine Intelligence

Fitting coupled potential energy surfaces is a critical step in simulating electronically nonadiabatic chemical reactions and energy transfer processes. Analytic representation of coupled potential energy surfaces enables one to perform detailed dynamics calculations. Traditionally, fitting is performed in a diabatic representation to avoid fitting the cuspidal ridges of coupled adiabatic potential energy surfaces at conical intersection seams. In this work, we provide an alternative approach by carrying out fitting in the adiabatic representation using a modified version of the Frobenius companion matrices, whose usage was first proposed by Opalka and Domcke. Their work involved minimizing the errors in fits of the characteristic polynomial coefficients (CPCs) and diagonalizing the resulting companion matrix, whose eigenvalues are adiabatic potential energies. We show, however, that this may lead to complex eigenvalues and spurious discontinuities. To alleviate this problem, we provide a new procedure for the automatic discovery of CPCs and the diagonalization of a companion matrix by using a special neural network architecture. The method effectively allows analytic representation of global coupled adiabatic potential energy surfaces and their gradients with only adiabatic energy input and without experience-based selection of a diabatization scheme. We demonstrate that the new procedure, called the companion matrix neural network (CMNN), is successful by showing applications to LiH, H3, phenol, and thiophenol.

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled 5A' States and Fourteen Coupled 3A' States of O + O2

We report new potential energy surfaces for six coupled 5A' states and 14 coupled 3A' states of O3. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled 5A' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled 3A' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (5A') and 20 meV (3A').

ChemPotPy: A Python Library for Analytic Representations of Potential Energy Surfaces and Diabatic Potential Energy Matrices

Constructing analytic representations of global and semiglobal potential energy surfaces is difficult and can be laborious, and it is even harder when one needs coupled potential energy surfaces and their electronically nonadiabatic couplings. When accomplished, however, the resulting potential functions are a valuable resource. To facilitate the convenient use of potentials that have been developed, we provide a collection of existing surfaces in a library with consistent units and formats. A potential energy surface library of this type, namely PotLib, was built more than 20 years ago. However, that library only provided pristine Fortran subroutines for each potential energy surface, and therefore, it is not as user-friendly as would be desirable. Here, we report the creation of ChemPotPy, a CHEMical library of POTential energy surfaces in PYthon. ChemPotPy is a user-friendly library for analytic representation of single-state and multistate potential energy surfaces and couplings. A given entry in the library contains an analytic potential energy function or analytic functions for a set of coupled potential energy surfaces, and depending on the case, it may also include analytic or numerical gradients, nonadiabatic coupling vectors, and/or diabatic potential energy matrices and their gradients. Only three inputs, namely, the chemical formula of the system, the name of the potential energy surface or surface set, and the Cartesian geometry, are required. ChemPotPy uses the same units for input and output quantities of all surfaces and surface sets to facilitate general interfaces with the dynamics programs. The initial version of the library contains 338 entries, and we anticipate that more will be added in the future.

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.

Semiclassical Multistate Dynamics for Six Coupled 5A' States of O + O2

Dynamics simulations of high-energy O₂-O collisions play an important role in simulating thermal energy content and heat flux in flows around hypersonic vehicles. To carry out such dynamics simulations efficiently requires accurate global potential energy surfaces and (in most algorithms) state couplings for many energetically accessible electronic states. The ability to treat collisions involving many coupled electronic states has been a challenge for decades. Very recently, a new diabatization method, the parametrically managed diabatization by deep neural network (PM-DDNN), has been developed. The PM-DDNN method uses a deep neural network architecture with an activation function parametrically dependent on input data to discover and fit the diabatic potential energy matrix (DPEM) as a function of geometry, and the adiabatic potential energy surfaces are obtained by diagonalization of a small matrix with analytic matrix elements. Here, we applied the PM-DDNN method to the six lowest-energy potential energy surfaces in the ⁵A' manifold of O₃ to perform simultaneous diabatization and fitting; the data are obtained by extended multistate complete-active-space second-order perturbation theory. We then used the adiabatic surfaces for dynamics calculations with three methods: coherent switching with decay of mixing (CSDM), curvature-driven CSDM (κCSDM), and electronically curvature-driven CSDM (eκCSDM). The κCSDM calculations require only adiabatic potential energies and gradients. The three dynamical methods are in good agreement. We then calculated electronically nonadiabatic, electronically inelastic, and dissociative cross sections for seven initial collision energies, five initial vibrational levels, and four initial rotational levels. Trends in the electronically inelastic cross sections as functions of the initial collision energy and vibrational level were rationalized in terms of the coordinate ranges where the gaps between the second and third potential energy surfaces are small.

Linearized Pair-Density Functional Theory

Multiconfiguration pair-density functional theory (MC-PDFT) is a post-SCF multireference method that has been successful at computing ground- and excited-state energies. However, MC-PDFT is a single-state method in which the final MC-PDFT energies do not come from diagonalization of a model-space Hamiltonian matrix, and this can lead to inaccurate topologies of potential energy surfaces near locally avoided crossings and conical intersections. Therefore, in order to perform physically correct ab initio molecular dynamics with electronically excited states or to treat Jahn-Teller instabilities, it is necessary to develop a PDFT method that recovers the correct topology throughout the entire nuclear configuration space. Here we construct an effective Hamiltonian operator, called the linearized PDFT (L-PDFT) Hamiltonian, by expanding the MC-PDFT energy expression to first order in a Taylor series of the wave function density. Diagonalization of the L-PDFT Hamiltonian gives the correct potential energy surface topology near conical intersections and locally avoided crossings for a variety of challenging cases including phenol, methylamine, and the spiro cation. Furthermore, L-PDFT outperforms MC-PDFT and previous multistate PDFT methods for predicting vertical excitations from a variety of representative organic chromophores.

Mode-dependent H atom tunneling dynamics of the S1 phenol is resolved by the simple topographic view of the potential energy surfaces along the conical intersection seam

Mode-dependent H atom tunneling dynamics of the O-H bond predissociation of the S₁ phenol has been theoretically analyzed. As the tunneling is governed by the complicated multi-dimensional potential energy surfaces that are dynamically shaped by the upper-lying S₁(ππ*)/S₂(πσ*) conical intersection, the mode-specific tunneling dynamics of phenol (S₁) has been quite formidable to be understood. Herein, we have examined the topography of the potential energy surface along the particular S₁ vibrational mode of interest at the nuclear configurations of the S₁ minimum and S₁/S₂ conical intersection. The effective adiabatic tunneling barrier experienced by the reactive flux at the particular S₁ vibrational mode excitation is then uniquely determined by the topographic shape of the potential energy surface extended along the conical intersection seam coordinate associated with the particular vibrational mode. The resultant multi-dimensional coupling of the specific vibrational mode to the tunneling coordinate is then reflected in the mode-dependent tunneling rate as well as nonadiabatic transition probability. Remarkably, the mode-specific experimental result of the S₁ phenol tunneling reaction [K. C. Woo and S. K. Kim, J. Phys. Chem. A 123, 1529-1537 (2019)] (in terms of the qualitative and relative mode-dependent dynamic behavior) could be well rationalized by semi-classical calculations based on the mode-specific topography of the effective tunneling barrier, providing the clear conceptual insight that the skewed potential energy surfaces along the conical intersection seam (strongly or weakly coupled to the tunneling reaction coordinate) may dictate the tunneling dynamics in the proximity of the conical intersection.

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.

Electronic Excitation of ortho-Fluorothiophenol

ortho-Fluorothiophenol (o-FTP) photodissociates through the well-known πσ* process. The fluorine atom of o-FTP introduces a feature in the photodissociation of o-FTP that does not occur in most other πσ* processes because the fluorine atom can form a hydrogen bond with the hydrogen atom of the SH group. Theoretical computations can serve as a good way to study these reactions because they usually proceed very quickly, and the current spectroscopies cannot probe the details of the processes as thoroughly as theory can. Here we use completely renormalized equation-of-motion coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations (CR-EOM-CCSD(T)) and quasidegenerate perturbation theory, in particular extended multistate complete-active-space second-order perturbation theory (XMS- CASPT2), to calculate the four lowest singlet states of o-FTP and hybrid density functional theory to optimize the geometries of the two lowest singlet states. We find that ten active electrons in nine active orbitals are sufficient to provide a good reference function for all four states. We find that the ground electronic state and the first excited singlet state both exhibit strongly bent hydrogen bonds. We also use density functional theory with the Tamm-Dancoff approximation and the SMD solvation model to successfully simulate the electronic spectrum of o-FTP in n-hexane solvent.

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.

Non-Born-Oppenheimer effects in molecular photochemistry: an experimental perspective

Non-adiabatic couplings between Born-Oppenheimer (BO)-derived potential energy surfaces are now recognized as pivotal in describing the non-radiative decay of electronically excited molecules following photon absorption. This opinion piece illustrates how non-BO effects provide photostability to many biomolecules when exposed to ultraviolet radiation, yet in many other cases are key to facilitating 'reactive' outcomes like isomerization and bond fission. The examples are presented in order of decreasing molecular complexity, spanning studies of organic sunscreen molecules in solution, through two families of heteroatom containing aromatic molecules and culminating with studies of isolated gas phase H₂O molecules that afford some of the most detailed insights yet available into the cascade of non-adiabatic couplings that enable the evolution from photoexcited molecule to eventual products. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Why the Photochemical Reaction of Phenol Becomes Ultrafast at the Air-Water Interface: The Effect of Surface Hydration

Photochemical reactions at the air-water interface can show remarkably different rates from those in bulk water. The present study elucidates the reaction mechanism of phenol characteristic at the air-water interface by the combination of molecular dynamics simulation and quantum chemical calculations of the excited states. We found that incomplete hydrogen bonding to phenol at the air-water interface affects excited states associated with the conical intersection and significantly reduces the reaction barrier, resulting in the distinctively facilitated rate in comparison with the bulk phase. The present study indicates that the reaction dynamics can be substantially different at the interfaces in general, reflecting the difference in the stabilization energy of the electronic states in markedly different solvation at the interface.

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.

Nonadiabatic Dynamics Algorithms with Only Potential Energies and Gradients: Curvature-Driven Coherent Switching with Decay of Mixing and Curvature-Driven Trajectory Surface Hopping

Direct dynamics by mixed quantum-classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive time steps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature-driven coherent switching with decay of mixing (κCSDM) and curvature-driven trajectory surface hopping (κTSH). We show how powerful these new methods are in terms of computation time and accuracy as compared to previous mixed quantum-classical nonadiabatic dynamics algorithms. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.

Insights into the hydrated electron generation from UV/aniline: Mechanism and quantum efficiency

The insight into the neglected reduction process accompanied by UV-based oxidation process may provide new ideas for the development of advanced oxidation and reduction technologies. In this study, aniline was comprehensively investigated as an unexpected indicator of hydrated electron (e_aq^-) under UV irradiation. Monochloroacetic acid (MCAA) was selected as the probe of e_aq^- and the balance of chloride ions indicated the reduction of MCAA. Further, laser flash photolysis experiments demonstrated the generation of e_aq^- in the UV/aniline process and the half-life period of formed e_aq^- was demonstrated to be 0.13 μs. The photolysis of aniline along with the decay of the excited state of aniline was responsible for the e_aq^- generation. Besides, the hydrogen atom (H) generated from the photolysis can subsequently reacted with OH^- to generate e_aq^-. The photolysis pathways of aniline were proposed by the results of GC-MS. Aniline was abstracted of H in solution to the formation of aniline radical (PhNH) or form aminophenol in three different isomers (orto-, meta- and para-aminophenol). Moreover, UV/aniline showed a higher reducing capacity of MCAA compared with other organic electron donors and sustained a highly reducing ability in a wide pH. And the calculation results of quantum efficiency (Φ) showed that excessive aniline was not conducive to the elevation of Φ. This study introduced a novel pathway of e_aq^- generation during the photolysis of aniline and provided a new perspective for e_aq^--based advanced reduction processes.

Unitary coupled-cluster based self-consistent polarization propagator theory: A quadratic unitary coupled-cluster singles and doubles scheme

The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H̄. The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles-singles block of H̄, single commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller-Plesset perturbation theory.

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.

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.

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.

Benzene, Toluene, and Monosubstituted Derivatives: Diabatic Nature of the Oscillator Strengths of S1 ← S0 Transitions

For benzene, toluene, aniline, fluorobenzene, and phenol, even sophisticated treatments of electron correlation, such as MRCI and XMS-CASPT2 calculations, show oscillator strengths typically lower than experiment. Inclusion of a simple pseudo-diabatization approach to perturb the S1 state with approximate vibronic coupling to the S2 state for each molecule results in more accurate oscillator strengths. Their absolute values agree better with experiment for all molecules except aniline. When the coupling between the S1 and S2 states is strong at the S0 geometry, the simple diabatization scheme performs less well with respect to the oscillator strengths relative to the adiabatic values. However, we expect the scheme to be useful in many cases where the coupling is weak to moderate (where the maximum component of the coupling has a magnitude less than 1.5 au). Such calculations give an insight into the effects of vibronic coupling of excited states on UV/vis spectra.

Signatures of light-induced nonadiabaticity in the field-dressed vibronic spectrum of formaldehyde

Nonadiabatic coupling is absent between the electronic ground X and first excited (singlet) A states of formaldehyde. As laser fields can induce conical intersections between these two electronic states, formaldehyde is particularly suitable for investigating light-induced nonadiabaticity in a polyatomic molecule. The present work reports on the spectrum induced by light-the so-called field-dressed spectrum-probed by a weak laser pulse. A full-dimensional ab initio approach in the framework of Floquet-state representation is applied. The low-energy spectrum, which without the dressing field would correspond to an infrared vibrational spectrum in the X-state, and the high-energy spectrum, which without the dressing field would correspond to the X → A spectrum, are computed and analyzed. The spectra are shown to be highly sensitive to the frequency of the dressing light allowing one to isolate different nonadiabatic phenomena.

Improved algorithm for the direct dynamics variational multi-configurational Gaussian method

The Direct Dynamics variational Multi-Configurational Gaussian (DD-vMCG) method provides a fully quantum mechanical solution to the time-dependent Schrödinger equation for the time evolution of nuclei with potential surfaces calculated on-the-fly using a quantum chemistry program. Initial studies have shown its potential for flexible and accurate simulations of non-adiabatic excited-state molecular dynamics. In this paper, we present developments to the DD-vMCG algorithm that improve both its accuracy and efficiency. First, a new, efficient parallel algorithm to control the DD-vMCG database of quantum chemistry points is presented along with improvements to the Shepard interpolation scheme. Second, the use of symmetry in describing the potential surfaces is introduced along with a new phase convention in the propagation diabatization. Benchmark calculations on the allene radical cation including all degrees of freedom then show that the new scheme is able to produce a consistent non-adiabatic coupling vector field. This new DD-vMCG version thus opens the route for effectively and accurately treating complex chemical systems using quantum dynamics simulations.

Conformer-Specific Tunneling Dynamics Dictated by the Seam Coordinate of the Conical Intersection

The dynamic role of the conical intersection "seam" coordinate has been first revealed in the H fragmentation reaction of ortho(o)-cresol conformers. One of the (3N - 8) dimensional seam coordinates of the S₁(ππ*)/S₂(πσ*) conical intersection has been identified as the CH₃ torsional potential function. The tunneling dynamics of the reactive flux is dictated by its nuclear layout with respect to the CH₃ torsional angle, as the multidimensional tunneling barrier is dynamically shaped along the conical intersection seam. The effective tunneling-barrier weight-averaged over the quantum-mechanical probability along the CH₃ torsional angle perfectly explains the experimental finding: the sharp variation of the tunneling rate ((700-400) ps^-1) with the CH₃ torsional mode excitations within the narrow (0-100 cm^-1) energetic window. The much longer S₁ lifetime of cis compared to trans is ascribed to the higher-lying S₁/S₂ conical intersection of the former. With the use of distinct lifetimes, vibronic bands of each conformer could be completely separated.

Revealing the role of excited state proton transfer (ESPT) in excited state hydrogen transfer (ESHT): systematic study in phenol-(NH3) n clusters

Excited State Hydrogen Transfer (ESHT), proposed at the end of the 20th century by the corresponding authors, has been observed in many neutral or protonated molecules and become a new paradigm to understand excited state dynamics/photochemistry of aromatic molecules. For example, a significant number of photoinduced proton-transfer reactions from X–H bonds have been re-defined as ESHT, including those of phenol, indole, tryptophan, aromatic amino acid cations and so on. Photo-protection mechanisms of biomolecules, such as isolated nucleic acids of DNA, are also discussed in terms of ESHT. Therefore, a systematic and up-to-date description of ESHT mechanism is important for researchers in chemistry, biology and related fields. In this review, we will present a general model of ESHT which unifies the excited state proton transfer (ESPT) and the ESHT mechanisms and reveals the hidden role of ESPT in controlling the reaction rate of ESHT. For this purpose, we give an overview of experimental and theoretical work on the excited state dynamics of phenol–(NH₃)_n clusters and related molecular systems. The dynamics has a significant dependence on the number of solvent molecules in the molecular cluster. Three-color picosecond time-resolved IR/near IR spectroscopy has revealed that ESHT becomes an electron transfer followed by a proton transfer in highly solvated clusters. The systematic change from ESHT to decoupled electron/proton transfer according to the number of solvent molecules is rationalized by a general model of ESHT including the role of ESPT.

A general model of excited state hydrogen transfer (ESHT) which unifies ESHT and the excited state proton transfer (ESPT) is presented from experimental and theoretical works on phenol–(NH₃)_n. The hidden role of ESPT is revealed.

Behavior of Hydroxyl Radicals on Water Ice at Low Temperatures

ConspectusBecause chemical reactions on/in cosmic ice dust grains covered by amorphous solid water (ASW) play important roles in generating a variety of molecules, many experimental and theoretical studies have focused on the chemical processes occurring on the ASW surface. In laboratory experiments, conventional spectroscopic and mass-spectrometric detection of stable products is generally employed to deduce reaction channels and mechanisms. However, despite their importance, the details of chemical reactions involving reactive species (i.e., free radicals) have not been clarified because of the absence of experimental methods for in situ detection of radicals. Because OH radicals can be easily produced in interstellar conditions by not only the photolysis and/or ion bombardments of H₂O but also the reaction of H and O atoms, they are thought to be one of the most abundant radicals on ice dust. In this context, the development of a close monitoring method of OH radicals on the ASW surface may help to elucidate the chemical reactions occurring on the ASW surface.Recently, to detect OH radicals adsorbed on the ASW surface, we applied our developed method to sensitively and selectively detect surface adsorbates with a combination of photostimulated desorption and resonance-enhanced multiphoton ionization techniques. Using this method, we showed that an OH radical on the ASW surface can be desorbed upon one-photon absorption at 532 nm, at which wavelength both the OH radical and H₂O molecule are transparent. Theoretical calculations addressing an OH radical adsorbed on water clusters indicated that the valence A-X transition of an OH radical significantly red-shifts by ∼2 eV when the OH radical is strongly adsorbed to ice through three hydrogen bonds. With this method, the number density of surface OH can be monitored as a snapshot so that the behaviors of OH radicals, such as surface diffusion, can be studied. Moreover, the development of a system for studying the wavelength dependence of photodesorption may establish a foundation for future research investigating the absorption spectra of surface adsorbed species.Owing to the large electron affinity of OH radicals on ice, they are expected to easily become OH^- by electron attachment on the ASW surface. We characterized the behavior of OH^- on ASW at low temperatures, which may be relevant not only to physicochemical processes on cosmic ice dust and planetary atmosphere but also to understanding the electrochemical properties of ice. A negative constant current was found when ASW at temperatures below 50 K was exposed to both UV photons and electrons. It was demonstrated that the negative current is initiated by the formation of OH^- ions on the ASW surface, and they are transported to the bulk via the proton-hole transfer mechanism, which was predicted 100 years ago as a mirror image of proton transfer known as the Grotthuss mechanism. These results indicate that OH^- ions are readily transported to the bulk ice and further induce reactions, even at low temperatures where thermal diffusion is negligible. Therefore, in-mantle chemical processes that have been considered inactive at low temperatures are worth reevaluating.

Compressed-State Multistate Pair-Density Functional Theory

Multiconfiguration pair-density functional theory (MC-PDFT) is a multireference method that can be used to calculate excited states. However, MC-PDFT potential energy surfaces have the wrong topology at conical intersections because the last step of MC-PDFT is not a diagonalization of a model-space Hamiltonian matrix, as done in, for example, multistate second-order perturbation theory (MS-CASPT2). We have previously proposed methods that solve this problem by diagonalizing a model-space effective Hamiltonian matrix, where the diagonal elements are MC-PDFT energies for intermediate states, and the off-diagonal elements are evaluated by wave function theory. One previous method is called variational multistate PDFT (VMS-PDFT), whose intermediate states maximize the trace of the effective Hamiltonian, namely, the sum of the MC-PDFT energies of the model-space states; the VMS-PDFT is very robust but is more computationally expensive than another method, extended multistate PDFT (XMS-PDFT), in which the transformation to intermediate states is accomplished without needing any density functional evaluations. However, although VMS-PDFT was accurate in all cases tested, XMS-PDFT was accurate in only some of them. In the present paper, we propose a new method, called compressed-state multistate PDFT (CMS-PDFT), that is as efficient as XMS-PDFT and as accurate as VMS-PDFT. The new method maximizes the trace of the classical Coulomb energy of the intermediate states such that the electron densities of the intermediate states are compressed. We show that CMS-PDFT performs robustly even where XMS-PDFT fails.

Effects of Ring Fluorination on the Ultraviolet Photodissociation Dynamics of Phenol

The dynamics of photoinduced O-H bond fission in five fluorinated phenols (2-fluorophenol, 3-fluorophenol, 2,6-difluorophenol, 3,4,5-trifluorophenol, and pentafluorophenol) have been investigated by H Rydberg atom photofragment translational spectroscopy following excitation at many wavelengths in the range 220 ≤ λ ≤ 275 nm. The presence of multiple fluorine substituents reduces the efficiency of O-H bond fission (by tunneling) from the first excited (1¹ππ*) electronic state, whereas all bar the perfluorinated species undergo O-H bond fission when excited at shorter wavelengths (to the 2¹ππ* state). As in bare phenol, O-H bond fission is deduced to occur by non-adiabatic coupling at conical intersections between the photoprepared "bright" ππ* states and the 1¹πσ* potential energy surface. In all cases, the fluorophenoxyl photoproducts are found to be formed in a range of vibrational levels, all of which include an odd number of quanta (typically one) in an out-of-plane (a″) vibrational mode; this product vibration is viewed as a legacy of the parent out-of-plane motions that promote non-adiabatic coupling to the dissociative 1¹πσ* potential. The radical products also show activity in in-plane vibrations involving coupled (both in- and out-of-phase) C-O and C-F wagging motions, which can be traced to the impulse between the recoiling O and H atoms and, in detail, are sensitive to the presence (or not) of an intramolecular F···H-O hydrogen bond. Upper limit values for the O-H bond dissociation energies are reported for all molecules studied apart from pentafluorophenol.

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.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Real-Time Tunneling Dynamics through Adiabatic Potential Energy Surfaces Shaped by a Conical Intersection

Dynamic shaping of the adiabatic tunneling barrier in the S-H bond extension coordinate of several ortho-substituted thiophenols has been found to be mediated by low-frequency out-of-plane vibrational modes, which are parallel to the coupling vector of the branching plane comprising the conical intersection. The S-H predissociation tunneling rate (k) measured when exciting to the S₁ zero-point level of 2-methoxythiophenol (44 ps)^-1 increases abruptly, to k ≈ (22 ps)^-1, at the energy corresponding to excitation of the 152 cm^-1 out-of-plane vibrational mode and then falls back to k ≈ (40 ps)^-1 when the in-plane mode is excited at 282 cm^-1. Similar resonance-like peaks in plots of S₁ tunneling rate versus internal energy are observed when exciting the corresponding low-frequency out-of-plane modes in the S₁ states of 2-fluorothiophenol and 2-chlorothiophenol. This experiment provides clear-cut evidence for dynamical "shaping" of the lower-lying adiabatic potential energy surfaces by the higher-lying conical intersection seam, which dictates the multidimensional tunneling dynamics.

Photolysis dynamics of m- and o-fluorophenol: Substitution effects on tunneling mechanism

The photolysis dynamics of m-fluorophenol (m-FPhOH) and o-fluorophenol (o-FPhOH) have been investigated with time-resolved velocity map imaging (TR-VMI) and time-resolved ion-yield (TR-IY) techniques. Following excitation to the origin of S₁ (ππ∗) state of m- and o-FPhOH, H atoms elimination mediated by tunneling through the potential barrier under the S₁ (ππ∗)/S₂ (πσ∗) conical intersection (CI) has been observed as a Gaussian feature signal centered at a total kinetic energy release (TKER) of ∼6000 cm^-1 for both molecules. The quantum tunneling mechanism has been identified as the main decay pathway of S₁ state for m-FPhOH, and the tunneling lifetime of 2.1 ns has been obtained from the TR-VMI measurements of H fragments. This tunneling mechanism is further confirmed by the studies on the selective O-H deuterated species, m-FPhOD, and consolidated by our theoretical calculations. However, the photolysis dynamics is quite different for the photoexcited o-FPhOH. The much lower yield of the H atoms originating from tunneling hinders the extraction of a reliable tunneling lifetime for o-FPhOH. Our theoretical calculations exhibit a broader and higher potential barrier exists beneath the S₁/S₂ CI of o-FPhOH, which increase the difficulty for tunneling. Furthermore, the special existence of intramolecular hydrogen bond in o-FPhOH is probably also the key factor that affects the tunneling rate, which would restrict the O-H stretch motion.

Time-Derivative Couplings for Self-Consistent Electronically Nonadiabatic Dynamics

Electronically nonadiabatic dynamics methods based on a self-consistent potential, such as semiclassical Ehrenfest and coherent switching with decay of mixing, have a number of advantages but are computationally slower than approximations based on an unaveraged potential because they require evaluation of all components of the nonadiabatic coupling vector. Here we introduce a new approximation to the self-consistent potential that does not have this computational drawback. The new approximation uses time-derivative couplings evaluated by overlap integrals of electronic wave functions to approximate the nonadiabatic coupling terms in the equations of motion. We present a numerical test of the method for ethylene that shows there is little loss of accuracy in the ensemble-averaged results. This new approximation to the self-consistent potential makes direct dynamics calculations with self-consistent potentials more efficient for complex systems and makes them practically affordable for some cases where the cost was previously too high.

Stimulated X-ray Resonant Raman Spectroscopy of Conical Intersections in Thiophenol

The conical intersection dynamics of thiophenol is studied by computing the stimulated X-ray resonant Raman spectroscopy signals. The hybrid probing field is constructed of a hard X-ray narrowband femtosecond pulse combined with an attosecond broadband X-ray pulse to provide optimal spectral and temporal resolutions for electronic coherences in the level crossing region. The signal carries phase information about the valence-core electronic coupling in the vicinity of conical intersections. Two conical intersections occurring during the course of the S-H dissociation dynamics can be distinguished by their valence-core transition frequencies computed at the complete active space self-consistent field level. The X-ray pulse is tuned such that the Raman transition at the first conical intersection between ¹πσ* and 1¹ππ* involves higher core levels, while the Raman transition at the second conical intersection between ¹πσ* and S₀ involves the lowest core level in the sulfur K-edge.

Conservation of Angular Momentum in Direct Nonadiabatic Dynamics

Direct nonadiabatic dynamics is used to study processes involving multiple electronic states from small molecules to materials. Compared with dynamics with fitted analytical potential energy surfaces, direct dynamics is more user-friendly in that it obtains all needed energies, gradients, and nonadiabatic couplings (NACs) by electronic structure calculations. However, the NAC that is usually used does not conserve angular momentum or the center of mass in widely used mixed quantum-classical nonadiabatic dynamics algorithms, in particular, trajectory surface hopping, semiclassical Ehrenfest, and coherent switching with decay of mixing. We show that by using a projection operator to remove the translational and rotational components of the originally computed NAC, one can restore the conservation.

Stimulated X-ray Raman Imaging of Conical Intersections

The conical intersection dynamics of thiophenol is studied theoretically using the stimulated X-ray Raman imaging (SXRI) technique. SXRI employs a hard X-ray narrowband/broadband hybrid probe field and provides a real-time and real-space image of the passage through conical intersections. The signal, calculated using the minimal-coupling radiation/matter Hamiltonian, carries the phase information, and the real-space image of the transition charge density can be reconstructed by its Fourier transform. The two conical intersections (S₂/S₁ (1¹ππ*/¹πσ*) and S₁/S₀ (¹πσ*/S₀)) can be distinguished and identified by the diffraction patterns in the level crossing regimes.

Insights into the Mechanism of Nonadiabatic Photodissociation from Product Vibrational Distributions. The Remarkable Case of Phenol

The fate of a photoexcited molecule is often strongly influenced by electronic degeneracies, such as conical intersections, which break the Born-Oppenheimer separation of electronic and nuclear motion. Detailed information concerning internal energy redistribution in a nonadiabatic process can be extracted from the product state distribution of a photofragment in photodissociation. Here, we focus on the nonadiabatic photodissociation of phenol and discuss the internal excitation of the phenoxyl fragment using both symmetry analysis and wave packet dynamics. It is shown that unique and general selection rules exist, which can be attributed to the geometric phase in the adiabatic representation. Further, our results provide a reinterpretation of the experimental data, shedding light on the impact of conical intersections on the product state distribution.

Real-Time Observation of Fermi Resonances in the S1 State of Phenol

Fermi resonances in the first electronically excited (S₁) state of phenol have been observed in real time. Quantum beats associated with coherent superposition of Fermi resonant eigenstates are manifested as temporal oscillations of the ionization cross sections of which the amplitudes are strongly dependent on the total ionization energy. This indicates that coherently excited eigenstates are effectively decomposed into their zeroth-order states, providing the unique opportunity for the investigation of nonstationary state dynamics in real-time. Energy gaps (Δν̃) of eigenstates within the laser coherence width have been most precisely determined up to date, giving Δν̃ ∼ 3.302 ± 0.001 or 1.655 ± 0.001 cm^-1 for the 1¹/4¹10b¹ or 12²/8a¹ Fermi doublets, respectively. Dephasing rate suddenly increases as the S₁ internal energy becomes above ∼1500 cm^-1, revealing the important role of energy randomization dynamics during the H atom tunneling process of phenol in S₁.

An experimental and computational study of the effect of aqueous solution on the multiphoton ionisation photoelectron spectrum of phenol

We revisit the photoelectron spectroscopy of aqueous phenol in an effort to improve our understanding of the impact of inhomogeneous broadening and inelastic scattering on solution-phase photoelectron spectra.

Identification of an Emitting Metastable State of p-Fluorophenol-Ammonia 1:2 Complex by Laser-Induced Fluorescence Spectroscopy

We have demonstrated here, for the first time to our knowledge, the formation of an emitting metastable species upon lowest electronic excitation (S₁) of a hydrogen-bonded 1:2 complex of para-fluorophenol (pFP) with ammonia (NH₃), which is known to be one of the smallest reactive complexes to undergo excited state H-atom transfer (HAT) reaction to produce ^•NH₄(NH₃) radical fragment. The emission spectrum of the species is characterized to be red-shifted, broad, and structureless. From the viewpoint of energy balance, an excited state proton transfer (ESPT) is unfavorable, but according to predicted electronic structure parameters, the metastable state species could be stabilized by charge transfer (CT) interaction at the hydrogen-bonded geometry of the complex. We propose that this species could act as an intermediate to the HAT process in the excited state. The observation of such a state could be valuable to understand the complex dynamics of similar events in biologically relevant systems.

Unraveling the Mechanisms of the Excited-State Intermolecular Proton Transfer (ESPT) for a D-π-A Molecular Architecture

Precise revealing the mechanisms of excited-state intermolecular proton transfer (ESPT) and the corresponding geometrical relaxation upon photoexcitation and photoionization remains a formidable challenge. In this work, the compound (E)-4-(((4H-1,2,4-triazol-4-yl)imino)methyl)-2,6-dimethoxyphenol (TIMDP) adopting a D-π-A molecular architecture featuring a significant intramolecular charge transfer (ICT) effect has been designed. With the presence of perchloric acid (35 %), TIMDP can be dissolved through the formation of a HClO₄ -H₂ O-OH(TIMDP)-N(TIMDP) hydrogen-bonding bridge. At the ground state, the ICT effect is dominant, giving birth to crystals of TIMDP. Upon external stimuli (e.g., UV light irradiation, electro field), the excited state is achieved, which weakens the ICT effect, and significantly promotes the ESPT effect along the hydrogen-bonding bridge, resulting in crystals of [HTIMDP]⁺ ⋅[H₂ O]⋅[ClO₄ ]^- . As a consequence, the mechanisms of the ESPT can be investigated, which distorted the D-π-A molecular architecture, tuned the emission color with the largest Stokes shift of 242 nm, and finally, high photoluminescence quantum yields (12 %) and long fluorescence lifetimes (8.6 μs) have achieved. These results not only provide new insight into ESPT mechanisms, but also open a new avenue for the design of efficient ESPT emitters.

Multidimensional H Atom Tunneling Dynamics of Phenol: Interplay between Vibrations and Tunneling

Multidimensional facets of the hydrogen tunneling dynamics of phenol excited in S₁ (ππ*) have been unraveled to give particular S₁ vibronic states strongly coupled or actively decoupled to the O-H tunneling coordinate. Strong mode-dependent variation of the tunneling rate measured with picosecond lasers indicates that tunneling probability is extremely sensitive to low-frequency vibrational modes seemingly orthogonal to the O-H elongation coordinate unless the rate of energy randomization exceeds that of tunneling. The multidimensional nature of tunneling has also been manifested in efficient internal-to-translational energy transfers observed at S₁ vibronic modes strongly coupled to the tunneling coordinate, giving insights into otherwise the formidable multidimensional map of tunneling process. The nonadiabatic bifurcation dynamics in the later stage of the chemical reaction has been disentangled by analyzing picosecond time-resolved product state distributions, resolving a long controversial issue regarding the origin of high or low kinetic energy component of the product translational energy distributions.