On-the-fly ab initio molecular dynamics with multiconfigurational Ehrenfest method

Semiclassical dynamics in Wigner phase space II: Nonadiabatic hybrid Wigner dynamics

We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman-Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects.

An Exhaustive Quantum-Classical Study of C6F6+ Using the Newly Formulated Parallel TDDVR Method

We recently implemented our parallelized quantum-classical dynamical approach, known as the Time-Dependent Discrete Variable Representation (TDDVR) method, which is applied to the spectroscopically important hexafluorobenzene (HFBz) radical cation, where several conical intersections exist in their seven lowest excited electronic states (S11B2u, S21E1g, S31B1u, S41E1u, and S51A2u) considering degeneracy among potential energy surfaces (PESs), to demonstrate their various dynamical aspects. This new parallel version shows almost linear scalability with increasing number of computing processors. To get photoelectron (PE) spectra, Mass-Analyzed Threshold Ionization (MATI) spectra, population dynamics, and many other dynamical observables, the first-principles dynamics is applied at the state-of-the-art level to the corresponding Hamiltonian, where the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) type interactions are involved in those coupled seven electronic states. The quantum-classical method is used to thoroughly analyze the effects of these couplings on the nuclear dynamics of the involved electronic states, and the findings are compared with those observables obtained from experiments. Intrinsic dynamical properties are explained using the reduced densities of the wave packet (WP) in a coupled electronic manifold. The PE and MATI spectra of HFBz computed using TDDVR are found to be in good agreement with earlier experimental data and other theoretically simulated spectra.

Using a multistate mapping approach to surface hopping to predict the ultrafast electron diffraction signal of gas-phase cyclobutanone

Using the recently developed multistate mapping approach to surface hopping (multistate MASH) method combined with SA(3)-CASSCF(12,12)/aug-cc-pVDZ electronic structure calculations, the gas-phase isotropic ultrafast electron diffraction (UED) of cyclobutanone is predicted and analyzed. After excitation into the n-3s Rydberg state (S2), cyclobutanone can relax through two S2/S1 conical intersections, one characterized by compression of the CO bond and the other by dissociation of the α-CC bond. Subsequent transfer into the ground state (S0) is then achieved via two additional S1/S0 conical intersections that lead to three reaction pathways: α ring-opening, ethene/ketene production, and CO liberation. The isotropic gas-phase UED signal is predicted from the multistate MASH simulations, allowing for a direct comparison to the experimental data. This work, which is a contribution to the cyclobutanone prediction challenge, facilitates the identification of the main photoproducts in the UED signal and thereby emphasizes the importance of dynamics simulations for the interpretation of ultrafast experiments.

Ultrafast electron diffraction of photoexcited gas-phase cyclobutanone predicted by ab initio multiple cloning simulations

We present the result of our calculations of ultrafast electron diffraction (UED) for cyclobutanone excited into the S2 electronic state, which is based on the non-adiabatic dynamics simulations with the Ab Initio Multiple Cloning (AIMC) method with the electronic structure calculated at the SA(3)-CASSCF(12,12)/aug-cc-pVDZ level of theory. The key features in the UED pattern were identified, which can be used to distinguish between the reaction pathways observed in the AIMC dynamics, although there is a significant overlap between representative signals due to the structural similarity of the products. The calculated UED pattern can be compared with the experiment.

High-order geometric integrators for the local cubic variational Gaussian wavepacket dynamics

Gaussian wavepacket dynamics has proven to be a useful semiclassical approximation for quantum simulations of high-dimensional systems with low anharmonicity. Compared to Heller's original local harmonic method, the variational Gaussian wavepacket dynamics is more accurate, but much more difficult to apply in practice because it requires evaluating the expectation values of the potential energy, gradient, and Hessian. If the variational approach is applied to the local cubic approximation of the potential, these expectation values can be evaluated analytically, but they still require the costly third derivative of the potential. To reduce the cost of the resulting local cubic variational Gaussian wavepacket dynamics, we describe efficient high-order geometric integrators, which are symplectic, time-reversible, and norm-conserving. For small time steps, they also conserve the effective energy. We demonstrate the efficiency and geometric properties of these integrators numerically on a multidimensional, nonseparable coupled Morse potential.

Benchmarking non-adiabatic quantum dynamics using the molecular Tully models

On-the-fly non-adiabatic dynamics methods are becoming more important as tools to characterise the time evolution of a system after absorbing light. These methods, which calculate quantities such as state energies, gradients and interstate couplings at every time step, circumvent the requirement for pre-computed potential energy surfaces. There are a number of different algorithms used, the most common being Tully Surface Hopping (TSH), but all are approximate solutions to the time-dependent Schrödinger equation and benchmarking is required to understand their accuracy and performance. For this, a common set of systems and observables are required to compare them. In this work, we validate the on-the-fly direct dynamics variational multi-configuration Gaussian (DD-vMCG) method using three molecular systems recently suggested by Ibele and Curchod as molecular versions of the Tully model systems used to test one-dimensional non-adiabatic behaviour [Ibele et al., Phys. Chem. Chem. Phys. 2020, 22, 15183-15196]. Parametrised linear vibronic potential energy surfaces for each of the systems were also tested and compared to on-the-fly results. The molecules, which we term the Ibele-Curchod models, are ethene, DMABN and fulvene and the authors used them to test and compare several versions of the Ab Initio Multiple Spawning (AIMS) method alongside TSH. The three systems present different deactivation pathways after excitation to their ππ* bright states. When comparing DD-vMCG to AIMS and TSH, we obtain crucial differences in some cases, for which an explanation is provided by the classical nature and the chosen initial conditions of the TSH simulations.

NWChem: Recent and Ongoing Developments

This paper summarizes developments in the NWChem computational chemistry suite since the last major release (NWChem 7.0.0). Specifically, we focus on functionality, along with input blocks, that is accessible in the current stable release (NWChem 7.2.0) and in the "master" development branch, interfaces to quantum computing simulators, interfaces to external libraries, the NWChem github repository, and containerization of NWChem executable images. Some ongoing developments that will be available in the near future are also discussed.

Charge Migration in HCCI Cations Probed by Strong Field Ionization: Time-Dependent Configuration Interaction and Vibrational Wavepacket Simulations

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations and results in charge migration between the CC π orbital and the iodine π-type lone pair. This charge migration causes oscillations in the rate of strong field ionization of the cation to the dication that can be monitored using intense few-cycle probe pulses. The dynamics and strong field ionization of the coherent superposition the X and A states of HCCI⁺ have been modeled by time-dependent configuration interaction (TDCI) simulations. When the nuclei are allowed to move, the electronic wavefunctions need to be multiplied by vibrational wavefunctions. Nuclear motion has been modeled by vibrational packets moving on quadratic approximations to the potential energy surfaces for the X and A states of the cation. The overlap of the vibrational wavepackets decays in about 10-15 fs. Consequently, the oscillations in the strong field ionization decay on the same time scale. A revival of the vibrational overlap and in the oscillations of the strong field ionization is seen at 60-110 fs. TDCI simulations show that the decay and revival of the charge migration can be monitored by strong field ionization with intense 2- and 4-cycle linearly polarized 800 nm pulses. The revival is also seen with 7-cycle pulses.

Extending the Applicability of the Multiple-Spawning Framework for Nonadiabatic Molecular Dynamics

Ab initio multiple-spawning (AIMS) describes the nonadiabatic dynamics of molecules by expanding nuclear wave functions in a basis of traveling multidimensional Gaussians called trajectory basis functions (TBFs). New TBFs can be spawned whenever nuclear amplitude is transferred between electronic states due to nonadiabatic transitions. While the adaptive size of the TBF basis grants AIMS its characteristic accuracy in describing nonadiabatic processes, it also leads to a fast and uncontrolled growth of the number of TBFs, penalizing computational efficiency. A different flavor of AIMS, called AIMS with informed stochastic selections (AIMSWISS), has recently been proposed to reduce the number of TBFs dramatically. Herein, we test the performance of AIMSWISS for a series of challenging nonadiabatic processes─photodynamics of two-dimensional model systems, 1,2-dithiane and chromium (0) hexacarbonyl─and show that this method is robust and extends the range of molecular systems that can be simulated within the multiple-spawning framework.

Trajectory Propagation of Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian Using Machine Learning

The long short-term memory recurrent neural network (LSTM-RNN) approach is applied to realize the trajectory-based nonadiabatic dynamics within the framework of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC). After construction, the LSTM-RNN model allows us to propagate the entire trajectory evolutions of all involved degrees of freedoms (DOFs) from initial conditions. The proposed idea is proven to be reliable and accurate in the simulations of the dynamics of several site-exciton electron-phonon coupling models and three Tully's scattering models. It indicates that the LSTM-RNN model perfectly captures the dynamical information on the trajectory evolution in the MM-SQC dynamics. Our work proposes a novel machine learning approach in the simulation of trajectory-based nonadiabatic dynamic of complex systems with a large number of DOFs.

Ultrafast coherent photoexcited dynamics in a trimeric dendrimer probed by X-ray stimulated-Raman signals

The photoinduced ultrafast coherent inter-chromophore energy redistribution in a triarylamine trimer is explored using nonadiabatic excited state molecular dynamics followed by simulations of X-ray Raman signals. The nitrogencentered system ensures strong interchromophore interactions and, thus, the presence of coherences. Nevertheless, the multitude of non-deterministic photoinduced pathways during the ultrafast inter-branch migration of the excitation results in random confinement on some branches and, therefore, spatial exciton scrambling and loss of phase information at long times. We show that the vibronic coherence dynamics evolving into the incoherent scrambling mechanism on ultrafast 50 fs timescale, is accurately probed by the TRUECARS X-ray stimulated Raman signal. In combination with previous results, where the technique has revealed long-lived coherences in a rigid heterodimer, the signal is most valuable for detecting ultrafast molecular coherences or their absence. We demonstrate that X-ray Raman spectroscopy is a useful tool in the chemical design of functional molecular building blocks.

The photoinduced ultrafast coherent inter-chromophore energy redistribution in a triarylamine trimer is explored using nonadiabatic excited state molecular dynamics followed by simulations of X-ray Raman signals.

The moving crude adiabatic alternative to the adiabatic representation in excited state dynamics

The choice of the electronic representation in on-the-fly quantum dynamics is crucial. The adiabatic representation is appealing since adiabatic states are readily available from quantum chemistry packages. The nuclear wavepackets are then expanded in a basis of Gaussian functions, which follow trajectories to explore the potential energy surfaces and approximate the potential using a local expansion of the adiabatic quantities. Nevertheless, the adiabatic representation is plagued with severe limitations when conical intersections are involved: the diagonal Born-Oppenheimer corrections (DBOCs) are non-integrable, and the geometric phase effect on the nuclear wavepackets cannot be accounted for unless a model is available. To circumvent these difficulties, the moving crude adiabatic (MCA) representation was proposed and successfully tested in low energy dynamics where the wavepacket skirts the conical intersection. We assess the MCA representation in the case of non-adiabatic transitions through conical intersections. First, we show that using a Gaussian basis in the adiabatic representation indeed exhibits the aforementioned difficulties with a special emphasis on the possibility to regularize the DBOC terms. Then, we show that MCA is indeed able to properly model non-adiabatic transitions. Tests are done on linear vibronic coupling models for the bis(methylene) adamantyl cation and the butatriene cation. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

Fewest switches surface hopping with Baeck-An couplings

In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

Fewest switches surface hopping with Baeck-An couplings

In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

A Mixed Deterministic-Stochastic Algorithm of the Branching Corrected Mean Field Method for Nonadiabatic Dynamics

We present a new algorithm of the branching corrected mean field (BCMF) method for nonadiabatic dynamics [J. Xu and L. Wang, J. Phys. Chem. Lett. 11, 8283 (2020)], which combines the key advantages of the two existed algorithms, i.e., the deterministic BCMF algorithm based on weights of trajectory branches (BCMF-w) and the stochastic BCMF algorithm with random collapse of the electronic wavefunction (BCMF-s). The resulting mixed deterministic-stochastic BCMF algorithm (BCMF-ws) is benchmarked in a series of standard scattering problems with potential wells on the excited-state surfaces, which are common in realistic systems. In all investigated cases, BCMF-ws holds the same high accuracy while the computational time is reduced about two orders of magnitude compared to the original BCMF-w and BCMF-s algorithms, thus promising for nonadiabatic dynamics simulations of general systems.

Dynamic signatures of electronically nonadiabatic coupling in sodium hydride: a rigorous test for the symmetric quasi-classical model applied to realistic, ab initio electronic states in the adiabatic representation

Sodium hydride (NaH) in the gas phase presents a seemingly simple electronic structure making it a potentially tractable system for the detailed investigation of nonadiabatic molecular dynamics from both computational and experimental standpoints. The single vibrational degree of freedom, as well as the strong nonadiabatic coupling that arises from the excited electronic states taking on considerable ionic character, provides a realistic chemical system to test the accuracy of quasi-classical methods to model population dynamics where the results are directly comparable against quantum mechanical benchmarks. Using a simulated pump-probe type experiment, this work presents computational predictions of population transfer through the avoided crossings of NaH via symmetric quasi-classical Meyer-Miller (SQC/MM), Ehrenfest, and exact quantum dynamics on realistic, ab initio potential energy surfaces. The main driving force for population transfer arises from the ground vibrational level of the D¹Σ⁺ adiabatic state that is embedded in the manifold of near-dissociation C¹Σ⁺ vibrational states. When coupled through a sharply localized first-order derivative coupling most of the population transfers between t = 15 and t = 30 fs depending on the initially excited vibronic wavepacket. While quantum mechanical effects are expected due to the reduced mass of NaH, predictions of the population dynamics from both the SQC/MM and Ehrenfest models perform remarkably well against the quantum dynamics benchmark. Additionally, an analysis of the vibronic structure in the nonadiabatically coupled regime is presented using a variational eigensolver methodology.

Ab initio symmetric quasi-classical approach to investigate molecular Tully models

We perform on-the-fly non-adiabatic molecular dynamics simulations using the symmetrical quasi-classical (SQC) approach with the recently suggested molecular Tully models: ethylene and fulvene. We attempt to provide benchmarks of the SQC methods using both the square and triangle windowing schemes as well as the recently proposed electronic zero-point-energy correction scheme (the so-called γ correction). We use the quasi-diabatic propagation scheme to directly interface the diabatic SQC methods with adiabatic electronic structure calculations. Our results showcase the drastic improvement of the accuracy by using the trajectory-adjusted γ-corrections, which outperform the widely used trajectory surface hopping method with decoherence corrections. These calculations provide useful and non-trivial tests to systematically investigate the numerical performance of various diabatic quantum dynamics approaches, going beyond simple diabatic model systems that have been used as the major workhorse in the quantum dynamics field. At the same time, these available benchmark studies will also likely foster the development of new quantum dynamics approaches based on these techniques.

AIMSWISS-Ab initio multiple spawning with informed stochastic selections

Ab initio multiple spawning (AIMS) offers a reliable strategy to describe the excited-state dynamics and nonadiabatic processes of molecular systems. AIMS represents nuclear wavefunctions as linear combinations of traveling, coupled Gaussians called trajectory basis functions (TBFs) and uses a spawning algorithm to increase as needed the size of this basis set during nonadiabatic transitions. While the success of AIMS resides in this spawning algorithm, the dramatic increase in TBFs generated by multiple crossings between electronic states can rapidly lead to intractable dynamics. In this Communication, we introduce a new flavor of AIMS, coined ab initio multiple spawning with informed stochastic selections (AIMSWISS), which proposes a parameter-free strategy to beat the growing number of TBFs in an AIMS dynamics while preserving its accurate description of nonadiabatic transitions. The performance of AIMSWISS is validated against the photodynamics of ethylene, cyclopropanone, and fulvene. This technique, built upon the recently developed stochastic-selection AIMS, is intended to serve as a computationally affordable starting point for multiple spawning simulations.

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

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

Velocity Adjustment in Surface Hopping: Ethylene as a Case Study of the Maximum Error Caused by Direction Choice

The most common surface hopping dynamics algorithms require velocity adjustment after hopping to ensure total-energy conservation. Based on the semiclassical analysis, this adjustment must be made parallel to the nonadiabatic coupling vector's direction. Nevertheless, this direction is not always known, and the common practice has been to adjust the velocity in either the linear momentum or velocity directions. This paper benchmarks surface hopping dynamics of photoexcited ethylene with velocity adjustment in several directions, including those of the nonadiabatic coupling vector, the momentum, and the energy gradient difference. It is shown that differences in time constants and structural evolution fall within the statistical uncertainty of the method considering up to 500 trajectories in each dynamics set, rendering the three approaches statistically equivalent. For larger ensembles beyond 1000 trajectories, significant differences between the results arise, limiting the validity of adjustment in alternative directions. Other possible adjustment directions (velocity, single-state gradients, angular momentum) are evaluated as well. Given the small size of ethylene, the results reported in this paper should be considered an upper limit for the error caused by the choice of the velocity-adjustment direction on surface hopping dynamics.

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

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

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.

On-the-Fly Ab Initio Semiclassical Evaluation of Electronic Coherences in Polyatomic Molecules Reveals a Simple Mechanism of Decoherence

Irradiation of a molecular system by an intense laser field can trigger dynamics of both electronic and nuclear subsystems. The lighter electrons usually move on much faster, attosecond timescale but the slow nuclear rearrangement damps ultrafast electronic oscillations, leading to the decoherence of the electronic dynamics within a few femtoseconds. We show that a simple, single-trajectory semiclassical scheme can evaluate the electronic coherence time in polyatomic molecules accurately by demonstrating an excellent agreement with full-dimensional quantum calculations. In contrast to numerical quantum methods, the semiclassical one reveals the physical mechanism of decoherence beyond the general blame on nuclear motion. In the propiolic acid, the rate of decoherence and the large deviation from the static frequency of electronic oscillations are quantitatively described with just two semiclassical parameters-the phase space distance and signed area between the trajectories moving on two electronic surfaces. Because it evaluates the electronic structure on the fly, the semiclassical technique avoids the "curse of dimensionality" and should be useful for preselecting molecules for experimental studies.

On-the-fly ab initio semiclassical evaluation of vibronic spectra at finite temperature

To compute and analyze vibrationally resolved electronic spectra at zero temperature, we have recently implemented the on-the-fly ab initio extended thawed Gaussian approximation [A. Patoz et al., J. Phys. Chem. Lett. 9, 2367 (2018)], which accounts for anharmonicity, mode-mode coupling, and Herzberg-Teller effects. Here, we generalize this method in order to evaluate spectra at non-zero temperature. In line with thermo-field dynamics, we transform the von Neumann evolution of the coherence component of the density matrix to the Schrödinger evolution of a wavefunction in an augmented space with twice as many degrees of freedom. Due to the efficiency of the extended thawed Gaussian approximation, this increase in the number of coordinates results in nearly no additional computational cost. More specifically, compared to the original, zero-temperature approach, the finite-temperature method requires no additional ab initio electronic structure calculations. At the same time, the new approach allows for a clear distinction among finite-temperature, anharmonicity, and Herzberg-Teller effects on spectra. We show, on a model Morse system, the advantages of the finite-temperature thawed Gaussian approximation over the commonly used global harmonic methods and apply it to evaluate the symmetry-forbidden absorption spectrum of benzene, where all of the aforementioned effects contribute.

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.

Identification of a receiver triplet state in the ultrafast intersystem crossing of carbonylpyrenes

The near-unity triplet quantum yield of photoexcited carbonyl functionalized pyrenes is theoretically investigated. The estimated energetics of singlet-triplet manifolds and relevant spin-orbit coupling parameters strongly suggest triplet state formation via the S₁→ T₄/T₅ pathway. Quantum wavepacket dynamics of triplet manifolds within the linear vibronic coupling approach reveal that the receiver triplet state would undergo rapid internal conversion decay to the lower triplet state(s), facilitating efficient triplet generation by minimizing the reverse intersystem crossing possibilities. On the basis of these results, a unified mechanism is proposed to describe the ultrafast intersystem crossing process in these molecules.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

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.

A molecular perspective on Tully models for nonadiabatic dynamics

We present a series of standardized molecular tests for nonadiabatic dynamics, reminiscent of the one-dimensional Tully models proposed in 1990.

Quasi-Diabatic Scheme for Nonadiabatic On-the-Fly Simulations

We use the quasi-diabatic (QD) propagation scheme to perform on-the-fly nonadiabatic simulations of the photodynamics of ethylene. The QD scheme enables a seamless interface between accurate diabatic-based quantum dynamics approaches and adiabatic electronic structure calculations, explicitly avoiding any efforts to construct global diabatic states or reformulate the diabatic dynamics approach to the adiabatic representation. Using the partial linearized path-integral approach and the symmetrical quasi-classical approach as the diabatic dynamics methods, the QD propagation scheme enables direct nonadiabatic simulation with complete active space self-consistent field on-the-fly electronic structure calculations. The population dynamics obtained from both approaches are in a close agreement with the quantum wavepacket-based method and outperform the widely used trajectory surface-hopping approach. Further analysis of the ethylene photodeactivation pathways demonstrates the correct predictions of competing processes of nonradiative relaxation mechanism through various conical intersections. This work provides the foundation of using accurate diabatic dynamics approaches and on-the-fly adiabatic electronic structure information to perform ab initio nonadiabatic simulation.

Nonadiabatic Quantum Molecular Dynamics in Dense Manifolds of Electronic States

Most nonadiabatic molecular dynamics methods require the determination of a basis of adiabatic or diabatic electronic states at every time step, but in dense manifolds of electronic states, such approaches become intractable. A notable exception is Ehrenfest molecular dynamics, which can be implemented without explicit determination of such a basis but suffers from unphysical behavior when propagation on a mean-field potential energy surface (PES) does not accurately reflect the true dynamics on multiple electronic states. Here we introduce the multiple cloning for dense manifolds of states (MCDMS) method, a systematically improvable approximation to the multiple cloning method. MCDMS avoids both the mean-field PES problem and the need to compute the full electronic spectrum. This is achieved by reformulating multiple cloning to use a subspace of approximate eigenstates constructed from the time-dependent Ehrenfest electronic wave function. By application to model systems, we show that this approach allows a substantial reduction in the size of the required electronic basis without significant loss in accuracy.

Single-Hessian thawed Gaussian approximation

To alleviate the computational cost associated with on-the-fly ab initio semiclassical calculations of molecular spectra, we propose the single-Hessian thawed Gaussian approximation in which the Hessian of the potential energy at all points along an anharmonic classical trajectory is approximated by a constant matrix. The spectra obtained with this approximation are compared with the exact quantum spectra of a one-dimensional Morse potential and with the experimental spectra of ammonia and quinquethiophene. In all cases, the single-Hessian version performs almost as well as the much more expensive on-the-fly ab initio thawed Gaussian approximation and significantly better than the global harmonic schemes. Remarkably, unlike the thawed Gaussian approximation, the proposed method conserves energy exactly, despite the time dependence of the corresponding effective Hamiltonian, and, in addition, can be mapped to a higher-dimensional time-independent classical Hamiltonian system. We also provide a detailed comparison with several related approximations used for accelerating prefactor calculations in semiclassical simulations.

Ab Initio Computation of Rotationally-Averaged Pump-Probe X-ray and Electron Diffraction Signals

We develop a new algorithm for the computation of the rotationally averaged elastic molecular diffraction signal for the cases of perpendicular or parallel pump-probe geometries. The algorithm first collocates the charge density from an arbitrary ab initio wave function onto a Becke quadrature grid [A. Becke, J. Chem. Phys. 1988 , 88 , 2457 ], providing a high-fidelity multiresolution representation of the charge density. A double sum is then performed over the Becke grid points, and the interaction between points computed using the scattering kernels of Williamson and Zewail [J. C. Williamson and A. H. Zewail, J. Phys. Chem. 1994 , 98 , 2766 ]. These kernels analytically average over the molecular orientations with the cos² γ selection factor appropriate for one-photon dipole absorption in a perpendicular pump-probe geometry. We show that the method is converged with small grids containing <500 points/atom. We implement the algorithm on a GPU for increased efficiency and emonstrate the algorithm for molecules with up to a few dozen atoms. We explore the accuracy of the independent atom model (IAM) by comparison with our new and more accurate method. We also investigate the possibility of detecting signatures of electronic transitions in polyatomic pump-probe diffraction experiments.

Improved Ehrenfest Approach to Model Correlated Electron-Nuclear Dynamics

Mixed quantum-classical mechanical descriptions are critical to modeling coupled electron-nuclear dynamics, i.e., nonadiabatic molecular dynamics, relevant to photochemical and photophysical processes. We introduce an efficient description of such dynamics in terms of an effective Hamiltonian that not only properly captures electron-nuclear correlation effects but also helps develop an efficient computational method. In particular, we introduce a coupled Gaussian wavepacket parametrization of the nuclear wave function, which generalizes the Ehrenfest approach to account for electron-nuclei correlations. We test this new approach, Ehrenfest-Plus, on a suite of model problems that probe electron-nuclear correlation in nonadiabatic transitions. The high accuracy of our approach, combined with mixed quantum-classical efficiency, opens a path for improved simulation of nonadiabatic molecular dynamics in realistic molecular systems.

The 3s Rydberg state as a doorway state in the ultrafast dynamics of 1,1-difluoroethylene

The deactivation dynamics of 1,1-difluoroethylene after light excitation is studied within the surface hopping formalism in the presence of 3s and 3p Rydberg states using multi-state second order perturbation theory (MS-CASPT2).