Evaluation of mixed quantum-classical molecular dynamics on cis-azobenzene photoisomerization

Construction of Highly Accurate Machine Learning Potential Energy Surfaces for Excited-State Dynamics Simulations Based on Low-Level Data Sets

Machine learning is capable of effectively predicting the potential energies of molecules in the presence of high-quality data sets. Its application in the construction of ground- and excited-state potential energy surfaces is attractive to accelerate nonadiabatic molecular dynamics simulations of photochemical reactions. Because of the huge computational cost of excited-state electronic structure calculations, the construction of a high-quality data set becomes a bottleneck. In the present work, we first built two data sets. One was obtained from surface hopping dynamics simulations at the semiempirical OM2/MRCI level. Another was extracted from the dynamics trajectories at the CASSCF level, which was reported previously. The ground- and excited-state potential energy surfaces of ethylene-bridged azobenzene at the CASSCF computational level were constructed based on the former low-level data set. Although non-neural network machine learning methods can achieve good or modest performance during the training process, only neural network models provide reliable predictions on the latter external test data set. The BPNN and SchNet combined with the Δ-ML scheme and the force term in the loss functions are recommended for dynamics simulations. Then, we performed excited-state dynamics simulations of the photoisomerization of ethylene-bridged azobenzene on machine learning potential energy surfaces. Compared with the lifetimes of the first excited state (S1) estimated at different computational levels, our results on the E isomer are in good agreement with the high-level estimation. However, the overestimation of the Z isomer is unimproved. It suggests that smaller errors during the training process do not necessarily translate to more accurate predictions on high-level potential energies or better performance on nonadiabatic dynamics simulations, at least in the present case.

Exact-Factorization-Based Surface Hopping without Velocity Adjustment

While surface hopping has emerged as a powerful method for simulating non-adiabatic dynamics in large molecules, the ad hoc nature of the necessary velocity adjustments and decoherence corrections in the algorithm somewhat reduces its reliability. Here we propose a new scheme that eliminates these aspects by combining the nuclear equation from the quantum-trajectory surface-hopping approach with the electronic equation derived from the exact-factorization approach. The resulting method, denoted QTSH-XF, yields a surface-hopping method on firmer ground than previous and is shown to successfully capture dynamics in Tully models and in a linear vibronic coupling model of the photoexcited uracil cation.

Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic Dynamics

Through approximating electron-nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the nonlocal nature of quantum nuclear dynamics that is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy. We analyze energy conservation in the coupled-trajectory mixed quantum-classical (CTMQC) algorithm and explore the performance of a modified algorithm, CTMQC-E, where some of the terms are redefined to restore energy conservation. A set of molecular models is used as a test, namely, 2-cis-penta-2,4-dienimium cation, bis(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.

Different flavors of exact-factorization-based mixed quantum-classical methods for multistate dynamics

The exact factorization approach has led to the development of new mixed quantum-classical methods for simulating coupled electron-ion dynamics. We compare their performance for dynamics when more than two electronic states are occupied at a given time, and analyze: (1) the use of coupled versus auxiliary trajectories in evaluating the electron-nuclear correlation terms, (2) the approximation of using these terms within surface-hopping and Ehrenfest frameworks, and (3) the relevance of the exact conditions of zero population transfer away from nonadiabatic coupling regions and total energy conservation. Dynamics through the three-state conical intersection in the uracil radical cation as well as polaritonic models in one dimension are studied.

Fewest-Switches Surface Hopping with Long Short-Term Memory Networks

The mixed quantum-classical dynamical simulation is essential for studying nonadiabatic phenomena in photophysics and photochemistry. In recent years, many machine learning models have been developed to accelerate the time evolution of the nuclear subsystem. Herein, we implement long short-term memory (LSTM) networks as a propagator to accelerate the time evolution of the electronic subsystem during the fewest-switches surface hopping (FSSH) simulations. A small number of reference trajectories are generated using the original FSSH method, and then the LSTM networks can be built, accompanied by careful examination of typical LSTM-FSSH trajectories that employ the same initial condition and random numbers as the corresponding reference. The constructed network is applied to FSSH to further produce a trajectory ensemble to reveal the mechanism of nonadiabatic processes. Taking Tully's three models as test systems, we qualitatively reproduced the collective results. This work demonstrates that LSTM can be applied to the most popular surface hopping simulations.

Exact Factorization Adventures: A Promising Approach for Non-Bound States

Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

Study of the Decoherence Correction Derived from the Exact Factorization Approach for Nonadiabatic Dynamics

We present a detailed study of the decoherence correction to surface hopping that was recently derived from the exact factorization approach. Ab initio multiple spawning calculations that use the same initial conditions and the same electronic structure method are used as a reference for three molecules: ethylene, the methaniminium cation, and fulvene, for which nonadiabatic dynamics follows a photoexcitation. A comparison with the Granucci–Persico energy-based decoherence correction and the augmented fewest-switches surface-hopping scheme shows that the three decoherence-corrected methods operate on individual trajectories in a qualitatively different way, but the results averaged over trajectories are similar for these systems.