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.

Excited-State Dynamics Simulations of a Light-Driven Molecular Motor in Solution

Molecular motors, where light can be transformed into motion, are promising in the design of nanomechanical devices. For applications, however, finding relationships between molecular motion and the environment is important. Here, we report the study of excited-state dynamics of an overcrowded alkene in solution using a hybrid quantum mechanics/molecular mechanics (QM/MM) approach combined with excited-state molecular dynamics simulations. Using QM/MM surface-hopping trajectories, we calculated time-resolved emission and transient absorption spectra. These show the rise of a short-lived Franck-Condon state, followed by the formation of a dark state in the first 150 fs before the molecular motor relaxes to the ground state in about 1 ps. From the analysis of radial distribution functions, we infer that the orientation of the solvent with respect to the molecular motor in the electronic excited state is similar to that in the ground state during the photoisomerization.

A Look Inside the Black Box of Machine Learning Photodynamics Simulations

ConspectusPhotochemical reactions are of great importance in chemistry, biology, and materials science because they take advantage of a renewable energy source, mild reaction conditions, and high atom economy. Light absorption can excite molecules to a higher energy electronic state of the same spin multiplicity. The following nonadiabatic processes induce molecular transformations that afford exotic molecular architectures and high-energy-isomers that are inaccessible by thermal means. Computational simulations now complement time-resolved instrumentation to reveal ultrafast excited-state mechanistic information for photochemical reactions that is essential in disentangling elusive spectroscopic features, excited-state lifetimes, and excited-state mechanistic critical points. Nonadiabatic molecular dynamics (NAMD), powered by surface hopping techniques, is among the most widely applied techniques to model the photochemical reactions of medium-sized molecules. However, the computational efficiency is limited because of the requisite thousands of multiconfigurational quantum-chemical calculations multiplied by hundreds of trajectories. Machine learning (ML) has emerged as a revolutionary force in computational chemistry to predict the outcome of the resource-intensive multiconfigurational calculations on the fly. An ML potential trained with a substantial set of quantum-chemical calculations can predict the energies and forces with errors under chemical accuracy at a negligible cost. The integration of ML potentials in NAMD dramatically extends the maximum simulation time scale by ∼10 000-fold to the nanosecond regime.In this Account, we present a comprehensive demonstration of ML photodynamics simulations and summarize our most recent applications in resolving complex photochemical reactions. First, we address three fundamental components of ML techniques for photodynamics simulations: the quantum-chemical data set, the ML potential, and NAMD. Second, we describe best practices in building training data and our procedure toward training the ML photodynamics model with our recent literature contributions. We introduce a convenient training data generation scheme combining Wigner sampling and geometrical interpolation. It trains reliable and effective ML potentials suitable for subsequent active learning to detect undersampled data. We demonstrate how active learning automatically discovers new mechanistic pathways and reproduces experimental results. We point out that atomic permutation is an essential data augmentation approach to improve the learnability of distance-based molecular descriptors for highly symmetric molecules. Third, we demonstrate the utility of ML-photodynamics by showing the results of ML photodynamics simulations of (1) photo-torquoselective 4π disrotatory electrocyclic ring closing of norbornyl cyclohexadiene, which reveals a thermal conversion from experimentally unobserved intermediates to the reactant in 1 ns; (2) [2 + 2] photocycloaddition of substituted [3]-syn-ladderdienes in competition with 4π and 6π electrocyclic ring-opening reactions, uncovering substituent effects to explain the reported increased quantum yield of substituted cubane precursors; and (3) photochemical 4π disrotatory electrocyclic reactions of fluorobenzenes in nanoseconds with XMS-CASPT2-level training data. We expect this Account to broaden understanding of ML photodynamics and inspire future developments and applications to increasingly large molecules within complex environments on long time scales.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.