Exploring molecular excited states holds immense significance across organic chemistry, chemical biology, and materials science. Understanding the photophysical properties of molecular chromophores is crucial for designing nature-inspired functional molecules, with applications ranging from photosynthesis to pharmaceuticals. Non-adiabatic molecular dynamics simulations are powerful tools to investigate the photochemistry of molecules and materials, but demand extensive computing resources, especially for complex molecules and environments. To address these challenges, the integration of machine learning has emerged. Machine learning algorithms can be used to analyse vast datasets and accelerate discoveries by identifying relationships between geometrical features and ground as well as excited-state properties. However, challenges persist, including the acquisition of accurate excited-state data and managing the complexity of the data. This article provides an overview of recent and best practices in machine learning for non-adiabatic molecular dynamics, focusing on pre-processing, surface fitting, and post-processing of data.

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• Review MeSH

ConspectusPhotochemical reactions have always been the source of a great deal of mystery. While classified as a type of chemical reaction, no doubts are allowed that the general tenets of ground-state chemistry do not directly apply to photochemical reactions. For a typical chemical reaction, understanding the critical points of the ground-state potential (free) energy surface and embedding them in a thermodynamics framework is often enough to infer reaction yields or characteristic time scales. A general working principle is that the energy profile along the minimum energy paths provides the key information to characterize the reaction. These well-developed concepts, unfortunately, rarely stretch to processes involving the formation of a nonstationary state for a molecular system after light absorption.Upon photoexcitation, a molecule is likely to undergo internal conversion processes, that is, changes of electronic states mediated by couplings between nuclear and electronic motion, precisely what the celebrated Born-Oppenheimer approximation neglects. These coupled electron-nuclear processes, coined nonadiabatic processes, allow for the molecule to decay from one electronic state to the other nonradiatively. Understanding the intricate nonadiabatic dynamics is pivotal to rationalizing and predicting the outcome of a molecular photoexcitation and providing insights for experiments conducted, for example, in advanced light sources such as free-electron lasers.Nowadays, most simulations in nonadiabatic molecular dynamics are based on approximations that invoke a near-classical depiction of the nuclei. This reliance is due to practical constraints, and the classical equations of motion for the nuclei must be supplemented by techniques such as surface hopping to account for nonadiabatic transitions between electronic states. A critical but often overlooked aspect of these simulations is the selection of initial conditions, specifically the choice of initial nuclear positions and momenta for the nonadiabatic dynamics, which can significantly influence how well the simulations mimic real quantum systems across various experimental scenarios. The conventional approach for generating initial conditions for nonadiabatic dynamics typically maps the initial state onto a nuclear phase space using a Wigner quasiprobability function within a harmonic approximation, followed by a second approximation where the molecule undergoes a sudden excitation.In this Account, we aim to warn the experienced or potential user of nonadiabatic molecular dynamics about the possible limitations of this strategy for initial-condition generation and its inability to accurately describe the photoexcitation of a molecule. More specifically, we argue that the initial phase-space distribution can be more accurately represented through molecular dynamics simulations by using a quantum thermostat. This method offers a robust framework that can be applied to large, flexible, or even solvated molecular systems. Furthermore, the reliability of this strategy can be benchmarked against more rigorous approaches such as path integral molecular dynamics. Additionally, the commonly used sudden approximation, which assumes a vertical and sudden excitation of a molecule, rarely reflects the excitation triggered by laser pulses used in actual photochemical and spectroscopic experiments. We discuss here a more general approach that can generate initial conditions for any type of laser pulse. We also discuss strategies to tackle excitation triggered by a continuous-wave laser.

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Liquid-jet photoemission spectroscopy (LJ-PES) directly probes the electronic structure of solutes and solvents. It also emerges as a novel tool to explore chemical structure in aqueous solutions, yet the scope of the approach has to be examined. Here, we present a pH-dependent liquid-jet photoelectron spectroscopic investigation of ascorbic acid (vitamin C). We combine core-level photoelectron spectroscopy and ab initio calculations, allowing us to site-specifically explore the acid-base chemistry of the biomolecule. For the first time, we demonstrate the capability of the method to simultaneously assign two deprotonation sites within the molecule. We show that a large change in chemical shift appears even for atoms distant several bonds from the chemically modified group. Furthermore, we present a highly efficient and accurate computational protocol based on a single structure using the maximum-overlap method for modeling core-level photoelectron spectra in aqueous environments. This work poses a broader question: to what extent can LJ-PES complement established structural techniques such as nuclear magnetic resonance? Answering this question is highly relevant in view of the large number of incorrect molecular structures published.

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The efficiency of machine learning algorithms for electronically excited states is far behind ground-state applications. One of the underlying problems is the insufficient smoothness of the fitted potential energy surfaces and other properties in the vicinity of state crossings and conical intersections, which is a prerequisite for an efficient regression. Smooth surfaces can be obtained by switching to the diabatic basis. However, diabatization itself is still an outstanding problem. We overcome these limitations by solving both problems at once. We use a machine learning approach combining clustering and regression techniques to correct for the deficiencies of property-based diabatization which, in return, provides us with smooth surfaces that can be easily fitted. Our approach extends the applicability of property-based diabatization to multidimensional systems. We utilize the proposed diabatization scheme to achieve higher prediction accuracy for adiabatic states and we show its performance by reconstructing global potential energy surfaces of excited states of nitrosyl fluoride and formaldehyde. While the proposed methodology is independent of the specific property-based diabatization and regression algorithm, we show its performance for kernel ridge regression and a very simple diabatization based on transition multipoles. Compared to most other algorithms based on machine learning, our approach needs only a small amount of training data.

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Solvent interactions, particularly hydration, are vital in chemical and biochemical systems. Model systems reveal microscopic details of such interactions. We uncover a specific hydrogen-bonding motif of the biomolecular building block indole (C8H7N), tryptophan's chromophore, in water: a strong localized N-H···OH2 hydrogen bond, alongside unstructured solvent interactions. This insight is revealed from a combined experimental and theoretical analysis of the electronic structure of indole in aqueous solution. We recorded the complete X-ray photoemission and Auger spectrum of aqueous-phase indole, quantitatively explaining all peaks through ab initio modeling. The efficient and accurate technique for modeling valence and core photoemission spectra involves the maximum-overlap method and the nonequilibrium polarizable-continuum model. A two-hole electron-population analysis quantitatively describes the Auger spectra. Core-electron binding energies for nitrogen and carbon highlight the specific interaction with a hydrogen-bonded water molecule at the N-H group and otherwise nonspecific solvent interactions.

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The wavelength control of photochemistry usually results from ultrafast dynamics following the excitation of different electronic states. Here, we investigate the CF3COCl molecule, exhibiting wavelength-dependent photochemistry both via (i) depositing increasing internal energy into a single state and (ii) populating different electronic states. We reveal the mechanism behind the photon-energy dependence by combining nonadiabatic ab initio molecular dynamics techniques with the velocity map imaging experiment. We describe a consecutive mechanism of photodissociation where an immediate release of Cl taking place in an excited electronic state is followed by a slower ground-state dissociation of the CO fragment. The CO release is subject to an activation barrier and is controlled by excess internal energy via the excitation wavelength. Therefore, a selective release of CO along with Cl can be achieved. The mechanism is fully supported by both the measured kinetic energy distributions and anisotropies of the angular distributions. Interestingly, the kinetic energy of the released Cl atom is sensitively modified by accounting for spin-orbit coupling. Given the atmospheric importance of CF3COCl, we discuss the consequences of our findings for atmospheric photochemistry.

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Characterizing the photochemical reactivity of transient volatile organic compounds (VOCs) in our atmosphere begins with a proper understanding of their abilities to absorb sunlight. Unfortunately, the photoabsorption cross-sections for a large number of transient VOCs remain unavailable experimentally due to their short lifetime or high reactivity. While structure-activity relationships (SARs) have been successfully employed to estimate the unknown photoabsorption cross-sections of VOCs, computational photochemistry offers another promising strategy to predict not only the vertical electronic transitions of a given molecule but also the width and shape of the bands forming its absorption spectrum. In this work, we focus on the use of the nuclear ensemble approach (NEA) to determine the photoabsorption cross-section of four exemplary VOCs, namely, acrolein, methylhydroperoxide, 2-hydroperoxy-propanal, and (microsolvated) pyruvic acid. More specifically, we analyze the influence that different strategies for sampling the ground-state nuclear density-Wigner sampling and ab initio molecular dynamics with a quantum thermostat-can have on the simulated absorption spectra. We highlight the potential shortcomings of using uncoupled harmonic modes within Wigner sampling of nuclear density to describe flexible or microsolvated VOCs and some limitations of SARs for multichromophoric VOCs. Our results suggest that the NEA could constitute a powerful tool for the atmospheric community to predict the photoabsorption cross-section for transient VOCs.

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