Combining SchNet and SHARC: The SchNarc Machine Learning Approach for Excited-State Dynamics

X2-GNN: A Physical Message Passing Neural Network with Natural Generalization Ability to Large and Complex Molecules

Neural network models excel in molecular property predictions but often struggle with generalizing from smaller to larger molecules due to increased structural diversity and complex interactions. To address this, we introduce an E(3) invariant (and equivariant capable) message passing graph neural network (GNN), namely, X2-GNN, that integrates physical insights via atomic orbital overlap integrals and core Hamiltonians. These features provide essential information about bond strength, electron delocalization, and many-body interactions, enhanced by an attention mechanism for improved learning efficiency. Benchmarked against mainstream GNNs on diverse data sets, X2-GNN trained solely on the QM9 data set (up to nine heavy atoms) effectively generalizes to larger molecules with tens of heavy atoms, achieving credible per-atom error rates. It also excels in potential energy surface modeling and accurately predicts the bond dissociation energy within subseconds. These results highlight X2-GNN's scalability and broad applicability, emphasizing the importance of integrating data-driven approaches with basic knowledge from electronic structure theory.

A simple approach to rotationally invariant machine learning of a vector quantity

Unlike with the energy, which is a scalar property, machine learning (ML) prediction of vector or tensor properties poses the additional challenge of achieving proper invariance (covariance) with respect to molecular rotation. For the energy gradients needed in molecular dynamics (MD), this symmetry is automatically fulfilled when taking analytic derivative of the energy, which is a scalar invariant (using properly invariant molecular descriptors). However, if the properties cannot be obtained by differentiation, other appropriate methods should be applied to retain the covariance. Several approaches have been suggested to properly treat this issue. For nonadiabatic couplings and polarizabilities, for example, it was possible to construct virtual quantities from which the above tensorial properties are obtained by differentiation and thus guarantee the covariance. Another possible solution is to build the rotational equivariance into the design of a neural network employed in the model. Here, we propose a simpler alternative technique, which does not require construction of auxiliary properties or application of special equivariant ML techniques. We suggest a three-step approach, using the molecular tensor of inertia. In the first step, the molecule is rotated using the eigenvectors of this tensor to its principal axes. In the second step, the ML procedure predicts the vector property relative to this orientation, based on a training set where all vector properties were in this same coordinate system. As the third step, it remains to transform the ML estimate of the vector property back to the original orientation. This rotate-predict-rotate (RPR) procedure should thus guarantee proper covariance of a vector property and is trivially extensible also to tensors such as polarizability. The RPR procedure has an advantage that the accurate models can be trained very fast for thousands of molecular configurations, which might be beneficial where many training sets are required (e.g., in active learning). We have implemented the RPR technique, using the MLatom and Newton-X programs for ML and MD, and performed its assessment on the dipole moment along MD trajectories of 1,2-dichloroethane.

Fast and accurate nonadiabatic molecular dynamics enabled through variational interpolation of correlated electron wavefunctions

We build on the concept of eigenvector continuation to develop an efficient multi-state method for the rigorous and smooth interpolation of a small training set of many-body wavefunctions through chemical space at mean-field cost. The inferred states are represented as variationally optimal linear combinations of the training states transferred between the many-body bases of different nuclear geometries. We show that analytic multi-state forces and nonadiabatic couplings from the model enable application to nonadiabatic molecular dynamics, developing an active learning scheme to ensure a compact and systematically improvable training set. This culminates in application to the nonadiabatic molecular dynamics of a photoexcited 28-atom hydrogen chain, with surprising complexity in the resulting nuclear motion. With just 22 DMRG calculations of training states from the low-energy correlated electronic structure at different geometries, we infer the multi-state energies, forces and nonadiabatic coupling vectors at 12 000 geometries with provable convergence to high accuracy along an ensemble of molecular trajectories, which would not be feasible with a brute force approach. This opens up a route to bridge the timescales between accurate single-point correlated electronic structure methods and timescales of relevance for photo-induced molecular dynamics.

Unsupervised Machine Learning in the Analysis of Nonadiabatic Molecular Dynamics Simulation

The all-atomic full-dimensional-level simulations of nonadiabatic molecular dynamics (NAMD) in large realistic systems has received high research interest in recent years. However, such NAMD simulations normally generate an enormous amount of time-dependent high-dimensional data, leading to a significant challenge in result analyses. Based on unsupervised machine learning (ML) methods, considerable efforts were devoted to developing novel and easy-to-use analysis tools for the identification of photoinduced reaction channels and the comprehensive understanding of complicated molecular motions in NAMD simulations. Here, we tried to survey recent advances in this field, particularly to focus on how to use unsupervised ML methods to analyze the trajectory-based NAMD simulation results. Our purpose is to offer a comprehensive discussion on several essential components of this analysis protocol, including the selection of ML methods, the construction of molecular descriptors, the establishment of analytical frameworks, their advantages and limitations, and persistent challenges.

SpaiNN: equivariant message passing for excited-state nonadiabatic molecular dynamics

Excited-state molecular dynamics simulations are crucial for understanding processes like photosynthesis, vision, and radiation damage. However, the computational complexity of quantum chemical calculations restricts their scope. Machine learning offers a solution by delivering high-accuracy properties at lower computational costs. We present SpaiNN, an open-source Python software for ML-driven surface hopping nonadiabatic molecular dynamics simulations. SpaiNN combines the invariant and equivariant neural network architectures of SchNetPack with SHARC for surface hopping dynamics. Its modular design allows users to implement and adapt modules easily. We compare rotationally-invariant and equivariant representations in fitting potential energy surfaces of multiple electronic states and properties arising from the interaction of two electronic states. Simulations of the methyleneimmonium cation and various alkenes demonstrate the superior performance of equivariant SpaiNN models, improving accuracy, generalization, and efficiency in both training and inference.

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.

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

MLatom Software Ecosystem for Surface Hopping Dynamics in Python with Quantum Mechanical and Machine Learning Methods

We present an open-source MLatom@XACS software ecosystem for on-the-fly surface hopping nonadiabatic dynamics based on the Landau-Zener-Belyaev-Lebedev algorithm. The dynamics can be performed via Python API with a wide range of quantum mechanical (QM) and machine learning (ML) methods, including ab initio QM (CASSCF and ADC(2)), semiempirical QM methods (e.g., AM1, PM3, OMx, and ODMx), and many types of ML potentials (e.g., KREG, ANI, and MACE). Combinations of QM and ML methods can also be used. While the user can build their own combinations, we provide AIQM1, which is based on Δ-learning and can be used out-of-the-box. We showcase how AIQM1 reproduces the isomerization quantum yield of trans-azobenzene at a low cost. We provide example scripts that, in dozens of lines, enable the user to obtain the final population plots by simply providing the initial geometry of a molecule. Thus, those scripts perform geometry optimization, normal mode calculations, initial condition sampling, parallel trajectories propagation, population analysis, and final result plotting. Given the capabilities of MLatom to be used for training different ML models, this ecosystem can be seamlessly integrated into the protocols building ML models for nonadiabatic dynamics. In the future, a deeper and more efficient integration of MLatom with Newton-X will enable a vast range of functionalities for surface hopping dynamics, such as fewest-switches surface hopping, to facilitate similar workflows via the Python API.

Machine Learning of Reactive Potentials

In the past two decades, machine learning potentials (MLPs) have driven significant developments in chemical, biological, and material sciences. The construction and training of MLPs enable fast and accurate simulations and analysis of thermodynamic and kinetic properties. This review focuses on the application of MLPs to reaction systems with consideration of bond breaking and formation. We review the development of MLP models, primarily with neural network and kernel-based algorithms, and recent applications of reactive MLPs (RMLPs) to systems at different scales. We show how RMLPs are constructed, how they speed up the calculation of reactive dynamics, and how they facilitate the study of reaction trajectories, reaction rates, free energy calculations, and many other calculations. Different data sampling strategies applied in building RMLPs are also discussed with a focus on how to collect structures for rare events and how to further improve their performance with active learning.

Explainable chemical artificial intelligence from accurate machine learning of real-space chemical descriptors

Machine-learned computational chemistry has led to a paradoxical situation in which molecular properties can be accurately predicted, but they are difficult to interpret. Explainable AI (XAI) tools can be used to analyze complex models, but they are highly dependent on the AI technique and the origin of the reference data. Alternatively, interpretable real-space tools can be employed directly, but they are often expensive to compute. To address this dilemma between explainability and accuracy, we developed SchNet4AIM, a SchNet-based architecture capable of dealing with local one-body (atomic) and two-body (interatomic) descriptors. The performance of SchNet4AIM is tested by predicting a wide collection of real-space quantities ranging from atomic charges and delocalization indices to pairwise interaction energies. The accuracy and speed of SchNet4AIM breaks the bottleneck that has prevented the use of real-space chemical descriptors in complex systems. We show that the group delocalization indices, arising from our physically rigorous atomistic predictions, provide reliable indicators of supramolecular binding events, thus contributing to the development of Explainable Chemical Artificial Intelligence (XCAI) models.

COSMIC: Molecular Conformation Space Modeling in Internal Coordinates with an Adversarial Framework

The fast and accurate conformation space modeling is an essential part of computational approaches for solving ligand and structure-based drug discovery problems. Recent state-of-the-art diffusion models for molecular conformation generation show promising distribution coverage and physical plausibility metrics but suffer from a slow sampling procedure. We propose a novel adversarial generative framework, COSMIC, that shows comparable generative performance but provides a time-efficient sampling and training procedure. Given a molecular graph and random noise, the generator produces a conformation in two stages. First, it constructs a conformation in a rotation and translation invariant representation─internal coordinates. In the second step, the model predicts the distances between neighboring atoms and performs a few fast optimization steps to refine the initial conformation. The proposed model considers conformation energy, achieving comparable space coverage, and diversity metrics results.

Machine-Learned Kohn-Sham Hamiltonian Mapping for Nonadiabatic Molecular Dynamics

In this work, we report a simple, efficient, and scalable machine-learning (ML) approach for mapping non-self-consistent Kohn-Sham Hamiltonians constructed with one kind of density functional to the nearly self-consistent Hamiltonians constructed with another kind of density functional. This approach is designed as a fast surrogate Hamiltonian calculator for use in long nonadiabatic dynamics simulations of large atomistic systems. In this approach, the input and output features are Hamiltonian matrices computed from different levels of theory. We demonstrate that the developed ML-based Hamiltonian mapping method (1) speeds up the calculations by several orders of magnitude, (2) is conceptually simpler than alternative ML approaches, (3) is applicable to different systems and sizes and can be used for mapping Hamiltonians constructed with arbitrary density functionals, (4) requires a modest training data, learns fast, and generates molecular orbitals and their energies with the accuracy nearly matching that of conventional calculations, and (5) when applied to nonadiabatic dynamics simulation of excitation energy relaxation in large systems yields the corresponding time scales within the margin of error of the conventional calculations. Using this approach, we explore the excitation energy relaxation in C60 fullerene and Si75H64 quantum dot structures and derive qualitative and quantitative insights into dynamics in these systems.

Theoretical trends in the dynamics simulations of molecular machines across multiple scales

Over the past few decades, molecular machines have been extensively studied, since they are composed of single molecules for functional materials capable of responding to external stimuli, enabling motion at scales ranging from the microscopic to the macroscopic level within molecular aggregates. This advancement holds the potential to efficiently transform external resources into mechanical movement, achieved through precise control of conformational changes in stimuli-responsive materials. However, the underlying mechanism that links microscopic and macroscopic motions remains unclear, demanding computational development associated with simulating the construction of molecular machines from single molecules. This bottleneck has impeded the design of more efficient functional materials. Advancements in theoretical simulations have successfully been developed in various computational models to unveil the operational mechanisms of stimulus-responsive molecular machines, which could help us reduce the costs in experimental trial-and-error procedures. It opens doors to the computer-aided design of innovative functional materials. In this perspective, we have reviewed theoretical approaches employed in simulating dynamic processes involving conformational changes in molecular machines, spanning different scales and environmental conditions. In addition, we have highlighted current challenges and anticipated future trends in the collective control of aggregates within molecular machines. Our goal is to provide a comprehensive overview of recent theoretical advancements in the field of molecular machines, offering valuable insights for the design of novel smart materials.

Fast and accurate excited states predictions: machine learning and diabatization

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.

Machine Learning Framework for Modeling Exciton Polaritons in Molecular Materials

A light-matter hybrid quasiparticle, called a polariton, is formed when molecules are strongly coupled to an optical cavity. Recent experiments have shown that polariton chemistry can manipulate chemical reactions. Polariton chemistry is a collective phenomenon, and its effects increase with the number of molecules in a cavity. However, simulating an ensemble of molecules in the excited state coupled to a cavity mode is theoretically and computationally challenging. Recent advances in machine learning (ML) techniques have shown promising capabilities in modeling ground-state chemical systems. This work presents a general protocol to predict excited-state properties, such as energies, transition dipoles, and nonadiabatic coupling vectors with the hierarchically interacting particle neural network. ML predictions are then applied to compute the potential energy surfaces and electronic spectra of a prototype azomethane molecule in the collective coupling scenario. These computational tools provide a much-needed framework to model and understand many molecules' emerging excited-state polariton chemistry.

Reinforcement Learning for Traversing Chemical Structure Space: Optimizing Transition States and Minimum Energy Paths of Molecules

In recent years, deep learning has made remarkable strides, surpassing human capabilities in tasks, such as strategy games, and it has found applications in complex domains, including protein folding. In the realm of quantum chemistry, machine learning methods have primarily served as predictive tools or design aids using generative models, while reinforcement learning remains in its early stages of exploration. This work introduces an actor-critic reinforcement learning framework suitable for diverse optimization tasks, such as searching for molecular structures with specific properties within conformational spaces. As an example, we show an implementation of this scheme for calculating minimum energy pathways of a Claisen rearrangement reaction and a number of SN2 reactions. The results show that the algorithm is able to accurately predict minimum energy pathways and, thus, transition states, providing the first steps in using actor-critic methods to study chemical reactions.

Encoding Hole-Particle Information in the Multi-Channel MolOrbImage for Machine-Learned Excited-State Energies of Large Photofunctional Materials

We present a novel class of one-electron multi-channel molecular orbital images (MolOrbImages) designed for the prediction of excited-state energetics in conjunction with the state-of-the-art VGG-type machine-learning architecture. By representing hole and particle states in the excitation process as channels of MolOrbImages, the revised VGG model achieves excellent prediction accuracy for both low-lying singlet and triplet states, with mean absolute errors (MAEs) of <0.08 and <0.1 eV for QM9 molecules and large photofunctional materials with up to 560 atoms, respectively. Remarkably, the model demonstrates exceptional performance (MAE < 1 kcal/mol) for the T1 state of QM9 molecules, making it a non-system-specific model that approaches chemical accuracy. The general rules attained, for instance, the improved performance with well-defined MO energies and the reduced overfitting concern via the inclusion of physically insightful hole-particle information, provide invaluable guidelines for the further design of orbital-based descriptors targeting molecular excited states.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Universal machine learning for the response of atomistic systems to external fields

Machine learned interatomic interaction potentials have enabled efficient and accurate molecular simulations of closed systems. However, external fields, which can greatly change the chemical structure and/or reactivity, have been seldom included in current machine learning models. This work proposes a universal field-induced recursively embedded atom neural network (FIREANN) model, which integrates a pseudo field vector-dependent feature into atomic descriptors to represent system-field interactions with rigorous rotational equivariance. This "all-in-one" approach correlates various response properties like dipole moment and polarizability with the field-dependent potential energy in a single model, very suitable for spectroscopic and dynamics simulations in molecular and periodic systems in the presence of electric fields. Especially for periodic systems, we find that FIREANN can overcome the intrinsic multiple-value issue of the polarization by training atomic forces only. These results validate the universality and capability of the FIREANN method for efficient first-principles modeling of complicated systems in strong external fields.

Ultrafast Photocontrolled Rotation in a Molecular Motor Investigated by Machine Learning-Based Nonadiabatic Dynamics Simulations

The thermal helix inversion (THI) of the overcrowded alkene-based molecular motors determines the speed of the unidirectional rotation due to the high reaction barrier in the ground state, in comparison with the ultrafast photoreaction process. Recently, a phosphine-based motor has achieved all-photochemical rotation experimentally, promising to be controlled without a thermal step. However, the mechanism of this photochemical reaction has not yet been fully revealed. The comprehensive computational studies on photoisomerization still resort to nonadiabatic molecular dynamics (NAMD) simulations based on electronic structure calculations, which remains a high computational cost for large systems such as molecular motors. Machine learning (ML) has become an accelerating tool in NAMD simulations recently, where excited-state potential energy surfaces (PESs) are constructed analytically with high accuracy, providing an efficient approach for simulations in photochemistry. Herein the reaction pathway is explored by a spin-flip time-dependent density functional theory (SF-TDDFT) approach in combination with ML-based NAMD simulations. According to our computational simulations, we notice that one of the key factors of fulfilling all-photochemical rotation in the phosphine-based motor is that the excitation energies of four isomers are similar. Additionally, a shortcut photoinduced transformation between unstable isomers replaces the THI step, which shares the conical intersection (CI) with photoisomerization. In this study, we provide a practical approach to speed up the NAMD simulations in photochemical reactions for a large system that could be extended to other complex systems.

Advances in the Application of Artificial Intelligence-Based Spectral Data Interpretation: A Perspective

The interpretation of spectral data, including mass, nuclear magnetic resonance, infrared, and ultraviolet-visible spectra, is critical for obtaining molecular structural information. The development of advanced sensing technology has multiplied the amount of available spectral data. Chemical experts must use basic principles corresponding to the spectral information generated by molecular fragments and functional groups. This is a time-consuming process that requires a solid professional knowledge base. In recent years, the rapid development of computer science and its applications in cheminformatics and the emergence of computer-aided expert systems have greatly reduced the difficulty in analyzing large quantities of data. For expert systems, however, the problem-solving strategy must be known in advance or extracted by human experts and translated into algorithms. Gratifyingly, the development of artificial intelligence (AI) methods has shown great promise for solving such problems. Traditional algorithms, including the latest neural network algorithms, have shown great potential for both extracting useful information and processing massive quantities of data. This Perspective highlights recent innovations covering all of the emerging AI-based spectral interpretation techniques. In addition, the main limitations and current obstacles are presented, and the corresponding directions for further research are proposed. Moreover, this Perspective gives the authors' personal outlook on the development and future applications of spectral interpretation.

Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach

The machine learning of potential energy surfaces (PESs) has undergone rapid progress in recent years. The vast majority of this work, however, has been focused on the learning of ground state PESs. To reliably extend machine learning protocols to excited state PESs, the occurrence of seams of conical intersections between adiabatic electronic states must be correctly accounted for. This introduces a serious problem, for at such points, the adiabatic potentials are not differentiable to any order, complicating the application of standard machine learning methods. We show that this issue may be overcome by instead learning the coordinate-dependent coefficients of the characteristic polynomial of a simple decomposition of the potential matrix. We demonstrate that, through this approach, quantitatively accurate machine learning models of seams of conical intersection may be constructed.

Nonadiabatic Derivative Couplings Calculated Using Information of Potential Energy Surfaces without Wavefunctions: Ab Initio and Machine Learning Implementations

In this work, we implemented an approximate algorithm for calculating nonadiabatic coupling matrix elements (NACMEs) of a polyatomic system with ab initio methods and machine learning (ML) models. Utilizing this algorithm, one can calculate NACMEs using only the information of potential energy surfaces (PESs), i.e., energies, and gradients as well as Hessian matrix elements. We used a realistic system, namely CH₂NH, to compare NACMEs calculated by this approximate PES-based algorithm and the accurate wavefunction-based algorithm. Our results show that this approximate PES-based algorithm can give very accurate results comparable to the wavefunction-based algorithm except at energetically degenerate points, i.e., conical intersections. We also tested a machine learning (ML)-trained model with this approximate PES-based algorithm, which also supplied similarly accurate NACMEs but more efficiently. The advantage of this PES-based algorithm is its significant potential to combine with electronic structure methods that do not implement wavefunction-based algorithms, low-scaling energy-based fragment methods, etc., and in particular efficient ML models, to compute NACMEs. The present work could encourage further research on nonadiabatic processes of large systems simulated by ab initio nonadiabatic dynamics simulation methods in which NACMEs are always required.

Nonadiabatic Forward Flux Sampling for Excited-State Rare Events

We present a rare event sampling scheme applicable to coupled electronic excited states. In particular, we extend the forward flux sampling (FFS) method for rare event sampling to a nonadiabatic version (NAFFS) that uses the trajectory surface hopping (TSH) method for nonadiabatic dynamics. NAFFS is applied to two dynamically relevant excited-state models that feature an avoided crossing and a conical intersection with tunable parameters. We investigate how nonadiabatic couplings, temperature, and reaction barriers affect transition rate constants in regimes that cannot be otherwise obtained with plain, traditional TSH. The comparison with reference brute-force TSH simulations for limiting cases of rareness shows that NAFFS can be several orders of magnitude cheaper than conventional TSH and thus represents a conceptually novel tool to extend excited-state dynamics to time scales that are able to capture rare nonadiabatic events.

Active sampling for neural network potentials: Accelerated simulations of shear-induced deformation in Cu-Ni multilayers

Neural network potentials (NNPs) can greatly accelerate atomistic simulations relative to ab initio methods, allowing one to sample a broader range of structural outcomes and transformation pathways. In this work, we demonstrate an active sampling algorithm that trains an NNP that is able to produce microstructural evolutions with accuracy comparable to those obtained by density functional theory, exemplified during structure optimizations for a model Cu-Ni multilayer system. We then use the NNP, in conjunction with a perturbation scheme, to stochastically sample structural and energetic changes caused by shear-induced deformation, demonstrating the range of possible intermixing and vacancy migration pathways that can be obtained as a result of the speedups provided by the NNP. The code to implement our active learning strategy and NNP-driven stochastic shear simulations is openly available at https://github.com/pnnl/Active-Sampling-for-Atomistic-Potentials.

Machine-Learned Electronically Excited States with the MolOrbImage Generated from the Molecular Ground State

We present a general machine learning framework for probing the electronic state properties using the novel quantum descriptor MolOrbImage. Each pixel of the MolOrbImage records the quantum information generated by the integration of the physical operator with a pair of bra and ket molecular orbital (MO) states. Inspired by the success of deep convolutional neural networks (NNs) in computer vision, we have implemented the convolutional-layer-dominated MO-NN model. Using the orbital energy and electron repulsion integral MolOrbImages, the MO-NN model achieves promising prediction accuracies against the ADC(2)/cc-pVTZ reference for transition energies to both low-lying singlet [mean absolute error (MAE) < 0.16 eV] and triplet (MAE < 0.14 eV) states. An apparent improvement in the prediction of oscillator strength, which has been shown to be challenging previously, has been demonstrated in this study. Moreover, the transferability test indicates the remarkable extrapolation capacity of the MO-NN model to describe the out of data set systems.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

High-throughput property-driven generative design of functional organic molecules

The design of molecules and materials with tailored properties is challenging, as candidate molecules must satisfy multiple competing requirements that are often difficult to measure or compute. While molecular structures produced through generative deep learning will satisfy these patterns, they often only possess specific target properties by chance and not by design, which makes molecular discovery via this route inefficient. In this work, we predict molecules with (Pareto-)optimal properties by combining a generative deep learning model that predicts three-dimensional conformations of molecules with a supervised deep learning model that takes these as inputs and predicts their electronic structure. Optimization of (multiple) molecular properties is achieved by screening newly generated molecules for desirable electronic properties and reusing hit molecules to retrain the generative model with a bias. The approach is demonstrated to find optimal molecules for organic electronics applications. Our method is generally applicable and eliminates the need for quantum chemical calculations during predictions, making it suitable for high-throughput screening in materials and catalyst design.

Machine learning of double-valued nonadiabatic coupling vectors around conical intersections

In recent years, machine learning has had an enormous success in fitting ab initio potential-energy surfaces to enable efficient simulations of molecules in their ground electronic state. In order to extend this approach to excited-state dynamics, one must not only learn the potentials but also nonadiabatic coupling vectors (NACs). There is a particular difficulty in learning NACs in systems that exhibit conical intersections, as due to the geometric-phase effect, the NACs may be double-valued and are, thus, not suitable as training data for standard machine-learning techniques. In this work, we introduce a set of auxiliary single-valued functions from which the NACs can be reconstructed, thus enabling a reliable machine-learning approach.

Graph neural networks for materials science and chemistry

Machine learning plays an increasingly important role in many areas of chemistry and materials science, being used to predict materials properties, accelerate simulations, design new structures, and predict synthesis routes of new materials. Graph neural networks (GNNs) are one of the fastest growing classes of machine learning models. They are of particular relevance for chemistry and materials science, as they directly work on a graph or structural representation of molecules and materials and therefore have full access to all relevant information required to characterize materials. In this Review, we provide an overview of the basic principles of GNNs, widely used datasets, and state-of-the-art architectures, followed by a discussion of a wide range of recent applications of GNNs in chemistry and materials science, and concluding with a road-map for the further development and application of GNNs.

Conical Intersection in Chemiluminescence of Cyclic Peroxides

Chemiluminescence (CL) utilizing chemiexcitation for energy transformation is one of the most highly sensitive and useful analytical techniques. The chemiexcitation is a chemical process of a ground-state reactant producing an excited-state product, in which a nonadiabatic event is facilitated by conical intersections (CIs), the specific molecular geometries where electronic states are degenerated. Cyclic peroxides, especially 1,2-dioxetane/dioxetanone derivatives, are the iconic chemiluminescent substances. In this Perspective, we concentrated on the CIs in the CL of cyclic peroxides. We first present a computational overview on the role of CIs between the ground (S₀) state and the lowest singlet excited (S₁) state in the thermolysis of cyclic peroxides. Subsequently, we discuss the role of the S₀/S₁ CI in the CL efficiency and point out misunderstandings in some theoretical studies on the singlet chemiexcitations of cyclic peroxides. Finally, we address the challenges and future prospects in theoretically calculating S₀/S₁ CIs and simulating the dynamics and chemiexcitation efficiency in the CL of cyclic peroxides.

Machine learning the Hohenberg-Kohn map for molecular excited states

The Hohenberg-Kohn theorem of density-functional theory establishes the existence of a bijection between the ground-state electron density and the external potential of a many-body system. This guarantees a one-to-one map from the electron density to all observables of interest including electronic excited-state energies. Time-Dependent Density-Functional Theory (TDDFT) provides one framework to resolve this map; however, the approximations inherent in practical TDDFT calculations, together with their computational expense, motivate finding a cheaper, more direct map for electronic excitations. Here, we show that determining density and energy functionals via machine learning allows the equations of TDDFT to be bypassed. The framework we introduce is used to perform the first excited-state molecular dynamics simulations with a machine-learned functional on malonaldehyde and correctly capture the kinetics of its excited-state intramolecular proton transfer, allowing insight into how mechanical constraints can be used to control the proton transfer reaction in this molecule. This development opens the door to using machine-learned functionals for highly efficient excited-state dynamics simulations.

Selected machine learning of HOMO-LUMO gaps with improved data-efficiency

Despite their relevance for organic electronics, quantum machine learning (QML) models of molecular electronic properties, such as HOMO-LUMO-gaps, often struggle to achieve satisfying data-efficiency as measured by decreasing prediction errors for increasing training set sizes. We demonstrate that partitioning training sets into different chemical classes prior to training results in independently trained QML models with overall reduced training data needs. For organic molecules drawn from previously published QM7 and QM9-data-sets we have identified and exploited three relevant classes corresponding to compounds containing either aromatic rings and carbonyl groups, or single unsaturated bonds, or saturated bonds The selected QML models of band-gaps (considered at GW and hybrid DFT levels of theory) reach mean absolute prediction errors of ∼0.1 eV for up to an order of magnitude fewer training molecules than for QML models trained on randomly selected molecules. Comparison to Δ-QML models of band-gaps indicates that selected QML exhibit superior data-efficiency. Our findings suggest that selected QML, e.g. based on simple classifications prior to training, could help to successfully tackle challenging quantum property screening tasks of large libraries with high fidelity and low computational burden.

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.

How Good Is the Vibronic Hamiltonian Repetition Approach for Long-Time Nonadiabatic Molecular Dynamics?

Multiple applied studies of slow nonadiabatic processes in nanoscale and condensed matter systems have adopted the "repetition" approximation in which long trajectories for such simulations are obtained by concatenating shorter trajectories, directly available from ab initio calculations, many times. Here, we comprehensively assess this approximation using model Hamiltonians with parameters covering a wide range of regimes. We find that state transition time scales may strongly depend on the length of the repeated data, although the convergence is not monotonic and may be slow. The repetition approach may under- or overestimate the time scales by a factor of ≤7-8, does not directly depend on the dispersion of energy gap and nonadiabatic coupling (NAC) frequencies, but may depend on the magnitude of the NACs. We suggest that the repetition-based nonadiabatic dynamics may be inaccurate in simulations with very small NACs, where intrinsic transition times are on the order of ≥100 ps.

Machine learning, artificial intelligence, and chemistry: how smart algorithms are reshaping simulation and the laboratory

Machine learning and artificial intelligence are increasingly gaining in prominence through image analysis, language processing, and automation, to name a few applications. Machine learning is also making profound changes in chemistry. From revisiting decades-old analytical techniques for the purpose of creating better calibration curves, to assisting and accelerating traditional in silico simulations, to automating entire scientific workflows, to being used as an approach to deduce underlying physics of unexplained chemical phenomena, machine learning and artificial intelligence are reshaping chemistry, accelerating scientific discovery, and yielding new insights. This review provides an overview of machine learning and artificial intelligence from a chemist’s perspective and focuses on a number of examples of the use of these approaches in computational chemistry and in the laboratory.

Orbital Mixer: Using Atomic Orbital Features for Basis-Dependent Prediction of Molecular Wavefunctions

Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous studies focuses on generating predictions for only a fixed set of properties. Recent lines of research instead aim to explicitly learn the electronic structure via molecular wavefunctions, from which other quantum chemical properties can be directly derived. While previous methods generate predictions as a function of only the atomic configuration, in this work we present an alternate approach that directly purposes basis-dependent information to predict molecular electronic structure. Our model, Orbital Mixer, is composed entirely of multi-layer perceptrons (MLPs) using MLP-Mixer layers within a simple, intuitive, and scalable architecture that achieves competitive Hamiltonian and molecular orbital energy and coefficient prediction accuracies compared to the state-of-the-art.

Combined fragment-based machine learning force field with classical force field and its application in the NMR calculations of macromolecules in solutions

We have developed a combined fragment-based machine learning (ML) force field and molecular mechanics (MM) force field for simulating the structures of macromolecules in solutions, and then compute its NMR chemical shifts with the generalized energy-based fragmentation (GEBF) approach at the level of density functional theory (DFT). In this work, we first construct Gaussian approximation potential based on GEBF subsystems of macromolecules for MD simulations and then a GEBF-based neural network (GEBF-NN) with deep potential model for the studied macromolecule. Then, we develop a GEBF-NN/MM force field for macromolecules in solutions by combining the GEBF-NN force field for the solute molecule and ff14SB force field for solvent molecules. Using the GEBF-NN/MM MD simulation to generate snapshot structures of solute/solvent clusters, we then perform the NMR calculations with the GEBF approach at the DFT level to calculate NMR chemical shifts of the solute molecule. Taking a heptamer of oligopyridine-dicarboxamides in chloroform solution as an example, our results show that the GEBF-NN force field is quite accurate for this heptamer by comparing with the reference DFT results. For this heptamer in chloroform solution, both the GEBF-NN/MM and classical MD simulations could lead to helical structures from the same initial extended structure. The GEBF-DFT NMR results indicate that the GEBF-NN/MM force field could lead to more accurate NMR chemical shifts on hydrogen atoms by comparing with the experimental NMR results. Therefore, the GEBF-NN/MM force field could be employed for predicting more accurate dynamical behaviors than the classical force field for complex systems in solutions.

Quantum machine learning for chemistry and physics

Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.

Deep learning study of tyrosine reveals that roaming can lead to photodamage

Amino acids are among the building blocks of life, forming peptides and proteins, and have been carefully 'selected' to prevent harmful reactions caused by light. To prevent photodamage, molecules relax from electronic excited states to the ground state faster than the harmful reactions can occur; however, such photochemistry is not fully understood, in part because theoretical simulations of such systems are extremely expensive-with only smaller chromophores accessible. Here, we study the excited-state dynamics of tyrosine using a method based on deep neural networks that leverages the physics underlying quantum chemical data and combines different levels of theory. We reveal unconventional and dynamically controlled 'roaming' dynamics in excited tyrosine that are beyond chemical intuition and compete with other ultrafast deactivation mechanisms. Our findings suggest that the roaming atoms are radicals that can lead to photodamage, offering a new perspective on the photostability and photodamage of biological systems.

UV-Visible Absorption Spectra of Solvated Molecules by Quantum Chemical Machine Learning

Predicting UV-visible absorption spectra is essential to understand photochemical processes and design energy materials. Quantum chemical methods can deliver accurate calculations of UV-visible absorption spectra, but they are computationally expensive, especially for large systems or when one computes line shapes from thermal averages. Here, we present an approach to predict UV-visible absorption spectra of solvated aromatic molecules by quantum chemistry (QC) and machine learning (ML). We show that a ML model, trained on the high-level QC calculation of the excitation energy of a set of aromatic molecules, can accurately predict the line shape of the lowest-energy UV-visible absorption band of several related molecules with less than 0.1 eV deviation with respect to reference experimental spectra. Applying linear decomposition analysis on the excitation energies, we unveil that our ML models probe vertical excitations of these aromatic molecules primarily by learning the atomic environment of their phenyl rings, which align with the physical origin of the π →π* electronic transition. Our study provides an effective workflow that combines ML with quantum chemical methods to accelerate the calculations of UV-visible absorption spectra for various molecular systems.

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.

Excited-State Distortions Promote the Photochemical 4π-Electrocyclizations of Fluorobenzenes via Machine Learning Accelerated Photodynamics Simulations

Benzene fluorination increases chemoselectivities for Dewar-benzenes via 4π-disrotatory electrocyclization. However, the origin of the chemo- and regioselectivities of fluorobenzenes remains unexplained because of the experimental limitations in resolving the excited-state structures on ultrafast timescales. The computational cost of multiconfigurational nonadiabatic molecular dynamics simulations is also currently cost-prohibitive. We now provide high-fidelity structural information and reaction outcome predictions with machine-learning-accelerated photodynamics simulations of a series of fluorobenzenes, C₆ F_6-n H_n , n=0-3, to study their S₁ →S₀ decay in 4 ns. We trained neural networks with XMS-CASPT2(6,7)/aug-cc-pVDZ calculations, which reproduced the S₁ absorption features with mean absolute errors of 0.04 eV (<2 nm). The predicted nonradiative decay constants for C₆ F₄ H₂ , C₆ F₆ , C₆ F₃ H₃ , and C₆ F₅ H are 116, 60, 28, and 12 ps, respectively, in broad qualitative agreement with the experiments. Our calculations show that a pseudo Jahn-Teller distortion of fluorinated benzenes leads to an S₁ local-minimum region that extends the excited-state lifetimes of fluorobenzenes. The pseudo Jahn-Teller distortions reduce when fluorination decreases. Our analysis of the S₁ dynamics shows that the pseudo-Jahn-Teller distortions promote an excited-state cis-trans isomerization of a π_C-C bond. We characterized the surface hopping points from our NAMD simulations and identified instantaneous nuclear momentum as a factor that promotes the electrocyclizations.

Fast Predictions of Reaction Barrier Heights: Toward Coupled-Cluster Accuracy

Quantitative estimates of reaction barriers are essential for developing kinetic mechanisms and predicting reaction outcomes. However, the lack of experimental data and the steep scaling of accurate quantum calculations often hinder the ability to obtain reliable kinetic values. Here, we train a directed message passing neural network on nearly 24,000 diverse gas-phase reactions calculated at CCSD(T)-F12a/cc-pVDZ-F12//ωB97X-D3/def2-TZVP. Our model uses 75% fewer parameters than previous studies, an improved reaction representation, and proper data splits to accurately estimate performance on unseen reactions. Using information from only the reactant and product, our model quickly predicts barrier heights with a testing MAE of 2.6 kcal mol^-1 relative to the coupled-cluster data, making it more accurate than a good density functional theory calculation. Furthermore, our results show that future modeling efforts to estimate reaction properties would significantly benefit from fine-tuning calibration using a transfer learning technique. We anticipate this model will accelerate and improve kinetic predictions for small molecule chemistry.

Internal conversion and intersystem crossing dynamics based on coupled potential energy surfaces with full geometry-dependent spin-orbit and derivative couplings. Nonadiabatic photodissociation dynamics of NH3(A) leading to the NH(X3Σ-, a1Δ) + H2 channel

We simulate the photodissociation of NH₃ originating from its first excited singlet state S₁ into the NH₂ + H (radical) and NH + H₂ (molecular) channels. The states considered are the ground singlet state S₀, the first excited singlet state S₁ and the lowest-lying triplet state T₁, which permit for the first time a uniform treatment of the internal conversion and intersystem crossing. The simulations are based on a diabatic potential energy matrix (DPEM) of S₀, S₁ coupled by a conical intersection seam, as well as a potential energy surface (PES) for T₁ coupled by spin-orbit coupling (SOC) to the two singlet states. The DPEM and PES are fitted to ab initio electronic structure data (ESD) including energies, energy gradients, and derivative couplings. The DPEM also defines an adiabatic to diabatic state (AtD) transformation, which is used to transform the singular adiabatic SOC into a smooth function of the nuclear coordinates in the diabatic representation, allowing the diabatic SOC to be fit to an analytical functional form. ESD and SOC data obtained from these surfaces can serve as input for either quantum or semi-classical characterization of the nonadiabatic dynamics. Using the SHARC suite of programs, nonadiabatic simulations based on over 40 000 semi-classical trajectories assess the convergence of our results. The production of NH + H₂ is not direct, but is only achieved through a quasi-statistical dissociation mechanism after internal conversion to the ground electronic state. This leads to a much lower yield comparing with the main NH₂ + H channel. The NH(X³Σ^_) radical produced through the intersystem crossing from S₀ to T₁ is rare (∼0.2%) compared to NH(a¹Δ) due to the process being spin forbidden.

Excited state non-adiabatic dynamics of large photoswitchable molecules using a chemically transferable machine learning potential

Light-induced chemical processes are ubiquitous in nature and have widespread technological applications. For example, photoisomerization can allow a drug with a photo-switchable scaffold such as azobenzene to be activated with light. In principle, photoswitches with desired photophysical properties like high isomerization quantum yields can be identified through virtual screening with reactive simulations. In practice, these simulations are rarely used for screening, since they require hundreds of trajectories and expensive quantum chemical methods to account for non-adiabatic excited state effects. Here we introduce a diabatic artificial neural network (DANN), based on diabatic states, to accelerate such simulations for azobenzene derivatives. The network is six orders of magnitude faster than the quantum chemistry method used for training. DANN is transferable to azobenzene molecules outside the training set, predicting quantum yields for unseen species that are correlated with experiment. We use the model to virtually screen 3100 hypothetical molecules, and identify novel species with high predicted quantum yields. The model predictions are confirmed using high-accuracy non-adiabatic dynamics. Our results pave the way for fast and accurate virtual screening of photoactive compounds.

Reconstruction of Nuclear Ensemble Approach Electronic Spectra Using Probabilistic Machine Learning

The theoretical prediction of molecular electronic spectra by means of quantum mechanical (QM) computations is fundamental to gain a deep insight into many photophysical and photochemical processes. A computational strategy that is attracting significant attention is the so-called Nuclear Ensemble Approach (NEA), that relies on generating a representative ensemble of nuclear geometries around the equilibrium structure and computing the vertical excitation energies (ΔE) and oscillator strengths (f) and phenomenologically broadening each transition with a line-shaped function with empirical full-width δ. Frequently, the choice of δ is carried out by visually finding the trade-off between artificial vibronic features (small δ) and over-smoothing of electronic signatures (large δ). Nevertheless, this approach is not satisfactory, as it relies on a subjective perception and may lead to spectral inaccuracies overall when the number of sampled configurations is limited due to an excessive computational burden (high-level QM methods, complex systems, solvent effects, etc.). In this work, we have developed and tested a new approach to reconstruct NEA spectra, dubbed GMM-NEA, based on the use of Gaussian Mixture Models (GMMs), a probabilistic machine learning algorithm, that circumvents the phenomenological broadening assumption and, in turn, the use of δ altogether. We show that GMM-NEA systematically outperforms other data-driven models to automatically select δ overall for small datasets. In addition, we report the use of an algorithm to detect anomalous QM computations (outliers) that can affect the overall shape and uncertainty of the NEA spectra. Finally, we apply GMM-NEA to predict the photolysis rate for HgBrOOH, a compound involved in Earth's atmospheric chemistry.