Deep Learning for Nonadiabatic Excited-State Dynamics

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.

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-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.

Training machine learning potentials for reactive systems: A Colab tutorial on basic models

In the last several years, there has been a surge in the development of machine learning potential (MLP) models for describing molecular systems. We are interested in a particular area of this field - the training of system-specific MLPs for reactive systems - with the goal of using these MLPs to accelerate free energy simulations of chemical and enzyme reactions. To help new members in our labs become familiar with the basic techniques, we have put together a self-guided Colab tutorial (https://cc-ats.github.io/mlp_tutorial/), which we expect to be also useful to other young researchers in the community. Our tutorial begins with the introduction of simple feedforward neural network (FNN) and kernel-based (using Gaussian process regression, GPR) models by fitting the two-dimensional Müller-Brown potential. Subsequently, two simple descriptors are presented for extracting features of molecular systems: symmetry functions (including the ANI variant) and embedding neural networks (such as DeepPot-SE). Lastly, these features will be fed into FNN and GPR models to reproduce the energies and forces for the molecular configurations in a Claisen rearrangement reaction.

AI in computational chemistry through the lens of a decade-long journey

This article gives a perspective on the progress of AI tools in computational chemistry through the lens of the author's decade-long contributions put in the wider context of the trends in this rapidly expanding field. This progress over the last decade is tremendous: while a decade ago we had a glimpse of what was to come through many proof-of-concept studies, now we witness the emergence of many AI-based computational chemistry tools that are mature enough to make faster and more accurate simulations increasingly routine. Such simulations in turn allow us to validate and even revise experimental results, deepen our understanding of the physicochemical processes in nature, and design better materials, devices, and drugs. The rapid introduction of powerful AI tools gives rise to unique challenges and opportunities that are discussed in this article too.

Artificial-Intelligence-Enhanced On-the-Fly Simulation of Nonlinear Time-Resolved Spectra

Time-resolved spectroscopy is an important tool for unraveling the minute details of structural changes in molecules of biological and technological significance. The nonlinear femtosecond signals detected for such systems must be interpreted, but it is a challenging task for which theoretical simulations are often indispensable. Accurate simulations of transient absorption or two-dimensional electronic spectra are, however, computationally very expensive, prohibiting the wider adoption of existing first-principles methods. Here, we report an artificial-intelligence-enhanced protocol to drastically reduce the computational cost of simulating nonlinear time-resolved electronic spectra, which makes such simulations affordable for polyatomic molecules of increasing size. The protocol is based on the doorway-window approach for the on-the-fly surface-hopping simulations. We show its applicability for the prototypical molecule of pyrazine for which it produces spectra with high precision with respect to ab initio reference while cutting the computational cost by at least 95% compared to pure first-principles simulations.

Estimating Nonradiative Excited-State Lifetimes in Photoactive Semiconducting Nanostructures

The time evolution of the exciton generated by light adsorption in a photocatalyst is an important feature that can be approached from full nonadiabatic molecular dynamics simulations. Here, a crucial parameter is the nonradiative recombination rate between the hole and the electron that form the exciton. In the present work, we explore the performance of a Fermi's golden rule-based approach on predicting the recombination rate in a set of photoactive titania nanostructures, relying solely on the coupling of the ground and first excited state. In this scheme the analysis of the first excited state is carried out by invoking Kasha's rule thus avoiding computationally expensive nonadiabatic molecular dynamics simulations and resulting in an affordable estimate of the recombination rate. Our results show that, compared to previous ones from nonadiabatic molecular dynamics simulations, semiquantitative recombination rates can be predicted for the smaller titania nanostructures, and qualitative values are obtained from the larger ones. The present scheme is expected to be useful in the field of computational heterogeneous photocatalysis whenever a complex and computationally expensive full nonadiabatic molecular dynamics cannot be carried out.

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.

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.

High-throughput virtual screening of organic second-order nonlinear optical chromophores within the donor-π-bridge-acceptor framework

In view of the theoretical importance and huge application potential of second-order nonlinear optical (NLO) materials, it is of great significance to conduct high-throughput virtual screening (HTVS) on a compound library to find candidate NLO chromophores. Under the donor-π-bridge-acceptor structural framework, a virtual compound library (size = 27 090) was constructed by enumeration of structural fragments. The kernel property adopted for optimization is the static first hyperpolarizability (β0). By combining machine learning and quantum chemical calculations, we have performed an HTVS procedure to sieve NLO chromophores out, and the response mechanism of the selected optimal NLO chromophores was examined. We have found: (a) The multi-layer perceptron/extended connectivity fingerprint combination with 20% selection ratio gives the highest prediction accuracy for the studied systems. (b) The two optimal donors are bis(4-diphenylaminophenyl)aminyl and bis(4-tert-butylphenyl)aminyl; the optimal π-bridges are composed of two thiophenyl, selenophenyl or furanyl units; and the two optimal acceptors are tri-s-triazinyl and 2,3-dicyanopyrazinyl. (c) The no. 1 candidate molecule can exhibit a calculated β0 equal to 8.55 × 104 a.u. (d) The difference in NLO responses of the optimal 16 molecules comes from the synergistic interaction of ES1, Δμ and f, by employing the two-level model. In addition, the sizable Δμ and f allow the studied optimal molecules to obtain a large NLO response in the meantime keeping a not-too-low excitation energy (retaining good optical transparency in the restricted range of the visible spectrum region). (e) With further modification on the acceptor, the designed DPA-π-TRZ-A' (A' = CN or NO2, π = oligo-thiophenyl or selenophenyl) systems can exhibit a rather large NLO response (maximum β0 = 3.17 × 105 a.u.), hence should have considerable potential as second-order NLO chromophores. With the above observations, we expect to provide some insight for the research community into the HTVS of organic second-order NLO chromophores.

Accurate fundamental invariant-neural network representation of ab initio potential energy surfaces

Highly accurate potential energy surfaces are critically important for chemical reaction dynamics. The large number of degrees of freedom and the intricate symmetry adaption pose a big challenge to accurately representing potential energy surfaces (PESs) for polyatomic reactions. Recently, our group has made substantial progress in this direction by developing the fundamental invariant-neural network (FI-NN) approach. Here, we review these advances, demonstrating that the FI-NN approach can represent highly accurate, global, full-dimensional PESs for reactive systems with even more than 10 atoms. These multi-channel reactions typically involve many intermediates, transition states, and products. The complexity and ruggedness of this potential energy landscape present even greater challenges for full-dimensional PES representation. These PESs exhibit a high level of complexity, molecular size, and accuracy of fit. Dynamics simulations based on these PESs have unveiled intriguing and novel reaction mechanisms, providing deep insights into the intricate dynamics involved in combustion, atmospheric, and organic chemistry.

Nonadiabatic Dynamics Simulations for Photoinduced Processes in Molecules and Semiconductors: Methodologies and Applications

Nonadiabatic dynamics (NAMD) simulations have become powerful tools for elucidating complicated photoinduced processes in various systems from molecules to semiconductor materials. In this review, we present an overview of our recent research on photophysics of molecular systems and periodic semiconductor materials with the aid of ab initio NAMD simulation methods implemented in the generalized trajectory surface-hopping (GTSH) package. Both theoretical backgrounds and applications of the developed NAMD methods are presented in detail. For molecular systems, the linear-response time-dependent density functional theory (LR-TDDFT) method is primarily used to model electronic structures in NAMD simulations owing to its balanced efficiency and accuracy. Moreover, the efficient algorithms for calculating nonadiabatic coupling terms (NACTs) and spin-orbit couplings (SOCs) have been coded into the package to increase the simulation efficiency. In combination with various analysis techniques, we can explore the mechanistic details of the photoinduced dynamics of a range of molecular systems, including charge separation and energy transfer processes in organic donor-acceptor structures, ultrafast intersystem crossing (ISC) processes in transition metal complexes (TMCs), and exciton dynamics in molecular aggregates. For semiconductor materials, we developed the NAMD methods for simulating the photoinduced carrier dynamics within the framework of the Kohn-Sham density functional theory (KS-DFT), in which SOC effects are explicitly accounted for using the two-component, noncollinear DFT method. Using this method, we have investigated the photoinduced carrier dynamics at the interface of a variety of van der Waals (vdW) heterojunctions, such as two-dimensional transition metal dichalcogenides (TMDs), carbon nanotubes (CNTs), and perovskites-related systems. Recently, we extended the LR-TDDFT-based NAMD method for semiconductor materials, allowing us to study the excitonic effects in the photoinduced energy transfer process. These results demonstrate that the NAMD simulations are powerful tools for exploring the photodynamics of molecular systems and semiconductor materials. In future studies, the NAMD simulation methods can be employed to elucidate experimental phenomena and reveal microscopic details as well as rationally design novel photofunctional materials with desired properties.

Cost-Efficient High-Resolution Linear Absorption Spectra through Extrapolating the Dipole Moment from Real-Time Time-Dependent Electronic-Structure Theory

We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require discrete Fourier transforms of the electric dipole moment. The spectral resolution is determined by the total propagation time, i.e., the trajectory length of the dipole moment, causing a high computational cost. Our developed method uses function fitting on shorter trajectories of the dipole moment, achieving arbitrary spectral resolution through extrapolation. Numerical testing shows that the fitting method can reproduce high-resolution spectra by using short dipole trajectories. The method converges with as little as 100 a.u. dipole trajectories for some systems, though the difficulty converging increases with the spectral density. We also introduce an error estimate of the fit, reliably assessing its convergence and hence the quality of the approximated spectrum.

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.

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.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Bidirectional Long Short-Term Memory Networks

Essential for understanding far-from-equilibrium processes, nonadiabatic (NA) molecular dynamics (MD) requires expensive calculations of the excitation energies and NA couplings. Machine learning (ML) can simplify computation; however, the NA Hamiltonian requires complex ML models due to its intricate relationship to atomic geometry. Working directly in the time domain, we employ bidirectional long short-term memory networks (Bi-LSTM) to interpolate the Hamiltonian. Applying this multiscale approach to three metal-halide perovskite systems, we achieve two orders of magnitude computational savings compared to direct ab initio calculation. Reasonable charge trapping and recombination times are obtained with NA Hamiltonian sampling every half a picosecond. The Bi-LSTM-NAMD method outperforms earlier models and captures both slow and fast time scales. In combination with ML force fields, the methodology extends NAMD simulation times from picoseconds to nanoseconds, comparable to charge carrier lifetimes in many materials. Nanosecond sampling is particularly important in systems containing defects, boundaries, interfaces, etc. that can undergo slow rearrangements.

DeePMD-kit v2: A software package for deep potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

Elucidating the Role of Hydrogen Bonding in the Optical Spectroscopy of the Solvated Green Fluorescent Protein Chromophore: Using Machine Learning to Establish the Importance of High-Level Electronic Structure

Hydrogen bonding interactions with chromophores in chemical and biological environments play a key role in determining their electronic absorption and relaxation processes, which are manifested in their linear and multidimensional optical spectra. For chromophores in the condensed phase, the large number of atoms needed to simulate the environment has traditionally prohibited the use of high-level excited-state electronic structure methods. By leveraging transfer learning, we show how to construct machine-learned models to accurately predict the high-level excitation energies of a chromophore in solution from only 400 high-level calculations. We show that when the electronic excitations of the green fluorescent protein chromophore in water are treated using EOM-CCSD embedded in a DFT description of the solvent the optical spectrum is correctly captured and that this improvement arises from correctly treating the coupling of the electronic transition to electric fields, which leads to a larger response upon hydrogen bonding between the chromophore and water.

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.

Adaptive regularized Gaussian process regression for application in the context of hydrogen adsorption on graphene sheets

We present a Gaussian process regression (GPR) scheme with an adaptive regularization scheme applied to the QM7 and QM9 test set, several protonated water clusters and specifically to the problem of atomic hydrogen adsorption on graphene sheets. For the last system our goal is to achieve good predictive accuracy with only a few training points. Therefore, we assess for these systems a self-correcting multilayer GPR model, in which the prediction is corrected by a chain of additional GPR models. In our adaptive regularization scheme, we impose no noise on the training data, but use an approach based on the data itself to account for its impurity. The strength of this strategy is that the data points are treated differently based on their importance and that the regularization can still be controlled by a single parameter. We assess how the accuracy of the prediction depends on this parameter. We can show that the new regularization scheme as well as the multilayer approach results in more robust predictors. Furthermore, we demonstrate that the predictor can be in good agreement with the density-functional theory results.

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.

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.

Combining machine learning and quantum chemical calculations for high-throughput virtual screening of thermally activated delayed fluorescence molecular materials: the impact of selection strategy and structural mutations

In view of the theoretical importance and huge application potential of Thermally Activated Delayed Fluorescence (TADF) materials, it is of great significance to conduct High-Throughput Virtual Screening (HTVS) on compound libraries to find TADF candidate molecules. This research focuses on the computational design of pure organic TADF molecules. By combining machine learning and quantum chemical calculations, using cheminformatics tools, and introducing the concept of selection and mutation from evolutionary theory, we have designed a computational program for HTVS of TADF molecular materials, especially the impact of selection strategy and structural mutations on the results of HTVS was explored. An initial compound library (size = 10³) constructed by enumeration of typical donors and acceptors was used to evolve by successively applying selection and 10 different structural mutations. And a group fingerprint similarity (Δ_MSPR) index was proposed to account for the similarity between two compound libraries with comparable sizes. Based on the computed data, we have found that the mix of selection and mutations into the evolution map does have great impact on the HTVS results: (a) except the fast mutation Sub2, all the rest of the mutations can effectively concentrate 'good' molecules in a compound library, and hence give large material abundance (typically >0.8) for high mutation generations (n _g ≥ 6). (b) The mean energy gap can exhibit a fast convergent trend toward very low values, hence the studied mutations (except Sub2) can cooperate very well with the studied DA substrates to generate optimal molecules, and the group fingerprint similarity can retain high enough values for large n _g, which can be associated with the apparent convergence in molecular skeletons as n _g increases. (c) The distribution of skeleton frequencies for a specific mutation is generally uneven with one dominant skeleton. The overall numbers of common and generic cores for all mutations are 11 and 7 as n _g = 9. Hence, in a sense, the 'optimal' skeletons seem unique and useful in realizing low energy gaps. With these observations and the development of related HTVS software, we expect to provide insight and tools to the research community of HTVS of molecular (TADF) materials.

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.

All-Atom Nonadiabatic Semiclassical Mapping Dynamics for Photoinduced Charge Transfer of Organic Photovoltaic Molecules in Explicit Solvents

Direct all-atom simulation of nonadiabatic dynamics in disordered condensed phases like liquid solutions and amorphous solids has been challenging. The first all-atom simulation of the photoinduced charge-transfer dynamics of a prototypical organic photovoltaic carotenoid-porphyrin-C₆₀ molecular triad in explicit tetrahydrofuran is presented. Based on the Meyer-Miller mapping Hamiltonian, various semiclassical and mixed quantum-classical dynamics are employed, including the linearized semiclassical, symmetrical quasiclassical, mean-field Ehrenfest, classical mapping model, and spin-mapping model approaches. The all-atom nonadiabatic dynamics were compared to multi-state harmonic models with a globally shared bath, and the models built using the ensemble averages on the initial electronic state could reproduce the all-atom results. The solvent effect was found to be critical for the photoinduced charge transfer, and the time-dependent solute-solvent radial distribution functions revealed that only the nonadiabatic dynamics started with the effective forces on the initial electronic state could capture the correct nuclear dynamics. The proposed strategy for modeling condensed-phase nonadiabatic dynamics with atomistic details is readily applied to complex condensed-phase systems.

Exploring Accurate Potential Energy Surfaces via Integrating Variational Quantum Eigensolver with Machine Learning

The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational cost. As an appealing application of quantum computing, we show in this work that variational quantum algorithms can be integrated with machine learning (ML) techniques as a promising scheme for exploring accurate PESs. Different from using a ML model to represent the potential energy, we encode the molecular geometry information into a deep neural network (DNN) to represent parameters of the variational quantum eigensolver (VQE), leaving the PES to the wave function ansatz. Once the DNN model is trained, the variational optimization procedure that hinders the application of the VQE to complex systems is avoided, and thus the evaluation of PESs is significantly accelerated. Numerical results demonstrate that a simple DNN model is able to reproduce accurate PESs for small molecules.

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.

Simulations of molecular photodynamics in long timescales

Nonadiabatic dynamics simulations in the long timescale (much longer than 10 ps) are the next challenge in computational photochemistry. This paper delimits the scope of what we expect from methods to run such simulations: they should work in full nuclear dimensionality, be general enough to tackle any type of molecule and not require unrealistic computational resources. We examine the main methodological challenges we should venture to advance the field, including the computational costs of the electronic structure calculations, stability of the integration methods, accuracy of the nonadiabatic dynamics algorithms and software optimization. Based on simulations designed to shed light on each of these issues, we show how machine learning may be a crucial element for long time-scale dynamics, either as a surrogate for electronic structure calculations or aiding the parameterization of model Hamiltonians. We show that conventional methods for integrating classical equations should be adequate to extended simulations up to 1 ns and that surface hopping agrees semiquantitatively with wave packet propagation in the weak-coupling regime. We also describe our optimization of the Newton-X program to reduce computational overheads in data processing and storage. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Accurate, affordable, and generalizable machine learning simulations of transition metal x-ray absorption spectra using the XANESNET deep neural network

The affordable, accurate, and generalizable prediction of spectroscopic observables plays a key role in the analysis of increasingly complex experiments. In this article, we develop and deploy a deep neural network-XANESNET-for predicting the lineshape of first-row transition metal K-edge x-ray absorption near-edge structure (XANES) spectra. XANESNET predicts the spectral intensities using only information about the local coordination geometry of the transition metal complexes encoded in a feature vector of weighted atom-centered symmetry functions. We address in detail the calibration of the feature vector for the particularities of the problem at hand, and we explore the individual feature importance to reveal the physical insight that XANESNET obtains at the Fe K-edge. XANESNET relies on only a few judiciously selected features-radial information on the first and second coordination shells suffices along with angular information sufficient to separate satisfactorily key coordination geometries. The feature importance is found to reflect the XANES spectral window under consideration and is consistent with the expected underlying physics. We subsequently apply XANESNET at nine first-row transition metal (Ti-Zn) K-edges. It can be optimized in as little as a minute, predicts instantaneously, and provides K-edge XANES spectra with an average accuracy of ∼±2%-4% in which the positions of prominent peaks are matched with a >90% hit rate to sub-eV (∼0.8 eV) error.

Multilayer Subsystem Surface Hopping Method for Large-Scale Nonadiabatic Dynamics Simulation with Hundreds of Thousands of States

We present a multilayer subsystem surface hopping (MSSH) method to deal with nonadiabatic dynamics in large-scale systems. A small subsystem instead of the full system is adopted for surface hopping and is updated on-the-fly to achieve a reliable description of important adiabatic states and the wave function evolution. Additional subsystems for molecular dynamics and statistical description are introduced to further improve the simulation reliability. The global flux hopping probabilities with optimal state assignments are utilized to treat the complex surface crossings. As demonstrated in a series of one- and two-dimensional Holstein models with up to hundreds of thousands of states, MSSH shows weak parameter dependence in all investigated systems. Especially, the computational costs are reduced by 2-6 orders of magnitude compared to traditional surface hopping simulations in full systems, and size-independent results are achieved with a large time-step size of 2-5 fs. The new method is compatible with different decoherence correction strategies and achieves a much better balance between efficiency and reliability, thus promising for applications in general charge and exciton dynamics simulations.

Generalized Ab Initio Nonadiabatic Dynamics Simulation Methods from Molecular to Extended Systems

Nonadiabatic dynamics simulation has become a powerful tool to describe nonadiabatic effects involved in photophysical processes and photochemical reactions. In the past decade, our group has developed generalized trajectory-based ab initio surface-hopping (GTSH) dynamics simulation methods, which can be used to describe a series of nonadiabatic processes, such as internal conversion, intersystem crossing, excitation energy transfer and charge transfer of molecular systems, and photoinduced nonadiabatic carrier dynamics of extended systems with and without spin-orbit couplings. In this contribution, we will first give a brief introduction to our recently developed methods and related numerical implementations at different computational levels. Later, we will present some of our latest applications in realistic systems, which cover organic molecules, biological proteins, organometallic compounds, periodic organic and inorganic materials, etc. Final discussion is given to challenges and outlooks of ab initio nonadiabatic dynamics simulations.

All-Atom Nonadiabatic Dynamics Simulation of Hybrid Graphene Nanoribbons Based on Wannier Analysis and Machine Learning

Trajectory surface hopping combined with ab initio electronic structure calculations is a popular and powerful approach for on-the-fly nonadiabatic dynamics simulations. For large systems, however, this remains a significant challenge because of the unaffordable computational cost of large-scale electronic structure calculations. Here, we present an efficient divide-and-conquer approach to construct the system Hamiltonian based on Wannier analysis and machine learning. In detail, the large system under investigation is first decomposed into small building blocks, and then all possible segments formed by building blocks within a cutoff distance are found out. Ab initio molecular dynamics is carried out to generate a sequence of geometries for each equivalent segment with periodicity. The Hamiltonian matrices in the maximum localized Wannier function (MLWF) basis are obtained for all geometries and utilized to train artificial neural networks (ANNs) for the structure-dependent Hamiltonian elements. Taking advantage of the orthogonality and spatial locality of MLWFs, the one-electron Hamiltonian of a large system at arbitrary geometry can be directly constructed by the trained ANNs. As demonstrations, we study charge transport in a zigzag graphene nanoribbon (GNR), a coved GNR, and a series of hybrid GNRs with a state-of-the-art surface hopping method. The interplay between delocalized and localized states is found to determine the electron dynamics in hybrid GNRs. Our approach has successfully studied GNRs with >10 000 atoms, paving the way for efficient and reliable all-atom nonadiabatic dynamics simulation of general systems.

Coupled- and Independent-Trajectory Approaches Based on the Exact Factorization Using the PyUNIxMD Package

We present mixed quantum-classical approaches based on the exact factorization framework. The electron-nuclear correlation term in the exact factorization enables us to deal with quantum coherences by accounting for electronic and nuclear nonadiabatic couplings effectively within classical nuclei approximation. We compare coupled- and independent-trajectory approximations with each other to understand algorithms in description of the bifurcation of nuclear wave packets and the correct spatial distribution of electronic wave functions along with nuclear trajectories. Finally, we show numerical results for comparisons of coupled- and independent-trajectory approaches for the photoisomerization of a protonated Schiff base from excited state molecular dynamics (ESMD) simulations with the recently developed Python-based ESMD code, namely, the PyUNIxMD program.

Significance of the Chemical Environment of an Element in Nonadiabatic Molecular Dynamics: Feature Selection and Dimensionality Reduction with Machine Learning

Using supervised and unsupervised machine learning (ML) on features generated from nonadiabatic (NA) molecular dynamics (MD) trajectories under the classical path approximation, we demonstrate that mutual information with the NA Hamiltonian can be used for feature selection and model simplification. Focusing on CsPbI₃, a popular metal halide perovskite, we observe that the chemical environment of a single element is sufficient for predicting the NA Hamiltonian. The conclusion applies even to Cs, although Cs does not contribute to the relevant wave functions. Interatomic distances between Cs and I or Pb and the octahedral tilt angle are the most important features. We reduce a typical 360-parameter ML force-field model to just a 12-parameter NA Hamiltonian model, while maintaining a high NA-MD simulation quality. Because NA-MD is a valuable tool for studying excited state processes, overcoming its high computational cost through simple ML models will streamline NA-MD simulations and expand the ranges of accessible system size and simulation time.

Mechanistic photophysics and photochemistry of unnatural bases and sunscreen molecules: insights from electronic structure calculations

Photophysics and photochemistry are basic subjects in the study of light-matter interactions and are ubiquitous in diverse fields such as biology, energy, materials, and environment. A full understanding of mechanistic photophysics and photochemistry underpins many recent advances and applications. This contribution first provides a short discussion on the theoretical calculation methods we have used in relevant studies, then we introduce our latest progress on the mechanistic photophysics and photochemistry of two classes of molecular systems, namely unnatural bases and sunscreens. For unnatural bases, we disclose the intrinsic driving forces for the ultrafast population to reactive triplet states, impacts of the position and degree of chalcogen substitutions, and the effects of complex environments. For sunscreen molecules, we reveal the photoprotection mechanisms that dissipate excess photon energy to the surroundings by ultrafast internal conversion to the ground state. Finally, relevant theoretical challenges and outlooks are discussed.

Forecasting nonadiabatic dynamics using hybrid convolutional neural network/long short-term memory network

Modeling nonadiabatic dynamics in complex molecular or condensed-phase systems has been challenging, especially for the long-time dynamics. In this work, we propose a time series machine learning scheme based on the hybrid convolutional neural network/long short-term memory (CNN-LSTM) framework for predicting the long-time quantum behavior, given only the short-time dynamics. This scheme takes advantage of both the powerful local feature extraction ability of CNN and the long-term global sequential pattern recognition ability of LSTM. With feature fusion of individually trained CNN-LSTM models for the quantum population and coherence dynamics, the proposed scheme is shown to have high accuracy and robustness in predicting the linearized semiclassical and symmetrical quasiclassical mapping dynamics as well as the mixed quantum-classical Liouville dynamics of various spin-boson models with learning time up to 0.3 ps. Furthermore, if the hybrid network has learned the dynamics of a system, this knowledge is transferable that could significantly enhance the accuracy in predicting the dynamics of a similar system. The hybrid CNN-LSTM network is thus believed to have high predictive power in forecasting the nonadiabatic dynamics in realistic charge and energy transfer processes in photoinduced energy conversion.

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

Fast Generation of Machine Learning-Based Force Fields for Adsorption Energies

Adsorption and desorption of molecules are key processes in extraction and purification of biomolecules, engineering of drug carriers, and designing of surface-specific coatings. To understand the adsorption process on the atomic scale, state-of-the-art quantum mechanical and classical simulation methodologies are widely used. However, studying adsorption using a full quantum mechanical treatment is limited to picoseconds simulation timescales, while classical molecular dynamics simulations are limited by the accuracy of the existing force fields. To overcome these challenges, we propose a systematic way to generate flexible, application-specific highly accurate force fields by training artificial neural networks. As a proof of concept, we study the adsorption of the amino acid alanine on graphene and gold (111) surfaces and demonstrate the force field generation methodology in detail. We find that a molecule-specific force field with Lennard-Jones type two-body terms incorporating the 3rd and 7th power of the inverse distances between the atoms of the adsorbent and the surfaces yields optimal results, which is surprisingly different from typical Lennard-Jones potentials used in traditional force fields. Furthermore, we present an efficient and easy-to-train machine learning model that incorporates system-specific three-body (or higher order) interactions that are required, for example, for gold surfaces. Our final machine learning-based force field yields a mean absolute error of less than 4.2 kJ/mol at a speed-up of ∼10⁵ times compared to quantum mechanical calculation, which will have a significant impact on the study of adsorption in different research areas.

Increasing Efficiency of Nonadiabatic Molecular Dynamics by Hamiltonian Interpolation with Kernel Ridge Regression

Nonadiabatic (NA) molecular dynamics (MD) goes beyond the adiabatic Born-Oppenheimer approximation to account for transitions between electronic states. Such processes are common in molecules and materials used in solar energy, optoelectronics, sensing, and many other fields. NA-MD simulations are much more expensive compared to adiabatic MD due to the need to compute excited state properties and NA couplings (NACs). Similarly, application of machine learning (ML) to NA-MD is more challenging compared with adiabatic MD. We develop an NA-MD simulation strategy in which an adiabatic MD trajectory, which can be generated with a ML force field, is used to sample excitation energies and NACs for a small fraction of geometries, while the properties for the remaining geometries are interpolated with kernel ridge regression (KRR). This ML strategy allows for one to perform NA-MD under the classical path approximation, increasing the computational efficiency by over an order of magnitude. Compared to neural networks, KRR requires little parameter tuning, saving efforts on model building. The developed strategy is demonstrated with two metal halide perovskites that exhibit complicated MD and are actively studied for various applications.

Physically Motivated Recursively Embedded Atom Neural Networks: Incorporating Local Completeness and Nonlocality

Recent advances in machine-learned interatomic potentials largely benefit from the atomistic representation and locally invariant many-body descriptors. It was, however, recently argued that including three-body (or even four-body) features is incomplete to distinguish specific local structures. Utilizing an embedded density descriptor made by linear combinations of neighboring atomic orbitals and realizing that each orbital coefficient physically depends on its own local environment, we propose a recursively embedded atom neural network model. We formally prove that this model can efficiently incorporate complete many-body correlations without explicitly computing high-order terms. This model not only successfully addresses challenges regarding local completeness and nonlocality in representative systems, but also provides an easy and general way to update local many-body descriptors to have a message-passing form without changing their basic structures.

Deep Learning-Based Three-Dimensional Oral Conical Beam Computed Tomography for Diagnosis

In order to deeply study oral three-dimensional cone beam computed tomography (CBCT), the diagnosis of oral and facial surgical diseases based on deep learning was studied. The utility model related to a deep learning-based classification algorithm for oral neck and facial surgery diseases (deep diagnosis of oral and maxillofacial diseases, referred to as DDOM) is brought out; in this method, the DDOM algorithm proposed for patient classification, lesion segmentation, and tooth segmentation, respectively, can effectively process the three-dimensional oral CBCT data of patients and carry out patient-level classification. The segmentation results show that the proposed segmentation method can effectively segment the independent teeth in CBCT images, and the vertical magnification error of tooth CBCT images is clear. The average magnification rate was 7.4%. By correcting the equation of R value and CBCT image vertical magnification rate, the magnification error of tooth image length could be reduced from 7.4. According to the CBCT image length of teeth, the distance R from tooth center to FOV center, and the vertical magnification of CBCT image, the data closer to the real tooth size can be obtained, in which the magnification error is reduced to 1.0%. Therefore, it is proved that the 3D oral cone beam electronic computer based on deep learning can effectively assist doctors in three aspects: patient diagnosis, lesion localization, and surgical planning.

On application of deep learning to simplified quantum-classical dynamics in electronically excited states

Deep learning (DL) is applied to simulate non-adiabatic molecular dynamics of phenanthrene, using the time-dependent density functional based tight binding (TD-DFTB) approach for excited states combined with mixed quantum–classical propagation. Reference calculations rely on Tully’s fewest-switches surface hopping (FSSH) algorithm coupled to TD-DFTB, which provides electronic relaxation dynamics in fair agreement with various available experimental results. Aiming at describing the coupled electron-nuclei dynamics in large molecular systems, we then examine the combination of DL for excited-state potential energy surfaces (PESs) with a simplified trajectory surface hopping propagation based on the Belyaev–Lebedev (BL) scheme. We start to assess the accuracy of the TD-DFTB approach upon comparison of the optical spectrum with experimental and higher-level theoretical results. Using the recently developed SchNetPack (Schütt et al 2019 J. Chem. Theory Comput. 15 448–55) for DL applications, we train several models and evaluate their performance in predicting excited-state energies and forces. Then, the main focus is given to the analysis of the electronic population of low-lying excited states computed with the aforementioned methods. We determine the relaxation timescales and compare them with experimental data. Our results show that DL demonstrates its ability to describe the excited-state PESs. When coupled to the simplified BL scheme considered in this study, it provides reliable description of the electronic relaxation in phenanthrene as compared with either the experimental data or the higher-level FSSH/TD-DFTB theoretical results. Furthermore, the DL performance allows high-throughput analysis at a negligible cost.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning Force Fields

In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.