Machine learning and excited-state 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.

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.

Optimized Machine learning techniques Enable prediction of organic dyes photophysical Properties: Absorption Wavelengths, emission Wavelengths, and quantum yields

Applications of organic dyes, ranging from basic research to industry, are functions of their photophysical properties. Two important aspects- (1) knowledge of the photophysical properties of existing dyes long before real applications and (2) discovery of new organic dyes with desired photophysical properties for either upgradation of existing or development of new applications-are needed to be addressed. These two cases are coupled together with the common goal of estimating photophysical properties with high accuracy at the minimum cost of time and money long before the hard-core laboratory experiment. For this purpose, machine learning-based techniques are the most suitable approach. In this study, we used optimized machine-learning techniques to assess a dataset of 3066 organic dyes, which were evaluated using three evaluation parameters: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R2). The Quadratic Support Vector Machine (QSVM) was the best predictive model for RMSE-16.614, MAE-10.837, and R2-0.961 for absorption wavelengths and RMSE-23.636, MAE-16.278, and R2-0.929 for emission wavelengths. These R2 values are 0.7% and 0.4% greater than the Gradient Boost Regression Tree (GBRT) model's recently reported values of 0.954 and 0.925 for absorption and emission wavelengths, respectively. Furthermore, we estimated the quantum yield and found that the Coarse Gaussian Support Vector Machine (CGSVM) outperformed all examined models. For more validation of these models, we compared the predicted results with the experimental results of selective dyes. The proposed automated approach can be used for predicting photophysical properties without much computer programming knowledge.

From Organic Fragments to Photoswitchable Catalysts: The OFF-ON Structural Repository for Transferable Kernel-Based Potentials

Structurally and conformationally diverse databases are needed to train accurate neural networks or kernel-based potentials capable of exploring the complex free energy landscape of flexible functional organic molecules. Curating such databases for species beyond "simple" drug-like compounds or molecules composed of well-defined building blocks (e.g., peptides) is challenging as it requires thorough chemical space mapping and evaluation of both chemical and conformational diversities. Here, we introduce the OFF-ON (organic fragments from organocatalysts that are non-modular) database, a repository of 7869 equilibrium and 67,457 nonequilibrium geometries of organic compounds and dimers aimed at describing conformationally flexible functional organic molecules, with an emphasis on photoswitchable organocatalysts. The relevance of this database is then demonstrated by training a local kernel regression model on a low-cost semiempirical baseline and comparing it with a PBE0-D3 reference for several known catalysts, notably the free energy surfaces of exemplary photoswitchable organocatalysts. Our results demonstrate that the OFF-ON data set offers reliable predictions for simulating the conformational behavior of virtually any (photoswitchable) organocatalyst or organic compound composed of H, C, N, O, F, and S atoms, thereby opening a computationally feasible route to explore complex free energy surfaces in order to rationalize and predict catalytic behavior.

Automated Exploration of Reaction Networks and Mechanisms Based on Metadynamics Nanoreactor Simulations

We developed an automated approach to construct a complex reaction network and explore the reaction mechanisms for numerous reactant molecules by integrating several theoretical approaches. Nanoreactor-type molecular dynamics was used to generate possible chemical reactions, in which the metadynamics was used to overcome the reaction barriers, and the semiempirical GFN2-xTB method was used to reduce the computational cost. Reaction events were identified from trajectories using the hidden Markov model based on the evolution of the molecular connectivity. This provided the starting points for further transition-state searches at the electronic structure levels of density functional theory to obtain the reaction mechanism. Finally, the entire reaction network containing multiple pathways was built. The feasibility and efficiency of the automated construction of the reaction network were investigated using the HCHO and NH3 biomolecular reaction and the reaction network for a multispecies system comprising dozens of HCN and H2O molecules. The results indicated that the proposed approach provides a valuable and effective tool for the automated exploration of the reaction networks.

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.

SchNetPack 2.0: A neural network toolbox for atomistic machine learning

SchNetPack is a versatile neural network toolbox that addresses both the requirements of method development and the application of atomistic machine learning. Version 2.0 comes with an improved data pipeline, modules for equivariant neural networks, and a PyTorch implementation of molecular dynamics. An optional integration with PyTorch Lightning and the Hydra configuration framework powers a flexible command-line interface. This makes SchNetPack 2.0 easily extendable with a custom code and ready for complex training tasks, such as the generation of 3D molecular structures.

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.

Semiclassical Dynamics on Machine-Learned Coupled Multireference Potential Energy Surfaces: Application to the Photodissociation of the Simplest Criegee Intermediate

Determination of high-dimensional potential energy surfaces (PESs) and nonadiabatic couplings have always been quite challenging. To this end, machine learning (ML) models, trained with a finite set of ab initio data, allow accurate prediction of such properties. To express the PESs in terms of atomic contributions is the cornerstone of any ML based technique because it can be easily scaled to large systems. In this work, we have constructed high fidelity PESs and nonadiabatic coupling terms at the CASSCF level of ab initio data using a machine learning technique, namely, kernel-ridge regression. Additional MRCI-level calculations were carried out to assess the quality of the PESs. We use these machine-learned PESs and nonadiabatic couplings to simulate excited-state molecular dynamics based on Tully's fewest-switches surface hopping method (FSSH). FSSH is a semiclassical method in which nuclei move on the PESs due to the electrons according to the laws of classical mechanics. Nonadiabatic effects are taken into account in terms of transitions between PESs. We apply this scheme to study the O-O photodissociation of the simplest Criegee intermediate (CH₂OO). The FSSH trajectories were initiated on the lowest optically bright singlet excited state (S₂) and propagated along the three most important internal coordinates, namely, O-O and C-O bond distances and the COO bond angle. Some of the trajectories end up on energetically lower PESs as a result of radiationless transfer through conical intersections. All of the trajectories lead to the dissociation of the O-O bond due to the dissociative nature of the excited PESs through one of the two dissociative channels. The simulation reveals that there is about 88.4% probability of dissociation through the lower channel leading to the H₂CO (X¹A₁) and O (¹D) products, whereas there is only 11.6% probability of dissociation through the upper channel leading to H₂CO (a³A″) and O (³P) products.

Machine Learning Exciton Hamiltonians in Light-Harvesting Complexes

We propose a machine learning (ML)-based strategy for an inexpensive calculation of excitonic properties of light-harvesting complexes (LHCs). The strategy uses classical molecular dynamics simulations of LHCs in their natural environment in combination with ML prediction of the excitonic Hamiltonian of the embedded aggregate of pigments. The proposed ML model can reproduce the effects of geometrical fluctuations together with those due to electrostatic and polarization interactions between the pigments and the protein. The training is performed on the chlorophylls of the major LHC of plants, but we demonstrate that the model is able to extrapolate well beyond the initial training set. Moreover, the accuracy in predicting the effects of the environment is tested on the simulation of the small changes observed in the absorption spectra of the wild-type and a mutant of a minor LHC.

An efficient protocol for excited states of large biochromophores

Efficient energy transport in photosynthetic antenna is a long-standing source of inspiration for artificial light harvesting materials. However, characterizing the excited states of the constituent chromophores poses a considerable challenge to mainstream quantum chemical and semiempirical excited state methods due to their size and complexity and the accuracy required to describe small but functionally important changes in their properties. In this paper, we explore an alternative approach to calculating the excited states of large biochromophores, exemplified by a specific method for calculating the Q_y transition of bacteriochlorophyll a, which we name Chl-xTB. Using a diagonally dominant approximation to the Casida equation and a bespoke parameterization scheme, Chl-xTB can match time-dependent density functional theory's accuracy and semiempirical speed for calculating the potential energy surfaces and absorption spectra of chlorophylls. We demonstrate that Chl-xTB (and other prospective realizations of our protocol) can be integrated into multiscale models, including concurrent excitonic and point-charge embedding frameworks, enabling the analysis of biochromophore networks in a native environment. We exploit this capability to probe the low-frequency spectral densities of excitonic energies and interchromophore interactions in the light harvesting antenna protein LH2 (light harvesting complex 2). The impact of low-frequency protein motion on interchromophore coupling and exciton transport has routinely been ignored due to the prohibitive costs of including it in simulations. Our results provide a more rigorous basis for continued use of this approximation by demonstrating that exciton transition energies are unaffected by low-frequency vibrational coupling to exciton interaction energies.

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.

Transition orbital projection approach for excited state tracking

Quantitively comparing the features between different electronic excited states (ESs) is a crucial task in both potential energy surface (PES) studies and excited-state fragmentation approaches. However, it is still a challenging problem in regard to the comparison of complex and highly degenerate systems. Herein, we present a transition orbital projection (TOP) method to calculate the similarity of different ESs based on the configuration vectors of two types of transition densities. It fully considers four significant problems, including phase, hole-particle bijectivity, orbital permutation, and sign of configuration coefficients. TOP state-tracking-based excited-state optimization shows high robustness in several high-symmetric systems, which are difficult to describe with traditional state-tracking approaches. The TOP state-tracking method is expected to be widely applied to the PES of photochemical reactions, ES molecular dynamics to track the diabatic states, and fragmentation approaches for local excitation of large systems.

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.

Machine learned calibrations to high-throughput molecular excited state calculations

Understanding the excited state properties of molecules provides insight into how they interact with light. These interactions can be exploited to design compounds for photochemical applications, including enhanced spectral conversion of light to increase the efficiency of photovoltaic cells. While chemical discovery is time- and resource-intensive experimentally, computational chemistry can be used to screen large-scale databases for molecules of interest in a procedure known as high-throughput virtual screening. The first step usually involves a high-speed but low-accuracy method to screen large numbers of molecules (potentially millions), so only the best candidates are evaluated with expensive methods. However, use of a coarse first-pass screening method can potentially result in high false positive or false negative rates. Therefore, this study uses machine learning to calibrate a high-throughput technique [eXtended Tight Binding based simplified Tamm-Dancoff approximation (xTB-sTDA)] against a higher accuracy one (time-dependent density functional theory). Testing the calibration model shows an approximately sixfold decrease in the error in-domain and an approximately threefold decrease in the out-of-domain. The resulting mean absolute error of ∼0.14 eV is in line with previous work in machine learning calibrations and out-performs previous work in linear calibration of xTB-sTDA. We then apply the calibration model to screen a 250k molecule database and map inaccuracies of xTB-sTDA in chemical space. We also show generalizability of the workflow by calibrating against a higher-level technique (CC2), yielding a similarly low error. Overall, this work demonstrates that machine learning can be used to develop a cost-effective and accurate method for large-scale excited state screening, enabling accelerated molecular discovery across a variety of disciplines.

Time-resolved photoelectron spectroscopy: the continuing evolution of a mature technique

Time-resolved photoelectron spectroscopy (TRPES) has become one of the most widespread techniques for probing nonadiabatic dynamics in the excited electronic states of molecules. Furthermore, the complementary development of ab initio approaches for the simulation of TRPES signals has enabled the interpretation of these transient spectra in terms of underlying coupled electronic-nuclear dynamics. In this perspective, we discuss the current state-of-the-art approaches, including efforts to push femtosecond pulses into vacuum ultraviolet and soft X-ray regimes as well as the utilization of novel polarizations to use time-resolved optical activity as a probe of nonadiabatic dynamics. We close this perspective with a forward-looking prospectus on the new areas of application for this technique.

Extending the Time Scales of Nonadiabatic Molecular Dynamics via Machine Learning in the Time Domain

A novel methodology for direct modeling of long-time scale nonadiabatic dynamics in extended nanoscale and solid-state systems is developed. The presented approach enables forecasting the vibronic Hamiltonians as a direct function of time via machine-learning models trained directly in the time domain. The use of periodic and aperiodic functions that transform time into effective input modes of the artificial neural network is demonstrated to be essential for such an approach to work for both abstract and atomistic models. The best strategies and possible limitations pertaining to the new methodology are explored and discussed. An exemplary direct simulation of unprecedentedly long 20 picosecond trajectories is conducted for a divacancy-containing monolayer black phosphorus system, and the importance of conducting such extended simulations is demonstrated. New insights into the excited states photophysics in this system are presented, including the role of decoherence and model definition.

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.

Choosing the right molecular machine learning potential

Quantum-chemistry simulations based on potential energy surfaces of molecules provide invaluable insight into the physicochemical processes at the atomistic level and yield such important observables as reaction rates and spectra. Machine learning potentials promise to significantly reduce the computational cost and hence enable otherwise unfeasible simulations. However, the surging number of such potentials begs the question of which one to choose or whether we still need to develop yet another one. Here, we address this question by evaluating the performance of popular machine learning potentials in terms of accuracy and computational cost. In addition, we deliver structured information for non-specialists in machine learning to guide them through the maze of acronyms, recognize each potential's main features, and judge what they could expect from each one.

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.

Ab Initio Machine Learning in Chemical Compound Space

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first-principles based virtual sampling of this space, for example, in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest subsets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an ab initio view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics.

Modern Theoretical Approaches to Modeling the Excited-State Intramolecular Proton Transfer: An Overview

The excited-state intramolecular proton transfer (ESIPT) phenomenon is nowadays widely acknowledged to play a crucial role in many photobiological and photochemical processes. It is an extremely fast transformation, often taking place at sub-100 fs timescales. While its experimental characterization can be highly challenging, a rich manifold of theoretical approaches at different levels is nowadays available to support and guide experimental investigations. In this perspective, we summarize the state-of-the-art quantum-chemical methods, as well as molecular- and quantum-dynamics tools successfully applied in ESIPT process studies, focusing on a critical comparison of their specific properties.

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.

Robustness and accuracy improvement of data processing with 2D neural networks for transient absorption dynamics

To achieve the goal of efficiently analyzing transient absorption spectra without arbitrary assumption and to overcome the limitations of conventional methods in fitting ability and highly noised backgrounds, it is essential to develop new tools to achieve more accurate and robust prediction based on the intrinsic properties of a spectrum even under strong noise. In this work, Lasso regression and neural network were combined to achieve an effective fitting. Compared to the conventional global fitting method, our network could automatically determine the exponential form on each wave unit, in which the accuracy was as high as 97%. Thereafter, the lifetime with the corresponding amplitude ratio could be easily predicted by the neural network on each wave unit. This kind of prediction is difficult to achieve by global fitting due to the limitation of computational resources. Furthermore, more accurate fitting even under weak signals could be achieved for the mean square error (MSE) decreasing by more than 100 times on average compared to conventional global fitting methods. Attributed to its improved accuracy and robustness, our developed algorithm could be readily applied to analyze time-resolved transient spectra.

Predicting phosphorescence energies and inferring wavefunction localization with machine learning

Phosphorescence is commonly utilized for applications including light-emitting diodes and photovoltaics. Machine learning (ML) approaches trained on ab initio datasets of singlet-triplet energy gaps may expedite the discovery of phosphorescent compounds with the desired emission energies. However, we show that standard ML approaches for modeling potential energy surfaces inaccurately predict singlet-triplet energy gaps due to the failure to account for spatial localities of spin transitions. To solve this, we introduce localization layers in a neural network model that weight atomic contributions to the energy gap, thereby allowing the model to isolate the most determinative chemical environments. Trained on the singlet-triplet energy gaps of organic molecules, we apply our method to an out-of-sample test set of large phosphorescent compounds and demonstrate the substantial improvement that localization layers have on predicting their phosphorescence energies. Remarkably, the inferred localization weights have a strong relationship with the ab initio spin density of the singlet-triplet transition, and thus infer localities of the molecule that determine the spin transition, despite the fact that no direct electronic information was provided during training. The use of localization layers is expected to improve the modeling of many localized, non-extensive phenomena and could be implemented in any atom-centered neural network model.

Perspective on integrating machine learning into computational chemistry and materials science

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

Molecular excited states through a machine learning lens

Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Automatic discovery of photoisomerization mechanisms with nanosecond machine learning photodynamics simulations

Photochemical reactions are widely used by academic and industrial researchers to construct complex molecular architectures via mechanisms that often require harsh reaction conditions. Photodynamics simulations provide time-resolved snapshots of molecular excited-state structures required to understand and predict reactivities and chemoselectivities. Molecular excited-states are often nearly degenerate and require computationally intensive multiconfigurational quantum mechanical methods, especially at conical intersections. Non-adiabatic molecular dynamics require thousands of these computations per trajectory, which limits simulations to ∼1 picosecond for most organic photochemical reactions. Westermayr et al. recently introduced a neural-network-based method to accelerate the predictions of electronic properties and pushed the simulation limit to 1 ns for the model system, methylenimmonium cation (CH₂NH₂⁺). We have adapted this methodology to develop the Python-based, Python Rapid Artificial Intelligence Ab Initio Molecular Dynamics (PyRAI²MD) software for the cis–trans isomerization of trans-hexafluoro-2-butene and the 4π-electrocyclic ring-closing of a norbornyl hexacyclodiene. We performed a 10 ns simulation for trans-hexafluoro-2-butene in just 2 days. The same simulation would take approximately 58 years with traditional multiconfigurational photodynamics simulations. We generated training data by combining Wigner sampling, geometrical interpolations, and short-time quantum chemical trajectories to adaptively sample sparse data regions along reaction coordinates. The final data set of the cis–trans isomerization and the 4π-electrocyclic ring-closing model has 6207 and 6267 data points, respectively. The training errors in energy using feedforward neural networks achieved chemical accuracy (0.023–0.032 eV). The neural network photodynamics simulations of trans-hexafluoro-2-butene agree with the quantum chemical calculations showing the formation of the cis-product and reactive carbene intermediate. The neural network trajectories of the norbornyl cyclohexadiene corroborate the low-yielding syn-product, which was absent in the quantum chemical trajectories, and revealed subsequent thermal reactions in 1 ns.

Photochemical reactions are widely used by academia and industry to construct complex molecular architectures via mechanisms that are often inaccessible by other means.

Machine Learning-Assisted Excited State Molecular Dynamics with the State-Interaction State-Averaged Spin-Restricted Ensemble-Referenced Kohn-Sham Approach

We present a machine learning-assisted excited state molecular dynamics (ML-ESMD) based on the ensemble density functional theory framework. Since we represent a diabatic Hamiltonian in terms of generalized valence bond ansatz within the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS) method, we can avoid singularities near conical intersections, which are crucial in excited state molecular dynamics simulations. We train the diabatic Hamiltonian elements and their analytical gradients with the SchNet architecture to construct machine learning models, while the phase freedom of off-diagonal elements of the Hamiltonian is cured by introducing the phase-less loss function. Our machine learning models show reasonable accuracy with mean absolute errors of ∼0.1 kcal/mol and ∼0.5 kcal/mol/Å for the diabatic Hamiltonian elements and their gradients, respectively, for penta-2,4-dieniminium cation. Moreover, by exploiting the diabatic representation, our models can predict correct conical intersection structures and their topologies. In addition, our ML-ESMD simulations give almost identical result with a direct dynamics at the same level of theory.

Prediction of Molecular Electronic Transitions Using Random Forests

Fluorescent molecules, fluorophores or dyes, play essential roles in bioimaging. Effective bioimaging requires fluorophores with diverse colors and high quantum yields for better resolution. An essential computational component to design novel dye molecules is an accurate model that predicts the electronic properties of molecules. Here, we present statistical machines that predict the excitation energies and associated oscillator strengths of a given molecule using the random forest algorithm. The excitation energies and oscillator strengths of a molecule are closely related to the emission spectrum and the quantum yields of fluorophores, respectively. In this study, we identified specific molecular substructures that induce high oscillator strengths of molecules. The results of our study are expected to serve as new design principles for designing novel fluorophores.