Excited-state nonadiabatic simulations with quantum mechanics/molecular mechanics (QM/MM) are essential to understand photoinduced processes in explicit environments. However, the high computational cost of the underlying quantum chemical calculations limits its application in combination with trajectory surface hopping methods. Here, we use FieldSchNet, a machine-learned interatomic potential capable of incorporating electric field effects into the electronic states, to replace traditional QM/MM electrostatic embedding with its ML/MM counterpart for nonadiabatic excited state trajectories. The developed method is applied to furan in water, including five coupled singlet states. Our results demonstrate that with sufficiently curated training data, the ML/MM model reproduces the electronic kinetics and structural rearrangements of QM/MM surface hopping reference simulations. Furthermore, we identify performance metrics that provide robust and interpretable validation of model accuracy.

Machine learning (ML) has shown to advance the research field of quantum chemistry in almost any possible direction and has recently also entered the excited states to investigate the multifaceted photochemistry of molecules. In this paper, we pursue two goals: i) We show how ML can be used to model permanent dipole moments for excited states and transition dipole moments by adapting the charge model of [Chem. Sci., 2017, 8, 6924-6935], which was originally proposed for the permanent dipole moment vector of the electronic ground state. ii) We investigate the transferability of our excited-state ML models in chemical space, i.e., whether an ML model can predict properties of molecules that it has never been trained on and whether it can learn the different excited states of two molecules simultaneously. To this aim, we employ and extend our previously reported SchNarc approach for excited-state ML. We calculate UV absorption spectra from excited-state energies and transition dipole moments as well as electrostatic potentials from latent charges inferred by the ML model of the permanent dipole moment vectors. We train our ML models on CH$_2$NH$_2^+$ and C$_2$H$_4$, while predictions are carried out for these molecules and additionally for CHNH$_2$, CH$_2$NH, and C$_2$H$_5^+$. The results indicate that transferability is possible for the excited states.

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 how machine learning is employed not only 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, approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine learning is employed at an increasing rate in the research field of quantum chemistry. While the majority of approaches target the investigation of chemical systems in their electronic ground state, the inclusion of light into the processes leads to electronically excited states and gives rise to several new challenges. Here, we survey recent advances for excited-state dynamics based on machine learning. In doing so, we highlight successes, pitfalls, challenges and future avenues for machine learning approaches for light-induced molecular processes. Keywords: machine learning, photodynamics, photochemistry, excited states, quantum chemistry, spin-orbit couplings, nonadiabatic couplings.

Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory computations or the limited accuracy of classical empirical force fields. Machine learning techniques can help to overcome these limitations by providing access to potential energies, forces and other molecular properties modeled directly after an electronic structure reference at only a fraction of the original computational cost. The present text discusses several practical aspects of conducting machine learning driven molecular dynamics simulations. First, we study the efficient selection of reference data points on the basis of an active learning inspired adaptive sampling scheme. This is followed by the analysis of a machine-learning based model for simulating molecular dipole moments in the framework of predicting infrared spectra via molecular dynamics simulations. Finally, we show that machine learning models can offer valuable aid in understanding chemical systems beyond a simple prediction of quantities.

Abstract: Photo-inducedprocesses are fundamental in nature, but accurate simulations are seriously limited by the cost of the underlying quantum chemical calculations, hampering their application for long time scales. Here we introduce a method based on machine learning to overcome this bottleneck and enable accurate photodynamics on nanosecond time scales, which are otherwise out of reach with contemporary approaches. Instead of expensive quantum chemistry during molecular dynamics simulations, we use deep neural networks to learn the relationship between a molecular geometry and its high-dimensional electronic properties. As an example, the time evolution of the methylenimmonium cation for one nanosecond is used to demonstrate that machine learning algorithms can outperform standard excited-state molecular dynamics approaches in their computational efficiency while delivering the same accuracy. Introduction Machine learning (ML) is revolutionizing the most diverse domains, like image recognition [1], playing board games [2], or society integration of refugees [3]. Also in chemistry, anincreasing range of applications is being tackled with ML, for example, the design and discovery of new molecules and materials [4, 5, 6]. In the present study, we show how ML enables efficient photodynamics simulations. Photodynamics is the study of photo-induced processes that occur after a molecule is exposed to light. Photosynthesis or DNA photodamage leading to skin cancer are only two examples of phenomena that involve molecules interacting with light [7, 8, 9, 10, 11]. The simulation of such processes has been key to learn structure-dynamicsfunction relationshipsthat can be used to guide the design of photonic materials, such as photosensitive drugs [12], photocatalysts [4] and photovoltaics [13, 14].

We introduce weighted atom-centered symmetry functions (wACSFs) as descriptors of a chemical system's geometry for use in the prediction of chemical properties such as enthalpies or potential energies via machine learning. The wACSFs are based on conventional atom-centered symmetry functions (ACSFs) but overcome the undesirable scaling of the latter with increasing number of different elements in a chemical system. The performance of these two descriptors is compared using them as inputs in high-dimensional neural network potentials (HDNNPs), employing the molecular structures and associated enthalpies of the 133855 molecules containing up to five different elements reported in the QM9 database as reference data. A substantially smaller number of wACSFs than ACSFs is needed to obtain a comparable spatial resolution of the molecular structures. At the same time, this smaller set of wACSFs leads to significantly better generalization performance in the machine learning potential than the large set of conventional ACSFs. Furthermore, we show that the intrinsic parameters of the descriptors can in principle be optimized with a genetic algorithm in a highly automated manner. For the wACSFs employed here, we find however that using a simple empirical parametrization scheme is sufficient in order to obtain HDNNPs with high accuracy.

Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate molecular infrared spectra with unprecedented computational efficiency. To account for vibrational anharmonic and dynamical effects -- typically neglected by conventional quantum chemistry approaches -- we base our machine learning strategy on ab initio molecular dynamics simulations. While these simulations are usually extremely time consuming even for small molecules, we overcome these limitations by leveraging the power of a variety of machine learning techniques, not only accelerating simulations by several orders of magnitude, but also greatly extending the size of systems that can be treated. To this end, we develop a molecular dipole moment model based on environment dependent neural network charges and combine it with the neural network potentials of Behler and Parrinello. Contrary to the prevalent big data philosophy, we are able to obtain very accurate machine learning models for the prediction of infrared spectra based on only a few hundreds of electronic structure reference points. This is made possible through the introduction of a fully automated sampling scheme and the use of molecular forces during neural network potential training. We demonstrate the power of our machine learning approach by applying it to model the infrared spectra of a methanol molecule, n-alkanes containing up to 200 atoms and the protonated alanine tripeptide, which at the same time represents the first application of machine learning techniques to simulate the dynamics of a peptide. In all these case studies we find excellent agreement between the infrared spectra predicted via machine learning models and the respective theoretical and experimental spectra.