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 enables excited-state molecular dynamics simulations including nonadiabatic couplings on nanosecond time scales.

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.

In recent years, deep learning has become a part of our everyday life and is revolutionizing quantum chemistry as well. In this work, we show how deep learning can be used to advance the research field of photochemistry by learning all important properties – multiple energies, forces, and different couplings – for photodynamics simulations. We simplify such simulations substantially by (i) a phase-free training skipping costly pre-processing of raw quantum chemistry data, (ii) rotationally covariant nonadiabatic couplings, which can either be trained, or (iii) alternatively be approximated from only ML potentials, their gradients, and Hessians, and (iv) incorporate spin-orbit couplings. As deep-learning method, we employ SchNet with its automatically determined representation of molecular structures and extend it for multiple electronic states. In combination with the molecular dynamics program SHARC, our approach termed SchNarc is tested on two polyatomic molecules and paves the way towards efficient photodynamics simulations of complex systems.

In recent years, we have been witnessing a paradigm shift in computational materials science. In fact, traditional methods, mostly developed in the second half of the XXth century, are being complemented, extended, and sometimes even completely replaced by faster, simpler, and often more accurate approaches. The new approaches, that we collectively label by machine learning, have their origins in the fields of informatics and artificial intelligence, but are making rapid inroads in all other branches of science. With this in mind, this Roadmap article, consisting of multiple contributions from experts across the field, discusses the use of machine learning in materials science, and share perspectives on current and future challenges in problems as diverse as the prediction of materials properties, the construction of force-fields, the development of exchange correlation functionals for density-functional theory, the solution of the many-body problem, and more. In spite of the already numerous and exciting success stories, we are just at the beginning of a long path that will reshape materials science for the many challenges of the XXIth century.

Machine learning (ML) has shown to advance the research field of quantum chemistry in almost any possible direction and has also recently been applied 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 Gastegger et al. [Chem. Sci. 8, 6924–6935 (2017)], 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 the 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 ${\mathrm{C}\mathrm{H}}_2{\mathrm{N}\mathrm{H}}_2^{+}$ and C₂H₄, while predictions are carried out for these molecules and additionally for CHNH₂, CH₂NH, and ${\mathrm{C}}_2{\mathrm{H}}_5^{+}$ . The results indicate that transferability is possible for the excited states.