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

Abstract

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 for photodynamics simulations. The properties are multiple energies, forces, nonadiabatic couplings and spin-orbit couplings. The nonadiabatic couplings are learned in a phasefree manner as derivatives of a virtually constructed property by the deep learning model, which guarantees rotational covariance. Additionally, an approximation for nonadiabatic couplings is introduced, based on the potentials, their gradients and Hessians. As deep-learning method, we employ SchNet extended for multiple electronic states. In combination with the molecular dynamics program SHARC, our approach termed SchNarc is tested on a model system and two realistic polyatomic molecules and paves the way towards efficient photodynamics simulations of complex systems.1 Excited-state dynamics simulations are powerful tools to predict, understand and explain photo-induced processes, especially in combination with experimental studies. Examples of photo-induced processes range from photosynthesis, DNA photodamage as the starting point of skin cancer, to processes that enable our vision [1][2][3][4][5]. As they are part of our everyday lives, their understanding can help to unravel fundamental processes of nature and to advance several research fields, such as photovoltaics [6,7], photocatalysis [8] or photosensitive drug design [9].Since the full quantum mechanical treatment of molecules remains challenging, exact quantum dynamics simulations are limited to systems containing only a couple of atoms, even if fitted potential energy surfaces (PESs) are used [10][11][12][13][14][15][16][16][17][18][19][20][21][22][23][24][25][26]. In order to treat larger systems in full dimensions, i.e., systems with up to 100s of atoms, and on long time scales, i.e., in the range of several 100 picoseconds, excited-state machine learning (ML) molecular dynamics (MD), where the ML model is trained on quantum chemistry data, has evolved as a promising tool in the last couple of years [27][28][29][30][31][32][33].Such nonadiabatic MLMD simulations are in many senses analog to excited-state ab initio molecular dynamics simulations. The only difference is that the costly electronic structure calculations are mostly replaced by a ML model, providing quantum properties like the PESs and the corresponding forces. The nuclei are assumed to move classically on those PESs. This mixed quantum-classical dynamics approach allows for a very fast on-the-fly evaluation of the necessary properties at the geometries visited during the dynamics simulations.In order to account for nonadiabatic effects, i.e., transitions from one state to another, further approximations have to be introduced [34]. One method, which is frequently used to account for such transitions, is the surface-hopping method originally developed by Tully [35]...

Automatic discovery of photoisomerization mechanisms with nanosecond machine learning photodynamics simulations

“…30,31 The forces and interstate couplings are trained as the derivatives of the energies and a virtual potential, respectively. 18 We used an atom-specic virtual potential for more accurate NACs predictions. The phase of NACs is internally corrected with a phase-less loss function.…”

“…The phase of NACs is internally corrected with a phase-less loss function. 18 We include a detailed discussion on force and NAC prediction in ESI. † The NN receives an inverse distancebased 17,18 feature representation.…”

Nanosecond Photodynamics Simulations of a Cis-Trans Isomerization Are Enabled by Machine Learning

“…Fully quantum chemical NAMD trajectory propagation requires millions of CASSCF calculations to determine the energies, forces, and NACs at each timestep. Westermeyr et al 15 describes the particular challenge of predicting forces and NACs because they have independent vector components. The direction of forces and NACs are rotationally covariant (i.e., they depend on the molecule's orientation).…”

“…We have implemented multilayer feedforward NNs as the primary ML model in our ML-NAMD approach. We used an inverse distance-based [14][15] feature representation to predict energies, forces, and NACs. 1 has 12 atoms (N = 12), which lead to 66 unique entries in the inverse distance matrix.…”

“…14 Recently they have extended the application of the NNs model in predicting excited-states electronic properties for other small molecules, such as SO2 and CSH2 employing a deep continuous-filter convolutional-layer neural network, SchNet, combined with Sharc. 15 Beyond the proof-of-concept models, applying ML-based NAMD on more complex molecules is challenging because of the exponential increase of conformational space arising from the degrees of freedom of flexible bonds and functional groups. Training ML models becomes increasingly difficult with the rapidly growing training dataset, including atom-wise molecular features.…”