Machine learning enables long time scale molecular photodynamics simulations

Abstract

Photo-induced processes 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.

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

“…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.…”

“…An option is to use a phase correction algorithm to pre-process data and remove these random phase jumps. Assuming that the effect of the Berry phase remains minor on the training set, smooth properties are obtained that are learnable by ML models [32]. However, this approach is expensive and many quantum chemistry reference computations are necessary to generate the training set.…”

“…The SchNarc approach can overcome the current limitations of existing MLMD simulations for excited states by allowing (i) a phase-free training to omit the costly pre-processing of raw quantum chemistry data and, to treat (ii) rotationally covariant NACs, which can either be trained, or (iii) alternatively be approximated from only ML potentials, their gradients, and Hessians, and to treat (iv) SOCs.To validate the phase-free training, a new loss function termed phase-less loss function is developed and tested for the methylenimmonium cation, CH 2 NH + 2 , of which we take a phase corrected training set from Ref. [32]. Using the same level of theory (MR-CISD(6,4)/aug-cc-pVDZ) with the program COLUMBUS [84], the training set is recomputed without applying phase correction to train ML models also on raw data obtained directly from quantum chemistry programs.…”

“…The virtual property is the multi-dimensional anti-derivative of the rightmost expression in equation (1), Ψ i | ∂H el R | Ψ j (a derivation is given in the SI). Compared to previous ML models for NACs [29,30,32,33], where NACs are learned and predicted as direct outputs or even single values, this approach provides rotational and translational covariance, which has recently been achieved in a similar way for the electronic friction tensor [85].However, even without the need of pre-processing the training set, the costly computations of NAC vectors for the training set generation remain. Approximations 4 Figure 1: Populations obtained from 90 QC (MR-CISD(6,4)/aug-cc-pVDZ) trajectories are shown by continuous lines and are compared to (A) populations resulting from 1000 initially excited trajectories obtained from SchNet (dotted lines) that is trained on not phase corrected data and takes the L 2 norm as loss function, (B) a similar SchNet model, but trained on phase corrected data, (C) a SchNet model trained on not phase corrected data, but using the new phase-less loss function, and (D) a SchNet model trained on phase corrected data using the new phase-less loss function .…”

“…33 for examples, where dynamics is not reproduced by ML although potentials seemingly are).The application of the NAC approximation is further tested on more realistic systems with properties obtained from quantum chemistry data including fast as well as slow population transfer. CH 2 NH + 2 serves as a testsystem for the former case, where ultrafast transitions from the second excited singlet state back to the ground state take place after excitation within 100 femtoseconds [32,98], which is only possible to repro-7 Figure 2: Potential energy curves and the norm of the NAC vectors between singlet states (A) and triplet states (B) along the asymmetric stretching mode of SO 2 . Continuous line represent LVC(MR-CISD) and dotted (dashed) lines show results obtained from SchNarc models trained on only energies and gradients (as well as NACs for comparison) of 3 singlets and 3 triplet states.Figure 3: Quantum populations using LVC(MR-CISD) (left panels), SchNarc trained on NACs (middle panels) and SchNarc using approximated NACs from energies and gradients (right panels).…”