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. 2019 Aug 5;10(35):8100-8107.
doi: 10.1039/c9sc01742a. eCollection 2019 Sep 21.

Machine learning enables long time scale molecular photodynamics simulations

Julia Westermayr  1 , Michael Gastegger  2 , Maximilian F S J Menger  1   3 , Sebastian Mai  1 , Leticia González  1 , Philipp Marquetand  1
Affiliations

Machine learning enables long time scale molecular photodynamics simulations

Julia Westermayr et al. Chem Sci. .

Abstract

Photo-induced processes are fundamental in nature but accurate simulations of their dynamics 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.

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Figures

Fig. 1
Fig. 1. Schematic workflow of surface hopping molecular dynamics with deep NNs: the scheme starts from a set of initial quantum chemical calculations, which are pre-processed using a phase-correction algorithm and constitute an initial training set. Using this set, two deep NNs (NN1 and NN2) are trained and replace the quantum chemical calculations of energies (E) and gradients (G), nonadiabatic couplings (NACs), spin–orbit couplings (SOCs) and dipole moments (μ). The dynamics calculation starts with an input geometry, for which the two NNs provide all electronic quantities. If the outcomes of both NNs are sufficiently similar, the configurational space around this input geometry is adequately represented by the training set and the electronic quantities are used for a propagation time step. If not, the nuclear configuration is recomputed with quantum chemistry, phase corrected and included in the training set – a process referred to as adaptive sampling. The NNs are then re-trained and a new dynamics cycle is started.
Fig. 2
Fig. 2. Molecular orbitals representing two different electronic states of the methylenimmonium cation, CH2NH2+. Panel A shows molecular geometries (with slightly different bond lengths) that are given as an input to a quantum chemistry program. The results for properties corresponding to off-diagonal matrix elements of the Hamiltonian are shown in panel B. Random signs are obtained due to random assignments of the phases of the involved wave functions. As can be seen in panel C, these random switches can be removed by phase correction, and smooth relations between a molecular geometry and any property can be found.
Fig. 3
Fig. 3. Population dynamics of CH2NH2+ based on deep NNs and traditional quantum chemistry: comparison between results obtained from (A) QC1 (90 trajectories) and NN (3846 trajectories) and (B) QC1 (90 trajectories) and QC2 (88 trajectories). For completeness, the populations from 90 trajectories propagated with NNs are given in Fig. S5A in the ESI along with geometrical analysis along the trajectories in Fig. S5B.
Fig. 4
Fig. 4. Nonadiabatic molecular dynamics simulations using deep NNs for one nanosecond. After excitation to the S2 state, ultrafast internal conversion to the S1 state takes place, followed by recovery of the S0 state within 300 fs. Until 10 ps, an ensemble of 200 trajectories is analyzed, followed by the population averaged from 2 trajectories.
Fig. 5
Fig. 5. Potential energy scans around the minimum energy conical intersections obtained with QC1 of the S2 and S1 states (A and B) and S1 and S0 states (C and D). Panels A and C show the PESs calculated with QC1, while panels B and D illustrate NN potentials. See the caption of Fig. S7 in the ESI for clarification of the dihedral angle.
Fig. 6
Fig. 6. Scatter plots showing the distribution of hopping geometries obtained with QC1, QC2, and NN as well as optimized S1/S0 (A) and S2/S1 (B) minimum energy conical intersections (CIs) along with the geometries that make up the training set with 4000 data points. The actual geometry is depicted on top (geometrical parameters are given in Fig. S7B†). A zoom-in of the regions near the optimized points is shown in Fig. S7A in the ESI together with a definition of the dihedral and pyramidalization angles.
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