Excited-state nonadiabatic dynamics in explicit solvent using machine learned interatomic potentials

TL;DR

We demonstrate that FieldSchNet can effectively replace QM/MM electrostatic embedding for excited-state nonadiabatic dynamics in explicit solvent by learning the field-dependent energies and gradients. Using furan in water and five coupled singlet states, the ML/MM approach reproduces key electronic kinetics and structural rearrangements when trained on carefully curated QM/MM data with an augmented loss that includes field-gradient contributions. Comparisons across data-splitting strategies reveal that random splits with full data perform best for dynamics prediction, while trajectory-based splits emphasize robust generalization and expose limitations near crossing seams via energy-gap-weighted metrics. The work provides a practical pathway to scalable, accurate nonadiabatic dynamics in complex environments and highlights active-learning strategies to efficiently sample critical regions of the potential-energy surfaces. The integrated ML/MM framework with SHARC enables accessible, solvent-explicit simulations that retain essential quantum phenomena in excited-state processes with reduced computational cost.

Abstract

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.

Figures (30)

• Figure 1: Depiction of the investigated system, furan, treated quantum mechanically (QM), solvated in water, which is described with molecular mechanics (MM). a) 3D rendering of furan, depicted as balls and sticks, surrounded by the water molecules of the first solvation shell, shown as sticks. The hydrogen bond present in this configuration is highlighted by a black dashed line. Hydrogen, carbon, and oxygen atoms are colored in white, black, and red, respectively. b) Lewis structure of furan with numbered carbon atoms.
• Figure 1: Absorption spectrum of furan based on the lowest 10 excited singlet states for a) solvated in explicit water obtained as average over 100 MM-MD snapshots and b) in the gas phase obtained from 100 Wigner samples.
• Figure 2: Timeline of the different molecular dynamics simulations performed for furan in water. Molecular mechanics (MM) is first used for heating (20 ps) and equilibration (600 ps) steps. The production run is divided into two parts, 400 ps and 2000 ps long. Frames are saved every 4 ps, resulting in 100 and 500 snapshots, respectively, which serve as potential initial conditions for two sets of QM/MM-SHARC trajectories. The number of selected trajectories (colored arrows) depends on whether an excitation can occur within a specific energy window (7.3 to 7.5 eV for set I and 6 to 7 eV for set II.). For furan in water, this results in 46 (set I, out of 600 initial conditions) and 66 (set II, out of 500 initial conditions) trajectories.
• Figure 2: Parity plots for the set I test set for the three "Split by Trajectory" models trained on 100 % of the available frames (every 0.5 fs) from the 36 training trajectories.
• Figure 3: Absorption spectrum of furan in water (solid black line) calculated at BP86/def2-SVP level of theory from the first 100 snapshots of the MM-MD production run. Contributions from different states are indicated by colors as indicated. Energies and oscillator strengths were convoluted with a Gaussian with a full width at half-maximum of 0.2 eV. Shaded vertical areas denote the two energy windows chosen to initiate the QM/MM-TSH dynamics, using the snapshots of set I and II, respectively.