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Nonadiabatic molecular dynamics (NA-MD) is a powerful tool to model far-from-equilibrium processes, such as photochemical reactions and charge transport. NA-MD application to condensed phase has drawn tremendous attention recently for development of next-generation energy and optoelectronic materials. Studies of condensed matter allow one to employ efficient computational tools, such as density functional theory (DFT) and classical path approximation (CPA). Still, system size and simulation timescale are strongly limited by costly ab initio calculations of electronic energies, forces, and NA couplings. We resolve the limitations by developing a fully machine learning (ML) approach in which all the above properties are obtained using neural networks based on local descriptors. The ML models correlate the target properties for NA-MD, implemented with DFT and CPA, directly to the system structure. Trained on small systems, the neural networks are applied to large systems and long timescales, extending NA-MD capabilities by orders of magnitude. We demonstrate the approach with dependence of charge trapping and recombination on defect concentration in MoS₂. Defects provide the main mechanism of charge losses, resulting in performance degradation. Charge trapping slows with decreasing defect concentration; however, recombination exhibits complex dependence, conditional on whether it occurs between free or trapped charges, and relative concentrations of carriers and defects. Delocalized shallow traps can become localized with increasing temperature, changing trapping and recombination behavior. Completely based on ML, the approach bridges the gap between theoretical models and realistic experimental conditions and enables NA-MD on thousand-atom systems and many nanoseconds. 

Non-adiabatic (NA) molecular dynamics (MD) is a powerful approach for studying far-from-equilibrium quantum dynamics in photophysical and photochemical systems. Most NA-MD methods are developed and tested with few-state models, and their validity with complex systems involving many states is not well studied. By modeling intraband equilibration and interband recombination of charge carriers in MoS2, we investigate the convergence of three popular NA-MD algorithms, fewest switches surface hopping (FSSH), global flux surface hopping (GFSH), and decoherence induced surface hopping (DISH) with the number of states. Only the standard DISH algorithm converges with the number of states and produces Boltzmann equilibrium. Unitary propagation of the wave function in FSSH and GFSH violates the Boltzmann distribution, leads to internal inconsistency between time-dependent Schrödinger equation state populations and trajectory counts, and produces non-convergent results. Introducing decoherence in FSSH and GFSH by collapsing the wave function fixes these problems. The simplified version of DISH that omits projecting out the occupied state and is applicable to few-state systems also causes problems when the number of states is increased. We discuss the algorithmic application of wave function collapse and Boltzmann detailed balance and provide detailed FSSH, GFSH, and DISH flow charts. The use of convergent NA-MD methods is highly important for modeling complicated quantum processes involving multiple states. Our findings provide the basis for investigating quantum dynamics in realistic complex systems.