Advancing nonadiabatic molecular dynamics simulations in solids with E(3) equivariant deep neural hamiltonians

Non-adiabatic molecular dynamics (NAMD) simulations have become an indispensable tool for investigating excited-state dynamics in solids. In this work, we propose a general framework, N²AMD (Neural-Network Non-Adiabatic Molecular Dynamics), which employs an E(3)-equivariant deep neural Hamiltonian to boost the accuracy and efficiency of NAMD simulations. Distinct from conventional machine learning methods that predict key quantities in NAMD, N²AMD computes these quantities directly with a deep neural Hamiltonian, ensuring excellent accuracy, efficiency, and consistency. N²AMD not only achieves impressive efficiency in performing NAMD simulations at the hybrid functional level within the framework of the classical path approximation (CPA), but also demonstrates great potential in predicting non-adiabatic coupling vectors and suggests a method to go beyond CPA. Furthermore, N²AMD demonstrates excellent generalizability and enables seamless integration with advanced NAMD techniques and infrastructures. Taking several extensively investigated semiconductors as the prototypical system, we successfully simulate carrier recombination in both pristine and defective systems at large scales where conventional NAMD often significantly underestimates or even qualitatively incorrectly predicts lifetimes. This framework offers a reliable and efficient approach for conducting accurate NAMD simulations across various condensed materials.