Advancing Semiempirical Quantum Chemistry with Extended Lagrangian and Machine Learning

Although semiempirical quantum chemistry provides better scalability and speed compared to sophisticated <i>ab initio </i>methods, Born-Oppenheimer Molecular Dynamics (BOMD) simulations within semiempirical formalism still suffer from the computational bottleneck of iterative self-consistent field (SCF) optimization at each time step, limiting their applicability to large-scale simulations. An advanced formulation of Extended Lagrangian Born–Oppenheimer Molecular Dynamics (XL-BOMD), implemented in the PyTorch-based semiempirical quantum chemistry code PySeQM software, eliminates the need for SCF optimization by simultaneously propagating the electronic degrees of freedom along with the nuclear motion. The implementation incorporates several key features, including consideration of finite electronic temperatures, the use of canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for density matrix propagation. With the new XL-BOMD formulated for the Neglect of Differential Diatomic Overlap (NDDO) semiempirical model, we can now simulate large and challenging chemical systems characterized by charge instabilities and low HOMO-LUMO gaps. Applied to molecular dynamics, simulation of 840 carbon atoms, one molecular dynamics time step executes in 4 s on a single GPU.<br/>The PyTorch implementation enables dynamic re-parameterization of semiempirical parameters by interfacing them with machine learning models, thereby enabling training to high-quality ab initio data, including reactive events. This approach leads to enhanced accuracy when compared to using static, pre-optimized semiempirical parameters.<br/>[1] M. Kulichenko, K. Barros, N. Lubbers, N. Fedik, G. Zhou, S. Tretiak, B. Nebgen, A. M. N. Niklasson. “Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation.” <i>J. Chem. Theory Comput.</i> (2023), 19, 11, 3209<br/>[2] A. M. N. Niklasson. “Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics.” <i>J. Chem. Theory Comput.</i> (2020) 6, 6, 3628.<br/>[3] G. Zhou, N. Lubbers, K. Barros, S. Tretiak, B. Nebgen. “Deep learning of dynamically responsive chemical Hamiltonians with semiempirical quantum mechanics.” <i>PNAS </i>(2022) 119, 27, e2120333119.<br/>[4] https://github.com/lanl/PYSEQM/tree/develop