Accelerating ab initio QM/MM Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semi-empirical QM/MM Hamiltonian

Abstract

Molecular dynamics (MD) simulations employing ab initio quantum mechanical and molecular mechanical (ai-QM/MM) potentials are considered to be the state of the art, but the high computational cost associated with the ai-QM calculations remains a theoretical challenge for their routine application. Here, we present a modified protocol of Multiple Time Step (MTS) method to accelerate ai-QM/MM MD simulations of condensed-phase reactions. Within a previous MTS protocol [Nam, J. Chem. Theory Comput., 2014, 10, 2175], reference forces are evaluated using a low-level (semi-empirical QM/MM) Hamiltonian and employed at inner time steps to propagate the nuclear motions. Correction forces, which arise from the force differences between high-level (ai-QM/MM) and low-level Hamiltonians, are applied at outer time steps, where the MTS algorithm allows the time-reversible integration of the correction forces. To increase the outer step size, which is bound by the highest-frequency component in the correction forces, the semi-empirical QM Hamiltonian is re-calibrated in this work to minimize the magnitude of the correction forces. The remaining high frequency modes, which are mainly bond stretches involving hydrogen atoms, are then removed from the correction forces. When combined with Langevin or SIN(R) thermostat, the modified MTS-QM/MM scheme remains robust with an up to 8 fs (with Langevin) or 10 fs (with SIN(R)) outer time step (with 1 fs inner time steps) for the chorismate mutase system. This leads to an over 5-fold speedup over standard ai-QM/MM simulations, without sacrificing the accuracy in the predicted free energy profile of the reaction.

Machine-Learning-Assisted Free Energy Simulation of Solution-Phase and Enzyme Reactions

“…To avoid such steep costs of direct ai -QM/MM free energy simulations, Gao, Warshel, and others − developed indirect free energy simulations, where sampling is carried out using a reference semiempirical QM/MM ( se -QM/MM) potential and then the free energy result is corrected with an se -QM/MM → ai -QM/MM thermodynamic perturbation or an interpolation between the two levels of potential, for example along the energy-minimized reaction path. , Alternatively, one can adopt the multiple-time-step simulation methodology from Tuckerman, − Schlick, , Nam, Roux, Rothlisberger, and others, where se -QM/MM trajectory propagation at regular/inner time steps is coupled with ai -QM/MM trajectory corrections at outer time steps. Needless to say, the accuracy of both indirect and multiple-time-step simulations is controlled by the quality of the se -QM/MM potential in use.…”