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

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.