Hamiltonian Grid-Based QM/MM Method with Mean-Field Embedding for Simulating Arbitrary Slab Geometries.

Abstract

The quantum mechanics/molecular mechanics (QM/MM) method is a powerful approach for investigating solid surfaces in contact with various types of media, since it allows for flexible modeling of complex interfaces while maintaining an all-atom representation. The mean-field QM/MM method is an average reaction field model within the QM/MM framework. The method addresses the challenges associated with the statistical sampling of interfacial atomic configurations of a medium and enables efficient calculation of free energies. In this study, we propose a grid-based mean-field QM/MM method that leverages the particle-mesh approach in fractional coordinates, enabling simulations for arbitrary slab models in parallelepiped simulation cells. The charges of the MM atoms are assigned to nearby grid points using a <i>C</i>^<i>n</i> class assignment function with <i>n</i> ≥ 1. The QM-MM electrostatic forces acting on atoms are analytically derived from the total energy using the derivatives of the assignment function. The method is thus rigorously grounded in a fully Hamiltonian formalism, ensuring energy conservation, correct interfacial distribution, and reliable dynamics of the medium atoms sampled from long-time simulations. Furthermore, we demonstrate the feasibility of numerically rigorous free energy calculations through the use of analytical free energy gradients.