Flexible-Boundary Quantum-Mechanical/Molecular-Mechanical Calculations:  Partial Charge Transfer between the...

Based on the principle of electronic chemical potential equalization, we propose a flexible-boundary scheme to account for partial charge transfers between the quantum-mechanical (QM) and molecular-mechanical (MM) subsystems in combined QM/MM calculations. The QM subsystem is viewed as an open system with a fluctuating number of electrons and is described by a statistical mixture of ensemble that consists of states of integer number of electrons. The MM subsystem serves as a reservoir that exchanges electrons with the QM subsystem. The electronic chemical potential of the MM subsystem varies whenever charges flow in or out, until equilibrium is established for the electronic chemical potentials between the QM and MM subsystems. Our scheme is demonstrated by calculations of the partial atomic charges for 7 small model systems, each consisting of a singly charged ion and a water molecule, as well as for the Eigen cation, a model system for the solvated structure of hydronium ion in water. Encouraging results are obtained for the partial atomic charges, which are in reasonable agreement with full-QM calculations on those model systems. The averaged mean unsigned deviations between the QM/MM and full-QM calculations are 0.16 e for the partial atomic charges of the entire systems and 0.13 e for the amount of charge transferred between the QM and MM subsystems.