Error estimate of short-range force calculation in inhomogeneous molecular systems

In the present paper, we develop an accurate error estimate of the nonbonded short-range interactions for the inhomogeneous molecular systems. The root-mean-square force error is proved to be decomposed into three additive parts: the homogeneity error, the inhomogeneity error, and the correlation error. The magnitude of the inhomogeneity error, which is dominant in the interfacial regions, can be more than one order of magnitude larger than the homogeneity error. This is the reason why a standard simulation with fixed cutoff radius is either less accurate if the cutoff is too small, or wastes considerable computational effort if the cutoff is too large. Therefore, based on the error estimate, the adaptive cutoff and long-range force correction methods are proposed to boost the efficiency and accuracy of the simulation, respectively. The way of correcting the long-range contribution of pressure is also developed for the inhomogeneous system. The effectiveness of the proposed methods is demonstrated by molecular dynamics simulations of the liquid-vapor equilibrium and the nanoscale particle collision. Different roles of the homogeneity error and inhomogeneity error are also discussed.