Atomic motion from the mean square displacement in a monatomic liquid

V-T theory is constructed in the many-body Hamiltonian formulation, and is being developed as a novel approach to liquid dynamics theory. In this theory the liquid atomic motion consists of two contributions, normal mode vibrations in a single representative potential energy valley, and transits, which carry the system across boundaries between valleys. The mean square displacement time correlation function (the MSD) is a direct measure of the atomic motion, and our goal is to determine if the V-T formalism can produce a physically sensible account of this motion. We employ molecular dynamics (MD) data for a system representing liquid Na, and find the motion evolves in three successive time intervals: on the first 'vibrational' interval, the vibrational motion alone gives a highly accurate account of the MD data; on the second 'crossover' interval, the vibrational MSD saturates to a constant while the transit motion builds up from zero; on the third 'random walk' interval, the transit motion produces a purely diffusive random walk of the vibrational equilibrium positions. This motional evolution agrees with, and adds refinement to, the MSD atomic motion as described by current liquid dynamics theories.