Atomic Motion from the Mean Square Displacement in a Monatomic Liquid

TL;DR

This paper introduces V-T theory, which models atomic motion in liquids as a combination of vibrations and transits, and demonstrates its effectiveness in explaining molecular dynamics data for liquid sodium.

Contribution

The paper develops a V-T formalism based on many-body Hamiltonian theory that accurately describes atomic motion in liquids, refining current liquid dynamics models.

Findings

Vibrational motion accounts for initial MSD behavior

Transit motion leads to diffusive random walk at long times

V-T theory aligns with molecular dynamics data for liquid Na

Abstract

V-T theory is constructed in the many-body Hamiltonian formulation, and differs at the foundation from current liquid dynamics theories. In V-T 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.