Isolating transits from molecular dynamics data with application to the equation of state

Abstract

In vibration-transit theory of liquid dynamics, the atomic motion consists of two contributions: First-principles vibrational motion in a $3N$-dimensional liquid potential energy valley, plus transits, which operate to move the atoms between valleys. In one time step, when an atom crosses the intersection between two valleys, moving a very small distance, the atom's equilibrium position moves the very large distance between the equilibrium positions of two neighboring valleys. A figure showing this simultaneous two-part motion is presented early in this paper. We recognize the motion of the equilibrium position as the transit motion, and we verify that this motion can be observed and measured. We present a collection of single-atom transit-motion profile graphs extracted from molecular dynamics liquid trajectories. These graphs confirm that vibrations plus transit motions constitute nearly the entire liquid atomic motion. While the transit motion is never fully resolved on the liquid trajectory, it is by definition fully resolved on the trajectory of equilibrium positions. The transit contribution to thermodynamics is calibrated via two adjustable parameters in the transit partition function. The transit contribution to the liquid thermal energy is graphed and discussed. The condensed-matter atomic motion theory of thermodynamic functions for crystals and liquids is outlined with particular attention to recent developments in the equation-of-state program.