Treatment of quantum zero‐point energy constraint in simulations of molecular dynamics

Abstract

Purpose

It has been well known that the quantum zero‐point energy (ZPE) cannot be conserved in simulations of atoms and molecules dynamics based on classical mechanics. The purpose of this paper is to examine fundamental issues related to the treatment of quantum ZPE constraint in simulations of atoms and molecules dynamics.

Design/methodology/approach

The ZPE is well known to be a quantum mechanical expectation value that is equivalent to an ensemble average when this value is interpreted to classical mechanics. An important point is that the ensemble‐averaged energies on simulations are expected to obey the ZPE criteria rather than those of individual simulation. The point is elucidated using quasiclassical trajectory calculations with a popular hydrogen atom‐diatom direct collision process incorporating a potential energy surface of a triatomic hydrogen system.

Findings

The results obtained by using standard classical trajectory calculations agree well with the quantum calculations. Using them, the author found that the classical results remain valid even if some trajectory calculations have vibrational energies that are less than the ZPE.

Originality/value

It is found that the ensemble‐average of each trajectory calculation can provide results that are consistent with quantum mechanical ones that obey the ZPE criteria, without the introduction of any additional constraint conditions for atoms and simulation algorithms.

Citation

Tada, S. (2011), "Treatment of quantum zero‐point energy constraint in simulations of molecular dynamics", Engineering Computations, Vol. 28 No. 4, pp. 508-523. https://doi.org/10.1108/02644401111131911