An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter

William A Angermeier,Thomas G White

doi:10.3390/plasma4020020

Abstract

Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool with which to study dynamical processes in warm dense matter beyond the Born–Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigated three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examined each of these approximations in regard to atomic and molecular hydrogen in addition to a dense hydrogen plasma. We found that the biggest improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match experimental pressures of dense hydrogen. Ultimately, we found that semi-empirical scaling parameters are necessary to correct for the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.

Highlights

Warm dense matter (WDM) is a critically important physical regime that bridges the gap between condensed matter and classical plasma physics
We focus our efforts on dense hydrogen, the prototypical test-bed for atomistic models, and investigate the accuracy of Wave packet molecular dynamics (WPMD) as the number of Gaussians in the basis is increased
Dense hydrogen is one of the simplest physical systems, and for this reason, it has become the prototypical test-bed for atomistic models of dense plasmas

Summary

Introduction

Warm dense matter (WDM) is a critically important physical regime that bridges the gap between condensed matter and classical plasma physics. The WDM state is found in several astrophysical environments (e.g., planetary interiors and white dwarfs) [1,2]. It has practical applications for understanding controlled thermonuclear fusion and material processing [3]. Described as a system of strongly coupled ions immersed in a degenerate electron sea, WDM may exist in either a compressed liquid or a highly excited solid state. In both states, the ions have a Coulomb energy comparable to the thermal energy, while the electrons, at temperatures below the Fermi temperature, exhibit strong quantum behavior [4]. Techniques that simulate WDM states must model the slow and longtime behavior of the strongly coupled ions while simultaneously capturing the electrons’

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