Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas

TL;DR

This paper evaluates various temperature-dependent quantum pair potentials, introduces an improved Kelbg potential, and applies these in simulations to accurately model thermodynamic properties of dense, partially ionized hydrogen plasmas.

Contribution

It presents a new simple temperature-dependent fit for the improved diagonal Kelbg potential and demonstrates its effectiveness in simulations of hydrogen plasmas.

Findings

The improved Kelbg potential accurately reproduces the exact pair potential across temperatures.

Classical MD with spin-dependent potentials effectively models hydrogen's internal energy at partial ionization.

Quantum potentials relate to effective potentials in density functional theory.

Abstract

Extending our previous work \cite{filinov-etal.jpa03ik} we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: i) the diagonal Kelbg potential, ii) the off-diagonal Kelbg potential iii) the {\em improved} diagonal Kelbg potential, iv) an effective potential obtained with the Feynman-Kleinert variational principle v) the ``exact'' quantum pair potential derived from the two-particle density matrix. For the {\em improved} diagonal Kelbg potential a simple temperature dependent fit is derived which accurately reproduces the ``exact'' pair potential in the whole temperature range. The derived pseudopotentials are then used in path integral Monte Carlo (PIMC) and molecular dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about $60 000$ K. Finally, we point out an interesting relation between the quantum potentials and effective potentials used in density functional theory.