Benchmarking Hydrogen-Helium Mixtures with QMC: Energetics, Pressures, and Forces

TL;DR

This study benchmarks various density functionals against quantum Monte Carlo results to evaluate their accuracy in modeling hydrogen-helium mixtures under conditions relevant for giant planets, focusing on energetics, pressures, and structural insights.

Contribution

It provides a comprehensive QMC-based benchmark of density functionals for hydrogen-helium mixtures, highlighting the most accurate functionals and analyzing error trends.

Findings

TPSS, BLYP, and vdW-DF are the most accurate functionals

Errors in enthalpy, energy, and pressure are well-behaved with helium concentration

Major error trends and differences among functionals are identified and analyzed

Abstract

An accurate understanding of the phase diagram of dense hydrogen and helium mixtures is a crucial component in the construction of accurate models of Jupiter, Saturn, and Jovian extrasolar planets. Though DFT based first principles methods have the potential to provide the accuracy and computational efficiency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quantification of the errors introduced. In this work, we present a quantum Monte Carlo based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures at thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC based force estimators and use them to gain insights into how well the local liquid structure is captured by different density functionals. We find that TPSS, BLYP and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative differences exhibited by the major classes of functionals, and estimate the magnitudes of these effects when possible.