Benchmarking exchange-correlation functionals for hydrogen at high pressures using quantum Monte Carlo

Abstract

The ab-initio phase diagram of dense hydrogen is very sensitive to errors in the treatment of electronic correlation. Recently, it has been shown that the choice of the density functional has a large effect on the predicted location of both the liquid-liquid phase transition and the solid insulator-to-metal transition in dense hydrogen. To identify the most accurate functional for dense hydrogen applications, we systematically benchmark some of the most commonly used functionals using Quantum Monte Carlo. By considering several measures of functional accuracy, we conclude that the van der Waals and hybrid functionals significantly out perform LDA and PBE. We support these conclusions by analyzing the impact of functional choice on structural optimization in the molecular solid, and on the location of the liquid-liquid phase transition.

Simulation and understanding of atomic and molecular quantum crystals

“…Nevertheless, the description of longranged and very weak interactions poses a serious challenge to some families of first-principles methods (also known as ab initio because do not rely on any predetermined knowledge of the atomic forces) as the analytical expression of the corresponding electronic exchange and correlation energies are intricate and difficult to approximate for computational purposes (Klimeš and Michaelides, 2012;Cazorla, 2015). This circumstance converts quantum solids into an ideal playground in which to perform benchmark calculations for assessing the performance of standard and advanced electronic band-structure first-principles methods like, for instance, density functional theory (DFT) and electronic quantum Monte Carlo (eQMC) [Driver et al, 2010;Henning et al, 2010;Clay III et al, 2014;Clay III et al, 2016] (see Sec. III.A).…”

Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces

“…In this study, we employ the same general methodology we used previously in our work on pure hydrogen 16 . Thus, we will in this section focus strictly on simulation details and extensions to the method, leaving the high level justification and detailed explanation of the approach to our previous paper.…”

“…In pure hydrogen, one can at least quantify the impact of density functional errors on the phase diagram, both because of explicit benchmarking studies, and because the phase diagram has been computed by many different groups and methods, ranging from slews of different functionals to highly accurate QMC methods. Various studies have found that the pure hydrogen phase diagram is extremely sensitive to the choice of exchange correlation functional, primarily because of the presence of multiple molecular disassociation and metallization phase transitions and crossovers [14][15][16][17] . In contrast, little is known of the impact that density functionals errors have on the demixing temperature in dense H+He mixtures.…”

The role of van der Waals and exchange interactions in high-pressure solid hydrogen

“…The phase diagram of high-pressure solid hydrogen has mainly been investigated using density functional theory (DFT) with local and semi-local exchange-correlation (XC) functionals [20][21][22][23][24][25][26][27][28][29]38 . In particular, DFT with generalized gradient approximation (GGA) functionals has been widely applied to search for candidate low-energy crystal structures and to calculate their vibrational properties.…”

“…It is now generally accepted that DFT results for high-pressure hydrogen strongly depend on the choice of exchange-correlation functional 26,29,38 and although PBE performs well in identifying candidate structures, it is poor at describing the relative energies of configurations and the properties of the molecular bond 26 . The sensitivity to choice of DFT-XC functional depends on the property being studied, and serious doubts about the accuracy of the results persist.…”