Reproducibility of Hybrid Density Functional Calculations for Equation-of-State Properties and Band Gaps

TL;DR

This study benchmarks the numerical reproducibility of four independent implementations of hybrid density functional calculations, focusing on properties like equations of state and band gaps for crystalline solids, revealing both promising accuracy and current limitations.

Contribution

It provides a systematic comparison of HSE hybrid functional implementations, highlighting the impact of numerical approximations and pseudopotential choices on reproducibility.

Findings

Band gaps are consistently reproduced across codes.

Lattice constants and bulk moduli show larger, code-dependent deviations.

Current implementations' precision limits the assessment of HDF physical accuracy.

Abstract

Hybrid density functional (HDF) approximations usually deliver higher accuracy than local and semilocal approximations to the exchange-correlation functional, but this comes with drastically increased computational cost. Practical implementations of HDFs inevitably involve numerical approximations -- even more so than their local and semilocal counterparts due to the additional numerical complexity arising from treating the exact-exchange component. This raises the question regarding the reproducibility of the HDF results yielded by different implementations. In this work, we benchmark the numerical precision of four independent implementations of the popular Heyd-Scuseria-Ernzerhof (HSE) range-separated HDF on describing key materials' properties, including both properties derived from equations of states (EOS) and band gaps of 20 crystalline solids. We find that the energy band gaps obtained by the four codes agree with each other rather satisfactorily. However, for lattice constants and bulk moduli, the deviations between the results computed by different codes are of the same order of magnitude as the deviations between the computational and experimental results. On the one hand, this means that the HSE functional is rather accurate for describing the cohesive properties of simple insulating solids. On the other hand, this also suggests that the numerical precision achieved with current major HSE implementation is not sufficiently high to unambiguously assess the physical accuracy of HDFs. It is found that the pseudopotential treatment of the core electrons is a major factor that contributes to this uncertainty.