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Hybrid density functional (HDF) approximations usually deliver higheraccuracy than local and semilocal approximations to the exchange-correlationfunctional, 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 theadditional numerical complexity arising from treating the exact-exchangecomponent. This raises the question regarding the reproducibility of the HDFresults yielded by different implementations. In this work, we benchmark thenumerical precision of four independent implementations of the popularHeyd-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 gapsobtained by the four codes agree with each other rather satisfactorily.However, for lattice constants and bulk moduli, the deviations between theresults computed by different codes are of the same order of magnitude as thedeviations between the computational and experimental results. On the one hand,this means that the HSE functional is rather accurate for describing thecohesive properties of simple insulating solids. On the other hand, this alsosuggests that the numerical precision achieved with current major HSEimplementation is not sufficiently high to unambiguously assess the physicalaccuracy of HDFs. It is found that the pseudopotential treatment of the coreelectrons is a major factor that contributes to this uncertainty.

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