Accuracy of the Heyd-Scuseria-Ernzerhof hybrid functional to describe many-electron interactions and charge localization in semiconductors

Hybrid functionals, which mix a fraction of Hartree-Fock exchange with local or semilocal exchange, have become increasingly popular in quantum chemistry and computational materials science. Here, we assess the accuracy of the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional to describe many-electron interactions and charge localization in semiconductors. We perform diffusion quantum Monte Carlo calculations to obtain the accurate ground-state spin densities of the negatively charged (SiV)- and the neutral (SiV)0 silicon-vacancy center in diamond and of the cubic silicon carbide (3C-SiC) with an extra electron. We compare our diffusion quantum Monte Carlo results with those obtained with the HSE functional and find a good agreement between the two methods for (SiV)- and (SiV)0, whereas the correct description of 3C-SiC with an extra electron crucially depends on the amount of Hartree-Fock exchange included in the functional. Also, we examine the case of the neutral Cd vacancy in CdTe, for which we assess the performance of HSE versus the many-body GW approximation for the description of the position of the defect states in the band gap.