On the accuracy of the HSE hybrid functional to describe many-electron interactions and charge localization in semiconductors

Hybrid functionals, which mix a fraction of Hartree-Fock (HF) 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 (DMC) 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 DMC results with those obtained with the HSE functional and find a good agreement between both methods for (SiV)$^-$ and (SiV)$^0$, whereas the correct description of 3C-SiC with an extra electron crucially depends on the amount of HF 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 against the many-body \emph{GW} approximation for the description of the position of the defect states in the band gap.