Calculated hybrid and semilocal functionals andGWelectronic structure of the metal trifluoridesMF3(M=Sc, Y, Al)

A thorough investigation of the effect of exchange and correlation on the electronic structure of wide-band-gap insulators ${\mathrm{ScF}}_{3},\phantom{\rule{0.16em}{0ex}}{\mathrm{YF}}_{3}$, and ${\mathrm{AlF}}_{3}$ is carried out using local, semilocal, and hybrid functionals in the density functional theory framework and the $GW$ approximation with four current plasmon-pole models. It is shown that the hybrid functionals, which attribute more weight to electron exchange, lead to a decent agreement with the state of the art $GW$ results, whereas the Tran-Blaha semilocal functional does not improve significantly the local density approximation results of the insulating transition-metal trifluorides, because of the high localization of the conduction band minimum states which are mainly of $d$ character, and underestimate considerably the valence-band width of the studied materials.