Better band gaps for wide-gap semiconductors from a locally corrected exchange-correlation potential that nearly eliminates self-interaction errors

This work constitutes a comprehensive and improved account of electronic-structure and mechanical properties of silicon-nitride (${Si}_3$ $N_4$) polymorphs via van Leeuwen and Baerends (LB) exchange-corrected local density approximation (LDA) that enforces the exact exchange potential asymptotic behavior. The calculated lattice constant, bulk modulus, and electronic band structure of ${Si}_3$ $N_4$ polymorphs are in good agreement with experimental results. We also show that, for a single electron in a hydrogen atom, spherical well, or harmonic oscillator, the LB-corrected LDA reduces the (self-interaction) error to exact total energy to  ∼10%, a factor of three to four lower than standard LDA, due to a dramatically improved representation of the exchange-potential. (paper)