  The accurate prediction of band gaps and structural properties in periodic
systems continues to be one of the central goals of electronic structure
theory. However, band gaps obtained from popular exchange-correlation
functionals (such as LDA and PBE) are severely underestimated partly due to the
spurious self-interaction error (SIE) inherent to these functionals. In this
work, we present a new formulation and implementation of Wannier
function-derived Fermi-L\"{o}wdin (WFL) orbitals for correcting the SIE in
periodic systems. Since our approach utilizes a variational minimization of the
self-interaction energy with respect to the Wannier charge centers, it is
computationally more efficient than the HSE hybrid functional and other
self-interaction corrections that require a large number of transformation
matrix elements. Calculations on several (17 in total) prototypical molecular
solids, semiconductors, and wide-bandgap materials show that our WFL
self-interaction correction approach gives better band gaps and bulk moduli
compared to semilocal functionals, largely due to the partial removal of
self-interaction errors.
