Efficient band gap prediction of semiconductors and insulators from a semilocal exchange-correlation functional

A semilocal exchange-correlation functional is proposed with the efficient prediction of the solid-state band gap. The underlying construction of the exchange functional is based on the modeling of the exchange hole and constructing the exchange energy functional. Being a meta-generalized gradient approximation (meta-GGA) level functional, it holds the key feature of the derivative discontinuity through the generalized Kohn-Sham (gKS) formalism. We validate our construction by demonstrating the functional performance for solid-state band gaps and comparing it with the other meta-GGA and hybrid functionals. It is shown that for the semiconductors having narrow, and moderate band gaps, as well as for layered materials the present functional performs as accurately as (or comparable to) the expensive hybrid functional, while for wide-band gap solids, it outperforms the hybrid functional. This indicates that the present functional holds promise for the multiscale modeling of materials with a very low computational cost. Also, the underlying construction is practically very useful as it can be easily implemented in any density functional platform that supports the gKS formalism.