Solid-state performance of a meta-GGA screened hybrid density functional constructed from Pauli kinetic enhancement factor dependent semilocal exchange hole

The semilocal form of an exchange hole is highly useful in developing non-local range-separated hybrid density functionals for finite and extended systems. The way to construct the conventional exact exchange hole model is based on either the Taylor series expansion or the reverse engineering technique from the corresponding exchange energy functional. Although the latter technique is quite popular in the context of generalized gradient approximation (GGA) functionals, the same for the meta-GGA functionals is not so much explored. Thus, in this study, we propose a reverse-engineered semilocal exchange hole of a meta-GGA functional, which only depends on the meta-GGA ingredient ? (also known as the Pauli kinetic energy enhancement factor). The model is subsequently used to design the short-range-separated meta-GGA hybrid density functional. We show that the present method can be successfully applied for several challenging problems in the context of solids, especially for which the GGA based hybrid fails drastically. This assessment proves that the present functional is quite useful for materials sciences. Finally, we also use this method for several molecular test cases, where the results are also as comparative as its base semilocal functional.