Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: Tests on solids

A recent study of Mejia-Rodriguez and Trickey [Phys. Rev. A 96, 052512 (2017)] showed that the deorbitalization procedure (replacing the exact Kohn-Sham kinetic-energy density by an approximate orbital-free expression) applied to exchange-correlation functionals of the meta-generalized gradient approximation (MGGA) can lead to important changes in the results for molecular properties. For the present work, the deorbitalization of MGGA functionals is further investigated by considering various properties of solids. It is shown that depending on the MGGA, common orbital-free approximations to the kinetic-energy density can be sufficiently accurate for the lattice constant, bulk modulus, and cohesive energy. For the bandgap, calculated with the modified Becke-Johnson MGGA potential, the deorbitalization has a larger impact on the results.