  The Pauli kinetic energy enhancement factor
$\alpha=(\tau-\tau^W)/\tau^{unif}$ is an important density ingredient, used to
construct many meta-generalized gradient approximations (meta-GGA)
exchange-correlation (XC) energy functionals, including the very successful
strongly constrained and appropriately normed (SCAN) semilocal functional.
Another meta-GGA functional, known as MGGAC [Phys. Rev. B 100, 155140 (2019)],
is also proposed in recent time depending only on the $\alpha$ ingredient and
based on the generalization of the Becke-Roussel approach with the cuspless
hydrogen exchange hole density. The MGGAC functional is proved to be a very
useful and competitive meta-GGA semilocal functional for electronic structure
properties of solids and molecules. Based on the successful implication of the
ingredient $\alpha$, which is also useful to construct the one-electron
self-interaction free correlation energy functional, here we propose revised
correlation energy for MGGAC exchange functional which is more accurate and
robust, especially for the high and low-density limits of the uniform density
scaling. The present XC functional, named as revised MGGAC (rMGGAC), shows an
impressive improvement for the structural and energetic properties of solids
compared to its previous version. Moreover, the assessment of the present
constructed functional shows to be quite useful in solid-state physics in terms
of addressing several current challenging solid-state problems.
