Partially deorbitalized meta-GGA

Mejia-Rodriguez and Trickey recently proposed a procedure for removing the explicit dependence of meta-GGA exchange-correlation energy functionals $E_{\rm xc}$ on the kinetic energy density $\tau$. We present a simple modification to this approach in which the exact Kohn-Sham $\tau$ is used as input for $E_{\rm xc}$ but the functional derivative of $\tau$ with respect to the density $\rho$, required to calculate the potential term $\int d^3r'\,\delta E_{\rm xc}/\delta\tau({\bf r}')|_{\rho}\cdot \delta\tau({\bf r}')/\delta\rho({\bf r})$, is evaluated using an approximate kinetic energy density functional. This ensures that the Kohn-Sham potential is a local multiplicative function as opposed to the non-local potential of a generalized Kohn-Sham approach. Electronic structure codes can be easily modified to use the new method. We validate it by quantifying the accuracy of the predicted lattice parameters, bulk moduli, magnetic moments and cohesive energies of a large set of periodic solids. An unanticipated benefit of this method is to gauge the quality of approximate kinetic energy functionals by checking if the self-consistent solution is indeed at the variational minimum.