Accurate and efficient computation of the Kohn-Sham orbital kinetic energy density in the full-potential linearized augmented plane wave method

TL;DR

This paper introduces a highly accurate and efficient computational scheme for the Kohn-Sham orbital kinetic energy density within the full-potential linearized augmented plane wave method, improving meta-GGA calculations and band gap predictions.

Contribution

The authors develop a new computational scheme for $ au_\sigma( )$ that is easy to implement and enhances the accuracy and efficiency of meta-GGA functionals in FLAPW methods.

Findings

Constructed Becke-Johnson meta-GGA exchange potentials with good agreement.

Improved convergence of the Tran-Blaha modified Becke-Johnson potential for band gaps.

The scheme is valuable for developing other meta-GGA functionals in FLAPW.

Abstract

The Kohn-Sham orbital kinetic energy density $\tau_\sigma(\vec{r}) = \sum_{i} w_{i\sigma} \big|\nabla \psi_{i\sigma}(\vec{r}) \big|^2$ is one fundamental quantity for constructing meta-generalized gradient approximations (meta-GGA) for use by density functional theory. We present a computational scheme of $\tau_\sigma(\vec{r})$ for full-potential linearized augmented plane wave method. Our scheme is highly accurate and efficient and easy to implement to existing computer code. To illustrate its performance, we construct the Becke-Johnson meta-GGA exchange potentials for Be, Ne, Mg, Ar, Ca, Zn, Kr, Cd atoms which are in very good agreement with the original results. For bulk solids, we construct the Tran-Blaha modified Becke-Johnson potential (mBJ) and confirm its capability to calculate band gaps, with the reported bad convergence of the mBJ potential being substantially improved. The present computational scheme of $\tau_\sigma(\vec{r})$ should also be valuable for developing other meta-GGA's in FLAPW as well as in similar methods utilizing atom centered basis functions.