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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 fundamentalquantity 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 wavemethod. Our scheme is highly accurate and efficient and easy to implement toexisting computer code. To illustrate its performance, we construct theBecke-Johnson meta-GGA exchange potentials for Be, Ne, Mg, Ar, Ca, Zn, Kr, Cdatoms which are in very good agreement with the original results. For bulksolids, we construct the Tran-Blaha modified Becke-Johnson potential (mBJ) andconfirm its capability to calculate band gaps, with the reported badconvergence of the mBJ potential being substantially improved. The presentcomputational scheme of $\tau_\sigma(\vec{r})$ should also be valuable fordeveloping other meta-GGA's in FLAPW as well as in similar methods utilizingatom centered basis functions.

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