The self-consistent implementation of exchange-correlation functionals depending on the local kinetic energy density

The self-consistent derivation and implementation of the true Kohn–Sham exchange-correlation potential (local, multiplicative and common for all orbitals) corresponding to a meta-GGA functional depending on the local kinetic energy density is reported. Our approach is based on the optimized effective potential (OEP) method. The method is compared to the less rigorous method of taking functional derivatives with respect to the molecular orbitals. The notable differences between these two approaches are illustrated by calculating nuclear shielding constants for 17 small main-group molecules.