First steps towards achieving both ultranonlocality and a reliable description of electronic binding in a meta-generalized gradient approximation

It has been demonstrated that a meta-generalized gradient approximation (meta-GGA) to the exchange-correlation energy of density functional theory can show a pronounced derivative discontinuity and significant ultranonlocality similar to exact exchange, and can accurately predict the band gaps of many solids. We here investigate whether within the meta-GGA form these properties are compatible with a reasonable accuracy for electronic binding energies. With the help of two transparent and inexpensive correlation functional constructions we demonstrate that this is the case. We report atomization energies, show that reliable bond lengths are obtained for many systems, and find promising results for reaction barrier heights, while keeping the strong derivative discontinuity and ultranonlocality, and thus accuracy for band gaps.