As a next step beyond GGA, one could make the exchange-correlation energy density depend upon some third ingredient, such as second derivatives of the density or (as suggested by Becke) the positive kinetic energy density of the occupied Kohn-Sham orbitals. The latter choice permits the satisfaction of more exact constraints on the hole density and on the functional for the energy. It also allows a meta-GGA to recognize and give an appropriate GGA-like description to covalent, metallic, and weak or van der Waals bonds. Meta-GGAs are in principle the most accurate of the computationally efficient semi-local functionals. The recent Strongly Constrained and Appropriately Normed (SCAN) meta-GGA is constructed to satisfy all 17 known exact constraints on the energy that a computationally-efficient semi-local functional can. SCAN is also fitted to appropriate norms, systems in which a semi-local functional is expected to be accurate (excluding bonded systems where semi-local functionals work only by imperfect error cancellation). Unlike GGAs, meta-GGAs can (and in SCAN they do) overcome the structure/energy dilemma, providing at the same time accurate structures and accurate binding energies for molecules and solids. Meta-GGAs are expected to be accurate, except when the exact exchange-correlation hole fails to be localized around its electron or when the self-consistent density displays spurious charge transfer.
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