SCAN meta-GGA, strong correlation, symmetry breaking, self-interaction correction, and semi-classical limit in density functional theory: Hidden connections and beneficial synergies

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA) for the exchange–correlation energy was constructed to satisfy 17 exact mathematical constraints and to fit non-bonded, normally correlated appropriate norms. It provides an excellent predictive description of the ground-state energies and electron spin densities of normally correlated systems in the absence of strong self-interaction error as in most sp atoms and covalent molecules at equilibrium geometries. A good self interaction-corrected SCAN would be exact in all one-electron regions of space, without degrading SCAN’s accuracy in many-electron regions. In other words, it should be accurate for nearly all normally correlated systems. Is it possible that such a self-interaction corrected SCAN would also reliably describe the energetic effects of strong correlation through symmetry breaking, thus killing two birds with one stone? An extreme symmetry-broken limit is semi-classical, with a separated blob of one-electron density for each electron, and the approach to this limit can only be described correctly by a self-interaction-free density functional. This article discusses these hidden connections and speculates on the future possibility of a much more reliable and accurate Kohn–Sham density functional theory.