Fractional Kohn–Sham Occupancies from a Strong-Correlation Density Functional

It is not always possible in Kohn–Sham density-functional theory for the non-interacting reference state to have integer-only occupancies. Cases of “strong” correlation, with very small HOMO-LUMO gaps, involve fractional occupancies. At the transition states of symmetric avoided-crossing reactions, for example, representation of the correct density requires a 50/50 mixing of degenerate HOMOs. In a recent paper (Becke, J Chem Phys 139:021104, 2013) the “B13” strong-correlation density functional of Becke (J Chem Phys 138:074109, 2013 and 138:161101, 2013) was shown to give excellent barrier heights in symmetric avoided-crossing reactions. However, the calculations were performed only at reactant and transition-state geometries, where the fractional HOMO-LUMO occupancies in the latter are 50/50 by symmetry. In the present chapter, we compute full reaction curves for avoided crossings in H₂ + H₂, ethylene (twisting around the double bond), and cyclobutadiene (double-bond automerization) by determining fractional occupancies variationally. We adopt a practical strategy for doing so which does not involve self-consistent B13 computations (not yet possible) and involves minimal cost. Single-bond dissociation curves for H₂ and LiH are also presented.