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

Abstract

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 H 2 + H 2 , 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 H 2 and LiH are also presented.

The Fractional Occupation Number Weighted Density as a Versatile Analysis Tool for Molecules with a Complicated Electronic Structure

“…The ρ FOD value additionally indicates the localization and the extent of the SEC effects. The PESs for double‐bond twists calculated by using FT‐DFT are smooth and parallel to CASSCF/NEVPT2 surfaces, as demonstrated for the examples of C 2 H 4 , TCNE, and retinal. Indeed, the robustness of FT‐DFT for PES computations has recently been the subject of several studies that used methods related to the FOD analysis . It has been compared with standard single‐reference methods in the exploration of the PES for the molecular‐dynamics‐based prediction of mass spectra, which due to many bond‐breaking events definitely requires exploration beyond single‐reference methods, see Ref.…”