Sanibel Symposium

The many instances of wave function theory being combined with density functional theory have been recounted in a recent review [Ghosh et al. Chem. Rev. 2018, 118, 7249-7292]. The idea is to try to take advantage of the strengths of both theories. At the level of constrained-search density-functional theory [Levy, Proc. Natl. Acad. Sci USA 1979, 76, 6062-6065] though, there is a synergy between these two theories. Here we attempt to harness that synergy by developing model “hybrid+U” functionals for stretched diatomic and ring molecules. The structure of the functionals for these molecules possess similar features, namely several subsidiary functionals on subspaces of covalent and excitonic wave functions, yielding an exchange hybrid energy, a scaled Hubbard-U , and delocalization influences on the Hubbard-U. These features express both dynamic and static correlation within a single functional. The hybrid exchange functional is obtained by separating a Kohn-Sham determinantal wave function from the multi-reference wave function that underlies the functional. Dissociation behavior is governed by closure of a bonding– anti-bonding gap that, in turn, allows contributions from the fundamental gap in different subsidiary functional to cancel exactly. Because there is an element of wave function theory in the functional, it has a dependence on the external potential, but the dependence weakens as a molecule is stretched.