  Static correlation is a difficult problem for density-functional theory (DFT)
as it arises in cases of degenerate or quasi-degenerate states where a
multideterminantal wave function provides the simplest reasonable first
approximation to the true interacting wave function. This is also where
Kohn-Sham DFT may also fail to be noninteracting v-representible (NVR). In
contrast, Kohn-Sham DFT typically works well for describing the missing dynamic
correlation when a single-determinantal reference wave function provides a good
first approximation to the true interacting wave function. Multiplet sum method
(MSM) DFT [Theor. Chim. Acta 4, 877 (1977)] provides one of the earliest and
simplest ways to include static correlation in DFT. MSM-DFT assumes that DFT
provides a good description of single-determant energies and uses symmetry and
simple ansatzes to include the effects of static correlation. This is
equivalent to determining the off-diagonal matrix elements in a small
configuration interaction (CI) eigenvalue problem. We have developed a
diagrammatic approach to MS-DFT facilitates comparison with wave function CI
and so allows educated guesses of off-diagonal CI matrix elements even in the
absence of symmetry. In every case, an additional exchange-only ansatz (EXAN)
allows the MSM-DFT formulae to be transformed into wave function formulae. This
EXAN also works for transforming time-dependent DFT into time-dependent
Hartree-Fock. Although not enough to uniquely guess DFT formulae from wave
function formulae, the diagrammatic approach and the EXAN provide important
constraints on any guesses that might be used. Some alternative guesses are
tried out for problems concerning the ground and excited states of H2 , LiH,
and O2 in order to assess how much difference might be involved for different
DFT guesses for off-diagonal matrix elements.
