The correlation factor approach: Combining density functional and wave function theory

Several of the limitations of approximate exchange-correlation functionals within Kohn-Sham density functional theory can be eliminated by extending the single-determinant reference system to a multi-determinant one. Here, we employ the correlation factor ansatz to combine multi-configurational, self-consistent field (MCSCF) with approximate density functionals. In the proposed correlation factor approach, the exchange-correlation hole ρ_XC(r, u), a function of the reference point r and the electron-electron separation u, is written as a product of the correlation factor f_C(r, u) and an exchange plus static-correlation hole ρ_XS(r, u), i.e., ρ_XC ^CFXS(r, u) = f_C(r, u)ρ_XS(r, u). ρ_XS(r, u) is constructed to reproduce the exchange-correlation energy of an MCSCF reference wave function. The correlation factor f_C(r, u) is designed to account for dynamic correlation effects that are absent in ρ_XS(r, u). The resulting approximation to the exchange-correlation energy, which we refer to as CFXStatic, is free of empirical parameters, and it combines the qualitatively correct description of the electronic structure obtainable with MCSCF with the advantages of approximate density functionals in accounting for dynamic correlation.