Rationale for mixing exact exchange with density functional approximations

Abstract

Density functional approximations for the exchange‐correlation energy E DFA xc of an electronic system are often improved by admixing some exact exchange E x: E xc≊E DFA xc+(1/n)(E x−E DFA x). This procedure is justified when the error in E DFA xc arises from the λ=0 or exchange end of the coupling‐constant integral ∫1 0 dλ E DFA xc,λ. We argue that the optimum integer n is approximately the lowest order of Görling–Levy perturbation theory which provides a realistic description of the coupling‐constant dependence E xc,λ in the range 0≤λ≤1, whence n≊4 for atomization energies of typical molecules. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second‐order perturbation theory with the generalized gradient approximation.