Rationale for mixing exact exchange with density functional approximations

Density functional approximations for the exchange-correlation energy E(XC)(DFA) of an electronic system are often improved by admixing some exact exchange E(X) : E(XC) approximate to E(XC)(DFA) + (1/n)(E(X) - E(X)(DFA)). This procedure is justified when the error in E(XC)(DFA) arises from the lambda = 0 or exchange end of the coupling-constant integral integral(0)(1) d lambda E(XC lambda)(DFA). We argue that the optimum integer n is approximately the lowest order of Gorling-Levy perturbation theory which provides a realistic description of the coupling-constant dependence E(XC,lambda) in the range 0 less than or equal to lambda 1, whence n approximate to 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 pertubation theory with the generalized gradient approximation. (C) 1996 American Institute of Physics.