On the Coulson-Fischer wave function and a local static correlation potential

Abstract

By using the optimized effective potential (OEP) method in conjunction with the Coulson–Fischer wave function, we develop a formalism, OEP-CF, for incorporating both exchange and static correlation effects. A local static correlation potential is presented which affords a qualitatively correct description of dissociative processes. The energies supported by the OEP-CF method are lower than the corresponding Hartree-Fock values and energies obtained from exchange–only OEP methods (x OEP) since, in the OEP-CF formalism, orbital orthogonality restrictions are relaxed. The OEP-CF equations, which determine a multiplicative correlation potential, are compared with those obtained with the more familiar x OEP method. A parametrized form of a local exchange-correlation Coulson–Fischer potential expressed in terms of the external potential is implemented for the diatomic systems H2 and HeH+. Such a representation allows the solution of both the one-electron Schrödinger equation and OEP-CF equations to be simplified. Applications to the dissociation of the H2 molecule and the HeH+ ion using the OEP-CF methodology demonstrate that the method is capable of describing the static correlation with an accuracy comparable with existing multiconfigurational-OEP-based methods. Potential energy curves computed with the OEP-CF method are compared with those obtained from the x OEP method. †