The Ornstein-Zernike equation in molecular electronic structure theory

The Ornstein-Zernike equation expresses a simple relationship between direct and full correlation effects of a many-body system. Although it was introduced in the context of fluids, it can be derived through simple physical arguments that are equally applicable to the electrons in a molecule. Direct correlation effects account for the correlation between two particles at a time. If a simple model for direct correlation can be found, the Ornstein-Zernike equation can be used to convert it into a treatment of the full correlation effect. We show that the independent electron pair approximation (IEPA) is a reasonable model for the description of direct correlation effects. IEPA followed by our Ornstein-Zernike treatment is closer to CCSD(T) than is CCSD for valence correlation energies of small molecules.