The Ornstein–Zernike equation in molecular electronic structure theory

Abstract

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.

Keywords:

• electron correlation
• IEPA
• coupled cluster
• fluids
• Ornstein–Zernike

This article is referred to by:

Molecular Physics Longuet-Higgins Young Author's Prize 2010

Acknowledgements

FRM is grateful for discussions on the Ornstein–Zernike equation with distinguished experts on the statistical mechanics of fluids, namely Prof. Jean-Pierre Hansen (Cambridge), Prof. Bob Evans (Bristol) and Prof. Ben Widom (Cornell). Some of the ideas presented here were developed while FRM was a visiting scholar at Cornell, hosted by Prof. Garnet Chan, and Prof. Chan's financial contribution to that trip and numerous insights on this project are very gratefully acknowledged. We are very grateful to Prof. Hans-Joachim Werner for converting the CCSD code in Molpro into an IEPA code in a period of about 20 minutes. On a personal note, it has been my great pleasure and honor to collaborate with Prof. Werner on local, density fitted and explicitly correlated electronic structure theory over the past years, and I thank him for his support, insight and friendship—FRM.