Correlation Energy Densities : E Pluribus Unum

For a given electron density n(r), the correlation energy Ec is unique while the correlation energy density n(r)ǫc(r) is not. Exact correlation energy densities for atoms or molecules have been calculated by Baerends et al [1, 2] and by Huang and Umrigar [3] from two wavefunctions: one for the system at full coupling strength and one for its non-interacting counterpart of the same electron density. Here we argue that this “endpoint” correlation energy density differs in its kinetic-energy component from the conventional correlation energy density, constructed from the correlation hole integrated over coupling constant from zero coupling to full coupling strength. To believe otherwise would require a local version of the adiabatic connection formula or coupling-constant integration [4, 5], which we have not been able to derive. While many exact correlation energy densities yield the same correlation energy, the conventional one has a special relevance to density functional theory and also has many known properties. We propose a sophisticated hybrid model which predicts the conventional correlation energy density from the conventional potential energy density of correlation. Our model satisfies all known properties,