Extensivity and the contracted Schrödinger equation

Abstract

We provide an extensive formulation of the contracted Schrödinger equation and other reduced eigenvalue equations. Nonextensive (unconnected) terms in these equations cancel exactly, leading to completely connected one- and two-electron equations that together are equivalent to the Schrödinger equation. We discuss how these equations can be solved for the one- and two-electron cumulants. These cumulants yield a two-electron reduced density matrix that is necessarily size consistent, even for an approximate solution. A diagram technique, introduced to aid the formal manipulations, clarifies the connection between density matrix reconstruction and solution of the CSE.