N -electron zero-momentum energy expression: A criterion for assessing the accuracy of approximate wave functions

A derivation and discussion of Armstrong's N-electron zero-momentum energy expression is presented. This functional Ezm(χ) is linear in the wave function χ, and thus is easier to compute and more sensitive to wave-function error than the variational upper bound Eᵥₐᵣ(χ). The smallness of the quantity Δ(χ)=Ezm(χ)-Eᵥₐᵣ(χ) provides an a priori criterion for assessment of the accuracy of an approximate wave function. Nontrivial numerical examples are given to illustrate the utility of this criterion.