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

The zero-momentum energy expression has been proposed as a sensitive criterion for assessing the accuracy of approximate wave functions. The original expression is shown to lead to an indeterminate 0/0 form for all states other than spatially symmetric one-electron doublets and two-electron singlets. This paper presents a modified version which extends its applicability to arbitrary N-electron states with no restriction on spatial symmetry or spin multiplicity. Since it is a linear functional of the wave function, it is more sensitive to wave-function error than is the usual expression for variational energy.