Reduced local energy as a criterion for the accuracy of approximate H2 wave-functions

The goodness of the local fit of an approximate wave-function, documentclass{article}pagestyle{empty}begin{document}$ tilde psi $end{document}, to the exact function, ψ₀, is documentclass{article}pagestyle{empty}begin{document}$ |tilde psi - psi _0 | $end{document}. From this quantity the global accuracy of documentclass{article}pagestyle{empty}begin{document}$ tilde psi $end{document} is defined and a “working supposition” is presented, which quantitatively relates the global accuracy to the accuracy of expectation values. Two criteria based on the accuracy of the reduced local energy and the density respectively, are presented as alternatives to documentclass{article}pagestyle{empty}begin{document}$ |tilde psi - psi _0 | $end{document}. The relative global accuracies of eight wave-functions for H₂ are determined using the two criteria. The ‘working supposition’ is applied and predictions are made concerning the relative accuracies of the expectation values of the following operators: z², r², x² + y², 3z² ?; r², ξ, r, r, and E_L (the reduced local energy). The success rate is high (>90%) except for those operators which are sensitive to interelectron coordinates or derivatives of the wave-function.