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

✍ Scribed by Frank Javor; Gerald F. Thomas; Stuart M. Rothstein

• Publisher: John Wiley and Sons
• Year: 1977
• Tongue: English
• Weight: 654 KB
• Volume: 11
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560110106

✦ Synopsis

Abstract

The goodness of the local fit of an approximate wave‐function, \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document}, to the exact function, ψ~0~, is \documentclass{article}\pagestyle{empty}\begin{document}$ |\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 H~2~ 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: z^2^, r^2^, x^2^ + y^2^, 3__z__^2^ −; r^2^, 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.