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Reduced local energy as a criterion for the accuracy of approximate H 2 wave‐functions
Author(s) -
Javor Frank,
Thomas Gerald F.,
Rothstein Stuart M.
Publication year - 1977
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560110106
Subject(s) - function (biology) , wave function , energy (signal processing) , physics , atomic physics , quantum mechanics , evolutionary biology , biology
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 A −1 , r 12 −1 , 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.