Abstract
The Lehmann-Maehly approach and Bazley’s method of special choice are matrix eigenvalue problems that allow the calculation of lower bounds to energies of atomic and molecular systems. We introduce a common derivation of their scalar versions using the overlap of a trial function with the unknown ground-state wave function. In the scalar setting, the Lehmann-Maehly approach reduces to the Temple formula. The common derivation allows us to easily unite and improve both methods in several stages within this restricted application. Finally we offer a different union that allows generalization to arbitrary dimension matrix methods. Calculations on the helium atom ground state illustrate the improvements and mergers.
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Marmorino, M.G. Comparison and union of the Temple and Bazley lower bounds. J Math Chem 51, 2062–2073 (2013). https://doi.org/10.1007/s10910-013-0199-7
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DOI: https://doi.org/10.1007/s10910-013-0199-7