Comparison and union of the Temple and Bazley lower bounds
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- Marmorino, M.G. J Math Chem (2013) 51: 2062. doi:10.1007/s10910-013-0199-7
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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.