Comparison and union of the Temple and Bazley lower bounds

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.