Abstract
The Temple formula is perhaps the most common method used in the uncommon endeavor of calculating a lower bound to the ground-state energy of an atomic or molecular system. We generalize the Temple formula by introducing a parameter that can be varied to optimize the lower bound. This generalization does not require any information that is not already used for the traditional Temple lower bound. Examples with the helium cation and neutral atom show that improvement is greatest when the approximate wave function poorly approximates the true ground-state wave function. The examples also show that in some cases the traditional Temple lower bound may already be optimal so that our generalization gives no improvement.
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Marmorino, M.G., Almayouf, A., Krause, T. et al. Optimization of the temple lower bound. J Math Chem 50, 833–842 (2012). https://doi.org/10.1007/s10910-011-9927-z
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DOI: https://doi.org/10.1007/s10910-011-9927-z