Journal of Mathematical Chemistry

, Volume 50, Issue 4, pp 833–842

Optimization of the temple lower bound

  • M. G. Marmorino
  • Abdullah Almayouf
  • Tyler Krause
  • Doan Le
Original Paper

DOI: 10.1007/s10910-011-9927-z

Cite this article as:
Marmorino, M.G., Almayouf, A., Krause, T. et al. J Math Chem (2012) 50: 833. doi:10.1007/s10910-011-9927-z
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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.

Keywords

Lower bound Temple Helium 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • M. G. Marmorino
    • 1
  • Abdullah Almayouf
    • 1
  • Tyler Krause
    • 1
  • Doan Le
    • 2
  1. 1.Department of Chemistry and BiochemistryIndiana University South BendSouth BendUSA
  2. 2.Department of Mathematical SciencesIndiana University South BendSouth BendUSA