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Bounds to electronic expectation values for atomic and molecular systems

✍ Scribed by M. G. Marmorino; Kayleigh Cassella

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 196 KB
Volume: 111
Category: Article
ISSN: 0020-7608
DOI: 10.1002/qua.22924

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✦ Synopsis

Abstract

A generalization of a method to calculate lower bounds to expectation values of non‐negative observables is presented. We consider bounds to three electronic expectation values 〈r^2^〉, 〈r〉, and 〈r^−1^〉 in the helium atom as an example. For both 〈r^2^〉 and 〈r〉, we are able to calculate improved lower bounds. The lower bound to 〈r^−1^〉 does not improve, but we are able to calculate an upper bound which is much closer to the expectation value than the lower bound. Although our generalization allows for improved bounds and/or upper bounds, these bounds to general observables are much less precise than energy bounds and even the expectation values calculated from variational wave functions. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

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