Energy Expectation Values and the Integral Hellmann–Feynman Theorem: H2+ Molecule

Rothstein, Stuart M.; Blinder, S. M.

Energy Expectation Values and the Integral Hellmann–Feynman Theorem: H2+ Molecule

dc.contributor.author	Rothstein, Stuart M.	en_US
dc.contributor.author	Blinder, S. M.	en_US
dc.date.accessioned	2010-05-06T21:37:38Z
dc.date.available	2010-05-06T21:37:38Z
dc.date.issued	1968-08-01	en_US
dc.identifier.citation	Rothstein, Stuart M.; Blinder, S. M. (1968). "Energy Expectation Values and the Integral Hellmann–Feynman Theorem: H2+ Molecule." The Journal of Chemical Physics 49(3): 1284-1287. <http://hdl.handle.net/2027.42/70096>	en_US
dc.identifier.uri	https://hdl.handle.net/2027.42/70096
dc.description.abstract	It is by now well known that the integral Hellmann–Feynman (IHF) theorem has little quantitative utility for chemically interesting problems, although the formalism potentially affords a ready physical interpretation of changes in molecular conformation. In this paper, the IHF theorem is applied to variational and simple LCAO wavefunctions for the H2+ ground state, which range in quality from crude to essentially exact. The IHF results improve quite dramatically with the quality of the wavefunctions. This suggests that errors in the IHF formula may be of the same order as those in the wavefunction. (In contrast, errors in variationally determined energies are of second order.) Our results suggest a convenient test which can be applied to any revised IHF formalism developed in the future.	en_US
dc.format.extent	3102 bytes
dc.format.extent	285078 bytes
dc.format.mimetype	text/plain
dc.format.mimetype	application/pdf
dc.publisher	The American Institute of Physics	en_US
dc.rights	© The American Institute of Physics	en_US
dc.title	Energy Expectation Values and the Integral Hellmann–Feynman Theorem: H2+ Molecule	en_US
dc.type	Article	en_US
dc.subject.hlbsecondlevel	Physics	en_US
dc.subject.hlbtoplevel	Science	en_US
dc.description.peerreviewed	Peer Reviewed	en_US
dc.contributor.affiliationum	Department of Chemistry, The University of Michigan, Ann Arbor, Michigan	en_US
dc.description.bitstreamurl	http://deepblue.lib.umich.edu/bitstream/2027.42/70096/2/JCPSA6-49-3-1284-1.pdf
dc.identifier.doi	10.1063/1.1670221	en_US
dc.identifier.source	The Journal of Chemical Physics	en_US
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dc.identifier.citedreference	M. P. Melrose and R. G. Parr, Theoret. Chim. Acta 8, 150 (1967).	en_US
dc.identifier.citedreference	S. M. Rothstein and S. M. Blinder, Theoret. Chim. Acta 8, 427 (1967), and Refs. 2–7 therein.	en_US
dc.identifier.citedreference	S. T. Epstein, A. C. Hurley, R. E. Wyatt, and R. G. Parr, J. Chem. Phys. 47, 1275 (1967).	en_US
dc.identifier.citedreference	S. Kim, T. Y. Chang, and J. O. Hirschfelder, J. Chem. Phys. 43, 1092 (1965).	en_US
dc.identifier.citedreference	ΔTΔT contains the volume integral ∫ dτ(ψR∇2ψR′−ψR′∇2ψR),∫dτ(ψR∇2ψR′−ψR′∇2ψR), By Green’s theorem, this can be transformed to a surface integral ∫ (ψR∇ψR′⋅dσ−ψR′∇ψR⋅dσ).∫(ψR∇ψR′⋅dσ−ψR′∇ψR⋅dσ). As the integration is extended over all space, there do indeed arise nonvanishing contributions from surface elements enclosing the nuclei, owing to the cusps in ψ, hence, discontinuities in ∇ψ.∇ψ. However, since ψ and ∇ψ.∇ψ. are both finite at the nuclei, these contributions, and hence ΔT,ΔT, approach zero in the limit as the surface elements about the nuclei are collapsed to points. See also J. O. Hirschfelder and G. V. Nazaroff, J. Chem. Phys. 34, 1666 (1961).	en_US
dc.identifier.citedreference	S.M.R. acknowledges a conversation with Prof. R. M. Pitzer on this and a closely related subject.	en_US
dc.identifier.citedreference	E. A. Magnusson and C. Zauli, Proc. Phys. Soc. (London) 78, 53 (1961).	en_US
dc.identifier.citedreference	D. R. Bates, K. Ledsham, and A. L. Stewart, Phil. Trans. Roy. Soc. (London) A246, 215 (1953).	en_US
dc.identifier.citedreference	J. I. Musher, J. Chem. Phys. 43, 2145 (1965).	en_US
dc.identifier.citedreference	J. P. Lowe and A. Mazziotti, J. Chem. Phys. 48, 877 (1968).	en_US
dc.identifier.citedreference	Further analysis to be published (S.M.R.).	en_US
dc.owningcollname	Physics, Department of

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