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International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 8.7, p. 715
Section 8.7.3.3.4. Hellmann–Feynman constrainta 732 NSM Building, Department of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260-3000, USA,bDigital Equipment Co., 129 Parker Street, PKO1/C22, Maynard, MA 01754-2122, USA, and cEcole Centrale Paris, Centre de Recherche, Grand Voie des Vignes, F-92295 Châtenay Malabry CEDEX, France |
According to the electrostatic Hellmann–Feynman theorem, which follows from the Born–Oppenheimer approximation and the condition that the forces on the nuclei must vanish when the nuclear configuration is in equilibrium, the nuclear repulsions are balanced by the electron–nucleus attractions (Levine, 1983![[link]](/graphics/greenarr.gif)
). The balance of forces is often achieved by a very sharp polarization of the electron density very close to the nuclei (Hirshfeld & Rzotkiewicz, 1974), which may be represented in the X-ray model by the introduction of dipolar functions with large values of ζ. The Hellmann–Feynman constraint offers the possibility for obtaining information on such functions even though they may contribute only marginally to the observed X-ray scattering (Hirshfeld, 1984).
As the Hellmann–Feynman constraint applies to the static density, its application presumes a proper deconvolution of the thermal motion and the electron density in the scattering model.
References
Hirshfeld, F. L. (1984). Hellmann–Feynman constraint on charge densities, an experimental test. Acta Cryst. B40, 613–615.Google Scholar
Hirshfeld, F. L. & Rzotkiewicz, S. (1974). Electrostatic binding in the first-row AH and A2 diatomic molecules. Mol. Phys. 27, 1319–1343.Google Scholar
Levine, I. L. (1983). Quantum chemistry, 3rd edition. Boston/London/Sydney: Allyn and Bacon Inc.Google Scholar
