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 8.7.3.3.3. Radial constraint

P. Coppens,a Z. Sub and P. J. Beckerc

a 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

8.7.3.3.3. Radial constraint

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Poisson's electrostatic equation gives a relation between the gradient of the electric field ∇2Φ(r) and the electron density at r. [ \nabla ^2\Phi ({\bf r}) =-4\pi \rho ({\bf r}). \eqno (8.7.3.14)]As noted by Stewart (1977[link]), this equation imposes a constraint on the radial functions R(r). For [R_l(r)=N_l r^{n(l)}\exp (-\zeta _lr)], the condition [n(l)\geq l] must be obeyed for [R_l r^{-l}] to be finite at r = 0, which satisfies the requirement of the non-divergence of the electric field ∇V, its gradient ∇2V, the gradient of the field gradient ∇3V, etc.

References

First citation Stewart, R. F. (1977). One-electron density functions and many-centered finite multipole expansions. Isr. J. Chem. 16, 124–131.Google Scholar








































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