Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20

Acta Crystallographica. Section A, Foundations and Advances
J Robert Michael, Anatoliy Volkov

Abstract

The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven signifi...Continue Reading

References

Aug 24, 2006·Acta Crystallographica. Section A, Foundations of Crystallography·Anatoliy VolkovLouis J Farrugia

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Citations

Mar 7, 2018·Journal of Applied Crystallography·Michał L ChodkiewiczPaulina Maria Dominiak
Oct 5, 2021·Acta Crystallographica. Section D, Structural Biology·Vedran VukovićChristian Jelsch

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