Table 8.7.3.2

Coppens, P.; Su, Z.; Becker, P. J.

doi:10.1107/97809553602060000615

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 8.7, p. 719

Table 8.7.3.2

P. Coppens,^a Z. Su^b and P. J. Becker^c

^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

Table 8.7.3.2 | top | pdf |
Expressions for the shape factors S for a parallelepiped with edges δ_x, δ_y, and δ_z (from Moss & Coppens, 1981)

j₀ and j₁ are the zero- and first-order spherical Bessel functions: j₀(x) = sin x/x, j₁(x) = sin x/x² − cos x/x; V_T is volume of integration.

$[\hat y]$	Property	$[S[\hat y({\bf r}), {\bf h}]]$
1	Charge	$[V_T\,j_0(2\pi h_x\delta_x)\, j_0(2\pi h_y\delta_y)\, j_0(2\pi h_z\delta_z)]$
r _α	Dipole μ_α	$[\eqalign { -i&V_T\delta_\alpha\,j_1(2\pi h_\alpha\delta_\alpha) \cr & \times\, j_0(2\pi h_\beta\delta_\beta)\,j_0(2\pi h_y\delta_y)}]$
r _α r _β	Second moment μ_αβ off-diagonal	$[\eqalign { -V_T&\delta_\alpha\delta_\beta\,j_1 (2\pi h_\alpha\delta_\alpha) \cr \times\,& j_1(2\pi h_\beta\delta_\beta)\,j_0(2\pi h_\gamma \delta_\gamma) }]$
r _α r _α	Second moment μ_αα diagonal	$[\eqalign { -V_T&\delta^2_\alpha\bigg\{\displaystyle{j_1(2\pi h_\alpha\delta_\alpha) \over \pi h_\alpha \delta_\alpha} - j_0(2\pi h_\alpha\delta_\alpha)\bigg\} \cr \quad \times\, &j_0(2\pi h_\beta\delta_\beta)\,j_0(2\pi h_\gamma\delta_\gamma) }]$