Table 8.7.3.3

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. 722

Table 8.7.3.3

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 8.7.3.3 | top | pdf |
The matrix M⁻¹ relating d-orbital occupancies P_ij to multipole populations P_lm (from Holladay, Leung & Coppens, 1983)

d-orbital populations	Multipole populations
d-orbital populations	P ₀₀	P ₂₀	P ₂₂₊	P ₄₀	P ₄₂₊	P ₄₄₊
	0.200	1.039	0.00	1.396	0.00	0.00
P_xz	0.200	0.520	0.942	−0.931	1.108	0.00
P _yz	0.200	0.520	−0.942	−0.931	−1.108	0.00
$[P_{x^2-y^2}]$	0.200	−0.039	0.00	0.233	0.00	1.571
P_xy	0.200	−1.039	0.00	0.233	0.00	−1.571

Mixing terms.

	P ₂₁	P ₂₁₋	P ₂₂₊	P ₂₂₋	P ₄₁₊	P ₄₁₋	P ₄₂₊	P ₄₂₋	P ₄₃₊	P ₄₃₋	P ₄₄₋
$[P_{z^{2}/xz}]$	1.088	0.00	0.00	0.00	2.751	0.00	0.00	0.00	0.00	0.00	0.00
$[P_{z^{2}/yz}]$	0.00	1.088	0.00	0.00	0.00	2.751	0.00	0.00	0.00	0.00	0.00
$[P_{z^2/x^2-y^2}]$	0.00	0.00	−2.177	0.00	0.00	0.00	1.919	0.00	0.00	0.00	0.00
$[P_{z^{2}/xy}]$	0.00	0.00	0.00	−2.177	0.00	0.00	0.00	1.919	0.00	0.00	0.00
$[P_{xz/yz}]$	0.00	0.00	0.00	1.885	0.00	0.00	0.00	2.216	0.00	0.00	0.00
$[P_{xz/x^{2}-y^{2}}]$	1.885	0.00	0.00	0.00	−0.794	0.00	0.00	0.00	2.094	0.00	0.00
$[P_{xz/xy}]$	0.00	1.885	0.00	0.00	0.00	−0.794	0.00	0.00	0.00	2.094	0.00
$[P_{yz/x^{2}-y^{2}}]$	0.00	−1.885	0.00	0.00	0.00	0.794	0.00	0.00	0.00	2.094	0.00
$[P_{yz/xy}]$	1.885	0.00	0.00	0.00	−0.794	0.00	0.00	0.00	−2.094	0.00	0.00
$[P_{x^{2}-y^{2}/xy}]$	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	3.142