Other types of model

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. 730

Section 8.7.4.5.3. Other types of model

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

8.7.4.5.3. Other types of model

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One may wish to take advantage of the fact that, to a good approximation, only a few molecular orbitals are involved in s(r). In an independent particle model, one expands the relevant orbitals in terms of atomic basis functions (LCAO ): $[\varphi_{i\sigma}=\textstyle\sum\limits_\mu\, c^\sigma_{i\mu}\chi^\sigma_\mu({\bf r}-{\bf R}_\mu) \eqno (8.7.4.69)]$ with σ = $[\uparrow]$ or $[\downarrow]$ , and the spin density is expanded according to (8.7.4.21) and (8.7.4.23). Fourier transform of two centre-term products is required. Details can be found in Forsyth (1980) and Tofield (1975).

In the case of extended solids, expansion (8.7.4.69) must refer to the total crystal, and therefore incorporate translational symmetry (Brown, 1986).

Finally, in the simple systems such as transition metals, like Ni, there is a d–s type of interaction, leading to some contribution to the spin density from delocalized electrons (Mook, 1966). If [s_l] and [s_d] are the localized and delocalized parts of the density, respectively, $[s({\bf r})=as_l({\bf r})+[1-a]s_d({\bf r}), \eqno (8.7.4.70)]$ where a is the fraction of localized spins. s_d(r) can be modelled as being either constant or a function with a very small number of Fourier adjustable coefficients.

References

Brown, P. J. (1986). Interpretation of magnetization density measurements in concentrated magnetic systems: exploitation of the crystal translational symmetry. Chem. Scr. 26, 433–439.Google Scholar

Forsyth, J. B. (1980). In Electron and magnetization densities in molecules and solids, edited by P. Becker. New York/London: Plenum.Google Scholar

Mook, H. A. (1966). Magnetic moment distribution of Ni metal. Phys. Rev. 148, 495–501.Google Scholar

Tofield, B. C. (1975). Structure and bonding, Vol. 21. Berlin: Springer-Verlag.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 8.7, p. 730