Moments of the magnetization density

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

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. C. ch. 8.7, p. 732

Section 8.7.4.7.2. Moments of the magnetization density

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

8.7.4.7.2. Moments of the magnetization density

| top | pdf |

Among the various properties that are derivable from the delocalized spin density function, the dipole coupling tensor is of particular importance: $[D_{nij}({\bf R}_n) = \int\, s({\bf r})\, \displaystyle{ [3\, r_{ni}r_{nj} - r^2_n\, \delta_{ij}] \over r^5_n}\, {\rm d} {\bf r}, \eqno (8.7.4.93)]$ where R_n is a nuclear position and r_n = r − R_n. This dipolar tensor is involved directly in the hyperfine interaction between a nucleus with spin $[{\bf I}_n]$ and an electronic system with spin s, through the interaction energy $[\textstyle\sum\limits_{i, j}\, I_{ni}\, D_{nij}\, S_j. \eqno (8.7.4.94)]$ This tensor is measurable by electron spin resonance for either crystals or paramagnetic species trapped in matrices. The complementarity with scattering is thus of strong importance (Gillon, Becker & Ellinger, 1983).

Computational aspects are the same as in the electric field gradient calculation, ρ(r) being simply replaced by s(r) (see Subsection 8.7.3.4).

References

Gillon, B., Becker, P. & Ellinger, Y. (1983). Theoretical spin density in nitroxides. The effect of alkyl substitutions. Mol. Phys. 48, 763–774.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 8.7, p. 732