Symmetrized multipole analysis of orientational distributions

Mikko Kara, Kaarle Kurki-Suonio

Research output: Contribution to journalArticleScientificpeer-review

56 Citations (Scopus)


A rigorous treatment of the constraints imposed by site and body symmetry on the orientational distribution of librating molecules is presented in terms of multipole expansions. Radial densities of the site-symmetric dynamic multipole expansion are linear combinations of the radial densities of the body-symmetric static multipole expansion of the same multipole order. The transformation from static to dynamic radial densities is transmitted by libration matrices, which can be included as parameters in a structure factor model. The matrix elements are connected to the rotational dynamics of the molecule. They are expansion coefficients of the orientational distribution in a basis obtained by site and body symmetrization of the real Wigner functions. Both symmetrizations are reduced to selecting terms from a general basis according to simple index rules. Independence of the kind of density function and Fourier invariance make the formalism useful in combined neutron and X-ray diffraction studies.
Original languageEnglish
Pages (from-to)201 - 210
Number of pages10
JournalActa crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography
Issue number2
Publication statusPublished - 1981
MoE publication typeNot Eligible

Fingerprint Dive into the research topics of 'Symmetrized multipole analysis of orientational distributions'. Together they form a unique fingerprint.

Cite this