Symmetrized multipole analysis of orientational distributions

Mikko Kara, Kaarle Kurki-Suonio

Research output: Contribution to journalArticleScientificpeer-review

52 Citations (Scopus)

Abstract

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
Volume37
Issue number2
DOIs
Publication statusPublished - 1981
MoE publication typeNot Eligible

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Neutrons
X-Ray Diffraction
multipoles
expansion
Molecules
libration
matrices
Invariance
Probability density function
molecules
invariance
formalism
neutrons
X ray diffraction
symmetry
coefficients
diffraction
x rays

Cite this

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title = "Symmetrized multipole analysis of orientational distributions",
abstract = "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.",
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Symmetrized multipole analysis of orientational distributions. / Kara, Mikko; Kurki-Suonio, Kaarle.

In: Acta crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, Vol. 37, No. 2, 1981, p. 201 - 210.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Symmetrized multipole analysis of orientational distributions

AU - Kara, Mikko

AU - Kurki-Suonio, Kaarle

PY - 1981

Y1 - 1981

N2 - 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.

AB - 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.

U2 - 10.1107/S0567739481000491

DO - 10.1107/S0567739481000491

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JO - Acta Crystallographica Section A: Foundations and Advances

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