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.