Low-symmetric coordination polyhedra - pseudosymmetry and idealization

A method is described for the analysis of symmetryless or low-symmetric coordination polyhedra with respect to their pseudosymmetry, regardless of coordination number. With lattice sums of spherical harmonics, symmetry-adapted orientations of the real polyhedra in the various point groups are ascertained by fitting procedures. The idealized polyhedra can then be constructed by averaging and optimizing the positional parameters of those atoms which are symmetry equivalent in the idealized arrangements. The degree of distortion of the real polyhedra with regard to the idealized polyhedra is specified by the mean value of relative atom displacements. The method can assist in the investigation of factors affecting crystal structure and in the interpretation of spectroscopic and magnetic properties of compounds with d and f elements. The analysis is applied to LiCeO₂ where a symmetryless arrangement of the O atoms around the Ce atom occurs with coordination number seven.