Journal
ACTA CRYSTALLOGRAPHICA SECTION A
Volume 60, Issue -, Pages 250-256Publisher
BLACKWELL MUNKSGAARD
DOI: 10.1107/S0108767304007688
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Relations between direct and reciprocal basis vectors and the atomic displacement matrix and anisotropic temperature-factor matrix are provided for generic dimension n, introducing a few new symbols. The moments of the probability distribution of the anisotropic thermal ellipsoids are provided as functions of dimension n. For specific dimensions n=2 and n=3, new explicit formulas for the semi-axis lengths and rotation angles of the thermal ellipsoids are derived from the atomic displacement matrix, taking into account certain special cases. For dimension n=3, the Euler angles are defined. The resulting formulas can be used, for example, to display the thermal ellipsoids of atoms or for further analysis of molecular vibrations.
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