Abstract
Evaluation of temperature factors from a harmonic lattice-dynamical theory of molecular crystals has been applied to some aromatic hydrocarbons in the non-rigid case: i.e. mixing of lattice vibrations with the lowest-frequency internal modes. The calculations start from known atomic coordinates, unit-cell parameters and symmetry operations, using Cailfano-Neto potentials for in-plane modes, Williams IVa potentials for intermolecular interactions, and an overall value of 0.9 nN Å for any twisting around C-C bonds. Molecular motions inside the crystal are described on the basis of normal coordinates of the isolated molecule, by applying Gwinn's method. For some molecules (benzene and naphthalene) the rigid-body approximation is adequate for the carbon-atom framework, and practically no coupling occurs between the lattice vibrations and the internal motion. For anthracene and phenanthrene, there are differences between rigid-body and non-rigid estimates of temperature factors. Molecular vibration tensors T, L, and S can be calculated, and also a general molecular displacement matrix (tensor). including even the internal modes (W), which permits extension of the rigid-body analysis to non-rigid molecules.
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