Anharmonic librations and the temperature dependence of NQR frequencies

The temperature dependence of NQR frequencies of nuclei in molecules undergoing quasi-harmonic rotational oscillations is calculated. Following the model proposed by Bayer, the instantaneous orientation of the electric field gradient principal axes is assumed to change from its average orientation as a result of rotational oscillations, while the EFG magnitude remains constant. The eigenstates and energy eigenvalues of a rotator in a potential of the form V(theta)=V-2 theta(2)-V4 theta(4) are calculated by standard perturbation methods, followed by the evaluation of statistical averages of square angular amplitudes. For molecular crystals with more than one molecule in a unit cell the angular displacements are expressed in terms of normal coordinates, and the same procedure is followed. The final expression for the change in the NQR frequency consists of two terms, the first one being related to the harmonic part of the potential and the second one to the quartic term. At the absolute zero it yields a nonzero contribution to [theta(2)], and for high temperatures it reproduces the nonlinear character of nu(Q) (T) observed experimentally. The model has been tested with measurements on solid Cl-2 performed by Nakamura and Chihara, combined with libration mode frequencies measured in Raman spectroscopy by Cahill and Leroi and analysed according to our anharmonic libration picture. The fitting of our equation to experimental data supports Cahill and Leroi's hypothesis about the existence of an undetected libration mode in Cl-2 Raman spectra of frequency near 60 cm(-1).