On the libration of 9,10-anthraquinone at five temperatures

Potential energy profiles corresponding to libration of 9,10-anthraquinone about its molecular axes were constructed for the five structures derived from data which were collected at - 170, - 112, -72, - 12.5 and 20.5°C [Lonsdale, Milledge & El Sayed (1966). Acta Cryst. 20, 1-13]. These profiles were represented by fourth-degree least-squares polynomials, whereafter r.m.s. libration amplitudes and rigid rotator frequencies of 9,10-anthraquinone were evaluated in the quadratic approximation. The temperature dependence of the calculated quantities is in most cases close to that of the observed ones thus reproducing, by comparison with observed Raman frequencies, the pseudoharmonic behaviour of 9,10-anthraquinone. Calculated r.m.s. libration amplitudes are only qualitatively comparable to the experimental ones and appear to be somewhat too low. The present representation of energy profiles makes it possible to estimate conveniently the contribution of anharmonicity to the profile shape.