The rotational kinetic energy in the orientationally disordered phase of solid methane. A quasi-classical approach

It is shown that, as a consequence of the orientational correlations, the quantum rotational kinetic energy of interacting molecules in the orientationally disordered phase of solid methane exceeds the free rotor value. The expectation value of kinetic energy is obtained from the initial terms of a quasiclassical high temperature expansion of the free energy. The calculation is based on an analytic function approximating the configuration representation of the statistical density operator of the free spherical top. It is demonstrated that in the classical limit the function tends asymptotically to the true density operator, the error being exponentially dependent on temperature. As an application, the quantum correction to the second moment of an infrared absorption band is estimated.