The Rotation of Molecules in Crystals

Abstract

The problem of the rotation of molecules in crystals has been generalized to embrace also polyatomic configurations. Two models, of which the homo‐ and heteropolar diatomic molecules are special cases, are considered. The potential energy expressions are taken to be harmonic functions of the coordinates, satisfying the symmetry of the model under consideration. Two limiting cases exist; one where the crystal fields are small and effecting the motion of the top only slightly; the other where the crystal fields are large, restraining the top to rotate principally about its axis of symmetry, which will oscillate isotropically about its position of equilibrium. The eigenvalues of the problem are approximated for small fields by applying Schrödinger perturbation theory to the rotator and for large fields by applying Schrödinger perturbation theory to the isotropic oscillator in two dimensions. The connection of the eigenvalues for extreme values of the field is considered in detail. The eigenfunctions may on the rotator side be expanded in terms of the hypergeometric functions, and on the oscillator side in terms of associated Laguerre polynomials.