Dynamics of a crystal containing a molecular impurity. II. Molecular vibrations included

Abstract

The dynamics of a crystal containing a molecular impurity is discussed with allowance for the effects of internal vibrations of the molecule. Cartesian co-ordinates are introduced to describe internal vibrations, angular oscillations and centre of mass motions of the impurity, and the displacements of the atoms of the host crystal. Next the Hamiltonian is set up and the equations of motion derived. In this process, use is made of Dirac brackets when dealing with coordinates having redundancy and constraints. From the dynamical matrix, some of the familiar results of the crystal-field approximation are recovered. The application of the partitioning technique is then discussed, and finally comparison is made with results of other approaches.