Interaction of translational and rotational modes of a molecular impurity in two-dimensional atomic crystals

Abstract

The interaction between the translational and rotational degrees of freedom of a diatomic homonu-clear molecule that executes a motion at the site of a two-dimensional close-packed atomic matrix located on a close-packed atomic substrate (a molecular substitutional impurity in the crystal field of the two-dimensional lattice of a solidified rare gas) is investigated theoretically. The relationships describing the effective dynamic properties of an impurity rotator in the presence of translational excitations of its center of inertia are derived in the framework of consistent procedures on the basis of the Lagrangian (the functional-integral method) and Hamiltonian (the canonical-transformation method) formalisms. The inclusion of the translational-rotational interaction leads to a radical change in the inertial properties of the molecule. This manifests itself in a change in the form of the operator for the rotational kinetic energy as compared to the corresponding expression for a free rotator. The inertia tensor components for the molecule become functions of molecular orientation, and the molecule, in terms of rotational motion, transforms into a “parametric rotator” whose effective kinetic energy is represented as a generalized quadratic form of the angular momentum (or the angular velocity) components with a symmetry corresponding to the symmetry of the external crystal field. The translational-rotational interaction also results in the renormalization of the parameters of the crystal potential without a change in its initial form.