On a Vibration-Rotation Hamiltonian for Bimolecular Collisions Analogous to the Wilson-Howard Vibration-Rotation Hamiltonian for Isolated Molecules

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Abstract
A bimolecular vibration-rotation Hamiltonian is derived which is analogous to the Wilson-Howard vibration-rotation Hamiltonian for isolated molecules. The bimolecular Hamiltonian involves the use of a ``complex-fixed'' axis system, i.e., a system with one of its axes along the line joining the centers of mass of the two interacting molecules. The bimolecular vibration-rotation Hamiltonian shows some similarities to the diatomic-molecule vibration-rotation-electronic Hamiltonian, the role of the two atoms in the diatomic molecule being played by the two interacting molecules, the role of the inter-nuclear axis by the line joining the molecular centers of mass, and the role of electronic orbital and spin angular momenta by the vibration-rotation angular momenta of the two interacting molecules. The application of permutation-inversion molecular symmetry group ideas to a bimolecular complex is described.

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