A DERIVATION OF MOLECULAR VIBRATIONAL-ROTATIONAL HAMILTONIANS

Abstract

The problem of collective molecular coordinates is examined within the Hamiltonian formalism by enlarging the number of degrees of freedom and transforming the model to a gauge theory (a theory where the solutions to the equations of motion include arbitrary functions of time). It turns out that in the case of a nonlinear molecule and within the harmonic approximation the most appropriate gauge fixing conditions are the Eckart conditions; thus the Wilson-Howard Hamiltonian is derived. The case of a linear molecule is examined as a second application, and it is found that there are two reasonable gauge choices. The question of the linear molecule as the limiting case of a nonlinear one is also elucidated.