For a study of the rotational and the vibrational motions of nonrigid molecular systems in terms of differential geometry, quantum molecular dynamics is set up without using the Eckart frame. The vibrational motions turn out to induce on the internal space a ‘‘gauge’’ field attached to the rotational motions. A method of obtaining the internal Hamiltonian for nonrigid molecules is presented. The space of internal wave functions on which the internal Hamiltonian acts is associated with the space of wave functions that are simultaneous eigenfunctions of P^ and J${^}^2$, where P^ and Ĵ denote the total linear momentum operator and the total angular momentum operator, respectively. The internal Hamiltonian to be obtained shows that the internal motions are coupled with the gauge field.

• Received 21 August 1985

DOI:https://doi.org/10.1103/PhysRevA.33.2262