General Internal Motion of Molecules, Classical and Quantum-Mechanical Hamiltonian

The dynamics and the Hamiltonian of a general asymmetric-top molecule undergoing almost arbitrary deformations are discussed. s vector notations are used for translational, rotational, and internal-velocity coordinates. The kinetic energy is formulated by generalizing the G-matrix technique known from the theory of molecular vibrations. A geometrical definition of the rotational coordinates referring to the instantaneous principal axis system is compared with a dynamical definition involving the over-all angular momentum. States of general internal motion are associated by definition with zero linear momentum and zero over-all angular momentum.