On the reaction path Hamiltonian

A vector-fiber bundle structure of the reaction path Hamiltonian, which has been introduced by Miller, Handy and Adams, is explored with respect to molecular vibrations orthogonal to the reaction path. The symmetry of the fiber bundle is characterized by the real orthogonal group O(3N - 7) for the dynamical system with N atoms. Under the action of group O(3N - 7), the kinetic energy of the reaction path Hamiltonian is left invariant. Furthermore, the invariant behaviour of the Hamiltonian vector fields is investigated.