On the reaction path Hamiltonian for polyatomic molecules

The classical reaction path Hamiltonian formulation of Miller, Handy, and A dams; is reformulated using a linear expansion of the gradient in internal coordinates. It leads to a correspondence between the are length: s, along the intrinsic reaction coordinate, and the whole set of internal coordinate s and, furthermore, to a dynamical equation for s, a second-order Bernoulli -type equation, which is analytically solvable inside the validity range of the quadratic expansion of the-potential. Therefore, by virtue of the abov e correspondence, the time dependence of the whole set of internal coordina tes is easily recovered, by means of a few functional and overlap evaluatio ns. It thus enhances the computational performance of the overall direct dy namics method. The unimolecular 1,2 hydrogen migration, between the (corres ponding) carbene and ethyne oxide, is considered as example for illustrativ e purposes.