Geometry of Phase‐Space Transition States: Many Dimensions, Angular Momentum

Abstract

The geometrical structure of a classical transition state is described in details, with a careful introduction of all necessary tools: Hamiltonian dynamics, stability analysis, invariant manifolds, Poincar'e surface of section. Thanks to recent progresses in the understanding of dynamics with many degrees of freedom, possibly including angular momentum, a description of the structure of phase space in the neighborhood of saddle equilibrium points is possible. A transition state that connects different regions of space is built and described, with a progression from 1 degree of freedom to n≥3 degrees of freedom. Applications are found in the isomerization and reaction dynamics of simple molecular systems. The importance of angular momentum is described. Its prominent role is underlined in low energy collisions that prevail is the chemistry of astrophysical gases.