Collective coordinates and an accompanying metric force in structural isomerization dynamics of molecules

Structural isomerization dynamics of three- and four-atom clusters of vanishing total angular momentum is studied in terms of internal coordinates of n-body systems on the basis of a gauge theory. The so-called principal-axis hyperspherical coordinates are employed effectively as collective variables for the study of isomerization reactions. It turns out that the non-Euclidean metric on the internal space gives rise to a force, which works in response to internal motions called the democratic (kinematic) rotations in the internal space. This metric force generally tends to induce an asymmetry in mass balance of a system, and is coupled with the usual potential force to give rise to trapped motions in the vicinity of the transition states of the cluster. This observation provides a different perspective for the so-called recrossing problem in chemical reaction dynamics.