A dynamic theory of the transition state in the phase space: Application to isomerization in the LiNC-LiCN molecule

A theoretical method for systematic calculations of all the periodic orbits resulting in isomerization in the LiNC → LiCN system was suggested. Calculations used the property of hyperbolic orbits at the saddle point separating isomers in the configuration space. These orbits formed invariant stable and unstable manifolds in the phase space, which served as guides in fairly entangled and usually chaotic molecular dynamics. Manifold intersections result in the formation of so-called homoclinic orbits, which, in turn, form infinite families of bifurcation orbits constituting the structural framework of the phase space of the system. This approach allows isomerization reactions in the LiNC-LiCN molecular system to be described in terms of a roadmap determining the transfer of classical density from one local minimum to another.