Hamiltonian systems isomerization

In order to demonstrate the efficiency of the present theory for systems with many degrees of freedom, we have applied it to a 4-D model of HCN CNH isomerization (i.e., isomerization in a plane). The system is described in terms of two vectors J n=c for the vector from N to C, and Ru for the vector from the center of mass of the system to H. A fixed spatial Cartesian framework is used, with the a -axis set to be parallel to the initial direction of Rn=c, and the y- and 2 -axes perpendicular to it. The center of mass of NC is assumed to be the same as that of the whole system so that the kinetic part of the Hamiltonian is diagonal. The potential energy surface and the dipole moment are taken from [32]. 

Since, as mentioned in Section 2, the spectroscopic states are fully determined by the set mj,Zj,Sj, isomeric systems with identical isotopic compositions share the same molecular Hamiltonian [10], implying that represent stationary states of isolated systems of nuclei... 

In a study of the rate of isomerization of HCN to CNH, Rice and co-workers [19] suggested exploiting a reaction path Hamiltonian as a device to permit extension of classical statistical reaction rate theory from few-dimensional to many-dimensional systems. In that approach the dynamics of the reacting molecule is reduced to that of a system with a complicated but one-dimensional reactive DOF coupled with other effective DOFs. Although their calculations based on this approach yield an accurate description of the isomerization rate as... 

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