On the classical theory of the rate of isomerization of HCN

We report the results of calculations, using classical mechanics, of the rate of the isomerization reaction HCN↔CNH. The three purposes of the calculations are (i) to test whether or not the Zhao–Rice approximate version of the Davis–Gray theory provides an accurate description of the rate of isomerization when there is a large scale atomic rearrangement; (ii) to determine if the quasi-two-dimensional reaction path representation of dynamical evolution on a multidimensional potential energy surface preserves the major features of the phase space mappings in two dimensions that are the key features of the Davis–Gray formulation of unimolecular reaction rate theory; and (iii) to determine if the reaction path representation is useful when the energy of the system is considerably greater than that along the minimum energy path. We find that both the Zhao–Rice (ZR) and the reaction path calculations of the isomerization rate constant are in reasonable agreement with the rate constant estimated from trajectory calculations; the ZR rate constant is about a factor of 2 smaller, and the reaction path rate constant is about a factor of 2 larger, than that obtained from trajectory calculations. For the few data points available, the energy dependence of the ZR rate constant agrees very well with that obtained from trajectory calculations. The energy dependence of the reaction path rate constant is uniformly accurate over the range we have studied, but is in moderately good agreement with the values obtained from the trajectory studies. We conclude that the reaction path representation remains useful even when the energy of the reacting system is considerably greater than that along the minimum energy path.