Highly excited energy levels of the coupled bend and stretch modes in HCN are calculated by a method based on (a) a semiclassical self-consistent field (SCF) approximation, in which each mode is influenced by the other modes through an interaction averaged over their motions, and (b) choosing variationally coordinates which are optimal for the SCF approximation. The optimal coordinates are in general energy- and state-dependent. In the case of HCN, a one-parameter family of spheroidal coordinates is considered, the variationally optimal result being related to motion along the minimum-energy path. The use of optimal coordinates is found to greatly improve the SCF approximation. The calculated OC-SCF energies are in remarkable agreement with the exact values (for levels where the latter are available), and the computational effort required is a modest one. The relative improvement of SCF results by using optimal coordinates increases for high-bending levels. The OC-SCF method is applied also to the calculation of the tunneling rate for the HCN → HNC reaction, with emphasis on the effect of bend-stretch coupling. It is found that the tunneling rate decreases sharply as the stretch is increased. A simply physical interpretation is offered. The validity range and potential applications of the OC-SCF method are discussed in light of the results.
ASJC Scopus subject areas
- Physical and Theoretical Chemistry