Accurate localized and delocalized vibrational states of HCN/HNC

Results of the first accurate quantum calculation of the delocalized, large amplitude motion vibrational (J = 0) levels of HCN/HNC, lying above the isomerization barrier, are presented. The recently developed DVR-DGB quantum method [Z. Bačić and J. C. Light, J. Chem. Phys. 85, 4594 (1986)] is employed in this work. A model, empirical surface by Murrell et al. is used. All modes are included; the energy level calculation does not involve any approximations. Over a hundred vibrational levels are calculated accurately for this model surface. A number of them lie above the isomerization barrier; some are extensively delocalized over both HCN and HNC minima. Analysis shows that for HCN/HNC the threshold for significant derealization is determined by the height of the vibrationally adiabatic bending barrier. In addition, the nearest neighbor level spacing distribution is obtained and compared to that of LiCN/LiNC. Various computational aspects of the DVR-DGB approach, which is applicable to any triatomic molecule, are also discussed. The method is very suitable for efficient, accurate treatment of floppy molecules and molecules which can isomerize. The DVR-DGB (i.e., ray eigenvector) basis provides a rapidly convergent expansion for the delocalized (and localized) states. Consequently, a single diagonalization of the DVR-ray eigenvector Hamiltonian matrix, whose size is modest relative to the number of accurately determined energy levels, yields the energies of both localized and delocalized states. Accurate evaluation of the two-dimensional integrals in the potential matrix elements requires only 3-4 Gauss-Hermite quadrature points per dimension.