Wave packet dynamics and phase space structure of HCN molecule

Abstract

The solution of the time-dependent Schrödinger equation by a mixed method of close coupling and discretization techniques is obtained for initial Gaussian wave packets localized at particular regions of phase space of HCN which is treated as a system with three vibrational degrees of freedom. This allows us to explore the correspondence of the classical phase space to quantum mechanics. The phase space structure is described by following the principal families of periodic orbits and some of their bifurcations. Irregular families of periodic orbits, those which are not associated with the principal or bifurcating families, are found at the energy of 1.87 eV, which is 0.37 eV above the barrier of isomerization of HCN to HNC. All irregular periodic orbits are of rotating type. It is shown that the wave packets initialized in the HCN well are trapped in that side of the potential for considerable time, even for energies 0.2 eV above the barrier of isomerization, in agreement with classical mechanics. Thus periodic orbits not only reveal the phase space structure of HCN but also indicate the localization of eigenfunctions in configuration space.