Periodic orbits and vibrational wave functions for DCP: nonlinear resonances in isotopically substituted molecules

Abstract

We investigate, by means of classical and quantum mechanics, how isotopic substitution (H/D) affects the vibrational dynamics of HCP. The analysis of periodic orbits, including the location of the principal families as well as saddle node bifurcations, reveals a totally different picture for the phase-space resonance structure for HCP and DCP. While HCP is characterized by a 1:2 resonance between the CP stretch and the bending mode, DCP shows a 1:2 resonance between the two stretching degrees of freedom. Saddle node bifurcations, which are associated with large-amplitude motion of H/D moving from the C- to the P-end, appear at considerably higher energies in DCP than in HCP. These results are in accord with exact quantum mechanical calculations of the vibrational levels.