Catastrophe map and the role of individual resonances in C2H2 bending dynamics

Abstract

A catastrophe map analysis is presented of the birth of new modes in bifurcations of the normal modes of the acetylene pure bending system using a spectroscopic fitting Hamiltonian that is nonseparable with multiple resonances. The map splits into two independent maps for subspaces defined by the resonance frequency conditions. Nonetheless, both resonance couplings act on each of the resonance subspaces, since the system is nonseparable. With this generalized notion of independent resonances, the map accounts for partial resemblances to single resonance models but maintains the full complexity inherent in the nonseparable Hamiltonian. This suggests a way to extend both the generalized Fermi resonance and the catastrophe map analysis to systems with higher degrees of freedom.