Detailed analysis of polyad-breaking spectroscopic Hamiltonians for multiple minima with above barrier motion: Isomerization in HO2

We present a two-dimensional model for isomerization in the hydroperoxyl radical (HO2). We then show that spectroscopic fitting Hamiltonians are capable of reproducing large scale vibrational structure above isomerization barriers. Two resonances, the 2: 1 and 3: 1, are necessary to describe the pertinent physical features of the system and, hence, a polyad-breaking Hamiltonian is required. We further illustrate, through the use of approximate wave functions, that inclusion of additional coupling terms yields physically unrealistic results despite an improved agreement with the exact energy levels. Instead, the use of a single diagonal term, rather than extra couplings, yields good fits with realistic results. Insight into the dynamical nature of isomerization is also gained through classical trajectories. Contrary to physical intuition the bend mode is not the initial reaction mode, but rather isomerization requires excitation in both the stretch and bend modes. The dynamics reveals a Farey tree formed between the 2: 1 and 3: 1 resonances with the prominent 5: 2 (2: 1 + 3: 1) feature effectively dividing the tree into portions. The 3: 1 portion is associated with isomerization, while the 2: 1 portion leads to localization and perhaps dissociation at higher energies than those considered in this work. Simple single resonance models analyzed on polyad phase spheres are able to account in a qualitative way for the spectral, periodic orbit, and wave function patterns that we observe. (C) 2011 American Institute of Physics. [doi:10.1063/1.3552086]