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

Abstract

We present a two-dimensional model for isomerization in the hydroperoxyl radical (HO(2)). 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.

Reduced dimension rovibrational variational calculations of the S1 state of C2H2. II. The S1 rovibrational manifold and the effects of isomerization

“…37,38 However, we are less hopeful that such a model could be developed for cis-trans isomerization in S 1 C 2 H 2 due to a number of significant complications: (i) acetylene exhibits an essentially complete mixing of normal modes along the isomerization path, whereas HO 2 , though requiring both stretch and bend excitation to isomerize, dominantly proceeds along the bending coordinate; (ii) acetylene contains other resonances, such as the coupling between trans ν 4 and ν 6 , which are not directly involved with the isomerization but would need to be accounted for in an effective Hamiltonian, complicating any conceivable model; and (iii) perhaps most importantly, the asymmetric double minimum potential of S 1 acetylene is a qualitatively distinct and more difficult system than that of a symmetric double well potential.…”

“…Such difficulties have been noted before, for example, in Jacobson and Child's semiempirical, semiclassical inversion model of large amplitude motion in HCP, 36 and in Barnes and Kellman's approach to the isomerization in HO 2 . 37,38 Though new empirical methods 39 have been proposed to model the multi-mode vibrational level structure resulting from the existence of a saddle point, an ab initio calculation that predicts the global rovibrational energy level structure and the associated wavefunctions is particularly useful for understanding both the physical nature and spectroscopic details of the emergent patterns caused by the isomerization. A further consequence of isomerization in the S 1 state is that cis vibrational levels appear weakly in theà −X spectra via tunneling into the trans well.…”

Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

“…2,3,[11][12][13][14][15][16] It has recently been shown how a polyadbreaking effective Hamiltonian is capable of describing the spectrum of systems with a reaction barrier (e.g., dissociation or isomerization systems). [17][18][19] The traditional description of molecular vibrations in terms of normal modes 20 involves harmonic collective nuclear motions, and works reasonably well for molecules without large mass differences in their constituents. However, when such mass differences are present, an approach based on local modes may be more convenient to explain the patterns appearing in the energy spectrum.…”

Visualizing the zero order basis of the spectroscopic Hamiltonian

“…In this section we describe: (1) The workings of the effective Hamiltonian, starting with the standard spectroscopic Hamiltonian for states confined to a single potential well; (2) the innovations of the generalized effective Hamiltonian that have allowed us to treat isomerizing systems.…”