In this thesis, we study the classical-quantum correspondence of polyatomic molecules to further understand their rotational and vibrational behavior. More specifically, we focus on two different scenarios: (1) completely rigid asymmetric top molecules and (2) molecules with purely vibrational behavior. In the first part, we study the dynamics of the two asymmetric top molecules ortho-aminobenzonitrile (OABN) and para-aminobenzonitrile (PABN) in a static electric field. These structural isomers feature differing asymmetries and dipole moments. We show that the dynamics of each molecule depends on the region of phase space of the initial rotational state, the asymmetry of the molecule, and the direction of the dipole. We also show that the ergodicity of the system varies gradually with energy, except where the rotational energy of the initial state is much less than the Stark interaction. We find that both molecules are far from full chaos for total angular momentum quanta $J\in[0,45]$, which counters the results presented in reference 1. However, the initial rotational states in OABN access much more of the available phase space than in PABN, which is a strong cause for the experimental discrepancies observed in the molecular beam deflection experiment of reference 1. In the second part, we address the 0.01-0.1 cm$^{-1}$ peak splittings found in high-resolution IR spectra of polyatomic molecules. Narrow splittings lead to energy flow on extremely long time scales. For polyatomics molecules, there are two main competing mechanisms that occur over such time scales: (1) dynamical tunneling, which connects classically disconnected regions of phase space by tunneling through dynamical barriers, and (2) Arnol'd Diffusion, which describes diffusion in phase space along a resonance network called the Arnol'd web. As a result of the ubiquitous numerical errors that accumulate during numerical studies of Arnol'd Diffusion, we use a physically motivated non-convex Hamiltonian that features fast diffusion along the Arnol'd web. Fast diffusion is a worst case scenario as a competitor to dynamical tunneling. We show how dynamical tunneling dominates fast diffusion, suggesting that dynamical tunneling is the prime culprit of the narrow peak splittings in high-resolution IR spectra of polyatomic molecules. / Physics
| Identifer | oai:union.ndltd.org:harvard.edu/oai:dash.harvard.edu:1/33493526 |
| Date | 25 July 2017 |
| Creators | Pittman, Suzanne Michelle |
| Contributors | Heller, Eric, Doyle, John, Kaxiras, Efthimios |
| Publisher | Harvard University |
| Source Sets | Harvard University |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation, text |
| Format | application/pdf |
| Rights | open |
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