Ab initio Semiclassical Initial Value Representation: Development of New Methods

  • Author / Creator
    Wong, Stephanie Y Y
  • Between the world of classical and quantum mechanics there lies a region where both are used to provide an accurate (quantum) but computationally tractable (classical) description of motion: semiclassical mechanics. The heart of semiclassical theory is the use of the classical path (or, alternatively, the classical trajectory), in a way to elucidate quantum mechanical properties. At the heart of this theory is the semiclassical expression of the quantum mechanical propagator: e^{-iHt/h_bar}. By reexpressing the propagator in semiclassical form (specifically, the Herman-Kluk initial value representation), we are able to use classical trajectories to determine the vibrational energies of molecules. We first develop the software tools for ab initio molecular dynamics in MMTK. In the process of doing so, we have examined the ground and excited state dynamics of the methyl hypochlorite CH3OCl molecule. Vertical excitation energies and transition dipole moments are calculated at the complete active space self-consistent field (CASSCF)/6-31+G(d) level of theory. With these proven tools, the semiclassical initial value representation (SC-IVR) method for the calculation of vibrational state energies is implemented into this framework. This is the main focus of the thesis. A thorough analysis of the vibrational energies for some of the fundamental, overtone and combination modes of H2CO is completed. Then, the time-averaged variant of SC-IVR is implemented on the same molecular system. Through this study, we have discovered many caveats of SC-IVR calculations which we discuss. We have shown that ab initio SC-IVR is a useful method to calculate vibrational energies and that its values approach that of quantum mechanical methods such as vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI).

  • Subjects / Keywords
  • Graduation date
    Fall 2013
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.