A combined experimental and theoretical study of the electronic structure of molecules by electron momentum spectroscopy and density functional theory
Creators: name: Duffy, Patrick
Publisher: name: University of British Columbia
Year: 2009

description: New theoretical models for the instrumental angular resolution function and for the experimental cross-section for electron momentum spectroscopy (EMS) are proposed, tested, and evaluated. For the experimental resolution function, the existing Gaussian Δp method is discussed and found inadequate as it is not representative of the spectrometer itself. A new model for the experimental resolution function, first proposed by Bawagan and Brion (Chem. Phys. 144, 167 (1990)), is considered in detail. An analytic form for the resulting resolution function, which involves the use of Gaussians in θ and φ, is developed, tested, and evaluated, and found to be both more realistic physically and to cause high-level quantum-mechanical calculations of the EMS angular cross-section to come into better agreement with experiment than when the Δp method (commonly employed previously) is used. The new experimental resolution function is further tested, in conjunction with existing theoretical methods, in an EMS study of acetylene. Three common ab initio methods for the calculation of approximate EMS angular cross-sections (Roothaan-Hartree-Fock, configuration interaction, and Green function) are considered. It is found that, for this molecule, the comparatively simple Hartree-Fock method provides an adequate description of the outer-valence electron angular cross-sections, and that the Green Function and multi-reference singles and doubles configuration interaction calculations also discussed are therefore not required when calculating angular cross-sections for acetylene. However, because of the pronounced breakdown of the single-particle model of ionization in the inner-valence region, these latter methods are found to be necessary for a quantitative prediction of the angular cross-sections in that region. Likewise, simple Koopmans' ionization potentials predict the binding energy spectrum of acetylene relatively accurately in the outer-valence region, while correlated treatments are found to be necessary to successfully predict the observed breakdown of the single-particle picture of ionization in the inner-valence region. Because of the general complexity of the calculations necessary for the calculation of EMS binding energies and cross-sections by conventional ab initio methods, and because electron momentum spectroscopy studies are evolving towards more complex systems, including biomolecules, a new method, less computationally intensive than conventional ab initio methods, is proposed for use: density functional theory (DFT). Binding energies and EMS cross-sections are calculated using DFT and compared with the appropriate ab initio (SCF and CI) results. DFT is found to provide very good predictions of binding energies for a wide range of molecules, and to provide EMS cross-sections of comparable quality to Hartree-Fock. The overall charge density provided by DFT within the local density approximation is further tested, in order to better determine the reliability of DFT for both EMS calculations and the prediction of other properties based on the electron density. It is found that while DFT (within the local density approximation) generally predicts outer-spatial properties based on the density with reasonable accuracy, it is unreliable for calculation of properties which depend on an accurate description of the electron density near the nucleus. Use of (spatially) non-local functionals is found to not improve calculated results significantly.