I. Theoretical studies of photoionization. II. The electronic structure of linear polyenes

Citation

Nascimento, Marco Antonio Chaer (1978) I. Theoretical studies of photoionization. II. The electronic structure of linear polyenes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/e7dw-3p39. https://resolver.caltech.edu/CaltechTHESIS:10292009-093916795

Abstract

Part I: The photoionization cross section is shown to be directly related to the imaginary part of the frequency dependent polarizability. Using this relation, an approximate representation of the frequency-dependent polarizability is constructed from a discrete set of transition frequencies and oscillator strengths. This approximate representation is used in an analytical continuation for complex values of the frequency using a sequence of (N+ J/N) Pade Approximants (with J ≥ 1). Once the representation of the frequency-dependent polarizability in the upper half part of the complex plane is known, we can calculate its value along the real axis and consequently the photo- ionization cross section. The great advantage of the method resides on the fact that the use of a discrete representation for the dynamic polarizability explicitly avoids the use of continuum functions. We have applied this method previously in the calculation of photoionization cross sections for the helium atom in its ground state and in the 2^1S and 2^3S metastable states. Calculations for the CO molecule are in progress. Here we present calculations for the H^- atom. For this system we also computed the dynamic polarizability in the normal dispersion region. A study of the basis set dependence is also presented. Part II: Self-consistent ab initio generalized valence bond (GVB) and configuration interaction (CI) calculations are presented for the ground states, valence and non-valence states, Rydberg states and π positive ion states of trans 1, 3-butadiene and all-trans 1, 3, 5-hexatriene molecules. It is shown that the electronic spectra of these molecules can be rationalized in terms of a few valence excited states and a series of Rydberg states. The first singlet excited states of these molecules (1^1B_u) correspond to non-valence, non-vertical states. It was found that to correctly describe the 1^1B_u and the 2^1A_g (valence) states of these molecules it is necessary to correlate not only the electrons of the π system but also the electrons of the (C-C)_σ subspace. It is also shown that the first two bands of the photoelectron spectrum (PE) of the butadiene molecule and the first three bands of the PE spectrum of hexatriene correspond to ionization out of the occupied π orbitals of these molecules. Another important conclusion from our studies is that for this type of system, good quality GVB (n/PP) wavefunctions with the 2n π electrons correlated can be obtained by carrying out a Hartree-Fock calculation on the ground state followed by a GVB (n/PP) calculation on just the 2nπ orbitals (keeping the σ HF space fixed). From this wavefunction accurate values for the transition energies of the valence states can be obtained. Work on all-trans 1, 3, 5, 7-octatetraene now in progress will provide a good test for this scheme.

Thesis Files