Development and testing of new theoretical methods for calculating Franck -Condon factors and density functional methods for calculating (hyper)polarizabilities

This research dissertation is composed of investigations into the polarizabilities (alpha) and second hyperpolarizabilities (gamma) for finite chain oligomers of polydiacetylene (PDA) and polybutatriene (PBT) using new methods in density functional theory (DFT) as well as an investigation into the calculation of Franck-Condon factors (FCFs) with simulation of the photoelectron (PE) spectra of the X˜2A2 ← X˜1A1 band of furan.;We applied a new procedure for calculating FCFs with anharmonicity fully included to simulate the PE spectra for the X˜ 2A2 ← X˜ 1A1 band of furan. Our simulation took into account anharmonic mode-mode coupling as well as Duschinsky rotations at the second-order perturbation theory level. At the present time except for previous work by Luis et al. on ethylene, there are no other practical procedures that incorporate these effects for larger than tetraatomic systems. All 21 vibrational modes were considered but in the end only 4 are needed to reproduce the spectrum. Based on these simulations we were able to improve and expand upon previous assignments as well as suggest further measurements.;It has been observed that conventional exchange-correlation (XC) functionals in DFT overestimate alpha and gamma values. We used the optimized effective potential for exact exchange (OEP-EXX) procedure developed by Yang and Wu to evaluate alpha and gamma for increasingly large PDA/PBT chains. A range of conventional atomic orbital basis sets were used for the exchange potential (X) as well as for the Kohn-Sham molecular orbital (MO) basis with comparisons made to ab initio coupled-perturbed Hartree Fock (CPHF) and correlated values. An informative analysis of basis set issues related to the OEP-EXX procedure was carried out.;The long-range correction (LC) method of Hirao and co-workers for treating electron exchange in DFT combined with the Becke-Lee-Yang-Parr (BLYP) XC functional was used to determine alpha and gamma for PDA/PBT oligomers. The performance of LC-BLYP was characterized by comparison with coupled-cluster calculations including single, double and perturbative triple excitations. Our results show that the tendency of conventional XC functionals to result in large overestimations is reduced but not eliminated. No clear-cut preference of LC-BLYP over HF values was obtained.