Multi-dimensional analyses of large amplitude vibrations

Typescript (photocopy).Computational methods were developed for correctly calculating the reduced masses for the ring-puckering and ring-twisting vibrations and for calculating the kinetic energy expansions for ring-puckering vibrations. Computer programs for two- and three-dimensional potential energy calculations were also developed and these were used to analyze three different ring molecules. For 1,3-disilacyclobutane a three-dimensional analysis of the interactions between the ring-puckering and the totally symmetric ring-deformation and between the ring-puckering and the SiH(,2) in-phase rocking vibrations gave the following potential (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) where x(,1), x(,2), and x(,3) are the ring-puckering, ring-deformation, and SiH(,2) rocking coordinates, respectively. The negative sign of the puckering-deformation crossterm indicates that the vibrations are co-operative while the positive sign on the puckering-rocking crossterm indicates that the vibrations are anti-cooperative. For cyclopentene a two-dimensional analysis of the ring-puckering with the ring-twisting interaction gave: (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) where x(,1) and x(,2) represent the ring-puckering and ring-twisting coordinates, respectively. For 1-silacyclopent-3-ene, additional spectral data were obtained. For this molecule a sideband series corresponding to ring-puckering in the first excited state of the ring-twisting was obtained. Combination bands and the pure puckering bands for the isotopically substituted molecule 1-silacyclopent-3-ene-1-d(,1) were also obtained. The two-dimensional analysis of 1-silacyclopent-3-ene for all the data gave the potential function (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) where x(,1) is the ring-puckering coordinate and x(,2) is the ring-twisting coordinate. The crossterm for both ring-twisting interactions was positive indicating that this vibration and the ring-puckering vibration are anti-cooperative