ANALYSIS OF THE VIBRATIONAL INTERACTION OF THE RING PUCKERING AND PH INVERSION VIBRATIONS IN 3-PHOSPHOLENE

Abstract

The complete Hamiltonian of internal motion for two vibrations in center of mass coordinates is given by $h=-1/2\eta^{2} \sum\limits^{2}{k,i=1}\left(\frac{\partial}{\partial q{k}}+1/4\frac{\partial ing}{\partial q_{k}}\right)\delta_{K1} \left(\frac{\partial}{\delta q_{1}}-1/4\frac{\partial ing}{\partial q_{1}}\right)+v(q_{1},q_{2}).$ The present work provides a close look at the form of this Hamiltonian when considering the interaction of the ring-puckering and PH inversion vibrations in 3-phospholene. This molecule shows a series of hot bands and difference bands involving these two vibrational modes. In going from the ground state to the excited state of the PH inversion, the ring-puckering transitions increase by as much as $3.3 cm^{-1}$. The far-infrared spectrum directly shows the ring inversion transitions in the PH inversion excited state as well as the ground $state.^{1}$ An appropriate expansion of harmonic oscillator wavefunctions (prediagonalized basis functions) was used as the basis functions for carrying out the two-dimensional analysis which was complicated by the asymmetry of the two-vibrations. In addition to examination of the potential energy terms the kinetic energy terms (including $8_{45}$ and pseudopotential terms) were also evaluated. The current status of this research will be discussed.