Knowledge Bank

The complete Hamiltonian of internal motion for two vibrations in center of mass coordinates is given by $h=-1/2\eta 2\sum k,i=12(\partial \partial qk+1/4\partial ing\partial qk)\delta K1(\partial \delta q1-1/4\partial ing\partial q1)+v(q1,q2).$ 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 $3.3cm-1$. 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 $845$ and pseudopotential terms) were also evaluated. The current status of this research will be discussed.