PERTURBATION-THEORY APPROACH TO DYNAMIC TUNNELING SPLITTING OF LOCAL MODE VIBRATIONAL-STATES IN ABA MOLECULES

We introduce a point of view for treating the dynamical tunneling spli tting of symmetric local mode vibrational states in ABA molecules (A = H typically) which is the one we have employed in treating the vibrat ional spectroscopy of CH overtones in molecules such as (CX3)3YCCH. Na mely, the vibrational coupling corresponding to the dynamical tunnelin g in semiclassical mechanics via many intermediate off-resonance weak transitions between initial and final states can be treated by a stand ard high-order perturbation theory. We apply that method to the presen t simpler problem of tunneling splittings in ABA molecules, and compar e the results with those of exact diagonalization, the semiclassical m ethod, and the periodic orbit quantization. Of all the approximate met hods, the perturbation theory was found to provide the best approximat ion to the results of exact diagonalization for the system treated. Th e relationship between these three methods and application to the prob lem of vibrational relaxation in polyatomic molecules with tunneling m echanism of intramolecular vibrational relaxation is discussed.