Perturbation theory approach to dynamical tunneling splitting of local mode vibrational states in ABA molecules

We introduce a point of view for treating the dynamical tunneling splitting of symmetric local mode vibrational states in ABA molecules (A = H typically) which is the one we have employed in treating the vibrational spectroscopy of CH overtones in molecules such as (CXs),YCCH. Namely, the vibrational coupling corresponding to the dynamical tunneling in semiclassical mechanics via many intermediate off-resonance weak transitions between initial and final states can be treated by a standard high-order perturbation theory. We apply that method to the present simpler problem of tunneling splittings in ABA molecules, and compare the results with those of exact diagonalization, the semiclassical method, and the periodic orbit quantization. Of all the approximate methods, the perturbation theory was found to provide the best approximation to the results of exact diagonalization for the system treated. The relationship between these three methods and application to the problem of vibrational relaxation in polyatomic molecules with tunneling mechanism of intramolecular vibrational relaxation is discussed.