Tunneling splittings in model 2D potentials. III.

Vibrational tunneling spectra for a ‘linear’ potential are calculated with the WKB trajectory method for a wide range of coupling strengths between coordinates, and compared to the quantum mechanical computations. Reasonable agreement is found between the WKB and quantum results, both in the tunneling splittings and wave functions at the ‘path-generated’ dividing line. The method is generalized to N-dimensional symmetric potentials with two equivalent minima. The results are exemplified by calculating the vibrational tunneling spectrum in a 3D ‘squeezed’ potential. The inhomogeneous broadening of tunneling doublets in supersonic beams is discussed. In rotationally excited states, the coupling strength depends on the rotational quantum number, because of the vibration-rotation interaction. The resultant line width is formed by an ensemble of coherently tunneling systems with a distribution of coupling strengths determined by the finite rotational temperature.