Va. Benderskii et al., TUNNELING SPLITTINGS IN MODEL 2D POTENTIALS .3. V(X,Y)=LAMBDA(X(2)-X(0)(2))-CXY+1 2KY(2)+(C-2/2K)X(2)/, Chemical physics, 198(3), 1995, pp. 281-295
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 computatio
ns. Reasonable agreement is found between the WKB and quantum results,
both in the tunneling splittings and wave functions at the 'path-gene
rated' dividing line. The method is generalized to N-dimensional symme
tric potentials with two equivalent minima. The results are exemplifie
d by calculating the vibrational tunneling spectrum in a 3D 'squeezed'
potential. The inhomogeneous broadening of tunneling doublets in supe
rsonic beams is discussed. In rotationally excited states, the couplin
g strength depends on the rotational quantum number, because of the vi
bration-rotation interaction. The resultant line width is formed by an
ensemble of coherently tunneling systems with a distribution of coupl
ing strengths determined by the finite rotational temperature.