Hindered rotation potential, tunneling

As seen from this table, the WKB approximation is reasonably accurate even for very shallow potentials. At 7 = 0 the hindered rotation is a coherent tunneling process like that studied in section 2.3 for the double well. If, for instance, the system is initially prepared in one of the wells, say, with cp = 0, then the probability to find it in one of the other wells is P( jn, t) = 5sin (2Ar), while the survival probability equals 1 — sin ( Ar). The transition amplitude A t), defined as P( + t) = A t), is connected with the tunneling frequency by... 

Methyl-substituted malonaldehyde (a-methyl-/3-hydroxyacrolein) provides an opportunity to study the role of asymmetry of the potential profile in the proton exchange. In the initial and final states, one of the C-H bonds of the methyl group is in the molecular plane and directed toward the proton position. The double well potential becomes symmetric only due to methyl group rotation over tt/6, when the C-H bond lies in the plane perpendicular to the molecular one. As a result, proton tunneling occurs in combination with CH3 hindered rotation and the... 

Latanowicz investigated the concepts of correlation time, autocorrelation function and spectral densities in the context of the tunnelling jumps through the potential barrier, superimposed on another type of motion. Two specific case were discussed hindered methyl rotation combined with isotropic overall reorientation and jumps within a double-well hydrogen bond potential in connection with librations of the whole molecule. 

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