Barrier height tunneling splitting

The symmetry and height of the rotational barriers and hence the tunnel splittings depend strongly on the orientation of the molecule and its adsorption site. The results of these measurements (a higher resolution experiment is planned) when combined with model calculations based on empirical atom-atom potentials (see below) may be able to provide corroborative evidence for the orientation of an adsorbed molecule as well as details of the molecule-substrate interaction. The principal obstacle to a wider application of the technique may simply be the small number of adsorbed systems in which these tunnel splittings can be observed. 

In connection with the aforementioned example, it is useful to note a simple method for estimating the height of a one-dimensional barrier when the values of A and the barrier width are known [Gomez et al., 1967]. For two displaced identical parabolic terms, the tunneling splitting... 

From (9.7) and (9.8) it follows that at = c, low-frequency TLS s appear with zero-point amplitude Sc — S()(D/hajn)U6. Since the tunneling splitting varies exponentially with the barrier height, as in Eq. (9.3), even a narrow distribution of R values near the critical value c results in creation of a continuous spectrum of tunneling states. 

The various energy levels of the system exhibit a tunnel splitting and the energy eigenfunctions split into two separate manifolds with even and odd symmetry. The height of the barrier determines the energy difference between the lowest even and odd symmetry. This so-called tunnel splitting can be expressed as a tunnel frequency Uf... 

In most cases the ground-state rotational tunnel splitting, as well as the two transitions to the split excited librational state, are observed. Because the tunnel splittings (typically 1-10 cm-1) can be measured with much better accuracy than the librational transitions, the value for the barrier height V2 is usually extracted from the former. Higher terms in the expansion of the potential are introduced only if the librational transitions derived do not agree well with other observations. For... 

If on the other hand AFJ is much smaller than Ipv, the eigenstates 1), 12) essentially coincide with the handed states L), /2). In that case the absolute value of the difference E2 — 1] between the eigenstates is approximately 2 V v - We can estimate the size of the tunneling splitting for typical chiral molecules for instance within the Wentzel-Kramers-Brillouin approximation. If we assume a quartic double well potential with a barrier height of 200 kJ mol a barrier Avidth of 200 pm and a tunneling mass... 

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