Tunnelling distance

A typical situation is when (5i > (5q, so that the tunneling distance Qo is overcome mostly at the expense of intermolecular vibration q. The probability p q) is exponentially small, but it is to be compared with the exponentially small barrier transparency, and reduction of the tunneling distance Qo — qhy promoting vibrations may be very large. 

For example, in the case of H tunneling in an asymmetric 0i-H - 02 fragment the O1-O2 vibrations reduce the tunneling distance from 0.8-1.2 A to 0.4-0.7 A, and the tunneling probability increases by several orders. The expression (2.77a) is equally valid for the displacement of a harmonic oscillator and for an arbitrary Gaussian random value q. In a solid the intermolecular displacement may be contributed by various lattice motions, and the above two-mode model may not work, but once q is Gaussian, eq. (2.77a) will still hold, however complex the intermolecular motion be. 

Suppose now that both types of vibrations are involved in the transition. The symmetric modes decrease the effective tunneling distance to 2Q, while the antisymmetric ones create the Franck-Condon factor in which the displacement 2Qq now is to be replaced by the shorter tunneling distance 2Q, [Benderskii et al. 1991a]... 

Fig. 4.60. Comparison of resonance Raman spectra with and without tip enhancement for 0.5 monolayers of brilliant cresyl blue on a smooth gold film. The tip increased the total Raman intensity by a factor of approximately 15, when positioned at a tunneling distance of 1 nm. Several other bands were made visible as a result of the tip enhancement [4.306].

There is currently much interest in electron transfer processes in metal complexes and biological material (1-16, 35). Experimental data for electron transfer rates over long distances in proteins are scarce, however, and the semi-metheme-rythrin disproportionation system appears to be a rare authentic example of slow electron transfer over distances of about 2.8 nm. Iron site and conformational changes may also attend this process and the tunneling distances from iron-coordinated histidine edges to similar positions in the adjacent irons may be reduced from the 3.0 nm value. The first-order rate constant is some 5-8 orders of magnitude smaller than those for electron transfer involving some heme proteins for which reaction distances of 1.5-2.0 nm appear established (35). 

If hole and electron transfer occurs interduplex, it follows that it will also occur interstrand. The tunneling distances are comparable. This is elaborated in Sec. 4.3. 

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