Tunneling energies

Figure 21. The energy band diagram (only the conduction band is shown) calculated for the silicon/electrolyte interface with a potential drop of 5 V and different radii of curvature. Ec is the conduction bandedge in the bulk and Ecs is the conduction bandedge at the surface. AE AEj, AE1/2, and AE1/5 are the possible tunneling energy ranges for different radii of curvature. The distribution of occupied states at the interface, Dred, is also schematically indicated. After Zhang.24...

Fig.6 The distance dependence of electron-transfer rates in DNA hairpins [51]. The acceptor is a photoexcited derivatized stilbene (SA) or phenanthrene (PA) the electron donor is guanine (G), deazaguanine (Z), or inosine (I). The decay is much more rapid in the Z-PA couple compared to the G-SA couple because the tunneling energy is further from the bridge states in the case of Z-PA...

If the tunneling energy Et lies below the band but close to its minimum, 8e — (Eq — V) — Et V, Green s function G(r,r E) may be obtained according to formula (21) where the energy levels and the wave functions of the band states are only used [20]. Then, the resulting expression is ... 

The simplest potential that we can use to interpret the measured tunnelling spectra is a ID torsional potential with threefold symmetry, V3. For this, the principal tunnelling energy between the rotational ground and the first excited state... 

Leforestier et al [53] have compared their experimental results for vibrational-rotational-tunneling energy levels of the water dimer for all six intermolecular vibrations with the corresponding data obtained from the MCY, RWK2 and ASP-w (I) and ASP-w (II). It turns out that while the structure of the dimer, quantified by the rotational constants, is well represented by all these four potentials, none of them is able to describe the tunneling dynamics of intermolecular vibrations even at a qualitatively correct level of accuracy. 

Fig. 15 Vibronic energy levels versus the warping factor p (both E and P are in units of 4a, where a is rotational quantum) in a JT elementary cell with quadratic coupling E (S> e [after O Brien [62]). Encircled is the domain of a very small tunneling energy gap where the concept of extended vibronic pseudo spin applies...

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