Vibration-assisted tunneling

To feature the vibration-assisted tunneling, a convenient object for simulations, is the hydrogenoxalate anion... 

G. V. Mil nikov, O. Kuhn, and H. Nakamura, Ground state and vibrationally assisted tunneling in the formic acid dimer. J. Chem. Phys. 123, 074308 (2005). 

This is quite different from the first two. Due to the reflection symmetry of this potential, the instanton path always remains directed along the Q axis. The transverse q vibration changes only the width of the reactive channel according to Eqs. (4.23) and (4.24). When C > 0, the vibrational-ly adiabatic squeezed barrier is greater than the bare one. This case of dynamically induced formation of the barrier was studied by Auerbach and Kivelson [1985] in context of nuclear physics. The opposite case C < 0, corresponding to the vibration-assisted tunneling, will be considered in Section 8.3. 

These studies provide direct experimental confirmation of the vibration-assisted tunneling model. The fluorescence excitation spectrum... 

This model is based on the weak coupling approximation and it takes into account neither reorganization nor vibration assistance in the sense of Section 2.5. Although the term vibration-assisted tunneling is also applied to the Skinner-Trommsdorf model, this assistance signifies only that vibrations supply the energy needed to provide a resonance. 

Another factor of which a nonclassical theory must take account is the quantisation of the internal modes of D and A, and the consequent relaxation of the Bom-Oppenheimer constraint that the electron must transfer within a fixed nuclear framework. In classical theory, the vibrational modes of D and A are treated as classical harmonic oscillators, but in reality their quantisation is usually significant (that is, one or more of the vibration frequencies v is sufficiently high that the classical limit hv IcT does not apply). Electron transfer then requires the overlap, not only of the electronic wavefunctions of R and P, but also of their vibrational wavefunctions. It is then possible that nuclear tunnelling may assist electron transfer. As shown in Fig. 4.12, the vibrational wave-functions of R and P extend beyond the classical parabolas and overlap to some extent. This permits nuclear tunnelling from the R to the P surface, particularly in the region just below the classical intersection point. Part of the reorganisation of D and A, required prior to ET in the classical picture, may then occur simultaneously withET, by the nuclei tunnelling short (typically < 0.1 A) distances from their R to their P positions. 

---