Tunneling motion

In the nonadiabatic limit ( < 1) B = nVa/Vi sF, and at 1 the adiabatic result k = k a holds. As shown in section 5.2, the instanton velocity decreases as t] increases, and the transition tends to be more adiabatic, as in the classical case. This conclusion is far from obvious, because one might expect that, when the particle loses energy, it should increase its upside-down barrier velocity. Instead, the energy losses are saturated to a finite //-independent value, and friction slows the tunneling motion down. 

A van der Waals attraction between the domain walls undergoing tunneling motions was argued to contribute to the puzzling negative expansivity, observed in a number of low T glasses. 

Coupled Tunneling Motions in Hydrogen-Bonded Dimers... 

Fig. 11. Schematic diagram for (a) the dynamic Jahn-Teller effect and (b) the Moskalenko-Suhl-Kondo mechanism. In the former, the distorted Cg molecule undergoes the tunneling motion between three equivalent configurations. This results in the formation of the orbital-singlet state. In the latter, as shown by the black arrows, the Cooper pairs are transferred from one Fermi sphere to another, which is the pair-transfer process, a remarkable feature of multiband superconductors, and stabilizes the superconductivity. Also, as shown by the white arrows, the Cooper pairs are scattered coherently within each Fermi sphere, which is the pair-scattering process in usual superconductors.

Thus, the general curve of E vs qH, as schematically represented in Figure 5-14, can be constructed without recourse to more complicated cluster rearrangements. This suggests that the tunneling motion is simple and does not involve solvent reorganization or fluctuations. 

Equation (1-13) or its body-fixed equivalent is of little use for Van der Waals complexes, as it discriminates one nuclear coordinate, e.g. y = 1. Specific mathematical forms of Hamiltonians describing the nuclear motions in Van der Waals dimers have been developed (7). This point will be discussed in more details in Section 12.4. Here we only want to stress that whatever the mathematical form of the Hamiltonian is used to solve the problem of nuclear motions, the results will be the same, if the Schrodinger equation is solved exactly. However, in weakly bound complexes there is a hierarchy of motions due to the strong intramolecular forces which determine the internal vibrations of the molecules, and to much weaker intermolecular forces which determine their relative translations and rotations. This hierarchy allows to make a separation between the intramolecular vibrations with high frequencies and the intermolecular modes with much lower frequencies. Such a separation of the fast intramolecular vibrations and slow rotation-vibration-tunneling motions can be performed if a suitable form of the Hamiltonian for the nuclear motions in Van der Waals molecules is used. 

Van der Avoird A, Wormer PES, Moszynski R (1997) Theory and computation of vibration, rotation and tunneling motions of van der waals complexes and their spectra. In Scheiner S (ed) Molecular interactions FromVan derWaals to strongly bound complexes, Wiley, New York, ppl05-153... 

Fig. 7. Tunneling motion of the two protons in hydrogen fluoride dimer. The cyclic structure of the dimer corresponds to a saddle point on the energy surface...

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