Tunneling of protons

Dolinsek et al.7 have reported the existence of quantum tunnelling in these systems. This has been observed from the temperature-independent behaviour of 8 Rb and 2H NMR SLR times at low temperatures (1.6Quantum tunnelling in these systems refers to the tunnelling of protons/deuterons in the double-well potential. In a 31P NMR relaxation time measurements by Chen et al.30 in D-RADP systems, have found an additional T1 minimum at low temperatures apart from the BPP T1 minimum at high temperatures. The low temperature minimum has been attributed to the extreme slowing down of the O-D—O intra-bond motion which is unique to the glassy phase. 

There is another reservation that should be mentioned for those who see Monte Carlo and MD techniques as all-conquering they use classical mechanics. This is all very well for some movements, e.g., translation in imperfect gases. But what of the quantized vibration Or what of quantal aspects in rate calculations or the tunneling of protons in the conduction of aqueous acid solutions (see Section 4.11.5), for example ... 

An interesting study concerning the tunneling of protons has been conducted by Willison [122], who has treated the phenomenon of sonoluminescence in liquid water just as caused by the proton tunneling between oxygens of nearest water molecules (see Appendix B). 

If the local tunnel integral J is small compared with Coulomb interaction U. the contribution on the side of the term proportional to p+ in expression (443) is negligible (its contribution is of the order of J/U single domain. Increasing of y involves an increase of the p term, which will suppress the coherent tunneling of protons. 

Figure 30. Role of the proton-phonon interaction in the coherent tunnel repolarization of a short chain. is the Euclidean renormalized action of phonons, and is their nonrenormalized action. The bond vibrations can effectively decrease the local proton tunneling (flo/tt < 0) and at the same time increase the coherent tunneling of protons ( 9 Et < // ).

Tunnelling of protons through their H-bonds is at the origin of disorder. This tunnelling is phonon-assisted, that is, they appear more easily when vibrational modes of the crystal, called phonons, are excited. When temperature increases from 0 K, such low-frequency phonons... 

The interpretation of the dehydroxylation process is consistent with the advancing interface concept rather than the inhomogeneous mechanism since the tunneling of protons explains the reaction of hydroxyl groups in adjacent layers. This mechanism also maintains electroneutrality, so the postulate of Mg2+ countermigration is no longer required. 

The situation presented in fig. 29 corresponds to the sudden limit, as we have already explained in the previous subsection. Having reached a bend point at the expense of the low-frequency vibration, the particle then cuts straight across the angle between the reactant and product valley, tunneling along the Q-direction. The sudden approximation holds when the vibration frequency (2 is less than the characteristic instanton frequency, which is of the order of In particular, the reactions of proton transfer (see fig. 2), characterised by high intramolecular vibration frequency, are being usually studied in this approximation [Ovchinnikova 1979 Babamov and Marcus 1981]. 

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

Concept of quantum-mechanical tunnelling in proton-uansfer reactions introduced (without experimental evidence) by several authors. 

Lifnbach et al. [92JA9657 97BBPG889] made an exhaustive study of proton transfer in solid pyrazoles. For instance, the activation barriers, isotope and tunneling effects of the dimer 67, the trimer 68, and the tetramer 69 were determined. Catemers, like pyrazole itself, do not show dynamic behavior. 

Fig. 2.15 Transport of protons in water. Proton tunnelling is a fast process but water molecules must first rotate to the position where the transfer is possible... 

First, we shall discuss reaction (5.7.1), which is more involved than simple electron transfer. While the frequency of polarization vibration of the media where electron transfer occurs lies in the range 3 x 1010 to 3 x 1011 Hz, the frequency of the vibrations of proton-containing groups in proton donors (e.g. in the oxonium ion or in the molecules of weak acids) is of the order of 3 x 1012 to 3 x 1013 Hz. Then for the transfer proper of the proton from the proton donor to the electrode the classical approximation cannot be employed without modification. This step has indeed a quantum mechanical character, but, in simple cases, proton transfer can be described in terms of concepts of reorganization of the medium and thus of the exponential relationship in Eq. (5.3.14). The quantum character of proton transfer occurring through the tunnel mechanism is expressed in terms of the... 

At not very low temperatures, the excited vibrational states of the tunneling particle make some contribution to the transition probability. Furthermore, at high enough frequencies of the vibrations of the medium atoms, quantum effects may be important for the medium. In the harmonic approximation for the tunneling particle we obtain, in a similar way as in the case of proton transfer, the expression for the transition probability in the Condon approximation48... 

Borgis, D. and Hynes, J. T. Dynamical theory of proton tunneling transfer rates in solution general formulation, Chem. Phys., 170(1993),315-346... 

Since the rate for the tunneling of a proton is strongly dependent on barrier width, it is necessary that the molecular systems to be studied constrain the distance of proton transfer. Also, since the various theoretical models make predictions as to how the rate of proton transfer should vary with a change in free energy for reaction as well as how the rate constant should vary with solvent, it is desirable to study molecular systems where both the driving force for the reaction and the solvent can be varied widely. 

The effect of the solvent upon the breaking of the symmetry of the potential energy surface for proton transfer has a profound consequence for the reaction dynamics for proton transfer. The tunneling of the proton out of the reactant state... 

The DKL model for nonadiabatic proton transfer at a fixed distance R allows for the tunneling of the proton out of any of the bound vibrations, n, associated with the proton-transfer coordinate, into any of the bound vibrations in the product state, m [10]. 

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