Tunnelling proton transfer

In the framework of the model, the difference Ei — E is within the acoustic phonon bandwidth, and that is why Skinner and Trommsdorff [21] reasonably assumed that the longitudinal acoustic modes could influence the tunneling proton transfer. The interaction potential (22) was chosen in the form of the deformation potential approximation (see Ref. 74)... 

Hammes-Schiffer expounds in Ch. 16 her group s theoretical formulation for proton-coupled electron transfer (PCET) mechanism and rates, pointing out the similarities with the separate spedal limits of electron transfer and (tunneling) proton transfer, and emphasizing the new features of PCET. The latter include the... 

B. Translational Tunneling Proton Transfer in Symmetric and Near-Symmetric Potential Energy Surface, 172... 

The transition from the adiabatic to tunneling proton transfer affects the temperature dependence of the transfer rate constant in such a way that the activation energy decreases with decreasing T and at T < d lnk/d( 1/7) = 0. The distance of pro-... 

Mavri, J., Berendsen, H.J.C., Van Gunsteren, W.F. Influence of solvent on intramolecular proton transfer in hydrogen malonate. Molecular dynamics study of tunneling by density matrix evolution and nonequilibrium solvation. J. Phys. Chem. 97 (1993) 13469-13476. 

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]. 

On the other hand, it is clear that in the classical regime, T> (T i is the crossover temperature for stepwise transfer), the transition should be step-wise and occur through one of the saddle points. Therefore, there should exist another characteristic temperature. r 2> above which there exist two other two-dimensional tunneling paths with smaller action than that of the one-dimensional instanton. It is these trajectories that collapse to the saddle points atlT = T i. The existence of the second crossover temperature, 7, 2, for two-proton transfer has been noted by Dakhnovskii and Semenov [1989]. 

We have seen that 10" M s is about the fastest second-order rate constant that we might expect to measure this corresponds to a lifetime of about 10 " s at unit reactant concentration. Yet there is evidence, discussed by Grunwald, that certain proton transfers have lifetimes of the order 10 s. These ultrafast reactions are believed to take place via quantum mechanical tunneling through the energy barrier. This phenomenon will only be significant for very small particles, such as protons and electrons. 

State Proton Transfer (Section VIII). The general problem of intramolecular proton transfers includes tunneling paths (91JPC10457). The most relevant results are reported in Table VI. 

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. 

Isotope effect between the HH, HD, DH, and DD isotopomers was used as an important tool to determine the mechanism of the double-proton transfer. For concerted degenerate double-proton transfers in the absence of tunneling, the rule of the geometrical mean (RGM) should hold in good approximation, which states that /chh/ hd = /cdh/ dd-Tunneling may lead to a breakdown of this rule but the relation /chh > hd = dh > dd should remain valid. In the absence of secondary isotope effects the relation /chh HD = DH = 2 /cdd sliould liold for a stepwise pathway, even if tunneling is involved. 

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

E. Caldin, Tunneling in proton-transfer reactions in solntion, Chem. Rev. 1969, 69, 135. 

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... 

Below we will use Eq. (16), which, in certain models in the Born-Oppenheimer approximation, enables us to take into account both the dependence of the proton tunneling between fixed vibrational states on the coordinates of other nuclei and the contribution to the transition probability arising from the excited vibrational states of the proton. Taking into account that the proton is the easiest nucleus and that proton transfer reactions occur often between heavy donor and acceptor molecules we will not consider here the effects of the inertia, nonadiabaticity, and mixing of the normal coordinates. These effects will be considered in Section V in the discussion of the processes of the transfer of heavier atoms. 

Equation (77) shows that if ph lp(R )/4 1 at an optimum distance R between the reactants, proton transfer occurs by means of tunneling between the unexcited states. However, the distance of the proton jump, 2r0(R ), is not equal to the distance between the points of minima of the potential wells of the proton in the equilibrium nuclear configuration. This case is a generalization of the results obtained in an earlier model by Dogonadze, Kuznetsov, and Levich36 (DKL model). 

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