Tunneling, proton

If a free particle hits a barrier, it is reflected, according to classical mechanics. In quantum mechanics, on the other hand, the solution of the time-independent Schrodinger equation (SE) in the barrier is a decreasing exponential in absolute value. The reason is that the wave function must have a continuous derivative. The wave function in the barrier does not become equal to zero. At the right boundary, it has to have a continuous derivative into the region with zero potential. It has a lower amplitude than to the left of the barrier. 

In the symmetric case, the proton is described by the wave functions  

In each of the eigenstates, the probability is thus equally large that the systan is described by or Pb. The situation when the proton is hydrogen-bonded to A (t = 0) is described as a superposition between Pi and T2. In time-dependent quantum mechanics, the proton will oscillate between A and B. 

A symmetric hydrogen bond is found in H2O-H-OHJ. A symmetric hydrogen bond, as defined here, is one where the proton equally likely sits on either of the heavy atoms. However, this does not mean that there is no activation barrier. In the case of H2O-H-OHJ, it has been found in the calculations that the activation barrier is in fact absent. 

In pure water too, the activation barrier for PT is shallow or even absent. PT reactions in water have proven to be very fast and this is referred to as the Grotthuss effect. Theodore von Grotthuss (1785-1822) was a German-Lithuanian baron who contributed to both electrolysis and photochemistry. At this time, neither protons nor the electrodissociation theory was known, of course (it was not even known that the formula for water is H2O). Still, Grotthuss developed a primitive theory that H+ and OH ions are involved in conductivity. This depends on the fact that the water molecules form chains of hydrogen bonds. Protons move stepwise and are almost activationless. Covalent bonds become hydrogen bonds as the charge is passed from 

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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... 

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. 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

Bell, R. P. (1981). Proton Tunnelling in Chemistry , Chapman and Hall, London Bender, M. L. (1971). Mechanisms of Homogeneous Catalysis from Protons to Proteins . Wiley Interscience, New York... 

For my first volume as Editor, I have invited Professor Colin D. Hubbard (University of Erlangen-Niirnberg, Erlangen, Germany and University of New Hampshire, Durham, NH, USA) as co-editor. Professor Hubbard studied chemistry at the University of Sheffield, and obtained his PhD with Ralph G. Wilkins. Following post-doctoral work at MIT, Cornell University and University of California in Berkeley, he joined the academic staff of the University of New Hampshire, Durham, where he became Professor of Chemistry in 1979. His interests cover the areas of high-pressure chemistry, electron transfer reactions, proton tunnelling and enzyme catalysis. 

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

M. V. Vener and J. Sauer, Vibrational spectra of the methanol tetramer in the OH stretch region. Two cyclic isomers and concerted proton tunneling. J. Chem. Phys. 114, 2623 2628 (2001). 

T. N. Wassermann, D. Luckhaus, S. Coussan, and M. A. Suhm, Proton tunneling estimates for malonaldehyde vibrations from supersonic jet and matrix quenching experiments. Phys. Chem. Chem. Phys. 8, 2344 2348 (2006). 

In 1989, Borgis and Hynes proposed a theory for nonadiabatic proton transfer that includes all the parameters contained with the DKL model. In addition, they addressed the important issue of low-frequency vibrations serving as promoting modes in proton tunneling [11]. For nonadiabatic proton transfer, the distance dependence of the tunneling coupling, C(Q), has the analytical form [13]... 

Large kinetic isotope effects are usually indicative of proton tunneling. However, if proton transfer is not rate-limiting or rate-contributing, proton tunneling may stiU be present, but its occurrence would be masked. 

Observation of the temperature dependence of ku/kj and Td/Tt and kn/ko kinetic isotope effects via Arrhenius plot is very useful in detecting and characterizing proton tunneling ... 

The equihbrium positions of each proton to the right or to the left of the bond centre are described by the pseudospin value with values + 1,-1, respectively. hi Fourier space J(q) is the proton-proton interaction with wave vector q. The operator accounts for proton tunnelling with timnel frequency The host lattice dynamics comprises the displacements along the z-axis of the K -ion, of the PO4 cores and of the PO4 shells. Its Hamiltonian is given by ... 

Brief History of Models and the Proton-Tunneling Model. 163... 

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