Tunneling coupling

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]... 

Sutcliffe, M.J. and Scrutton, N.S. (2002). A new conceptual framework for enzyme catalysis. Hydrogen tunnelling coupled to enzyme dynamics in flavoprotein and quinoprotein enzymes. Eur. J. Biochem. 269, 3096-3102... 

Since the probability amplitude for tunneling is exponentially sensitive to the position of the dot, the maximum of the tunnel exchange interaction between an electron on the dot and an electron in one lead occurs when the tunneling coupling to the other lead is negligible. This is why we will assume the following property of tunneling amplitude ALjR t) to be fulfilled ... 

The first two terms are the Hamiltonians of the left and right parts, the third term describes the left-right (tunneling) coupling. The equivalent matrix representation of this Hamiltonian is... 

The scattering matrix elements implicitly depend on x via the parametric coordinate dependence of Edot and F. The tunnel coupling F homogeneously broadens the resonance energy levels E t- Therefore, the Lorentzian distribution of the scattering matrix element implies an exponential decay via the coupling of electrons to the environment across only a resonance window of density of states p(E)... 

The Franck-Condon principle implies locality in phase space x, p. It states that the coordinate and momentum of a massive dot stay unchanged during the electron transitions, i.e. electron tunneling in our case. For detailed balance, the tunnel coupling Ta has to be invoked as the main prerequisite for the Coulomb blockade. The additional relaxation due to molecular collisions and electromagnetic radiation may have to be favored for the steady state. This is similar to the dissipation necessitated in the orthodox theory of the Coulomb blockade [Kulik 1975 Averin 1991],... 

The first term in Eq. (10.53) is the activation energy contribution from the thermally averaged square coupling 0-) Eq. (10.40), and as such is extremely sensitive to parameters affecting the H-bond mode-tunneling coupling, namely T, ha>Q, and Eah- For the present system, this term dominates the activation energy for both H (60%) and D (66%). Furthermore, since F l tn-i is mass sensitive, the... 

Kohen, A. (2003) Kinetic isotope effects as probes for hydrogen tunneling, coupled motion and dynamics contributions to enzyme catalysis, Progr. React. Kinet. Mech. 28, 119-156. 

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