Electron coupled

Blake N P and Metiu H 1995 Efficient adsorption line shape calculations for an electron coupled to many quantum degrees of freedom, applications to an electron solvated in dry sodalites and halo-sodalites J. Chem. Phys. 103 4455... 

Figure C3.2.6. Zones associated witlr the distinctive decay of electronic coupling tlrrough a-helical against p-sheet stmctures in proteins. Points shown refer to specific rates in mtlrenium-modified proteins aird in tire photosyntlretic reaction centre. From Gray H B aird Wiirkler J R 1996 Electron trairsfer in proteins A . Rev. Biochem. 65 537.

The cross relation has proven valuable to estimate ET rates of interest from data tliat might be more readily available for individual reaction partners. Simple application of tire cross-relation is, of course, limited if tire electronic coupling interactions associated with tire self exchange processes are drastically different from tliose for tire cross reaction. This is a particular concern in protein/protein ET reactions where tire coupling may vary drastically as a function of docking geometry. 

DeRege P J F, Williams S A and Therien M J 1995 Direct evaluation of electronic coupling mediated by hydrogen bonds—implications for biological electron transfer Sc/e/ ce 269 1409-13... 

Knox R S and Gulen D 1993 Theory of polarized fluorescence from molecular pairs—Forster transfer at large electronic coupling Photochem. Photobiol. 57 40-3... 

The simplest way to write down the 2 x 2 Hamiltonian for two states such that its eigenvalues coincide at trigonally symmetric points in (x,y) or (q, ( )), plane is to consider the matrices of vibrational-electronic coupling of the e Jahn-Teller problem in a diabatic electronic state representation. These have been constructed by Haiperin, and listed in Appendix TV of [157], up to the third... 

The Bom-Oppenheimer approximation is usually very good. For the hydrogen molecule the error is of the order of 10 ", and for systems with heavier nuclei, the approximation becomes better. As we shall see later, it is only possible in a few cases to solve the electronic part of the Schrodinger equation to an accuracy of 10 ", i.e. neglect of the nuclear-electron coupling is usually only a minor approximation compared with other errors. 

Dipole-bound anions (5a, 4f) in which the extra electron is attracted primarily by the dipole force field of the polar molecule and for which rotation-to-electronic coupling is most important in inducing electron ejection. 

NH (X n) for which (4d) vibration of the N-H bond couples only weakly to the non-bonding 2pn orbital and for which rotation-to-electronic coupling can be dominant in causing electron ejection for high rotational levels. 

That is, the semi-classical approximation to the photon absorption rate is equivalent to a Landau-Zener treatment of the probability of hopping from Vj -i-hco to Vf induced by the electronic coupling perturbation p, f (s,0,Q). 

These transition-metal catalysts contain electronically coupled hydridic and acidic hydrogen atoms that are transferred to a polar unsaturated species under mild conditions. The first such catalyst was Shvo s diruthenium hydride complex reported in the mid 1980s [41 14], Noyori and Ikatiya developed chiral ruthenium catalysts showing excellent enantioselectivity in the hydrogenation of ketones [45,46]. 

The factor k takes into acount the effects of nonadiabatic transition and tunneling properly. Also note that the electronic coupling //ad is assumed to be constant in the Marcus formula, but this is not necessary in the present formulation. The coupling Had cancels out in k of Eq. (126) and the ZN probability can be calculated from the information of adiabatic potentials. 

The present formula Eq. (126) is tested in comparison with the Bixon-Jortner perturbation theory in the weak electronic coupling regime [109]. The Arrhenius plot is shown in Fig. 23, where the electronic coupling Had is taken... 

Figure 23. Arrhenius plot of the electron transfer rate. The electronic coupling strength is TIad = 0.0001 a.u. Solid line-Bixon-Jortner perturbation theory Ref. [109]. FuU-circle present results of Eq. (26 ). Dashed line-results of Marcus s high temperature theory [Eq.(129)]. Taken from Ref. [28].

Figure 25. Electron-transfer rate the electronic coupling strength at T = 500 K for the asymmetric reaction (AG = —3ffl2, oh = 749 cm ). Solid line-present full dimensional results with use of the ZN formulas. Dotted line-full dimensional results obtained from the Bixon-Jortner formula. Filled dotts-effective ID results of the quantum mechanical flux-flux correlation function. Dashed line-effective ID results with use of the ZN formulas. Taken from Ref. [28].

Hess, B.A. and Kaldor, U. (2000) Relativistic all-electron coupled-cluster calculations on Au2 in the framework of the Douglas—Kroll transformation. Journal of Chemical Physics, 112, 1809-1813. 

Patrone, L.. Palacin, S. and Bourgoin, J.P. (2003) Direct comparison of the electronic coupling efficiency of sulfur and selenium alligator dips for molecules adsorbed onto gold electrodes. Applied Surface Science, 212—213, 446—451. 

The left (solid) parabolic curve represents the oxidized state, the right one, the reduced state. Let us assume that the system is initially at the oxidized state (left curve). When the interaction metal-reaction species is small, the electronic coupling between is small and the system may oscillate many times on the left parabolic curve (ox) before it is transferred to the curve on the right (red). On the other hand, if the interaction is strong, the free energy should no longer be represented by the two solid curves in the intermediate region of the reaction coordinate, but rather, by the dashed... 

For highly ordered 3D systems, Terril et al. showed that the electron-hopping conductivity depends on the activation energy of the electron transfer and the electronic coupling term [3 [71]. They took the latter as a... 

Fig. 1. Schematic one-dimensional cross section through the Gibbs free energy surface G(R) of a spin-state transition system along the totally symmetric stretching coordinate. The situation for three characteristic temperatures is shown (B = barrier height, ZPE = zero-point energy, 28 = asymmetry parameter, J = electronic coupling parameter, AG° = Gh — GJ...

Let us consider the possible relations of LS and HS potential energy surfaces as shown schematically in Fig. 9. As long as the zero-order or diabatic surfaces are considered, the eleetrons remain localized on the particular spin state, no eleetron transfer being possible. In order that a conversion between the LS and HS state takes place, electronic coupling of the states is required. This coupling effectively removes the degeneracy at the interseetion of the zero-order surfaces... 

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