Electron-Transfer Matrix Element

The transition dipole between the free energy surfaces F (X) is not the only parameter that depends on the nuclear configuration of the solvent. The effective ET matrix element following from the trace of the 

Under the special condition that mu and Am i, are parallel, one obtains the 

Equations [140]-[143] provide a connection between the preexponential factor entering the nonadiabatic ET rate and the spectroscopically measured adiabatic transition dipole mu- It turns out that the Mulliken-Hush matrix element, commonly considered as an approximation valid for m b = 0, enters exactly the rate constant preexponent as long as the non-Condon solvent effects are accurately taken into account. Equation [142] stresses the importance of the orientation of the adiabatic transition dipole relative to the direction of ET set up by the difference diabatic dipole Am. The value of is zero when the vectors mi2 and Am are perpendicular. 

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Different quantum chemical approaches can be invoked to calculate the electronic couplings. In many cases one can reliably estimate electron-transfer matrix elements on the basis of a one-electron approximation [27-29]. 

In summary, these computational results suggest that the GMH and FCD methods are quite robust and can be applied to DNA fragments where donor and acceptor levels are far from resonance. On the other hand, the results demonstrate that the electron-transfer matrix element does not vary significantly when a perturbation by an external electric field is applied. This find-... 

Rates of non-adiabatic intramolecular electron transfer were calculated in Ref. [331] using a self-consistent perturbation method for the calculation of electron-transfer matrix elements based on Lippman-Schwinger equation for the effective scattering matrix. Iteration of this perturbation equation provides the data that show the competition between the through-bond and through-space coupling in bridge structures. 

R. J. Cave and M. D. Newton, Generalization of the Mulliken-Hush treatment for the calculation of electron transfer matrix elements, Chem. Phys. Lett., 249 (1996) 15-19. 

The Fermi Golden rule describes the first-order rate constant for the electron transfer process, according to equation (11), where the summation is over all the vibrational substates of the initial state i, weighted according to their probability Pi, times the square of the electron transfer matrix element in brackets. The delta function ensures conservation of energy, in that only initial and final states of the same energy contribute to the observed rate. This treatment assumes a weak coupling between D and A, also known as the nonadiabatic limit. 

The state splittings discussed above for rl are based on individual reactants which, aside from the bond length constraint (r1 ), are otherwise non-interacting. If we now consider the full initial and final states associated with the exchange reaction (Equations 2-7), we note that the relative energies of high-spin and low-spin states in the bimolecular transition-state complex may be affected by differences in initial and final state coupling, as represented by the electron-transfer matrix element, Hj f, discussed in the introduction. While for the "three-electron ... 

The principal effects of the electron-electron interaction can be embodied in a disordered Hubbard model containing three parameters t, the nearest-neighbor electron transfer matrix element assumed constant U, the Coulomb repulsion between electrons of... 

Li, X.Y. and He, E.C., Electron transfer between biphenyl and biphenyl anion radicals Reorganization energies and electron transfer matrix elements, J. Comp. Chem., 20, 597, 1999. 

L. Yu Zhang, R. Murphy, and R. A. FHesner, Ab Initio quantum chemical calculation of electron transfer matrix element for large molecules. Preprint of Schrodinger, Inc. (1997). 

Here Gab is the electron-transfer matrix element, which depends on the orbital overlap of the reactants (V)a is an average of the energy gap over molecular dynamics trajectories in the initial state and y(t) is given by... 

The well-established semiempirical ZINDO/S method has been used to calculate the hole and electron transfer matrix elements for all the selected dimers. Both and show a monotonic decreasing behavior due to the fact that the interaction... 

In Eq. (12) V is an effective nearest neighbor electron transfer matrix element ( V > as B > ), m is the effective mass of the reference model, and d is the dimension of the model. No ultraviolet catastrophe occurs for d < 2, but it does occur for d > 2 leading to a shift of the unperturbed band edge to When energies are measured relative to... 

Model calculations have been employed in elucidating the mechanism of electron transfer reactions in aqueous solution. The contribution of inner shell OH bonds to activation barriers has been estimated from calculation for metal ion hydrates. Calculated electron transfer matrix elements (Hjf) for redox processes of the type, MLe + MLe =... 

M. D. Newton, Electronic structure analysis of electron transfer matrix elements for transition metal redox pairs, J. Phys. Chem., submitted. 

Recently Zhang and Frienser have developed and applied a PS method for calculating electron transfer matrix elements at the HF level. The largest calculation performed utilizing 1778 basis functions required 14 h on an IBM 390 work station. 

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