A recursion relation is formulated for the Green's function for calculating the effective electron coupling in bridge-assisted electron transfer systems, within the framework of the tight-binding Hamiltonian. The non-perturbative recursion expression relates the Green’s function of a chain bridge to that of a bridge which is one unit less. The method is used to calculate the electronic coupling between a gold electrode and each of the molecules. (η⁵-C₅H₅)Fe(η⁵-C₅H₄)CO₂(CH₂)ₙSH and (η⁵-C₅H₅)Fe(η⁵-C₅H₄)(CH₂)ₙSH (n = 3 to 50). At larger numbers of bridge units, the effective coupling strength shows an exponential decay as the number of methylene units increases. This sequential formalism shows numerical stability even for a very long chain bridge and. since it uses only small matrices, requires much less computer time for the calculation. Identical bridge units are not a requirement, and so the method can be applied to more complicated systems, such as proteins. Most of the calculated coupling strengths, if converted to rate constants according to a nonadiabatic expression, agree well with the experimental results.
The time-dependent dynamic Stokes shift function, which describes the solvent response to a sudden change in the charge distribution of a solute molecule, is expressed in terms of experimentally measured dielectric dispersion data of the solvent, using a simple dielectric continuum model. The result is applied to photoexcited coumarin 343 in water, and encouraging agreement with the experimental data is obtained. A simple formula is also derived which includes the effect of a pump pulse of finite duration. Such an effect is negligible when the frequency of a pump pulse is close to the maximum in the absorption spectrum, but a deviation from the standard formula can be expected for the pump pulse tuned to a far wing of the absorption band of the chromophore. To calculate further the time-dependent fluorescence spectral lineshapes, a method is described for incorporating the vibronic transitions of a solute molecule. The intramolecular vibrational relaxation is assumed to be much faster
than the observation delay time. Calculations are made for coumarin 153 in acetonitrile. The results are again in encouraging agreement with experimental spectra. Results are also given for the dynamic Stokes shift in methanol.</p
