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

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... -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 solut [...]