We introduce a general and versatile MS Windows application for solving the spherically symmetric diffusion problem, involving up to two coupled spherically symmetric Smoluchowski equations. The application is based on a modular, configurable, user‐friendly graphical interface, in which input parameters are introduced through a graphical representation of the system of partial differential equations and output attributes can be obtained graphically during propagation. The numerical algorithm consists of finite differencing in space and Chebyshev propagation in time; it includes an implementation of virtual gridding, which enhances the accuracy of calculating boundary conditions and steep potentials. The program has b een checked against a wide collection of analytical solutions and applied to an experimentally open problem in excited‐state proton‐transfer to solvent. © 1996 by John Wiley & Sons, Inc.

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Nanosecond time-resolved absorption studies in a magnetic field ranging from zero to 3.0 T have been performed on a series of covalently linked donor-Ru(bipyridine) 3 -acceptor complexes (D-C 2+ -A 2+ ). In these complexes the electron donor is a phenothiazine moiety linked to a bipyridine by a (-CH 2 -) p (p ) 1, 4, 5, 7) chain, and the electron acceptor is an N,N′-diquaternary-2,2′-bipyridinium moiety, linked to a bipyridine by a (-CH 2 -) 2‚ chain. On the nanosecond time scale the first detectable photoinduced electron-transfer product after exciting the complex C 2+ is the charge-separated (CS) state, D + -C 2+ -A + , where an electron of the phenothiazine moiety, D, has been transferred to the diquat moiety, A 2+ . In zero field the lifetime of the CS state is about 150 ns. At low fields (B 0 < 0.5 T) the magnetic field strongly affects the decay kinetics, splitting it up into a major component, the rate constant of which decreases by a factor of about 10 at fields of several 100 mT, and a minor component with an approximately field independent rate constant. At high fields (B 0 > 0.5 T) the total amplitude of the CS absorption signal decreases and the relative contribution of the fast decaying component increases. The magnetic field effects can be consistently interpreted and quantitatively modeled by taking into account the mechanisms and kinetics of the spin multiplicity changes in the CS state and its precursor, a short-lived CT state (D-C 3+ -A + ) formed upon primary electron transfer from the triplet excited complex to the diquat moiety. Exploiting the magnetic field dependent kinetics, the rate constants of the triplet-singlet transitions in the two types of linked radical pairs and of all the electron-transfer processes following the primary one can be assessed. Magnetic-field-dependent investigations thus can be essential for the understanding of the complex kinetics in supramolecular systems with sequential cyclic electron transfer.