Specifying bounds on the rate constants of intramolecular two-state excited-state processes by global compartmental analysis of the fluorescence decay surface

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This report is an extension of the identifiability study [Boens et al., J. Phys. Chem. 96 (1992) 6331-6342] of intramolecular two-state excited-state processes. The identifiability study is expressed in terms of the rate constants and the parameters b̃ 1 and c̃ 1, where b̃ 1 is the relative absorbance of ground-state species 1 and c̃ 1 is the normalized spectral emission weighting factor of the corresponding excited-state species 1 *. From the decay times and the preexponential factors of a single fluorescence decay trace, it is generally possible to derive two sets of rate constants when one rate constant, b̃ 1 and c̃ 1 are known beforehand. A unique set of rate constants can be obtained when one rate constant is known in combination with the following sets of values for ( b̃ 1, c̃ 1): (0.5, 1), (0.5, 0), (1, 0.5), (0, 0.5), (0.5, 0.5), (1, 1) or (0, 0). It is further shown that when ( b̃ 1, c̃ 1) equals (1, 1) or (0, 0), i.e. a single species is excited and the fluorescence of only that species is observed, upper and lower bounds on all rate constants can be specified without any a priori information about the rate constant values. The bounds on the rate constants can be specified in terms of the decay times and the preexponential factors estimated from the biexponential analysis of a single fluorescence decay trace with b̃ 1 = 1 and c̃ 1 = 1 or, equivalently, b̃ 1 = 0 and c̃ 1 = 0. This analysis approach can provide kinetic information of intramolecular electron transfer and exciplex formation when no suitable model compound is available.