Extended model for photochemical dissociation reactions

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Abstract
The model for photodissociation reactions introduced by Rice, McLaughlin, and Jortner is generalized by allowing the excited molecule to decompose into several decay channels. In accordance with models for unimolecular reactions, intermediate resonance states having similar energies are assumed to couple to different channels and only resonances separated by a sufficiently large energy spacing, ε2, are taken to couple to the same channels. The molecule is shown to decay exponentially from the initially excited state at the nonradiative rate Γ1/(1+r)ℏ, where Γ1/ℏ is the nonradiative rate in the absence of resonance‐channel coupling and r=πΓ2/2ε2 measures the ratio of the nonradiative resonance widths Γ2 to the energy spacing ε2. Plots of the resonance populations Pman and the channel populations Pdiss versus time consist of exponential segments linked at times t=p h/ε2, p=1,2,3,…, to yield continuous but only piecewise smooth curves. For t < h/ε2, decay from the initially prepared state populates the resonances and the channels in parallel and maintains a 1:r ratio between Pman and Pdiss. For t > h/ε2, Pman eventually approaches zero while Pdiss continues to rise towards a value of unity. The detailed shape of the population versus time curves is sensitive to the values of r, Γ1/(1+r) and ε2. This general behavior is termed ``quasisequential'' because although the populations do not satisfy conventional kinetic rate equations for consecutive decay, the evolution still resembles decay from the initial state to the resonances ``followed'' by decay from the resonances to the channels. True sequential decay occurs only when ε2 is so large that ε2≫Γ2, while the nonsequential decay previously obtained for the Rice‐McLaughlin‐Jortner model occurs only if ε2 is so small that h/ε2 exceeds the physically relevant time scale. We do not expect the former limiting case to be generally realized since it is inconsistent with models for unimolecular reactions which postulate that ε2≈Γ2. Although the latter limiting case may be realized for certain large molecules, we expect that many molecules will decay, instead, according to the more general quasisequential expressions which we present. The general formulas we derive are valid for all times following photoexcitation and are therefore applicable to relatively small as well as large molecules.