Formalism of the excitation transfer matrix element applicable for any multiconfigurational wave functions is made. On the basis of the resultant formulas, the excitation transfer matrix elements between the S2 or S1 state of a carotenoid, neurosporene, and the S2 or S1 state of bacteriochlorophyll a are calculated at various stacked configurations of the two molecules. The results show that the excitation transfer from the carotenoid S1 state to the bacteriochlorophyll S1 state via the Coulomb mechanism including multipole–multipole interactions takes place very efficiently in a speed more rapid than that via the electron-exchange mechanism. The results also show that the excitation transfer from carotenoid to bacteriochlorophyll occurs directly from the carotenoid S2 state, as well as from the carotenoid S1 state. Furthermore, it is shown that the excitation transfer matrix element due to the electron-exchange interaction has an oscillatory dependence on the displacement of one molecule from the other when the distance between the planes of the π systems is kept constant. Based on these results, a possible mechanism of the excitation transfer from carotenoid to bacteriochlorophyll in vivo is discussed.
A typical example of electron transfer (ET) mediated by a midway molecule M is the initial ultrafast ET from the special pair to bacteriopheophytin in the reaction center of bacterial photosynthesis, where the donor D and the acceptor A are so far apart (∼17 Å) that ET is mediated by a bacteriochlorophyll monomer located in-between. An analytic formula for the rate constant k a,d of such an ET is presented with attention to its morphology to the resonance Raman scattering in second-order optical processes. When M is located in the same energy region as D and A, important roles are played by the dephasing-thermalization time of phonons τ m at M, relative to the lifetime of an electron l m at M. In the limit of τ m . l m , the superexchange ET occurs where M mediates the ET as a virtual intermediate state of quantum mechanics, while in the opposite limit of τ m , l m , the ordinary sequential ET occurs where ET to M from D is followed by ET to A from M after thermalization of phonons at M. The analytic formula correctly bridges the two limits. It describes intermediate cases as a single process, different from the expediency of assuming two channels by the superexchange and the ordinary sequential ET's, which cannot coexist. Occurring earlier than τ m in the course of ET are the superexchange ET and the subsequent hot sequential ET where ET to A from M occurs during reorganization of the medium around M after ET to M from D. Since they cannot be unambiguously separated, we can determine only the degree of ordinary sequentiality D OS of the ET, with D OS , 1 for the superexchange ET and 1 -D OS , 1 for the ordinary sequential ET. An analytic formula for D OS is also presented. D OS , in combination with k a,d , describes reasonably various aspects of the initial ET in bacterial photosynthesis, including its artificial modifications with respect to energy positions relative among D, M, and A.
Abstract— The contributions of different factors that might be responsible for the 500 nm absorption maximum of bovine rhodopsin are evaluated in detail. These include: (1) electrostatic interactions between the chromophore and a charged amino acid on the apoprotein; (2) exciton interactions with aromatic amino acids; (3) twisting about single bonds which have considerable double bond character; (4) weak interactions between the Schiff base and a putative counter‐ion. Analysis of these mechanisms in terms of theoretical and experimental results suggests that(2–4) are all capable of contributing to the protein induced spectral shifts. However, the “external point charge” model proposed previously, i.e. mechanism (1), appears to provide the crucial interaction. In this paper, the theoretical basis for this model is discussed in detail. The model is briefly evaluated in light of the amino‐acid sequence of bovine rhodopsin and possible implications for other visual pigments are considered.
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