A superexchange mechanism for the primary charge separation in photosynthetic reaction centers

We analyse the superexchange model for the primary charge separation from the electronically excited singlet state (¹P^*) of the bacteriochlorophyll dimer (P) to the bacteriopheophytin (H) across the A branch of the bacterial photosynthetic reaction centers, which is mediated by the accessory bacteriochlorophyll (B). The dominant contribution to the superexchange electronic interaction between the initial ¹P^* BH and the final P⁺BH^- states originates from the mixing with the mediating electronic state P⁺P^-H, the energy of which is above ¹P^*. The superexchange electronic interaction is V=V_PBV_BH/δE, where V_PB and V_BH are the electronic couplings of ¹P^*BH with P⁺B^-H and P⁺B^-H with P⁺BH^-, respectively, while δE is the vertical energy difference. The nonadiabatic electron-transfer rate is proportional to V²F, where F is the nuclear Franck-Condon factor, which is determined by the (free) energy gap ΔG=-2000 cm^-1, the medium reorganization energy λ (λ<2500 cm^-1) and the medium characteristic frequency ω≈100 cm^-1. Indirect information on the constituents of the effective electronic coupling V≈25 cm^-1 was inferred from the ration |V_BH/V_PB| calculated from the intermolecular overlap approximation in conjunction with an activated sequential channel and the utilization of kinetic constraints on the dynamics of the primary electron transfer, which result in V_PB≥60 cm^-1, V_BH≥360 cm^-1 and δE≥1100 cm^-1. We discuss several physical phenomena and observables, i.e., electric field effects on the prompt fluorescence, the unidirectionality of charge separation across the A branch and magnetic interactions in the primary radial pair in the framework of the superexchange mechanism. The electric field (∈) dependence of the fluorescence quantum yield (Y_f(∈)) for isotropic samples at 75 K predicts Y_f(∈)=5 mV/Å)/Y_f(0)=1.39 and Y_f(∈=9 mV/Å)/Y_f(0)=3.5. The fluorescence polarization data at constant field (Lock-hart, D.J., Goldstein R.F. and Boxer, S.G. (1988) J. Chem. Phys. 89, 1408-1415) can be well accounted for in terms of the energetic parameters λ=1600 cm^-1 and ΔG=-2000 cm^-1 together with the value ψ=61^o for the angle between the dipole P⁺H^- and the transition moment of P. The unidirectionality of the charge separation across the A branch originates predominantly from structural symmetry breaking, which affects the electronic coupling, while the contribution of the nuclear contribution has been shown to be small. The predicted ratio of the electronic transfer rates k(A)/k(B)=82(+190; -70) at T=80 K is consistent with the recent experimental result k(A)/k(B)≥25 at this temperature. Finally we examined magnetic interactions of the primary P⁺H^- radical pair, establishing the interrelationship between the singlet energy shifts and the triplet energy shift with the primary electron transfer rate, k, and the triplet recombination rate k_T whereupon the singlet-triplet splitting of P⁺H^- is J=αk-βk_T where the coefficients α and β depend on energetic parametes and Franck-Condon factors. The estimate of J within the superexchange mechanism rests on the incorporation of an assumed configurational relaxation and essential cancellation effects.