Electron spin polarization in consecutive spin-correlated radical Pairs: Application to short-lived and long-lived precursors in type 1 photosynthetic reaction centres

An analytical treatment of the spin dynamics in sequential photoinduced correlated coupled radical pairs is presented and applied to the spectra of the states P⁺A ₁ ^? and P⁺F _x ^? in type 1 photo-synthetic reaction centres. Expressions for the spin polarized spectra are derived for the specific limiting cases of a very short-lived and very long-lived primary radical pair which correspond to the situation found in heliobacteria and photosystem I (PSI), respectively. The inhomogeneous line-broadening due to the unresolved hyperfine couplings is taken explicitly into account. It is shown that the density matrix of the secondary pair ρ₂ can be written as the sum of two terms corresponding to (i) the part which is independent of the spin dynamics in the precursor, (ii) the additional spin polarization which is generated during the lifetime of the precursor and transferred to the secondary pair. The latter term contains two contributions which arise from the difference of the Zeeman interactions of the radicals in the primary pair and from the inhomogeneous line broadening. The predicted polarization patterns are compared to those established for chemically induced dynamic electron polarization (CIDEP) when uncoupled radicals are generated from a radical pair precursor. The expressions are then used to simulate the experimental spectra of the consecutive pairs P⁺A ₁ ^? and P⁺F _x ^? in PSI using parameters derived entirely from independent experimental data. Excellent agreement with the experimental results is obtained. The spectra of P⁺F _x ^? in heliobacteria at X- and K-band are also simulated and it is shown that the observed polarization patterns can be reproduced assuming direct electron transfer from A₀ to F_x with a time constant ofτ = 600 ps.