Theoretical study of the mechanism of electron transfer at photosynthetic reaction centers. I. Singlet excited states of free base porphin

Free base porphin is a key unit in the electron transfer reaction at photosynthetic reaction centers. For the electron transfer reaction, the transfer integral of the rate constant depends strongly on the quality of the wave functions of porphin-based chromophores. Therefore, we need a stable method for calculating the wave functions of optically allowed excited states of the porphin. We developed such a method and verified its stability by calculating the wave functions for an ethylene molecule. We confirmed that the optically allowed excited states required the entire amount of valence molecular orbitals for the active space to adequately describe the wave function with molecular in–out polarization. We applied our calculation method to investigate the wave function of free base porphin. Our ab initio calculation used 4-31 G plus d polarization functions for the carbon and nitrogen atoms, and Rydberg $\text{2d}$ basis functions on the center of each pyrrol ring simultaneously. We also proposed an assignment for the controversial B and N bands. This assignment is reasonably consistent with experimental data within 0.36 eV for Q and B bands, and 0.75 eV for N bands. The reproduction accuracy of the lower excitation spectra up to B band confirms the reliability of the transfer integral part to calculate the rate constants of the electron transfer reaction at photosynthetic reaction centers.