In the present study, the electronic energy transfer pathways in trimeric and hexameric aggregation state of cyanobacteria C-phycocyanin (C-PC) were investigated in term of the Förster theory. The corresponding excited states and transition dipole moments of phycocyanobilins (PCBs) located into C-PC were examined by model chemistry in gas phase at time-dependent density functional theory (TDDFT), configuration interaction-singles (CIS), and Zerner's intermediate neglect of differential overlap (ZINDO) levels, respectively. Then, the long-range pigment-protein interactions were approximately taken into account by using polarizable continuum model (PCM) at TDDFT level to estimate the influence of protein environment on the preceding calculated physical quantities. The influence of the short-range interaction caused by aspartate residue nearby PCBs was examined as well. Only when the protonation of PCBs and its long- and short-range interactions were properly taken into account, the calculated energy transfer rates (1/K) in the framework of Förster model at TDDFT/B3LYP/6-31+G* level were in good agreement with the experimental results of C-PC monomer and trimer. Furthermore, the present calculated results suggested that the energy transfer pathway in C-PC monomer is predominant from β-155 to β-84 (1/K = 13.4 ps), however, from α-84 of one monomer to β-84 (1/K = 0.3-0.4 ps) in a neighbor monomer in C-PC trimer. In C-PC hexamer, an additional energy flow was predicted to be from β-155 (or α-84) in top trimer to adjacent β-155 (or α-84) (1/K = 0.5-2.7 ps) in bottom trimer.

Within the framework of the Förster theory, the electronic excitation energy transfer pathways in the cyanobacteria allophycocyanin (APC) trimer and hexamer were studied. The associated physical quantities (i.e., excitation energy, oscillator strength, and transition dipole moments) of the phycocyanobilins (PCBs) located in APC were calculated at time-dependent density functional theory (TDDFT) level of theory. To estimate the influence of protein environment on the preceding calculated physical quantities, the long-range interactions were approximately considered with the polarizable continuum model at the TDDFT level of theory, and the short-range interaction caused by surrounding aspartate residue of PCBs were taken into account as well. The shortest energy transfer time calculated in the framework of the Förster model at TDDFT/B3LYP/6-31+G* level of theory are about 0.10 ps in the APC trimer and about 170 ps in the APC monomer, which are in qualitative agreement with the experimental finding that a very fast lifetime of 0.43-0.44 ps in APC trimers, whereas its monomers lacked any corresponding lifetime. These results suggest that the lifetime of 0.43-0.44 ps in the APC trimers determined by Sharkov et al. was most likely attributed to the energy transfer of α(1) -84 ↔ β(3) -84 (0.23 ps), β(1) -84 ↔ α(2) -84 (0.11 ps) or β(2) -84 ↔ α(3) -84 (0.10 ps). So far, no experimental or theoretical energy transfer rates between two APC trimmers were reported, our calculations predict that the predominate energy transfer pathway between APC trimers is likely to occur from α(3) -84 in one trimer to α(5) -84 in an adjacent trimer with a rate of 32.51 ps.