Energy transfer efficiency in the chromophore network strongly coupled to a vibrational mode

Using methods from condensed matter and statistical physics, we examine the transport of excitons through the photosynthetic complex from a receiving antenna to a reaction center. Writing the equations of motion for the exciton creation-annihilation operators, we are able to describe the exciton dynamics, even in the regime when the reorganization energy is of the order of the intrasystem couplings. We determine the exciton transfer efficiency in the presence of a quenching field and protein environment. While the majority of the protein vibrational modes are treated as a heat bath, we address the situation when specific modes are strongly coupled to excitons and examine the effects of these modes on the energy transfer efficiency in the steady-state regime. Using the structural parameters of the Fenna-Matthews-Olson complex, we find that, for vibrational frequencies below 16 meV, the exciton transfer is drastically suppressed. We attribute this effect to the formation of a “mixed exciton-vibrational mode” where the exciton is transferred back and forth between the two pigments with the absorption or emission of vibrational quanta, instead of proceeding to the reaction center. The same effect suppresses the quantum beating at the vibrational frequency of 25 meV. We also show that the efficiency of the energy transfer can be enhanced when the vibrational mode strongly couples to the third pigment only, instead of coupling to the entire system.

Figure 1

Environment spectral function $J\left(\omega \right)$ including contributions from the heat bath and a specific vibrational mode with frequency $\mathrm{\Omega }$ = 10 meV.

Figure 2

Energy transfer efficiency as a function of the coupling to the quenching field at various couplings to the reaction center.

Figure 3

Energy transfer efficiency as a function of the coupling to the reaction center at various couplings to the quenching field.

Figure 4

Energy transfer efficiency as a function of the vibrational mode frequency $\mathrm{\Omega }$ at various couplings to the quenching field.

Figure 5

Time dependencies of the pigment populations for various frequencies of the vibrational mode.

Figure 6

Energy transfer efficiency as a function of the frequency $\mathrm{\Omega }$ of the vibrational mode coupled only to the third pigment.

Figure 7

Time dependencies of pigment populations for various frequencies of the vibrational mode coupled only to the third pigment.