Transport of excitation energy in a molecular aggregate. VIII. Numerical simulation of exciton processes in thylakoid membrane

Abstract We investigate the exciton dynamics in a molecular crystal. The dynamics is based on the exciton Hamiltonian, the phonon Hamiltonian, and the exciton–phonon interaction linear in phonon coordinates. Using the interaction picture, expressions were previously obtained for the rate of coherent migration of the exciton clothed by phonons, and the rate of incoherent or hopping motion. In this work we derive an expression for the clothed exciton propagator, which permits an explicit calculation of the hopping rate. Thus, the rates of exciton generation, coherent transfer, and hopping are determined completely from theory. These velocity constants, along with the experimental fluorescence decay constants and reaction rate constants for the excited molecules, are used to write a generalized master equation that describes the rate of change of exciton population at each site. The master equation can be numerically solved by using a time step of the order of a few femtoseconds, while the excited‐state reactions and exciton transfer occur in the picosecond scale. Exciton dynamics is numerically simulated for a simple model of thylakoid membrane in green plants. The model is based on the known characteristics of thylakoid architecture. The membrane is divided into 97 zones, each zone in the bulk containing 1,442 chlorophylls, one P700, and one P680. The latter two pigments are randomly placed in each zone, while keeping their distance between 55 and 60 Å. This accounts for the randomness in orientation. The disorder of the chlorophyll molecules within the domains of photosystems is neglected. Our findings are as follows. On average, about 6 million photons within the range of 655–681 nm pass through a membrane in 1 s. About 2.3% of incident photons are absorbed by the membrane chlorophyll molecules. For an excitation bandwidth of 70–175 cm −1 , the coherent transfer rate between two adjacent molecules is 1.138 ± 0.488 ps −1 . Because the Debye frequency is expected to be much smaller, the slow phonon limit applies. The exciton–phonon coupling constant that can be determined from the transition dipole–transition dipole interaction model leads to a hopping rate of 0.088 ps −1 at 300 K. A steady state is effectively achieved for each zone in the bulk in ∼5 ns. After a period of 50 ns, P700 and P680 in average trap at the rate of 650–702 and 629–679 excitons per second, respectively. The average rate of charge separation and subsequent reactions of each excited photosystem varies as 592–639 per second for PSI and 630–680 per second for PSII. These numbers lead to a reasonable estimate for the amount of glucose produced in each square meter of leaf area in a day. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005