A short description of two theories of the primary photosynthetic processes is given. Generally accepted in 1950s–1990s, the localized excited states theory has been changed to the modern exciton theory. Appearance of the new experimental data and the light-harvesting complex crystal structure are reasons why the exciton theory has become important. The bulk of data for the old theory and outstanding experiments that have been the driving force for a new theory are discussed in detail.

Based on single molecule spectroscopy analysis and our preliminary theoretical studies, the linear and fluorescence spectra of the PSI trimer from Arthrospira platensis with different realizations of the static disorder were modeled at cryogenic temperature. Considering the previously calculated spectral density of chlorophyll, an exciton model for the PSI monomer and trimer including the red antenna states was developed taking into account the supposed similarity of PSI antenna structures from Thermosynechococcus e., Synechocystis sp. PCC6803, and Arthrospira platensis. The red Chls in the PSI monomer were assumed to be in the nearest proximity of the reaction center. The PSI trimer model allowed the simulation of experimentally measured zero phonon line distribution of the red states considering a weak electron-phonon coupling for the antenna exciton states. However, the broad absorption and fluorescence spectra of an individual emitter at 760 nm were calculated by adjusting the Huang-Rhys factors of the chlorophyll lower phonon modes assuming strong electron-phonon coupling.