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Cyanobacterial photosystem I (PSI) constitutes monomeric and trimeric pigment-protein complexes [1], the optical properties of which are marked by the presence of long-wavelength absorption bands. In spite of numerous experimental studies, the nature of these bands is still under debate and requires intensive theoretical analysis. Collecting together the data of linear spectroscopy, single molecule spectroscopy and pump-probe measurements of PSI from Arthrospira platensis, we performed the quantum modeling of optical response based on the molecular exciton theory and the multimode Brownian oscillator model [2-4]. Within the framework of our PSI exciton model, the long-wavelength bands of the spectra are attributed to so-called antenna red chlorophylls. Discussion of exciton model micro parameters of these chlorophylls such as site energies, interaction between pigment molecules, the electron-phonon coupling (Huang-Rhys factors), and also the red chlorophyll localization in PSI monomer and trimer are the subjects of our presentation.