Frequency domain spectra of the photosystem I (PS1) of Synechococcus elongatus are measured in a wide temperature range and explained in an exciton model based on the recently determined X-ray crystal structure. Using the known spatial positions and orientations of the chlorophylls (Chls) the dipole-dipole couplings between the chromophores are calculated. In contrast, the Chl Qy site energies are determined by a simultaneous fit of low-temperature absorption, linear dichroism, and circular dichroism spectra. The best fit is achieved by an evolutionary algorithm after assigning some chromophores to the red- most states. Furthermore, a microscopically founded homogeneous line width is included and the influence of inhomogeneous broadening is discussed. To confirm the quality of the resulting PS1 model, time-dependent fluorescence spectra are calculated, showing a good agreement with recent experimental results.