The Qy absorption spectrum of Photosystem-I from Thermosynecochoccus elongatus (formerly Synecochoccus elongatus) is calculated using the CAM-B3LYP density functional and INDO schemes based on a quantum-mechanically refined structure for the entire photosystem obtained using the PW91 density functional. These methods present a priori predictions of the absorption and linear dichroism spectra and include protein electrostatic effects, short range inductive effects, long-range and short-range exciton couplings, and superexchange effects involving aromatic residues and carotenes. CAM-B3LYP is used as it is the only known density functional that correctly describes the Q bands of chlorophylls, all other methods contaminating them with erroneous charge-transfer excitations. A critical feature is found to be the use of fully optimized heavy-atom coordinates, with those obtained from just X-ray crystallography providing a poor description of the electronic properties of the chromophores. The result is a realistic first-principles prediction of the observed absorption band that identifies the nature of the red-shifted chlorophylls as well as the energies of the reaction-center chlorophylls and the exciton couplings acting between them. The "special pair" appears more like a dimer of dimers than a self-contained functional unit, with the exciton couplings between its members and the accessory chlorophylls exceeding the internal coupling.