Absorption of light by light-harvesting complexes and transfer of electronic excitation to the photosynthetic reaction center (RC) constitute the primary light-harvesting process of photosynthesis. This process is investigated on the basis of an atomic level structure of the so-called photosynthetic unit of the photosynthetic bacterium Rhodobacter sphaeroides. The photosynthetic unit combines in the intracytoplasmic membrane a nanometric assembly of three pigment-protein complexes : (i) the photosynthetic reaction center, (ii) a ring-shaped light-harvesting complex LH-I, and (iii) multiple copies of a similar complex, LH-II. The unit has been modeled using the known structure of (i) and for (ii) a model structure complexed appropriately with (i); for (iii) the structure of LH-II of Rhodospirillum molischianum is substituted. The model describes in detail the organization of chromophores involved in primary light absorption and excitation transfer : a hierarchy of ring-shaped bacteriochlorophyll aggregates that surround four centrally located bacteriochlorophylls of the photosynthetic reaction center. The bacteriochlorophylls involved in the overall transfer are found in a coplanar arrangement. On the basis of the modeled structure a quantum-mechanical description of the entire light-harvesting process is developed. For this purpose an effective Hamiltonian is established a priori and then employed to describe the LH-II --> LH-II --> LH-I --> RC cascade of excitation transfer. The transfer times calculated are in agreement with measured transfer times. The results suggest that excitons are the key carriers of the excitation transferred; i.e., electronic excitations are coherently delocalized in the photosynthetic unit. This suggestion is corroborated by an investigation of the effect of inhomogeneous broadening on the predicted excitons in LH-II and LH-I, an effect that is found to be significant but small. A particularly important role is played by the lowest energy excitons to which the circular arrangement of bacteriochlorophylls imparts vanishing oscillator strength. Despite the lack of oscillator strength, the low-energy excitons are well suited for exciton transfer on a subpicosecond and picosecond time scale. The accessory bacteriochlorophylls of the photosynthetic reaction center are found to be critical for the LH-I --> RC transfer, which would take several hundred picoseconds without these bacteriochlorophylls.