An effective Frenkel-exciton Hamiltonian for the entire LH2 photosynthetic complex (B800, B850, and carotenoids) from Rhodospirillum molischianum is calculated by combining the crystal structure with the Collective Electronic Oscillators (CEO) algorithm for optical response. Electronic couplings among all pigments are computed for the isolated complex and in a dielectric medium, whereby the protein environment contributions are incorporated using the Self-Consistent Reaction Field approach. The absorption spectra are analyzed by computing the electronic structure of the bacteriochlorophylls and carotenoids forming the complex. Interchromophore electronic couplings are then calculated using both a spectroscopic approach, which derives couplings from Davydov's splittings in the dimer spectra, and an electrostatic approach, which directly computes the Coulomb integrals between transition densities of each chromophore. A comparison of the couplings obtained using these two methods allows for the separation of the electrostatic (Forster) and electron exchange (Dexter) contributions. The significant impact of solvation on intermolecular interactions reflects the need for properly incorporating the protein environment in accurate computations of electronic couplings. The Forster incoherent energy transfer rates among the weakly coupled B800-B800, B800-B850, Lyc-B850, arid Lyc-B850 molecules are calculated, and the effects of the dielectric medium on the LH2 light-harvesting function are analyzed and discussed.