The liaht-harvesting system 11 (LH2) from Rhodospirillum (Rs.) molischianum is a two-ring circular aggregate composed of eight weakly coupled bacteriochlorophylls-a (BChls-a) in the B800 ring and sixteen strongly Coupled BChls-a in the B850 ring. The linear-scaling localized-density-matrix (LDM) method has been implemented at the INDO/S level to probe the electronic structures of monomers, dimers, trimers, pentamers, and entire rings of BChls. The low-lying excited states of a B850 ring are found to fit extremely well with a Frenkel exciton model with long-range dipolar interactions. More importantly, the nearest neighboring BChls-a exciton Coupling constants on a B850 ring are found to be close to those evaluated directly from dimers, and C thus, an existing discrepancy between calculated results of dimers and B850 rings has been resolved. In addition. solvent effects are simulated and the results are compared to the experimental findings.