The light-harvesting system II (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 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.