In this work we explain the spectral heterogeneity of the absorption band (. Biochim. Biophys. Acta. 1229:373-380), as well as the spectral evolution of pump-probe spectra for membranes of Rhodopseudomonas (Rps.) viridis. We propose an exciton model for the LH1 antenna of Rps. viridis and assume that LH1 consists of 24-32 strongly coupled BChl b molecules that form a ring-like structure with a 12- or 16-fold symmetry. The orientations and pigment-pigment distances of the BChls were taken to be the same as for the LH2 complexes of BChl a-containing bacteria. The model gave an excellent fit to the experimental results. The amount of energetic disorder necessary to explain the results could be precisely estimated and gave a value of 440-545 cm(-1) (full width at half-maximum) at low temperature and 550-620 cm(-1) at room temperature. Within the context of the model we calculated the coherence length of the steady-state exciton wavepacket to correspond to a delocalization over 5-10 BChl molecules at low temperature and over 4-6 molecules at room temperature. Possible origins of the fast electronic dephasing and the observed long-lived vibrational coherence are discussed.