Using time-dependent density functional theory (TDDFT), we obtained the excitation energy transfer coupling (Coulombic coupling) between the S-1 state of rhodopin glucoside (RG) and the Q(y) state of bacteriochlorophylls (BCh1) in the light-harvesting complex II (LH2) of purple photosynthetic bacterium Rhodopseudomonas (Rps.) acidophila. Our results suggest that the small mixing of S-2 character arising from symmetry-breaking of the carotenoid plays an important role in the Coulombic coupling. As a result the carotenoid (car) S-1 couplings to chlorophylls are similar to a set of scaled down Car(S2)-BCh1(Q(y)) couplings. We also report results for 6,10,15,19-tetramethyl-2-cis-4,6,8,10,12,14,16,18,20-all trans-22-cis-tetracosaundecaene, the polyene backbone of RG with six methyl groups attached, in two different structures: an optimized planar structure and the crystal structure of RG with hydrogen atoms replacing the two end groups, which is distorted from its planar structure. The mixing of S-2 configuration is strictly forbidden in the planar structure due to symmetry. In this case the polyene still couples moderately strongly to the nearby BCh1s. In the distorted structure derived from RG crystal structure, coupling strengths and the role of S-2 character mixing are similar to those of the full RG. Using an exciton model simulation, the calculated coupling strengths yield Car(S-1)-to-BCh1(Q(y)) excitation energy transfer times that are in good agreement with recent experimental results.