Chlorophylls are light-capturing units found in photosynthetic proteins. We study here the ground and excited state properties of monomeric, dimeric, and tetrameric models of the special chlorophyll/bacteriochlorophyll (Chl/BChl) pigment (P) centers P700 and P680/P870 of type I and type II photosystems, respectively. In the excited state calculations, we study the performance of the algebraic diagrammatic construction through second-order (ADC(2)) method in combination with the reduced virtual space (RVS) approach and the recently developed Laplace-transformed scaled-opposite-spin (LT-SOS) algorithm, which allows us, for the first time, to address multimeric effects at correlated ab initio levels using large basis sets. At the LT-SOS-RVS-ADC(2)/def2-TZVP level, we obtain vertical excitation energies (VEEs) of 2.00-2.07 and 1.52-1.62 eV for the P680/P700 and the P870 pigment models, respectively, which agree well with the experimental absorption maxima of 1.82, 1.77, and 1.43 eV for P680, P700, and P870, respectively. In the P680/P870 models, we find that the photoexcitation leads to a π → π* transition in which the exciton is delocalized between the adjacent Chl/BChl molecules of the central pair, whereas the exciton is localized to a single chlorophyll molecule in the P700 model. Consistent with experiments, the calculated excitonic splittings between the central pairs of P680, P700, and P870 models are 80, 200, and 400 cm(-1), respectively. The calculations show that the electron affinity of the radical cation of the P680 model is 0.4 V larger than for the P870 model and 0.2 V larger than for P700. The chromophore stacking interaction is found to strongly influence the electron localization properties of the light-absorbing pigments, which may help to elucidate mechanistic details of the charge separation process in type I and type II photosystems.