We have carried out quantum chemical computations on the special pairs of chlorophyll-a molecules so as to resolve the ambiguity of the large oxidation odor potential of P680 and establish the identities of P680 and P700 by comparing the calculated potentials with the observed ones. The methodology adopted here has been INDO. At first the oxidation potential of chlorophyll-a has been determined from the calculations on model structures prepared from the crystallographic structure of ethyl chlorophyllide-a dihydrate with variously truncated side chains. A good value of the oxidation potential is found only for structures that have most of the side chains and hydrogen-bonded water molecules intact. The calculated oxidation potentials are about 0.68 V in dichloromethane and 0.77 V in acetonitrile at pH 4.5 at 298.15 K. The calculated numbers are in good agreement with the observed values 0.74-0.86 and 0.76 V, respectively, for chlorophyll-a in these solvents. The intact structures have been used to form the special pairs. The pairs studied include the Shipman model, Strouse model, Svensson model, and a trial model. The new model for the structure of the special pair is a result of the synthesis of the basic chlorophyll-a structure and the optimum Jr-Jr interaction between two macrocycles facing each other, and it has been specifically studied to complete investigations on structures that, in principle, fill the gap between the Shipman model and the Svensson pair model. The theoretically determined redox potentials are: (1) 0.45-0.56 V for the Strouse model, 0.56-0.57 V for the Shipman model, 0.54 V for the Svensson dimer, 0.16 V for the trial model (dimer of monohydrates), and 0.34 V for the trial model (dimer of dihydrates) in the absence of a methionine neighbor; and (2) in the presence of a methionine electrostatically interacting with one of the chlorophylls, 0.97-1.08 V for the Strouse model, 1.07-1.08 V for the Shipman model, 1.05 V for the Svensson pair, 0.68 V for the trial model (monohydrate dimer) and 0.85-0.86 V for the trial model (dihydrate dimer). Comparing these values with 0.46-0.52 V for P700, one can identify P700 with all of the dimers except the trial dimer of chlorophyll monohydrates. Pigment P680 that has a redox potential of 1.1 V can be identified with the Strouse, Shipman, and Svensson pair models. Interaction with the surrounding dielectric medium and possible bare ions holds the key for the increase of the redox potential from its monomeric value. The formation of the Shipman model from two chlorophyll-a molecules is, in principle, not kinetically favored. The formation of the trial dimer from the mono- or dihydrates is not thermodynamically favored. A reexamination of the experimental spectroscopic data for P700 is necessary to decide whether the Svensson dimer (without the neighboring methionine) can qualify as P700. Hence the issue remains open. Relatively recent crystallographic data rule out water as a ligand of magnesium of the chlorophylls in P680 and thus discount the Strouse, Shipman, and trial models. Our INDO calculations show that the structure of P680 proposed by Svensson et al. from homology modeling successfully explains the abnormally large oxidation redox potential of this pigment.