Density functional and second order Moller-Plesset perturbation theoretical methods, coupled with a polarizable continuum model of water, were applied to determine the structures, binding affinities, and reduction potentials of Cu(II) and Cu(I) bound to models of the Asp1, Ala2, His6, and His13His14 regions of the amyloid beta peptide of Alzheimer's disease. The results indicate that the N-terminal Asp binds to Cu(II) together with His6 and either His13 or His14 to form the lower pH Component I of Aβ. Component II of Aβ is the complex between Cu(II) and His6, His13, and His14, to which an amide O (of Ala2) is also coordinated. Asp1 does not bind to Cu(II) if three His residues are attached nor to any Cu(I) species to which one or more His residues are bound. The most stable Cu(I) species is one in which Cu(I) bridges the Nδ of His13 and His14 in a linear fashion. Cu(I) binds more strongly to Aβ than does Cu(II). The computed reduction potential that closely matches the experimental value for Cu(II)/Aβ corresponds to reduction of Component II (without Ala2) to the Cu(I) complex after endergonic attachment of His6.