Different reconstructions of the polar, cation-terminated (100) surface of Cu2O have been investigated. All surfaces have been fully relaxed employing a pair-potential and shell-model description of the interactions within the crystal. A (1 x 1) missing-row reconstruction gave the lowest surface energy, while the experimentally reported (3 root 2 x root 2)R45 degrees surface structure could not be made stable. Quantum chemical models of the (1 x 1)-reconstructed surface were studied and the Cu+ (d(10)-->d(9) s(1)) excitation energy computed; relaxation of the surface leads to an increased excitation energy (1.89 eV) and a more ionic description compared with the reconstructed but unrelaxed surface (1.38 eV). The hydrogen atomic chemisorption energy was also computed; for the relaxed surface the computed binding energy of 2.06 eV is sufficiently below half the binding energy of H-2 that hydrogen dissociation can be excluded. This is in agreement with experiment. For the unrelaxed surface the binding energy is higher, 2.26 eV, which would allow energetically for H-2 to dissociate. The convergence of the Madelung potential for these nontrivial surfaces is investigated with the conclusion that it is favorable to perform the full Ewald summation. A program to compute the Gaussian integrals over the Madelung potential is reported.