All planar homopairings of the DNA base thymine and the RNA base uracil are reported for the first time in this study. Using the idea of binding sites discussed in our previous work (Kelly et al. J. Phys. Chem. B 2005, 109, 11933; J. Phys. Chem. B 2005, 109, 22045) and ab initio density functional theory, we predict and relax 10 thymine and 10 uracil homopairs. The stabilization energies of the homopairs vary from just below zero to -0.82 eV. The results on the pair geometry and energetics are compared with those available in the literature. The collected data on all planar thymine and uracil homopairs can be used to construct the thymine and uracil superstructures seen experimentally on various surfaces.