Using geometry optimizations with nonlocal density functional theory, we have carried out a broad survey of the molecular structures of porphyrin variants including inverted porphyrin, true carbaporphyrin, azuliporphyrin, and oxacarba- and thiacarbaporphyrins. For each ring system studied, we have calculated the relative energies of different tautomeric forms and the energies have been correlated with structural features of the central region of the macrocycles such as hydrogen-bonding interactions and hydrogen-hydrogen repulsions. The molecular geometry of azuliporphyrin, which is not available from experiment, provides an interesting illustration of the structural effect of intersecting [10]- and [18]annulene substructures that are present in this molecule. We propose that the energies of the carbenic tautomers of these molecules are related to their ability to form metal complexes with metal-carbon bonds. Finally, the energetics of carbon nucleophilicity of these molecules is examined by calculating the energies of protonation at various carbon centers. By this measure, we find that the central carbon is the most nucleophilic carbon atom for all the molecules examined. This is consistent with available experimental data on the regioselectivity of electrophilic substitution of inverted porphyrins.