The energetics, structure, and vibrational spectra of a wide variety of H+(H2O)(8) structures are calculated using density functional theory and second-order Moller-Plesset ab initio methods. In these isomers of H+(H2O)(8) the local environment of the excess proton sometimes resembles a symmetric H5O2+ structure and sometimes H3O+, but many structures are intermediate between these two limits. We introduce a quantitative measure of the degree to which the excess proton resembles H5O2+ or H3O+. Other bond lengths and, perhaps most useful, the position of certain vibrational bands track this measure of the symmetry in the local structure surrounding the excess proton. The general trend is for the most compact structures to have the lowest energy. However, adding zero-point energy counteracts this trend, making prediction of the most stable isomer impossible at this time. At elevated temperatures corresponding to recent experiments and atmospheric conditions (150-200 K), calculated Gibbs free energies clearly favor the least compact structures, in agreement with recent thermal simulations [Singer, McDonald, and Ojamae, J. Chem. Phys. 112, 710 (2000)].