Bond dissociation energies, electron affinities, and proton affinities are computed for a variety of molecules containing C-H, N-H, O-H, and S-H bonds using density functional theory with the B3LYP functional. Thermochemistry in which these bonds are broken or ions are formed is particularly relevant to understanding proton transfer (acid-base), electron transfer (redox), and H-atom transfer (free radical) reactions. A series of basis set experiments has led to an optimum compromise between computational speed and accuracy. Several theoretical models are defined and tested, and the medium and higher-level models approach an accuracy of 1 kcal/mol. Use of the above methodology to obtain absolute bond dissociation energies for X-H bonds, isodesmic reaction schemes, substituent effects, redox potentials, and gas-phase acid dissociation constants shows the usefulness of this approach.