Identity proton-transfer reactions between 21 acids, Y-X-H, and their conjugate bases, X--Y, were studied according to the reaction scheme, Y-X-H + X--Y --> (Y-X-H....-X-Y)(cx) --> [Y-(XHX)-H-...-X-...-Y](ts) --> (Y-X-....H-X-Y)(cx) --> Y-X- + H-X-Y, where cx indicates an ion-molecule complex and ts indicates the proton-transfer transition state. All species were optimized at the MP2/6-311+G** level, and these geometries were used for single-point calculations by other methods: coupled-cluster, DFT (gas phase), and a polarizable continuum aqueous solvent model (COSMO). All methods gave enthalpies of deprotonation which correlate well with experimental measurements of DeltaH(ACID) (gas) or pK(a) (aq). Calculated gas-phase enthalpies of deprotonation (DeltaH(ACID)) and enthalpies of activation (DeltaH(double dagger)) are poorly correlated except for small, carefully selected sets. This result stands in contrast to the many aqueous phase Bronsted correlations of kinetic and equilibrium acid strength. On the other hand, gas-phase enthalpies of complexation and DeltaH(double dagger) are well correlated, indicating that factors which stabilize the transition state are at work in the bimolecular ion-molecule complex although to a smaller degree. We infer that intermoiety electrostatic and other interactions, similar within the complex and the transition state, but absent in the separated reactants (products), cause the lack of correlation between DeltaH(ACID) and the other two quantities. Such differences are strongly attenuated in water because reactants and products do interact with polar/polarizable matter (the solvent) if not with each other. Charge distributions (NPA) were computed, allowing calculation of Bernasconi's "transition state imbalance parameter". Such measures provide intuitively satisfactory trends, but only if the reaction termini, X, are kept the same. As X is made more electronegative, the magnitude of the apparent imbalance increases, a result of greater negative charge on X in the transition state. This result gives additional support for the importance of the ion-triplet structure, [YX-...H+....-XY], to the stability of the transition state. Additional qualitative support for this conclusion is provided by the inverse relationship between the activation barrier and the charge on the in-flight hydrogen in the transition state, and by the dominance of polar over resonance substituent effects on the stability of the transition state. Calculations also show that the "nitroalkane anomaly", well established in solution, does not exist in the gas phase. The COSMO model partly reproduces this anomaly and performs adequately except when strong, specific intermolecular forces such as hydrogen bonding between solvent and anions are important.