The CBS-QB3 method was used to calculate the gas-phase free energy difference between nine tetrazole derivatives and their anions, and the DPCM and CPCM continuum solvation methods were applied to calculate the free energy differences of solvation. The calculations were performed on both gas-phase and solvent-phase optimized structures. Absolute pKa calculations using the CPCM method and the gas-phase optimized structures yielded mean unsigned error of 0.4 pKa unit. The calculations were made with the routine settings implemented in Gaussian 98. The study is as accurate as the best reported so far for six carboxylic acids and phenols and, to our knowledge, the best reported for the acidities of heterocyclic compounds in solution.

The multidimensional similarity measure, operating in the space spanned by potential values, and introduced recently for benzoic acids and monosubstituted benzenes, was applied to tetrazoles, hydrogenated tetrazoles, and phenyltetrazoles. High correlation of potentials at individual atoms constituting five-membered ring in tetrazoles was also found in hydrogenated tetrazoles despite the loss of aromatic character of the latter. Quality of the similarity measure was estimated by correlating it with Hammett constants and with free energy of dissociation for tetrazoles and phenyltetrazoles and methylation reactions for tetrazoles in gas phase. The correlations with the similarity measure were likened to correlations with the potentials at corresponding single atoms in the molecules. As the latter correlations were as good as (or even better than) the correlations with the multidimensional similarity introduced previously, we propose that potentials at the nuclei of congener molecules can be used as the simplest similarity measures. In addition to other systems where potentials at single atoms (sites of binding) were proven to be good reactivity descriptors, this investigation expands their applicability over some heterocyclic systems. Particularly, when similarity of acidic molecules is quantified by the potential at the dissociating hydrogen, it is a good measure of the acid strength both in gas phase as well as in water.