On the relative acidities of organic compounds:: Electronic and geometric relaxation energies

The energy for deprotonation of a molecule in the gas phase may be divided into an initial-state electrostatic part and a relaxation part. The electrostatic part is dominating in determining the relative acidities of organic compounds, but the relaxation part is not negligible. The relaxation energy may be split up in two parts, and accurate calculations (MP2/6-311++G**//RHF/6-311++G**) of these electronic and geometric relaxation energies are presented for 13 small organic molecules (four alkanes, three alcohols, two enols, and three carboxylic acids). It is shown that although the electronic relaxation energy is 2 orders of magnitude larger than the geometric relaxation energy, the difference in electronic relaxation energy and the difference in geometric relaxation energy between a pair of molecules may be of the same size. For example, while the electronic relaxation energy of the acetate anion is 6.1 kcal/mol smaller than that of the 2-propanoxide anion, the geometric relaxation energy is 4.6 kcal/mol larger. Hence, the two relaxation contributions partially cancel each other, and the total difference in deprotonation energy is approximately equal to the shift in initial-state electrostatic potential between the two compounds. The electronic relaxation energies are largest for the most easily polarizable molecules, and the geometric relaxation energies are largest for molecules where classical resonance arguments suggest strongly stabilized anions (carboxylic acids and enols). The MP2/6-311++G**//RHF/6-311++G** level of theory, including zero-point and thermal energy corrections, give computed absolute acidities, Delta H(298), very close to experimental gas-phase acidities (root-mean square deviation 1.1 kcal/mol).