Energies of solute molecules from an atom charge–dipole interaction model with a surrounding dielectric: Application to Gibbs energies of proton transfer between carboxylic acids in water

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Abstract
An expression is derived for the electrostatic energy of an array of charged, polarizable atoms representing a solute molecule in a cavity in a dielectric continuum, using a generalization of the theory of the reaction field. Explicit formulas are obtained for the case of a spherical cavity. The formulas are used to calculate Gibbs energies and entropies of proton transfer between carboxylic acids in water, using atom polarizabilities from previous studies and atom charges on the COOH and COO− groups which are optimzed to fit experimental Gibbs energies of proton transfer between acyclic carboxylic acids involving monovalent anions. A cavity radius increment is likewise optimized. The optimized fit is good, and the parameters are reasonably consistent with data from other sources (charges from molecular orbital theory, experimental dipole moments, and partial molal volumes). Calculations for reactions involving divalent anions or bicyclo[2.2.2]octane-1-carboxylic acids yield correct Gibbs energies with the same atom charges, but small adjustments are required in the cavity radius increment. Entropies for the reactions involving acyclic acids are calculated assuming that the entropy change arises solely from changes of bulk solvent properties with temperature. The results are in fair agreement with experiment in some cases, but show large discrepancies in others, due in part to a large sensitivity of the entropy to the parameters of the model. Overall, the results support the view that variations in ionization energies of carboxylic acids arise largely from electrostatic interactions.

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