An electrostatic model for energies of molecules in solution

Abstract

A model for solute-solvent interactions is considered, in which the solute molecule is placed in a cavity surrounded by a dielectric, as originally treated by Kirkwood and Westheimer. In the present version, each atom of the solute molecule is assigned a polarizability and a fixed partial charge, determined by semiempirical methods. These charges induce dipole moments at the atoms and polarize the dielectric. Each induced dipole is calculated by a rigorous treatment of its interactions with the charges and dipoles of the other atoms and with the dielectric. The electrostatic free energy for the molecule is determined as the reversible work to polarize the atoms and the surrounding dielectric and to assemble the charges and induced dipoles in their final positions within the cavity. In turn, molecular dipole moments and free energies of proton and electron transfer among related molecules may be calculated. Explicit formulas are derived for the case of a spherical cavity. Semiempirical determinations for some of the input parameters re­ quired by this model were made for several groups of related compounds, based on experimental dipole moments and free energies of charge transfer at 25°C. Generally, single most stable conformations of the molecules were used, and systematic procedures were developed to center each molecule inside its cavity and to generate the cavity radii. In this manner, a single radius increment (used to generate cavity radii based on molecular size and shape) and set of atom charges for the carboxyl and carboxylate groups of six monoand dicarboxylic acids were determined, for which the calculated free energies of proton transfer with acetic acid in water agreed with experimental values to within an average deviation of 0.65 kJ/mol. When these same charges were used for calcula­ tions of proton transfer between the rather elongated bicyclo[2.2.2]octane1-carboxylic acid and the 4-substituted acid in water, the radius increo ment s used had to be modified by as much as 0.12 A to produce comparable agreement with experiment. Moreover, a single set of atom charges for the amino groups of five primary amines in the gas phase was determined, for which the calculated free energies of electron transfer with methylamine and calculated dipole moments agreed with the corresponding experi­ mental values to within average deviations of 2.52 kJ/mol and 0.13 D, respectively. Finally, a series of calculations was done for the mole­ cules CXY^, CX^Yg, and CX^Y (X, Y = H, F, CI, Br, or I) to determine single sets of charges for atoms X and Y which produced agreement with experimental gas phase dipole moments to within an average deviation of 0.09 D. These results suggest that free energies of charge transfer may be explained largely in terms of electrostatic free energies. In ad­ dition, it was noted that interactive atom polarization contributes significantly to the total molecular dipole moment.