Solvation Energy Profile

In 1991, Kharkats and Ulstrnp calculated the Gibbs solvation energy profile for a sharp interface nsing a simple electrostatic continuum model [25]. The gist 

FIGURE 1.7 Distribution of an acid in neutral and ionized form. 

By considering the image of an ion of radius a located at a distance h from the other electrolyte, we have the following relations for h a  

FIG U RE 1.8 Left Ion located near a dielectric boundary. Right Gibbs solvation energy profile. (Kharkats, Y. I., and J. Ulstrup, 1991, J Electroanal Chem, Vol. 308, p. 17. Used with permission.) 

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Example Solvation can have a profound effect on the potential energy profile for a reaction. Jorgensen s research group provided important insights into the role of solvation. Consider the nucleophilic addition of the hydroxide anion to formaldehyde ... 

Ab initio molecular orbital calculations are being used to study the reactions of anionic nucleophiles with carbonyl compounds in the gas phase. A rich variety of energy surfaces is found as shown here for reactions of hydroxide ion with methyl formate and formaldehyde, chloride ion with formyl and acetyl chloride, and fluoride ion with formyl fluoride. Extension of these investigations to determine the influence of solvation on the energy profiles is also underway the statistical mechanics approach is outlined and illustrated by results from Monte Carlo simulations for the addition of hydroxide ion to formaldehyde in water. 

Fig. 13 Energy profiles for C C, Cl in DMF. Curve a potential energy in the gas phase. Curve b potential energy in the solvent (D p = 62 meV). Curve c variation of the solvation free energy. Curve d solvent reorganization energy.

The difference between the energy profiles in the solvent and in the gas phase provides the solvation free energy, Gr.wx- (profile c in Fig. 13). The solvent reorganization energy, Ao, may then be obtained from equation (60) as a function of the R—X distance (profile d in Fig. 13). 

FIGURE 3.25. Potential energy profiles (from B3LYP/6-13G calculations) for the clevage of 3- and 4-nitrobenzyl chloride anion radicals (a and b, respectively) in the gas phase (top) and in a solvent (middle and bottom) (from COSMO solvation calculations with a dielectric constant of 36.6 and 78.4, respectively). Dotted and solid lines best-fitting Morse and dissociative Morse curves, respectively. Adapted from Figure 3 of reference 43, with permission from the American Chemical Society. 

Figure 7 Qualitative depiction of the energy profile along the reaction co-ordinate for the Sn2 reaction Cl ICII3CI >CICn3 I Cl, which involves nucleophilic substitution of the chloride of methylchloride by a chloride ion. The potential energy curves drop as the two reactants approach until a loose complex is formed. Then the energy rises rapidly to the transition state, which has two equal C-Cl interatomic distances (zero on the abscissa). The energy profile looks quite different in the gas and solution phases. Compared to the reactants (or products), the loose complex and the TS are poorly solvated, so the energies for these are much higher in solution than in a vacuum.

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