Energy of solvation

Free energy perturbation (FEP) theory is now widely used as a tool in computational chemistry and biochemistry [91]. It has been applied to detennine differences in the free energies of solvation of two solutes, free energy differences in confonnational or tautomeric fonns of the same solute by mutating one molecule or fonn into the other. Figure A2.3.20 illustrates this for the mutation of CFt OFl CFt CFt [92]. 

Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... 

Kirkwood generalized the Onsager reaction field method to arbitrary charge distributions and, for a spherical cavity, obtained the Gibbs free energy of solvation in tenns of a miiltipole expansion of the electrostatic field generated by the charge distribution [12, 1 3]... 

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

McDonald, N. A., Carlson, H. A., Jorgensen, W. L. Free energies of solvation in chloroform and water from a linear response approach. J. Phys. Org. Chem. 10 (1997) 563-576... 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

The total electrostatic free energy G j of a system is given by the sum of the Coulomb energy and the Bom free energy of solvation (Eq. (39)) ... 

The Electrostatic Contribution to the Free Energy of Solvation The Born and Onsager Models... 

The energy of solvation can be further broken down into terms that are a function of the bulk solvent and terms that are specifically associated with the first solvation shell. The bulk solvent contribution is primarily the result of dielectric shielding of electrostatic charge interactions. In the simplest form, this can be included in electrostatic interactions by including a dielectric constant k, as in the following Coulombic interaction equation ... 

The solvent accessible surface area (SASA) method is built around the assumption that the greatest amount of interaction with the solvent is in the area very close to the solute molecule. This is accounted for by determining a surface area for each atom or group of atoms that is in contact with the solvent. The free energy of solvation AG° is then computed by... 

The accuracy of these methods is tested by finding the mean absolute error between the computed and experimental free energies of solvation. The SM4 method does well for neutral molecules in alkane solvents with a mean absolute error of 0.3 kcal/mol. For neutral molecules, the SM5 methods do very well with mean absolute errors in the 0.3 to 0.6 kcal/mol range, depending on the method and solvent. For ions, the SMI method seems to be most accurate with... 

The free energy of activation at the QCISD(T)/6-31 H-- -G(d,p) level amounts to 21.1 kcal/mol. According to the authors, the large electron density redistribution arising upon cyclization makes it necessary to use extended basis sets and high-order electron correlation methods to describe the gas-phase thermodynamics, which indicates clearly the gas-phase preference of the azido species. However, the equilibrium is shifted toward the tetrazole as the polarity of a solvent is increased. For instance, SCRF calculations (e = 78.4) yield a relative free energy of solvation with respect to the cw-azido isomer of —2.4 kcal/mol for the tmns-zziAo compound and of —6.8 kcal/mol for the tetrazole isomer. At a much lower level, the... 

It will also be shown that the absolute electrode potential is not a property of the electrode but is a property of the electrolyte, aqueous or solid, and of the gaseous composition. It expresses the energy of solvation of an electron at the Fermi level of the electrolyte. As such it is a very important property of the electrolyte or mixed conductor. Since several solid electrolytes or mixed conductors based on ZrC>2, CeC>2 or TiC>2 are used as conventional catalyst supports in commercial dispersed catalysts, it follows that the concept of absolute potential is a very important one not only for further enhancing and quantifying our understanding of electrochemical promotion (NEMCA) but also for understanding the effect of metal-support interaction on commercial supported catalysts. 

It is thus clear from the previous discussion that the absolute electrode potential is not a property of the electrode material (as it does not depend on electrode material) but is a property of the solid electrolyte and of the gas composition. To the extent that equilibrium is established at the metal-solid electrolyte interface the Fermi levels in the two materials are equal (Fig. 7.10) and thus eU 2 (abs) also expresses the energy of transfering an electron from the Fermi level of the YSZ solid electrolyte, in equilibrium with po2=l atm, to a point outside the electrolyte surface. It thus also expresses the energy of solvation of an electron from vacuum to the Fermi level of the solid electrolyte. 

R. Gomer, and G. Tryson, An experimental determination of absolute half-cell emfs and single ion free energies of solvation, J. Chem. Phys. 66, 4413-4424 (1977). 

The real energy of ion solvation, af, defined by Eq. (2), expresses the change in ion energy upon its transfer from a gas phase into a solution. Unlike the chemical energy of solvation, psi, the value of the real energy of solvation, also in the standard state, can be calculated from experimental data using the formula, e.g., for the hydration of the cation ... 

The determination of the real energies of solvation from measurements of the voltaic cells (Section VI) makes it possible to find the absolute electrode potentials in nonaqueous solvents owing to the relation... 

Real Free Energy of Solvation of H+ and Absolute Potential of h( s) in Different Solvents ... 

The published experimental estimates of the surface potentials of various organic solvents have been derived mainly from the data on the real, asi, and chemical, gSi, energies of solvation of ions ... 

---