Solvation Energy Estimates

Some early computations for cations are given below. In all cases, the loss of two hydrogen bonding positions per water molecule was assumed (i.e., 20.9 kJ/mole of water), and the dipole is in the axial position. In the Verwey positions, only one hydrogen bonding position may be assumed to be lost. Solvation energies are the quasi-absolute values from Ref. 95. p. 106. Distances are ion to dipole center. 

Inner shell dielectric constant, 1.599. Outer shell dielectric 

This work suggested that the distances obtained for monovalent cations were also too long. For K+, the inner and second shell were examined on this basis, and a fit could be made at a first shell ion-dipole center distance of 2.253 A, with an induced dipole of 0.461 D (eA = 3.094), with a second shell just apparent at 4.560 A, where the induced dipole was 0.050 D (eA = 6.650). This distance is certainly too 

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This fomuila does not include the charge-dipole interaction between reactants A and B. The correlation between measured rate constants in different solvents and their dielectric parameters in general is of a similar quality as illustrated for neutral reactants. This is not, however, due to the approximate nature of the Bom model itself which, in spite of its simplicity, leads to remarkably accurate values of ion solvation energies, if the ionic radii can be reliably estimated [15],... 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

The main point of this exercise and considerations is that you can easily examine the feasibility of the desolvation hypothesis by using well-defined thermodynamic cycles. The only nontrivial numbers are the solvation energies, which can however be estimated reliably by the LD model. Thus for example, if you like to examine whether or not an enzymatic reaction resembles the corresponding gas-phase reaction or the solution reaction you may use the relationship... 

Thus it is concluded that while destabilization of the ground-state charges may be used in enzymes to reduce Ag, it is not used in enzymes that optimize kzJKM. Furthermore, we argue that the feasibility of any proposed desolvation mechanism can be easily analyzed (and in most cases disproved) by the reader once the relevant thermodynamic cycle is defined and the solvation energies of the reacting fragments are estimated. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

The reliability of the experimental A / MX) values was checked for systems containing nitrobenzene, nitromethane, and 1,2-dichlo-roethane as organic solvent by comparing the differences in these values for various pairs of salts with the differences in the Galvani (i.e.,distribution) potemtials, A cp MX) for the same pairs. The differences should be the same. The A cp or Afip data can be used to estimate ion solvation energies in a water-saturated solvent. ... 

Dissolution of an ionic salt is essentially a separation process carried out by the interaction of the salt with water molecules. The separation is relatively easy in water because of its high dielectric constant. Comparison of the energies needed to separate ions of NaCl from 0-2 nm to infinity shows that it takes 692-89 kJ mol" in vacuum, but only 8-82 kJ moF in aqueous solution (Moore, 1972). Similar arguments have been used to try to estimate solvation energies of ions in aqueous solution, but there are difficulties caused by the variations in dielectric constant in the immediate vicinity of individual ions. 

In principle, it should be possible to use computational thermochemistry to calculate free energies of formation for unknown tetrahedral intermediates. In practice this remains difficult because of the problem of estimating solvation energies. There is no doubt that computational methods will become increasingly important in this as in other areas. 

Simonson, T. Briinger, A.T., Solvation free energies estimated from macroscopic continuum theory an accuracy assessment, J. Phys. Chem. 1994, 98, 4683-4694... 

Kamlet, M. J., Doherty, R. M., Carr, P. W., Mackay, D., Abraham, M. H., Taft, R. W. (1988) Linear solvation energy relationships. 44. Parameter estimation rules that allow accurate prediction of octanol/water partition coefficients and other solubility and toxicity properties of polychlorinated biphenyls and polycyclic aromatic hydrocarbons. Environ. Sci. Technol. 22, 503-509. 

These definitions are interpreted as follows environment atoms recognize the average weighted states of the ligands each ligand recognizes only the environment atoms and itself with the full scale for estimation of its effective Bom radius. Alternate definitions of the electrostatic solvation energy and the effective Bom radius at the intermediate states are also possible.81... 

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