Solvation energies

The simplest model for a solvent is one of a continuous dielectric which effectively reduces charge-charge interactions but does not influence energies due to covalence. No matter how naive this model may be it stresses a very simple point. As the dielectric constant increases and ionic energies diminish then the effect of covalence in bringing about association becomes dominant. Consider the equilibrium 

The slope of the AHion plot as a function of halide for the gaseous ions, plotting the halides with equal increment on the abscissae, 

Reduction of the dielectric constant of the solvent decreases the slope of the hydration energy such that the solvation energy becomes less important as a background against which the equilibrium 

Of course, change of ligand around the cation does not affect the hydration energy of the anion in the equilibrium 

However, it affects the slope of MX in Fig. 10. From the above considerations any atoms Y which reduce the charge (or increase the size of M) without equally lowering the electron affinity of the orbital acting as 

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On correcting to unit activity Ag (aq), we can obtain E g/Ag - Electron solvation energy is neglected in this definition. 

The solute-solvent interaction in equation A2.4.19 is a measure of the solvation energy of the solute species at infinite dilution. The basic model for ionic hydration is shown in figure A2.4.3 [5] there is an iimer hydration sheath of water molecules whose orientation is essentially detemiined entirely by the field due to the central ion. The number of water molecules in this iimer sheath depends on the size and chemistry of the central ion ... 

The FI2O molecules of these aquo-complexes constitute the iimer solvation shell of the ions, which are, in turn, surrounded by an external solvation shell of more or less uncoordinated water molecules fomiing part of the water continuum, as described in section A2.4.2 above. Owing to the difference in the solvation energies,... 

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],... 

Eisenberg D and A D McLachlan 1986. Solvation Energy in Protein Folding and Binding. Nature 319 199-203. 

Gilson M K and B Honig 1988. Calculation of the Total Electrostatic Energy of a Macromoleculai System Solvation Energies, Binding Energies and Conformational Analysis. Proteins Structure Function and Genetics 4 7-18. 

There is no one best method for describing solvent effects. The choice of method is dependent on the size of the molecule, type of solvent effects being examined, and required accuracy of results. Many of the continuum solvation methods predict solvation energy more accurately for neutral molecules than for ions. The following is a list of preferred methods, with those resulting in the highest accuracy and the least amount of computational effort appearing first ... 

LORG (localized orbital-local origin) technique for removing dependence on the coordinate system when computing NMR chemical shifts LSDA (local spin-density approximation) approximation used in more approximate DFT methods for open-shell systems LSER (linear solvent energy relationships) method for computing solvation energy... 

Considering Highest Occupied Molecular Orbital and Lowest Unoccupied Molecular Orbital (providing that solvation energies are equal) 44 might be.a better reducer than 43 (Schemes 65-68). 

Correlation methods discussed include basic mathematical and numerical techniques, and approaches based on reference substances, empirical equations, nomographs, group contributions, linear solvation energy relationships, molecular connectivity indexes, and graph theory. Chemical data correlation foundations in classical, molecular, and statistical thermodynamics are introduced. 

Linear Free Energy—Linear Solvation Energy Relationships. Linear free energy (LFER) and linear solvation energy (LSER) relationships are used to develop correlations between selected properties of similar compounds. These are fundamentally a collection of techniques whereby properties can be predicted from other properties for which linear dependency has been observed. Linear relationships include not only simple y = rax + b relationships, but also more compHcated expressions such as the Hammett equation (254) which correlates equiUbrium constants for ben2enes,... 

Kamlet-Taft Linear Solvation Energy Relationships. Most recent works on LSERs are based on a powerfiil predictive model, known as the Kamlet-Taft model (257), which has provided a framework for numerous studies into specific molecular thermodynamic properties of solvent—solute systems. This model is based on an equation having three conceptually expHcit terms (258). 

Low sulfate selectivity of the ion-selective electrodes (ISE) based on lipophilic quaternary ammonium salts (QAS) is usually explained by unfavorable ratio of sulfate hydration and solvation energies. We have been shown that another reason does exist as well namely, low efficiency of sulfate-QAS cation interaction caused by steric hindrance for simultaneous approach of two QAS cations, containing four long-chain hydrocarbon substituents, to sulfate ion. 

Eor instance, the contribution of water beyond 12 A from a singly charged ion is 13.7 kcal/mol to the solvation free energy or 27.3 kcal/mol to the solvation energy of that ion. The optimal treatment is to use Ewald sums, and the development of fast methods for biological systems is a valuable addition (see Chapter 4). However, proper account must be made for the finite size of the system in free energy calculations [48]. 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

Stabilization of the syn conformer in the gas phase is explained rather intuitively in terms of the extra stabilization due to increased interactions between the H atom in the OH group and the O atom in C=0 group. As one can see in Figure 5, the extra stabilization in the anti confonner in aqueous solution arises from the solvation energy, especially at the carbonyl oxygen site. 

It has been possible to obtain thermodynamic data for the ionization of alkyl chlorides by reaction with SbFs, a Lewis acid, in the nonnucleophilic solvent S02C1F. It has been foimd that the solvation energies of the carbocations in this medium are small and do not differ much from one another, making comparison of the nonisomeric systems possible. As long as subsequent reactions of the carbocation can be avoided, the thermodynamic characteristics of this reaction provide a measure of the relative ease of carbocation formation in solution. 

Many properties have an influence on nucleophilicity. Those considered to be most significant are (1) the solvation energy of the nucleophile (2) the strength of the bond being formed to carbon (3) the size of the nucleophile (4) flie electronegativity of the attacking atom and (5) the polarizability of the attacking atom. Let us consider how each of these factors affects nucleophilicity ... 

Solvation can be studied by thermodynamic methods, often combined with ex-trathermodynamic assumptions so as to express results for individual ions (rather than for neutral electrolytes). The solvation energy is the free energy change upon transferring a molecule or ion from the gas phase into a solvent at infinite dilution. This sometimes can be obtained from a consideration of the following processes, written for a 1 1 electrolyte ... 

In Section 8.2 solvation energy AGsoiv was defined as the free energy change upon transferring a solute from the gas into a solvent. We can now relate the transfer free energy to solvation energies ... 

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