Energy chemical solvation

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 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 ... 

The surface potential of a solution can be calculated, according to Eq. (10.18), from the dilference between the experimental real energy of solvation of one of the ions and the chemical energy of solvation of the same ion calculated from the theory of ion-dipole interaction. Such calculations lead to a value of -1-0.13 V for the surface potential of water. The positive sign indicates that in the surface layer, the water molecules are oriented with their negative ends away from the bulk. 

MD simulations in expHcit solvents are stiU beyond the scope of the current computational power for screening of a large number of molecules. However, mining powerful quantum chemical parameters to predict log P via this approach remains a challenging task. QikProp [42] is based on a study [3] which used Monte Carlo simulations to calculate 11 parameters, including solute-solvent energies, solute dipole moment, number of solute-solvent interactions at different cutoff values, number of H-bond donors and acceptors (HBDN and HBAQ and some of their variations. These parameters made it possible to estimate a number of free energies of solvation of chemicals in hexadecane, octanol, water as well as octanol-water distribution coefficients. The equation calculated for the octanol-water coefficient is ... 

This dependence is fundamental for electrochemistry, but its key role for liquid-liquid interfaces was first recognized by Koryta [1-5,35]. The standard transfer energy of an ion from the aqueous phase to the nonaqueous phase, AGf J, denoted in abbreviated form by the symbol A"G is the difference of standard chemical potential of standard chemical potentials of the ions, i.e., of the standard Gibbs energies of solvation in both phases. 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

Fig. 2.5. Possible applications of a coupling parameter, A, in free energy calculations, (a) and (b) correspond, respectively, to simple and coupled modifications of torsional degrees of freedom, involved in the study of conformational equilibria (c) represents an intramolecular, end-to-end reaction coordinate that may be used, for instance, to model the folding of a short peptide (d) symbolizes the alteration of selected nonbonded interactions to estimate relative free energies, in the spirit of site-directed mutagenesis experiments (e) is a simple distance separating chemical species that can be employed in potential of mean force (PMF) calculations and (f) corresponds to the annihilation of selected nonbonded interactions for the estimation of e.g., free energies of solvation. In the examples (a), (b), and (e), the coupling parameter, A, is not independent of the Cartesian coordinates, x. Appropriate metric tensor correction should be considered through a relevant transformation into generalized coordinates...

The present chapter thus provides an overview of the current status of continuum models of solvation. We review available continuum models and computational techniques implementing such models for both electrostatic and non-electrostatic components of the free energy of solvation. We then consider a number of case studies, with particular focus on the prediction of heterocyclic tautomeric equilibria. In the discussion of the latter we center attention on the subtleties of actual chemical systems and some of the dangers of applying continuum models uncritically. We hope the reader will emerge with a balanced appreciation of the power and limitations of these methods. 

The simplest generalization of free-energy-of-solvation concepts to dynamics in solution is provided by transition state theory. In conventional transition state theory, the rate constant of a chemical reaction at temperature T is given by... 

Figure 11.1 A two-dimensional gas-phase PES and the corresponding PES derived from adding the free energy of solvation to every point. This process is illustrated for point (x,y). Thick lines on the two surfaces indicate some chemical reaction proceeding from one minimum-energy structure to another. Note that there is no requirement for the x and y coordinates of equivalent stationary points on the two surfaces to be the same...

Of particular relevance to understanding the influence of solvation on chemical processes is the concept of the free energy of solvation, AGsol, which can be defined as the reversible work required to transfer the solute from the ideal gas phase to solution at a given temperature, pressure and chemical composition [10]. This definition is well suited for molecular formulations of the solvation problem, because it permits AGsol to be related to the difference in the reversible works necessary to build up the solute both in solution and in the gas phase. 

These findings indicate the complexity of the solvent polarization effect on the solute charge distribution, which shows differential trends depending on the nature of the solute. In conjunction with the free energy of solvation, the analysis of the solvent-induced changes in the solute s electron density should be valuable to shed light on the influence of solvation on the chemical reactivity of solutes. 

The calculation of solvation energies for ions is much more complicated. As discussed, e.g., by Kelly et the fact that it is not possible to measure the electrostatic potential between two media means that the free energy of formation or chemical potential of an individual ion has no operational meaning. Instead, it is common practice to set, arbitrarily, the free energy of a proton equal to 0 and, then, to study well-defined free energies of solvation for neutral combinations of anions and cations, whereby those of the individual cations and anions can be estimated. 

A comparison of anion solvation by methanol, a protic solvent, and dimethylformamide, a dipolar aprotic solvent, is instructive. The electrostatic contribution, d/i , to the Gibbs free energy of solvation per mole of an ion is sometimes estimated quite successfully (Stokes, 1964) from the Bom model, in which a charged sphere of radius r is transferred from vacuum to a medium of uniform dielectric constant, c. The Bom equation (17) suggests that an anion should be similarly solvated in methanol and in DMF, because these solvents have effectively the same dielectric constant (33-36). The Born equation makes no allowance for chemical interactions, such as hydrogen-bonding and mutual... 

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