Free energy Gibbs solvation

Equation (12.8) states that the apparent and intrinsic differential activation energies AAG obs and AAG /inlr differ by the differential Gibbs free solvation energy AGS, with AGs relating the saturation solubilities of N-Ac-L-Phe-OEt in a solvent to acetone as the standard state [Eq. (12.9)], so that, with AG = AH - T AS, Eq. (12.10) follows. 

These results allow us to say that the static cluster model is valid to provide a first account of the aqueous solvation with the first water shell around the solute. This also gives us confidence about the estimation of the Gibbs free microsolvation energy obtained from the static optimizations. 

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

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... 

Mass spectrometry has been used to study the energetics of solvation and has shown that the enthalpies of attachment of successive water molecules to either alkali metal or halide ions become less exothermic as the number of water molecules increases (Kebarle, 1977). The Gibbs free energies of attachment for water molecules have also been found to be negative. 

Figure 3. Change in Gibbs free energy upon formation of a nanoparticle from solvated atoms.

Bornian theory of the Gibbs free energy of ion resolvation, a vast amount of work dealing with ion solvation and resolvation could not fully be reviewed. The reader is referred to some books [2-5] and review articles [6-10] for a general survey. 

Fig. 12.2. Free energy data for electron transfer between the protein cytochrome c and the small acceptor microperoxidase-8 (MP8), from recent simulations [47]. Top Gibbs free energy derivative versus the coupling parameter A. The data correspond to solvated cytochrome c the MP8 contribution is not shown (adapted from [47]) Bottom the Marcus diabatic free energy curves. The simulation data correspond to cyt c and MP8, infinitely separated in aqueous solution. The curves intersect at 77 = 0, as they should. The reaction free energy is decomposed into a static and relaxation component, using the two steps shown by arrows a static, vertical step, then relaxation into the product state. All free energies in kcalmol-1. Adapted with permission from reference [88]...

In principle, Gibbs free energies of transfer for trihalides can be obtained from solubilities in water and in nonaqueous or mixed aqueous solutions. However, there are two major obstacles here. The first is the prevalence of hydrates and solvates. This may complicate the calculation of AGtr(LnX3) values, for application of the standard formula connecting AGt, with solubilities requires that the composition of the solid phase be the same in equilibrium with the two solvent media in question. The other major hurdle is that solubilities of the trichlorides, tribromides, and triiodides in water are so high that knowledge of activity coefficients, which indeed are known to be far from unity 4b), is essential (201). These can, indeed, be measured, but such measurements require much time, care, and patience. 

The enthalpies of solution and solubilities reviewed here provide much of the experimental information required in the derivation of single-ion hydration and solvation enthalpies, Gibbs free energies, and entropies for scandium, yttrium, and lanthanide 3+ cations. 

A widely-used alternative is the free energy perturbation technique (FEP),9"11,72"74 which will be discussed for the Gibbs free energy G. It involves a thermodynamic cycle such as the following, in which X and Y are two different molecules that are undergoing solvation in a particular solvent ... 

M. D. Tissandier, K.A. Cowen, W.Y. Feng, E. Gundlach, M. H. Cohen,A. D. Earhart, J. V Coe, T. R. Tuttle Jr. The Proton s Absolute Aqueous Enthalpy and Gibbs Free Energy of Solvation from Cluster-Ion Solvation Data. J. Phys. Chem. A 1998, 102, 7787-7794. 

The stronger the solvating ability of a solvent is, the more it decreases the thermodynamic activity of the reactants and their reactivity, that is, their availability for the reaction. A linear correlation has been found between the activation Gibbs free energy of a series of Sn2 reactions and the acceptor number (AN) of the solvents (Marcus, 1998). 

The Gibbs free energy of solution is the difference between the Gibbs free energy of solvation of the solute in the solvent and any Gibbs free energy of interaction in the pure solute that are lost on dissolution, if it is a solid, a liquid, or a nondilute gas. 

The differences in solvation of the reactants and the products constitute in general the major difference between the driving force for the equilibrium reaction in solution and that in the gas phase. The molar Gibbs free energy of solvation for any species I that participates in the equilibrium in a given solvent S can be written as... 

These differences stimulated our interest and prompted us to study the effects of solvation on (R,R )-tartaric acid amides. Encouraged by the widespread usage ofAMSOL [42] (vide infra) we decided to use it to calculate Gibbs free energies of hydratation. We performed the calculations with the use of the solvation model SM5.4 [43-46] and hamiltonian PM3 [47] for all structures, optimized at the RHF/6-31G level [20],... 

In the present context, the solvation of a solvent molecule in its own liquid (i.e., condensation from the vapour, the opposite of evaporation) is of interest, and molar quantities are employed, rather than quantities pertaining to a single particle (Ben-Naim and Marcus 1984). The Gibbs free energy of solvation of a solvent in itself is ... 

Returning to the solvation of gaseous or liquid solutes in solvents, the Gibbs free energy of solvation is given by ... 

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