Solute free energy

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]. 

Schafer, H., Daura, X., Mark, A. E., and van Gunsteren, W. F. (2001). Entropy calculations on a reversibly folding peptide Changes in solute free energy cannot explain folding behavior. Proteins Strud. Fund. Genet. 43, 45-56. 

Cieplak, P., Caldwell, J. W., Kollman, P. A., Molecular mechanical models for organic and biological systems going beyond the atom centered two body additive approximation aqueous solution free energies of methanol and IV-methyl acetamide, nucleic acid base, and amide hydrogen bonding and chloroform/water partition coefficients of the nucleic acid bases, J. Comput. Chem. 2001, 22, 1048-1057... 

Key words osmotic pressure, polymeric solutions, free energy of conformation. 

It is useful to know, that for a given type of crystals (oxides, sulfates, carbonates), the interfacial mineral-aqueous solution free energy, y (or ycw), increases with decreasing solubility (Schindler, 1967). Nielsen (1986) cites the following empirical relationship... 

Edwards and co-workers (Edwards and Jeffers, 1979 Edwards and Singh, 1979) adapted these techniques to determine chain dimensions in semidilute solutions. Subsequently, Muthukumar and Edwards (1982) formulated RG expressions for the solution free-energy and derived IT explicitly in the low and high concentration limits. The general expression for the free-energy density relative to that of an infinitely dilute solution is... 

Let us consider mixing of two gases A and 5to form a homogeneous mixture (a solution). Free energy changes of the constituents involved are... 

Mechanical Models for Organic and Biological Systems Going Beyond the Atom Centered Two Body Additive Approximation Aqueous Solution Free Energies of Methanol and N-Methyl Acetamide, Nucleic Acid Base, and Amide Hydrogen Hydrogen Bonding and Chloroform/Water Partition Coefficients of the Nucleic Acid Bases. 

There are several conclusions to be drawn from this worked example. The broadest conclusion is that these PDT-based approaches provide flexibility for interrogation of physical issues underlying models of solution free energies. 

The influence of the interaction in binary solvents on AG r ions was analyzed by Y. Marcus [261], who assumed a quasi-lattice model for the electrolyte in such solutions. Free energies of transfer of various ions were collected and discussed [75, 76]. Ion solvation including mixed solvent media has been reviewed by several authors [45, 76, 262-265]. 

The above techniques have been used in numerous calculations of solute free energy profiles. Wilson and Pohorille [52] and Benjamin[53] have determined the free energy profiles for small ions at the water liquid/vapor interface and compared the results to predictions of continuum electrostatic models. The transfer of small ions to the interface involves a monotonic increase in the free energy which is in qualitative agreement with the continuum model. This behavior is consistent with the increase in the surface tension of water with the increase in the concentration of a very dilute salt solution, and it represents the fact that small ions are repelled from the liquid/vapor interface. On the other hand, calculations of the free energy profile at the water liquid/vapor interface of hydrophobic molecules, such as phenol[54] and pentyl phenol[57] and even molecules such as ethanol [58], show that these molecules are attracted to the surface region and lower the surface tension of water. In addition, the adsorption free energy of solutes at liquid/liquid interfaces[59,60] and at water/metal interfaces[61-64] have been reported. 

Table II. Bulk Solution Free Energy of Solvation for Alkali Metal and Halide Ions In Methanol Solutions...

The solutus curve, in binary SSAS systems with ideal or positive solid-solution free-energies of mixing and with large differences (more than an order of magnitude) in end-member solubility products, will closely follow the pure-phase saturation curve of the least soluble end-member (except at high aqueous activity fractions of the more soluble component, e . figure 1). In contrast, ideal solid-solutions with very close end-member solubility products (less than an order of magnitude apart) will have a solutus curve up to 2 times lower in EH than the pure end-member saturation curves. The factor of 2 is obtained for the case where the two end-member solubility products are equal and can be derived from equations 4, 16 and 17. 

In comparing Figs. 8.11 and 8.13, the similarities between the nonstoichiometric compound and solid solution free-energy versus composition curves should be obvious. It follows that an instructive way to look at the nonstoichiometric phase A1/2B1/2O is to consider it to be for X q < 1/2 a solid solution between A3/4B1/4O and A1/2B1/2O, and for X q > 1/2 a solid solution between A1/4B3/4O and A1/2B1/2O. Note that for this to occur, the cations in the nonstoichiometric phase must exist in more than one oxidation state. 

Table 2 contrasts the free energy cycle for association of a proton with NH3 (a very strong gas phase electrostatic dominated interaction) with that of two methane molecules (a very weak gas phase association). As one can see, the aqueous solution free energies are very different from those in the gas phase. 

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