Hydration free energies

Jorgensen, Blake, and Buckner reported a staged FEP calculation of the hydration free energy of methane, which was treated as a Lennard-Jones (LJ) sphere. The size (a) and well depth (e) LJ parameters were each scaled linearly with the coupling parameter lambda  

In a related study. Garde et al. used a test-particle approach to perform a systematic comparison of hydration free energies for nine different LJ particles along with their WCA and HS equivalents. Their results indicate that the attractive part of the LJ solute-water potential is very well modeled as a perturbation of the WCA result. The excess chemical potential was calculated 

Agreement between pjj calculated from the test particle method and from Eq. [41] was nearly exact. Garde et al. also found that the contribution of the attractive part of the solute-water interaction energy to p, is reasonably well represented by even a very crude model and that this contribution shows little temperature dependence. These observations suggest that purely repulsive models capture many of the essential features of hydrophobicity for small solute molecules. Note, however, that this conclusion does not hold for large solutes or for interfaces.  

Wallqvist and Berne used an FEP method to determine hydration free energies for hard-sphere cavities as a function of both size and shape. They observed a nearly linear relationship between solute surface area and hydration free energy for both spherical and ellipsoidal cavities. The hydration free energy also exhibited a significant dependence on solute curvature.  

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Sitkoff, D., Sharp, K. A., Honig, B. Accurate calculation of hydration free energies using macroscopic solvent models. J. Phys. Chem. 98 (1994) 1978-1988... 

Schafer, H., van Gunsteren, W. F., Mark, A. E. Estimating relative binding free energies from an initial state Hydration free energies. J. Phys. Chem. (submitted)... 

Schafer H, W F van Gunsterten and A E Mark 1999. Estimating Relative Free Energies from a Sing] Ensemble Hydration Free Energies, Journal of Computational Chemistry 20 1604-1617. 

Sitkoff D, K A Sharp and B Honig 1994. Accurate Calculation of Hydration Free Energies Usin Macroscopic Solvent Models. Journal of Physical Chemistry 98 1978-1988. 

X Chen, A Tropsha. A generalized linear response method Application to the hydration free energy calculations. J Comput Chem 20 749-759, 1999. 

Ion Atomic Number Ionic Radius (nm) Hydration Free Energy, AG (kj/mol)... 

Lamoureux G, Roux B (2006) Absolute hydration free energy scale for alkali and halide ions established from simulations with a polarizable force field. J Phys Chem B 110(7) 3308-3322... 

Warren GL, Patel S (2007) Hydration free energies of monovalent ions in transferable intermolecular potential four point fluctuating charge water an assessment of simulation methodology and force field performance and transferability. J Chem Phys 127(6) 064509... 

Table 7. Hydration Free Energies of Doubly Charged Anions3...

Figure 14. Hydration free energies -ACjUi at 293 K for reaction A (H20)n-1 + H2O = A2-(H20) versus n for several doubly charged acid anions as indicated for each plot. Hydration strength increases in the order 1,5-naphthalenedisulfonate to SOi. From Blades, A. T. Klassen, J. S. Kebarle, P. ]. Am. Chem. Soc. 1995, 117, 10563, with permission.

Table 8. Hydration Free Energies of Some Protonated Alkylamines, Alkyldiamines, and Peptides3...

Table 9. Hydration Free Energies of Singly Charged Anions of Dicarboxylic Acids3...

Fig. 4. A schematic two-dimensional illustration of the idea for an information theory model of hydrophobic hydration. Direct insertion of a solute of substantial size (the larger circle) will be impractical. For smaller solutes (the smaller circles) the situation is tractable a successful insertion is found, for example, in the upper panel on the right. For either the small or the large solute, statistical information can be collected that leads to reasonable but approximate models of the hydration free energy, Eq. (7). An important issue is that the solvent configurations (here, the point sets) are supplied by simulation or X-ray or neutron scattering experiments. Therefore, solvent structural assumptions can be avoided to some degree. The point set for the upper panel is obtained by pseudo-random-number generation so the correct inference would be of a Poisson distribution of points and = kTpv where v is the van der Waals volume of the solute. Quasi-random series were used for the bottom panel so those inferences should be different. See Pratt et al. (1999).

Equation (15) permits a straightforward analysis of dielectric continuum models of hydration that have become popular in recent decades. The dielectric model, also called the Bom approximation, for the hydration free energy of a spherical ion of radius R with a charge q at its center is... 

Asthagiri, D. Pratt, L. R. Ashbaugh, H. S., Absolute hydration free energies ofions, ion-water clusters and quasichemical theory, J. Chem. Phys. 2003,119, 2702-2708... 

Intermediate states do not have to be physically meaningful, i.e., they do not have to correspond to systems that actually exist. As an example, assume that we want to calculate the difference in hydration free energies of a Lennard-Jones particle and an ion with a positive charge q of le. For simplicity, we further assume that the Lennard-Jones parameters remain unchanged upon charging the particle. Since a direct calculation of the free energy difference is not likely to succeed in this case, we construct intermediate states in which the particle carries fractional charges [Pg.46]

Fig. 2.6. The thermodynamic cycle for estimating the hydration free energy, zl/Ihydration, of a small solute (the right side of the figure). One route is the direct evaluation of A/lhydrauon along the upper vertical arrow. The solute, originally placed in vacuum (a) is moved to the bulk water (b). Another route consists of annihilating, or creating, the solute both in vacuo and in the aqueous medium and corresponds to the vertical lines in the thermodynamic cycle. As suggested by the cycle, these two routes are formally equivalent, as A/lhydrnt,ion = A A0 — A A1...

Mezei, M., Test of overlap ratio metho on the calculation of the aqueous hydration free energy difference between acetone and dimethyl amine, Mol. Phys. 1988, 65, 219-223... 

In Fig. 9.2 we present results of a first-of-a-kind study of the hydration of the first-transition-row metals within the quasichemical framework. The biphasic behavior of the actual hydration free energy is consistent with features inferred experimentally. Removing the ligand field effects reveals the linear decrease [12]. The results shown in Fig. 9.2 are largely outside the purview of extant simulation techniques, but are treated simply in the quasichemical framework developed below. 

As an example of importance-weighting ideas, consider the situation that the actual interest is in hydration free energies of a distinct conformational states of a complex solute. Is there a good reference system to use to get comparative thermodynamic properties for all conformers There is a theoretical answer that is analogous to the Hebb training rule of neural networks [36, 37], and generalizes a procedure of [21]... 

The right-most term is similar to the familiar PDT formula except that the indicator function combinations forbid binding of solution molecules to the defined inner shell. That last factor is recognized as the Boltzmann factor of the hydration free energy that would result if inner-shell binding were prohibited. The Km are recognizable ratios of equilibrium concentrations - equilibrium constants - that are discussed... 

The second necessary ingredient in the primitive quasichemical formulation is the excess chemical potential of the metal-water clusters and of water by itself. These quantities p Wm — can typically be obtained from widely available computational packages for molecular simulation [52], In hydration problems where electrostatic interactions dominate, dielectric models of those hydration free energies are usually satisfactory. The combination /t xWm — m//, wx is typically insensitive to computational approximations because the water molecules coat the surface of the awm complex, and computational errors can compensate between the bound and free ligands. 

For the metal ions that have been tried [12], this procedure works remarkably well in determining hydration free energies. There has been little [47] detailed attempt to determine hydration entropies and volumes in this way, and those properties are not... 

Sakane, S. Yezdimer, E. M. Liu, W. B. Barriocanal, J. A. Doren, D. J. Wood, R. H., Exploring the ab initio/classical free energy perturbation method the hydration free energy of water, 7. Chem. Phys. 2000,113, 2583-93... 

Gallicchio, E. Kubo, M. M. Levy, R. M., Enthalpy-entropy and cavity decomposition of alkane hydration free energies numerical results and implications for theories of hydrophobic solvation, J. Phys. Chem. B 2000,104, 6271-6285... 

Schafer, H. Mark, A. van Gunsteren, W.F., Estimating relative free energies from a single ensemble hydration free energies, J. Comput. Chem. 1999, 20, 1604—1617... 

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