Hydration of free energy

Here is the distance between the atoms, and g(r) is a cut-off factor which provides a continuous function to make vanish at ri3- = r0. 

This function is very nearly equal to 1-0 when r 0-9 r0, then drops to a value of 0-5 when r = 0-95 r0, and to zero when r = r0 furthermore, it is continuous and has a continuous derivative (which are required properties for computing gradients). The quantity Vj is a factor proportional to the volume of the jth atom. The total amount of solvent removed from the ith atom by the approach of all other atoms will then be 

In practice, the values of Vj were set equal to the volumes of the atoms in l3, as given by Bondi (1964), divided by 30. A further consideration in 

to Ai when Wt Ait and is continuous in between. The total solvent free energy is then obtained by summing over all atoms  

This is nearly linear up to W=0-75A, then turns sharply but smoothly to a constant value of A. A simpler function, consisting of two polynomials 

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Van Oss and Good [148] have compared solubilities and interfacial tensions for a series of alcohols and their corresponding hydrocarbons to determine the free energy of hydration of the hydroxyl group they find -14 kJ/mol per —OH group. 

The relative acidities in the gas phase can be detennined from ab initio or molecular orbital calculations while differences in the free energies of hydration of the acids and the cations are obtained from FEP sunulations in which FIA and A are mutated into FIB and B A respectively. 

Jorgenson W L and Ravimohan C 1985 Monte Carlo simulation of the differences in free energy of hydration J. Chem. Phys. 83 3050... 

Fig. 6. Free energies of hydration calculated, for a series of polar and non-polar solute molecules by extrapolating using (3) from a 1.6 ns trajectory of a softcore cavity in water plotted against values obtained using Thermodynamic Integration. The solid line indicates an ideal one-to-one correspondence. The broken line is a line of best fit through the calculated points.

Carlson, H. A., Jorgensen, W. L. An extended linear response method for determining free energies of hydration. J. Phys. Chem. 99 (1995) 10667-10673... 

Carlson H A and W L Jorgensen 1995. An Extended Linear Response Method for Determining Free Energies of Hydration. Journal of Physical Chemistry 99 10667-10673. 

Table 10. Free Energies of Hydration of Anions A and of Acid Dissociation, AH = A" + H+...

Chipot, C. Millot, C. Maigret, B. Kollman, P. A., Molecular dynamics free energy perturbation calculations. Influence of nonbonded parameters on the free energy of hydration of charged and neutral species, J. Phys. Chem. 1994, 98,11362-11372... 

In this second example, we examine simple systems near the water-hexane interface. Specifically, we calculate the difference in the free energy of hydrating a hard-sphere solute of radius a, considered as the reference state, and a model solute consisting of a point dipole p located at the center of a cavity [11]. We derive the formula for A A assuming that the solute is located at a fixed distance z from the interface, and subsequently we examine the dependence of the free energy on z. The geometry of the system is shown in Fig. 2.3. 

Jorgensen, W.L., Ravimohan, C., Monte Carlo simulation of differences in free energies of hydration, J. Chem. Phys. 1985, 83, 3050-3054... 

Henchman, R.H., Essex, J.W., Free energies of hydration using restrained electrostatic potential derived charges via free energy perturbations and linear response, J. Comput. Chem. 1999, 20, 499-510... 

Jorgensen, W. L. Tirado-Rives, J., Free energies of hydration for organic molecules from Monte Carlo simulations, Perspectives in Drug Discovery and Design 1995, 3,123-138. 

V. Helms and R. C. Wade, Free energies of hydration from thermodynamic integration ... 

The basic formalism of the X-dynamics method has taken various forms in its application to problems of interest. In an early prototype calculation to assess umbrella sampling in chemical coordinates, the X-dynamics method was used to evaluate the relative free energy of hydration for a set of small molecules which included both nonpolar (C2H6,) and polar (CH3OH, CH3SH, and CH3CN) solutes.1 By assigning a separate X variable to the Lennard-Jones and Coulomb interactions, a linear partition of the potential part of the hybrid Hamiltonian was constructed... 

Our extension of the LIE approach to calculate free energies of hydration (AGhyd) incorporated a third term proportional to the solute s solvent-accessible surface area (SASA), as an index for cavity formation within the solvent.19,27 The latter term is needed for cases with positive AGhyd such as alkanes and additional improvement occurred when both a and P were allowed to vary. Equation 8 gives the corresponding LIE/SA equation for... 

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