Electrostatic hydration free energies

Modeling of n (e) can be motivated by a simple thermodynamic model for this electrostatic contribution. The Bom model [34] for the hydration free energy of a spherical ion of radius Ra with a charge qa at its center is... 

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. 

Applications of spatially nonlocal electrostatic theory are not so numerous. Limited by simple models reducible to a one-dimensional problem, they only include systems obeying spherical or planar symmetry. A traditional treatment of hydration free energies... 

Inspection of the free energy components points out the dominant role of AGeie in water, which amounts to around 145% of the experimental hydration free energy (Table 4-1). In turn, the non-electrostatic term, AGn-eie, gives rise to an unfavorable contribution to the hydration of these compounds, which reflects the larger magnitude of the cavitation term compared to the van der Waals one in water [15], Overall, except for hydrocarbons, the transfer of polar solutes from the gas phase to water is a favorable process, which mainly originates from the electrostatic interactions between solute and water molecules. 

Table 4-3. Enthalpic and entropic components of the electrostatic and non-electrostatic terms of the hydration free energy (kcal/mol). The non-electrostatic enthalpy and entropy were determined by subtracting the electrostatic enthalpy and entropy from the corresponding experimental data...

We developed the Analytical Generalized Born plus Non-Polar (AGBNP) model, an implicit solvent model based on the Generalized Born model [37-40,44, 66] for the electrostatic component and on the decomposition of the nonpolar hydration-free energy into a cavity component based on the solute surface area and a solute-solvent van der Waals interaction free energy component modeled using an estimator based on the Born radius of each atom. 

We focus first on the outer-shell contribution of Eq. (7.8), p. 145. That contribution is the hydration free energy in liquid water for a distinguished water molecule under the constraint that no inner-shell neighbors are permitted. We will adopt a van der Waals model for that quantity, as in Section 4.1. Thus, we treat first the packing issue implied by the constraint Oy [1 i>a (7)] of Eq. (7.8) then we append a contribution due to dispersion interactions, Eq. (4.6), p. 62. Einally, we include a contribution due to classic electrostatic interactions on the basis of a dielectric continuum model. Section 4.2, p. 67. 

Figure 7.6 Cluster-variation of the hydration free energy of water. The open circles give the chemical contribution, A 7 lnxo. The open squares give the packing contribution, —kTlnpQ. The open triangles give the sum of outer-sphere electrostatic and dispersion contributions. The net free energy is shown by a solid line. The minimum is within 1 kcal/mol. of the experimental value of —6.1 kcal/mol.

A hybrid approach of the extended scaled particle theory (SPT) and the Poisson-Boltzmann (PB) equation for the solvation free energy of non-polar and polar solutes has been proposed by us. This new method is applied for the hydration free energy of the protein, avian pancreatic polypeptide (36 residues). The contributions form the cavity formation and the attractive interaction between the solute and the solvent to the solvation free energy compensate each other. The electrostatic conffibution is much larger than other terms in this hyelration free energy, because hydrophilic residues are ionized in water. This work is the first step toward further applications of our new method to free energy difference calculation appeared in the stability analysis of protein. 

Recently, the study of aqueous ionic solutions has been extended to supercritical conditions. Balbuena et al [202] have computed the hydration free energy of several ions (C1 , OH, Na" ", K, Rb" ", Ca " ", Sr " ") using the SPC/E model for water and different ion-water potentials, e.g. OPLS [197] for Cl and Aqvist [190] potentials for cations. They found that hydration free energy of CT is much more affected by the transition from ambient to supercritical conditions than that of Na", due to its stronger electrostatic interaction with water. Also, Balbuena et al observe an overestimated local density for bivalent cations with respect to experimental data [203] that is attributed to differences in concentration and to the potentials adopted. Aqvist potentials, on the other hand, as well as the SPC/E model, have been parametrized to reproduce thermodynamic properties of the ionic solution under ambient conditions and may lack the transferability necessary to describe correctly a solution at supercritical conditions. 

For many chemical problems, it is crucial to consider solvent effects. This was demonstrated in our recent studies on the hydration free energy of U02 and the model reduction of uranyl by water [232,233]. The ParaGauss code [21,22] allows to carry out DKH DF calculations combined with a treatment of solvent effects via the self-consistent polarizable continuum method (PCM) COSMO [227]. If one aims at a realistic description of solvated species, it is not sufficient to represent an aqueous environment simply as a dielectric continuum because of the covalent nature of the bonding between an actinide and aqua ligands [232]. Ideally, one uses a combination model, in which one or more solvation shells (typically the first shell) are treated quantum-mechanically, while long-range electrostatic and other solvent effects are accounted for with a continuum model. Both contributions to the solvation free energy of U02 were... 

Table 6 Non-electrostatic and electrostatic contributions to the Gibbs free energy of hydration, Gj[oq), the total hydration free energy, AAG c, v(aq), and the Gibbs free energy change in aqueous solution.

---