Dielectric models, electrostatic solvation free energies

The non-polar component of the solvation free energy is especially important for implicit membrane models as it decreases from a significant positive contribution in aqueous solvent to near zero at the center of the phospholipid bilayer. Without a non-polar term, even hydrophobic solutes would in fact prefer the high-dielectric environment where the electrostatic solvation free energy is more favorable than in a low-dielectric medium. The functional form of the non-polar term may follow a simple switching function [79,80], a calculated free energy insertion profile for molecular oxygen [82,84], or may be parameterized as well with respect to simulation or experimental data. 

The final class of methods that we shall consider for calculating the electrostatic compone of the solvation free energy are based upon the Poisson or the Poisson-Boltzmann equatior Ihese methods have been particularly useful for investigating the electrostatic properties biological macromolecules such as proteins and DNA. The solute is treated as a body of co stant low dielectric (usually between 2 and 4), and the solvent is modelled as a continuum high dielectric. The Poisson equation relates the variation in the potential (f> within a mediu of uniform dielectric constant e to the charge density p ... 

The Self-Consistent Reaction Field (SCRF) model considers the solvent as a uniform polarizable medium with a dielectric constant of s, with the solute M placed in a suitable shaped hole in the medium. Creation of a cavity in the medium costs energy, i.e. this is a destabilization, while dispersion interactions between the solvent and solute add a stabilization (this is roughly the van der Waals energy between solvent and solute). The electric charge distribution of M will furthermore polarize the medium (induce charge moments), which in turn acts back on the molecule, thereby producing an electrostatic stabilization. The solvation (free) energy may thus be written as... 

Some work has also appeared describing MD with implicit solvation for solutes described at the DFT level. Fattebert and Gygi (2002) have proposed making the external dielectric constant a function of the electron density, thereby achieving a smooth transition from solute to solvent instead of adopting a sudden change in dielectric constant at a particular cavity surface. Non-electrostatic components of the solvation free energy have not been addressed in this model. 

A short overview of the quantum chemical and statistical physical methods of modelling the solvent effects in condensed disordered media is presented. In particular, the methods for the calculation of the electrostatic, dispersion and cavity formation contributions to the solvation energy of electroneutral solutes are considered. The calculated solvation free energies, proceeding from different geometrical shapes for the solute cavity are compared with the experimental data. The self-consistent reaction field theory has been used for a correct prediction of the tautomeric equilibrium constant of acetylacetone in different dielectric media,. Finally, solvent effects on the molecular geometry and charge distribution in condensed media are discussed. 

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... 

GB models evaluate electrostatic part of solvation free energy as a sum of pairwise interaction terms between atomic charges. For a typical case of aqueous solvation of molecules with interior dielectric of 1, these interactions are approximated by an analytical function introduced by Still et al. [24] ... 

As shown above the size of the explicit water simulations can be rather large, even for a medium sized protein as in the case of the sea raven antifreeze protein (113 amino acid residues and 5391 water). Simulations of that size can require a large amount of computer memory and disk space. If one is interested in the stability of a particular antifreeze protein or in general any protein and not concerned with the protein-solvent interactions, then an alternative method is available. In this case the simulation of a protein in which the explicit waters are represent by a structureless continuum. In this continuum picture the solvent is represented by a dielectric constant. This replacement of the explicit solvent model by a continuum is due to Bom and was initially used to calculate the solvation free energy of ions. For complex systems like proteins one uses the Poisson-Boltzmann equation to solve the continuum electrostatic problem. In... 

Following earlier work by Wood et al., Luo and Tucker have relaxed the constant density restriction, and developed a continuum model in which the dielectric constant may be position-dependent. This dielectric function, s(7), is defined, at each point r in the fluid, in terms of the local density of the fluid at , pi(f), which is itself determined by the local values of the electric field and the compressibility. However, the local value of the electric field at 7 must be found from electrostatic equations (see Poisson-Boltzmann Type Equations Numerical Methods) which depend upon the dielectric function s(r) everywhere. Hence, all of the relevant equations must be solved self-consistently, and this is done using a numerical grid algorithm (see Poisson-Boltzmann Type Equations Numerical Methods). The result of such calculations are the density profile of the fluid around the solute and the position-dependent electric field, from which the free energy of solvation may be evaluated. The effects of solvent compression on solvation energetics can be quite substantial. Compression-induced enhancements to the solvation free energy of nearly 15 kcal mol" have been calculated for molecular ions in SC water at Tt = 1.01 and pr = 0.8. ... 

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]... 

It is often the case that the solvent acts as a bulk medium, which affects the solute mainly by its dielectric properties. Therefore, as in the case of electrostatic shielding presented above, explicitly defined solvent molecules do not have to be present. In fact, the bulk can be considered as perturbing the molecule in the gas phase , leading to so-called continuum solvent models [14, 15]. To represent the electrostatic contribution to the free energy of solvation, the generalized Bom (GB) method is widely used. Wilhin the GB equation, AG equals the difference between and the vacuum Coulomb energy (Eq. (38)) ... 

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