Solvation free energy continuum methods

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 ... 

Much like the RISM method, the LD approach is intermediate between a continuum model and an explicit model. In the limit of an infinite dipole density, the uniform continuum model is recovered, but with a density equivalent to, say, the density of water molecules in liquid water, some character of the explicit solvent is present as well, since the magnitude of the dipoles and their polarizability are chosen to mimic the particular solvent (Papazyan and Warshel 1997). Since the QM/MM interaction in this case is purely electrostatic, other non-bonded interaction terms must be included in order to compute, say, solvation free energies. When the same surface-tension approach as that used in many continuum models is adopted (Section 11.3.2), the resulting solvation free energies are as accurate as those from pure continuum models (Florian and Warshel 1997). Unlike atomistic models, however, the use of a fixed grid does not permit any real information about solvent structure to be obtained, and indeed the fixed grid introduces issues of how best to place the solute into the grid, where to draw the solute boundary, etc. These latter limitations have curtailed the application of the LD model. 

Hybrid solvation Implicit solvation plus Explicit solvation microsolvation subjected to the continuum method. Here the solute molecule is associated with explicit solvent molecules, usually no more than a few and sometimes as few as one, and with its bound (usually hydrogen-bonded) solvent molecule(s) is subjected to a continuum calculation. Such hybrid calculations have been used in attempts to improve values of solvation free energies in connection with pKp. [42], and also [45] and references therein. Other examples of the use of hybrid solvation are the hydration of the environmentally important hydroxyl radical [52] and of the ubiquitous alkali metal and halide ions [53]. Hybrid solvation has been surveyed in a review oriented toward biomolecular applications [54]. 

Keeping in mind the intrinsic features associated with the definition of the cavity in the most popular QM-SCRF methods, it can be questioned what is the influence of the fine details of the cavity definition on the computed solvation free energies. This question has been investigated in a recent study by Takano and Houk [61], who have examined the dependence of the solvation free energies estimated for a series of 70 compounds, including neutral and charged species, on both the choice of the cavity and the level of theory used in computations within the framework of the conductor-like polarizable continuum model (CPCM). The mean absolute deviation (MAD) between calculated... 

Apart from methods based on continuum approaches, methods based on the division of the total solvation energy by atom or group contributions that are independent from each other are quite popular. The solvation free energy in these methods is computed as a sum of products of an empirical constant depending on the nature of atom or group (wy), and a solvent accessible area of this atom or group (Si) ... 

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... 

To illustrate this approach, let us consider a recent paper by Toth et al. [117]. The authors used CBS methods (Petersson et al. [21]) and the G2 family of methods to compute gas-phase energy differences between six different carboxylic acids and their respective anions. Two different continuum solvation methods, SM5.42R (Li et al. [139]) and CPCM (Barone and Cossi [118]) were used to calculate the differences in solvation free energies for the acids and their anions. By using this data, relative pK values were determined for each acid using one of the acids as reference. They found that the pKa value of an unknown from a known molecule can be predicted with an average error of 0.4 pK units. It must be noted, however, that this level of accuracy was reached using different levels of theory to describe the processes occurring in the gas phase and in solution. 

The main benefits of this approach are that (i) this is a molecular theory, and that (ii) due to the spherical symmetry of the correlation fnnctions in the ID RISM approach, the computational costs are significantly rednced compared to explicit solvent methods and high-dimensional molecular theories like 3D RISM [80-82, 93], MOZ [82, 83], and MDFT [69, 70]. For an average drug-like molecule a ID RISM calculation of solvation free energy takes less than a minute on a desktop PC [67, 71, 72, 92]. This time scale is already comparable with the compntational time scale for continuum methods (seconds). We note that an explicit solvent calculation for the same kind of molecules would take between honrs and days [38,47-58]. 

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