Atomic surface tension

Given the somewhat ad hoc nature of most specific schemes for evaluating the non-electrostatic components of the solvation free energy, a reliance on a simpler, if somewhat more empirical, scheme has become widely accepted within available continuum models. In essence, the more empirical approach assumes that the free energy associated with the non-electrostatic solvation of any atom will be characteristic for that atom (or group) and proportional to its solvent-exposed surface area. Thus, the molecular Geos may be computed simply as 

It should be noted that SASA itself can be defined in many ways (see, for instance, Pascual-Ahuir, Silla, and Tunon 1994). In the simplest approach, one imagines solvent molecules to be spheres having some characteristic radius. The SASA is then generated by the center of 

6 cal moD which may be taken as the o value for alkane surface area in Eq. (11.22) (Giesen, Cramer, and Truhlar 1994) 

In the majority of continuum solvation models incorporating a surface-tension approach to estimating the non-electrostatic solvation components, the index k in Eq. (11.22) runs over a list of atom types, and die user assigns the appropriate type to each atom of the solute. This is particularly straightforward for MM models, like the Generalized Bom/Surface Area (GB/SA) model (Still el al. 1990 see also Best, Merz, and Reynolds 1997), since atom types are already intrinsic to the force field approach. This same formalism has been combined with the CHARMM and Cornell et al. force fields (see Table 2.1) to define GB models for proteins and nucleic acids (Dominy and Brooks 1999 Jayaram, Sprous, and Beveridge 1998). Considering this approach applied within the QM arena, the MST-ST models of Orozco and Luque have been the most extensively developed (see, for instance, Curutchet, Orozco, and Luque 2001). 

The surface tensions themselves in the GB/SA and MST-ST models were developed by taking collections of experimental data for the free energy of solvation in a specific solvent, removing the electrostatic component as calculated by the GB or MST model, and fitting the surface tensions to best reproduce the residual free energy given the known SASA of the solute atoms. Such a multilinear regression procedure requires a reasonably sized collection of data to be statistically robust, and limitations in data have thus restricted these models to water, carbon tetrachloride, chloroform, and octanol as solvents. 

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There are three popular ways to treat the nonelectrostatic effects (i) ignore them, (ii) combine specialized models for cavitation, dispersion, exchange repulsion, and so forth,46 48 70 (iii) employ atomic surface tensions.12 27, 83 86 In the third approach, which is the most accurate in an empirical sense, one writes22 27... 

Because surface curvature depends on radius and different atoms have different sizes, and because the atomic surface tension depends on atomic number, the atomic surface tensions also include surface curvature effects, which has recently been studied as a separate effect.7 Local surface curvature may also correlate with nearest-neighbor proximity and thus may be implicitly included to some extent when semiempirical atomic surface tensions depend on interatomic distances in the solute. 

It is actually possible to create a model based entirely on atomic surface tensions, and, at least for species with no net charge, it does quite well. Such a model can be quite useful for drug design because of its speed and simplicity, but it is somewhat unsatisfactory theoretically because the correct physics is not manifest. 

G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Parameterized model for aqueous free energies of solvation using geometry-dependent atomic surface tensions with implicit electrostatics, J. Phys. Chem. B 101 7147 (1997) erratum to be published. 

In order to be more generally applicable, the SMx models of Cramer and Truhlar address the issue of data scarcity by making the atomic surface tensions a function of quantifiable solvent properties, i.e.,... 

MST-ST MST model augmented with atomic surface tensions... 

Pratt and co-workers have proposed a quasichemical theory [118-122] in which the solvent is partitioned into inner-shell and outer-shell domains with the outer shell treated by a continuum electrostatic method. The cluster-continuum model, mixed discrete-continuum models, and the quasichemical theory are essentially three different names for the same approach to the problem [123], The quasichemical theory, the cluster-continuum model, other mixed discrete-continuum approaches, and the use of geometry-dependent atomic surface tensions provide different ways to account for the fact that the solvent does not retain its bulk properties right up to the solute-solvent boundary. Experience has shown that deviations from bulk behavior are mainly localized in the first solvation shell. Although these first-solvation-shell effects are sometimes classified into cavitation energy, dispersion, hydrophobic effects, hydrogen bonding, repulsion, and so forth, they clearly must also include the fact that the local dielectric constant (to the extent that such a quantity may even be defined) of the solvent is different near the solute than in the bulk (or near a different kind of solute or near a different part of the same solute). Furthermore... 

One special difficulty of applying parameterized models to chemical reactions deserves a special mention, namely that transition states often have charge distributions quite different from those against which solvation models are parameterized. For example, the partial atomic charge on Cl in the (Cl... CH3... Cl)-1 SN2 transition state is about -0.7, midway between the values (-1.0 and about -0.4, respectively) found in Cl-monatomic anion and typical alky chlorides. Thus the atomic radii and atomic surface tensions optimized against equilibrium free energies needs to be re-validated for transition structures. 

Finally, the van der Waals term (Gvw) is computed using a linear relationship to the solvent-exposed surface of each atom, as noted in Eq. 4-8, where the atomic surface tensions, , are determined by fitting to the experimental free energies of solvation for large series of solutes. Note then that those surface tensions not only account for dispersion-repulsion interactions between solute and solvent, but also correct for the implicit assumptions introduced in the evaluation of the remaining components of AGsoi ... 

The electrostatic term GENP is accompanied by a second term GCDS which, as the acronym indicates, collects cavitation, dispersion, and solvent structure contributions, the latter regarding dielectric saturation and other reorganization effects, when present. GCDS is modeled in terms of an interfacial atomic surface tension term, <7fc, and of the parameter Ak giving the solvent-accessible surface area for atom k ... 

Marenich, A.V., Cramer, C.J., Truhlar, D.G. Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J. Phys. Chem. B 2009,113(18), 6378-96. 

J. Liu, C.P Kelley, A.C. Goren, A.V. Marenich, C.J. Cramer, D.G. Truhlar, and C.G. Zhan, Free energies of solvation with surface, volume, and local electrostatic effects and atomic surface tensions to represent the first solvation shell, J. Chem. Theory Comput. 6 (2010), pp. 1109-1117. 

Maienich, A. V. Cramer, C. J. Truhlar, D. G., Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009,113,6378-6396. 

Dispersion-repulsion (van der Waals) contribute favorably to the solvation of the solute. The strength of these interactions depends on the nature of solvent, the size of the solute, and the type of atoms forming the solute. It has been shown [5-10] that, in general, the van der Waals contribution to solvation is related to the solvent exposure of the different atoms of the solute, as shown in equation (1), where SASi is the solvent-accessible surface of atom i and stands for the microscopic atomic surface tension. 

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