Solvation electrostatic component

Another way of calculating the electrostatic component of solvation uses the Poisson-Boltzmann equations [22, 23]. This formalism, which is also frequently applied to biological macromolecules, treats the solvent as a high-dielectric continuum, whereas the solute is considered as an array of point charges in a constant, low-dielectric medium. Changes of the potential within a medium with the dielectric constant e can be related to the charge density p according to the Poisson equation (Eq. (41)). 

Two important contributions to the study of solvation effects were made by Bom (in 192( and Onsager (in 1936). Bom derived the electrostatic component of the free energ) c solvation for placing a charge within a spherical solvent cavity [Bom 1920], and Onsagi extended this to a dipole in a spherical cavity (Figure 11.21) [Onsager 1936]. In the Bor... 

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 ... 

Considering that, roughly speaking, the electrostatic component of the solvation free energy varies as the cube of the molecular dipole moment, it becomes obvious that the corrective term (13.1) should be taken into account in the determination of differential solvation properties of very polar solutes. In the computation of transfer free energies across an interface, it has been suggested that equation (13.1) be expressed as a function of the number density of one of the two media, so that the correction is zero in solvent 1 and zl,l lsl lll in solvent 2 [115]. 

Abstract This chapter reviews the theoretical background for continuum models of solvation, recent advances in their implementation, and illustrative examples of their use. Continuum models are the most efficient way to include condensed-phase effects into quantum mechanical calculations, and this is typically accomplished by the using self-consistent reaction field (SCRF) approach for the electrostatic component. This approach does not automatically include the non-electrostatic component of solvation, and we review various approaches for including that aspect. The performance of various models is compared for a number of applications, with emphasis on heterocyclic tautomeric equilibria because they have been the subject of the widest variety of studies. For nonequilibrium applications, e.g., dynamics and spectroscopy, one must consider the various time scales of the solvation process and the dynamical process under consideration, and the final section of the review discusses these issues. 

The present chapter thus provides an overview of the current status of continuum models of solvation. We review available continuum models and computational techniques implementing such models for both electrostatic and non-electrostatic components of the free energy of solvation. We then consider a number of case studies, with particular focus on the prediction of heterocyclic tautomeric equilibria. In the discussion of the latter we center attention on the subtleties of actual chemical systems and some of the dangers of applying continuum models uncritically. We hope the reader will emerge with a balanced appreciation of the power and limitations of these methods. 

CM1 charges in the calculation of AGenp, corrections for charge inadequacies appear in G " )s and it is not possible to separate the electrostatic and non-electrostatic components of the free energy of solvation. 

The electrostatic component of the free energy of solvation of the sphere is then the difference between doing this charging in a vacuum (e = 1) and in the medium ... 

This indicates a lack of dynamic cohesion within the adducts i.e. the substrate has considerable freedom for reorientation within the receptor. The apparent reason for an absence of mechanical coupling is the nearly cylindrical symmetry of cucurbituril, which allows the guest an axis of rotational freedom when held within the cavity. Hence, the bound substrates show only a moderate increase in tc relative to that exhibited in solution. No relationship exists between values and the thermodynamic stability of the complexes as gauged by K (or K, cf. Tables 1 and 2). It must be concluded that the interior of cucurbituril is notably nonsticky . This reinforces previous conclusions that the thermodynamic affinity within adducts is chiefly governed by hydrophobic interactions affecting the solvated hydrocarbon components, plus electrostatic ion-dipole attractions between the carbonyls of the receptor and the ammonium cation of the ligands. 

In describing the results from SCRF calculations, it is useful to keep careful track of the various components of die energy. The electrostatic component of the solvation free energy is the difference between the energy in the gas phase and the energy in solution. This may be written... 

Most of the models described above have also been implemented at correlated levels of tlieory, including perturbation theory. Cl, and coupled-cluster theory (of course, the DFT SCRF process is correlated by construction of the functional). Unsurprisingly, if a molecule is subject to large correlation effects, so too is the electrostatic component of its solvation free energy. 

It is important to re-emphasize that the electrostatic component of the solvation free energy is not a physical observable. Thus, it is impossible to assert on any basis other... 

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... 

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. 

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. 

The structure of yint depends, in general, on the nature of the solute-solvent interaction considered by the solvation model. As already noted in the contribution by Tomasi, a good solvation model must describe in a balanced way all the four fundamental components of the solute-solvent interaction electrostatic, dispersion, repulsion, charge transfer. However, we limit our exposition to the electrostatic components, this being components of central relevance, also for historical reason, for the development of QM continuum models. This is not a severe limitation. As a matter of fact, the QM problem associated with the solute-solvent electrostatic component defines a general framework in which all the other solute-solvent interaction components may be easily collocated, without altering the nature of the QM problem [5],... 

Support to these assumptions has recently come from the analysis of the coupling between electrostatic and dispersion-repulsion contributions to the solvation of a series of neutral solutes in different solvents [31]. It has been found that the explicit inclusion of both electrostatic and dispersion-repulsion forces have little effect on both the electrostatic component of the solvation free energy and the induced dipole moment, as can be noted from inspection of the data reported in Table 3.1. These results therefore support the separate calculation of electrostatic and dispersion-repulsion components of the solvation free energy, as generally adopted in QM-SCRF continuum models. 

C. Curutchet, C. J. Cramer, D. G. Truhlar, D. Rinaldi, M. F. Ruiz-Lopez, M. Orozco and F. J. Luque, Electrostatic component of solvation comparison of SCRF continuum models, J. Comput. Chem., 24 (2003) 284—297. 

The solution of these differential equations yields the total electrostatic potential at any point r. Assuming a linear response approximation the electrostatic component of solvation can be obtained as of the work necessary to generate the solvent reaction potential, which can be determined by simply computing the ratio of potential generated by the solute in vacuo to the total potential around the solute (Equation (4.34)). 

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