Electrostatic contribution, continuum

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)) ... 

In this chapter we provide an introductory overview of the imphcit solvent models commonly used in biomolecular simulations. A number of questions concerning the formulation and development of imphcit solvent models are addressed. In Section II, we begin by providing a rigorous fonmilation of imphcit solvent from statistical mechanics. In addition, the fundamental concept of the potential of mean force (PMF) is introduced. In Section III, a decomposition of the PMF in terms of nonpolar and electrostatic contributions is elaborated. Owing to its importance in biophysics. Section IV is devoted entirely to classical continuum electrostatics. For the sake of completeness, other computational... 

We can exploit the new results for packing contributions to reconsider the outer shell contribution in Eq. (33). For ionic solutes, the outer shell term would represent the Born contribution because it describes a hard ion stripped of any inner shell ligands. A Born model based on a picture of a dielectric continuum solvent is reasonable (see Section III,B, and Fig. 9, color insert). With that motivation, we first separate the outer shell term into an initial packing contribution and an approximate electrostatic contribution as... 

The electrostatic contributions, identified as /t x born and modeled on the basis of a dielectric continuum, are typically a substantial part of the... 

To exploit the concept of PMF to represent solvent in free energy calculations, practical approximations must be constructed. A common approach is to treat the two components Z H/"P(X) and Z lYelec(X) separately. Approximations for the nonpolar term are usually derived from geometric considerations, as in scaled particle theory, for example [62], The electrostatic contribution is usually derived from continuum electrostatics. We consider these two contributions in turn. 

Jean-Charles, A. Nicholls, A. Sharp, K. Honig, B. Tempzyck, A. Hendrickson, T. Still, W.C., Electrostatic contributions to solvation energies comparison of free energy perturbation and continuum calculations., J. Am. Chem. Soc. 1991,113, 1454-1455... 

Classification of continuum models that include both electrostatic and non-electrostatic contributions. 

A key issue in any continuum model is the definition of the solute-solvent interface, since it largely modulates the electrostatic contribution to the solvation free energy. Generally, cavities are built up from the intersection of atom-centred spheres, whose size is determined from fixed standard atomic radii [32-36], However, other strategies have been proposed, such as the use of variable atomic radii, whose values depend... 

The electrostatic solvation energy is only a part of the total solvation energy. Cavitation, dispersion and repulsion terms must be added. We show below that the MPE method leads to similar electrostatic energies than the polarizable continuum model (PCM) of Tomasi and co-workers [10], provided the same cavities are used. Therefore, non-electrostatic terms in these methods may be computed using the same computational strategies [15]. We emphasize the fact that accurate non-electrostatic contributions are often difficult to compute since they are based on parameterized formulae that cannot be directly compared to experiment. The obtained data must therefore be used with prudence, especially if they are expected to play a major role in the process under study. Fortunately, in many circumstances, non-electrostatic terms are small and/or vary little, so that they can be neglected. Tunon et al. [80] developed a parameterized expression for the MPE method using an expression of the type... 

Continuum Model Calculations of Solvation Free Energies Accurate Evaluation of Electrostatic Contributions. 

A. Jean-Charles, A. Nicholls, K. Sharp, B. Honig, A. Tempczyk, T. F. Hendrickson, and W. C. Still,/. Am. Chem. Soc., 113, 1454 (1991). Electrostatic Contributions to Solvation Energies Comparison of Free Energy Perturbation and Continuum Calculations. 

It is a serious drawback that it is not possible to determine the transfer activity coefficient of the proton (or of any other single-ion species) directly by thermodynamic methods, because only the values for both the proton and its counterion are obtained. Therefore, approximation methods are used to separate the medium effect on the proton. One is based on the simple sphere-in-continuum model of Born, calculating the electrostatic contribution of the Gibb s free energy of transfer. This approach is clearly too weak, because it does not consider solvation effects. Different ex-trathermodynamic approximation methods, unfortunately, lead not only to different values of the medium effect but also to different signs in some cases. Some examples are given in the following log yH+ for methanol -1-1.7 (standard deviation 0.4) ethanol -1-2.5 (1.8), n-butanol -t-2.3 (2.0), dimethyl sulfoxide -3.6 (2.0), acetonitrile -1-4.3 (1.5), formic acid -1-7.9 (1.7), NH3 -16. From these data, it can be seen that methanol has about the same basicity as water the other alcohols are less basic, as is acetonitrile. Di-... 

Mohan, V., M. E. Davis, J. A. McCammon and B. M. Pettitt. (1992). Continuum Model Calculations of Solvation Free Energies - Accurate Evaluation of Electrostatic Contributions. Journal of Physical Chemistry. 96 6428-6431. 

Still, J. Am. Chem. Soc., 113, 145 (1991). Electrostatic Contributions to Solvation Free Energy Perturbation and Continuum Calculations. 

The original formal theory is expressed in terms of quanttun electrodynamics with the continuum mediwn characterized by its spectnun of complex dielectric frequencies. A more recent formulation, derived from this theory, is based on the extension of the reaction field concept to a dipole subject to fluctuations exclusively electric in origin. Another procedme has been formulated starting, as for the repulsion contribution, from the theory of intermolecular forces. Following the scheme commonly exploited to derive the electrostatic contribution to the interaction energy, the molecule B is substituted by a continuum medium, the solvent S, described by a surface charge density as induced by the solute transition densities of M (the equivalent of A) and spreading on the cavity surface. 

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