Electrostatic solute-solvent interaction models

As an example, consider assessment of classic electrostatic solute-solvent interactions associated with solute partial charges in force-field models. The contribution of electrostatic interactions is then isolated as... 

In this chapter we consider the extension of continuum solvent models to nonlocal theories in the framework of the linear response approximation (LRA). Such an approximation is mainly applicable to electrostatic solute-solvent interactions, which usually obey the LRA with reasonable accuracy. The presentation is confined to this case. 

The description of the electrostatic solute-solvent interactions has represented, historically, the keystone of continuum models. Within the continuum electrostatic frameworks the solvent is substituted with a dielectric medium and the solute occupies a cavity C within the dielectric. The main aspects to consider is thus the definition of the macroscopic characteristics of the dielectric, i.e. the form of the dielectric constant and the definition of the cavity C. Following this analysis we can define different systems ... 

Basically, the continuum solvation models consider the solvent as a uniform polarizable medium with dielectric constant e, where the solute (M) is immersed inside a cavity. Once placed inside the dielectric, the solute charge distribution polarizes the medium that in turn acts back (reaction field) polarizing the solute molecule. The system is then stabilized by the electrostatic interaction between the polarized solute and the polarized medium. Calling the charge distribution of the solute and the solvent reaction potential, the electrostatic solute-solvent interaction can be written as... 

As for the theoretical treatment, we could only try to include the electrostatic solute-solvent interactions and, in fact, we corrected the electronic potential energies for the solvation effeets by simply adding E , as calculated according to the solvaton model [eq. (2)]. The resulting potential curves are to be seen as effective potentials at equilibrium, i.e. refleeting orientational equilibrium distributions of the solvent dipoles around the charged atoms of the solute molecule. In principle, the use of potentials thus corrected involves the assumption that solvent equilibration is more rapid than internal rotation of the solute molecule. Fig. 4 points out the effects produced on the potential... 

Computer simulations of both equilibrium and dynamic properties of small solutes indicate that the solubility-diffusion model is not an accurate approximation to the behavior of small, neutral solutes in membranes. This conclusion is supported experimentally [57]. Clearly, packing and ordering effects, as well as electrostatic solute-solvent interactions need to be included. One extreme example are changes in membrane permeability near the gel-liquid crystalline phase transition temperature [56]. Another example is unassisted ion transport across membranes, discussed in the following section. 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

The physical properties of atoms and molecules embedded in polar liquids have usually been described in the frame of the effective medium approximation. Within this model, the solute-solvent interactions are accounted for by means of the RF theory [1-3], The basic quantity of this formalism is the RF potential. It is usually variationally derived from a model energy functional describing the effective energy of the solute in the field of an external electrostatic perturbation. For instance, if a singly negative or positive charged atomic system is considered, the RF potential is simply given by... 

Self-consistent reaction field (SCRF) models are the most efficient way to include condensed-phase effects into quantum mechanical calculations [8-11]. This is accomplished by using SCRF approach for the electrostatic component. By design, it considers only one physical effect accompanying the insertion of a solute in a solvent, namely, the bulk polarization of the solvent by the mean field of the solute. This approach efficiently takes into account the long range solute-solvent electrostatic interaction and effect of solvent polarization. However, by design, this model cannot describe local solute-solvent interactions. 

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],... 

A weakness of this model is that the separation of the electrostatic and the so-called specific solute-solvent interactions is not defined. In practice, two main approaches are used to account for solvent effects on the spin-spin coupling constants the continuum and the supermolecular methods. The combined MD/QM approach is rarely used for the purpose, since calculations of the spin-spin coupling constants are much more time consuming than those of the shielding constants and the MD/QM approach is too expensive for the former. 

Continuum solvation models are generally focused on purely electrostatic effects the solvent is a homogeneous continuous medium and its response is determined by its dielectric constant. Electrostatic effects usually constitute the dominating part of the solute - solvent interaction but in some cases explicit solute-solvent (or solute-solute)... 

In the following, the modelling of solute-solvent interactions at the interface will be discussed in Section Electrostatic and in Section Nonelectrostatic Interactions (cavitation, dispersion, and repulsion). Applications of the methods developed to the modelling of molecular properties at liquid surfaces will be described in the Section Energetics and Properties at Liquid-Gas and Liquid-Liquid Interface. 

Different solvation methods can be obtained depending on the way the (Vs(r p)) xj tern1 is calculated. So, for instance, in dielectric continuum models ( Vs(r p)) x is a function of the solvent dielectric constant and of the geometric parameters that define the molecular cavity where the solute molecule is placed. In ASEP/MD, the information necessary to calculate Vs(r, p))[Xj is obtained from molecular dynamics calculations. In this way (Vs(r p))[Xj incorporates information about the microscopic structure of the solvent around the solute, furthermore, specific solute-solvent interactions can be properly accounted for. For computational convenience, the potential Vs(r p)) X is discretized and represented by a set of point charges, that simulate the electrostatic potential generated by the solvent distribution. The set of charges, is obtained in three steps [26] ... 

For the dispersion contribution, we assume that the solute-solvent interaction, in the outer shell, is of the form C/r and that the distribution of water outside the inner shell is uniform. Thus the dispersion contribution is —4TTpC/(3i ), where for the SPC/E water model, 4ttpC/3 is 87.3kcalmol A . The electrostatic effects were modeled with a dielectric continuum approach (Yoon and Lenhoff, 1990), using a spherical cavity of radius R. The SPC/E (Berendsen et al, 1987) charge set was used for the water molecule in the center of the cavity. 

F. J. Olivares del Valle and -M. A. Aguilar,/. Mol. Struct. (THEOCHEM), 280, 25 (1993). Solute-Solvent Interactions. Part 5. An Extended Polarizable Continuum Model Including Electrostatic and Dispersion Terms and Electronic Correlation in the Solute. 

Since the main parts of the solute-solvent interactions are of electrostatic nature, one may improve the models mentioned in the previous subsection by including the response of the solvent molecules to the electric field generated by the solvent and the solute. In the general case, the dipole moment of a (solvent) molecule changes under the influence of an electrostatic field,... 

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