Interaction-radii solute, solvent

A simplihed approach to the description of AV starts from the statement made by Hamann [270] that the partial molar volume of any dissolved species in solution is the sum of the intrinsic volume of the species, corresponding to its van der Waals radius (intrinsic contribution), and of the contribution due to interaction with the solvent and with the other dissolved species (environmental... 

We developed the Analytical Generalized Born plus Non-Polar (AGBNP) model, an implicit solvent model based on the Generalized Born model [37-40,44, 66] for the electrostatic component and on the decomposition of the nonpolar hydration-free energy into a cavity component based on the solute surface area and a solute-solvent van der Waals interaction free energy component modeled using an estimator based on the Born radius of each atom. 

For purely electrostatic solute/solvent interactions, the Kirkwood equation, Eq. (4-27) [56], is applicable, which relates the standard molar Gibbs free energy of transfer of spherical dipolar molecules of radius r and dipole moment // from the gas phase (fir = 1) to a continuous medium of relative permittivity r-... 

In the case of nonpolar solute molecules, the third and fourth as well as the fifth term in Eq. (6-2) is zero, thus the solvent dependence will be determined by dispersion interactions and only the second term is essential. The solvent shift, compared to the vapour state, will be approximately 70 to 3000 cm to lower wavenumbers (general red shift) depending only on the function f (cf Eq. (6 )). If, on excitation, there is a sufficiently large change in dipole moment, the third and fourth terms have to be taken into account. In the case of an increase in the dipole moment, these terms cause a batho-chromic shift, and in the case of a decrease, a hypsochromic shift of the absorption band. It has been calculated that for a molecule with an interaction radius aw = 6 10 cm, a dipole moment = 10 Cm (6 D), and a dipole change (// — =... 

Veg and Veg are the wavenumbers of the electronic transitions for absorption and fluorescence in the gas phase, respectively the other terms are as in Eq. (6-2). Eq. (6-5a) has been widely used for the determination of dipole moment changes from the solvent dependence of spectra. The main source of error is the Hmited accuracy of the estimated value for the interaction radius uw of the solute molecule since Av is a cubic function of Uw. 

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. 

Self-consistent reaction-field (SCRF) theories are obtained by introducing solute-solvent interactions into the Hamiltonian. (Cf. Tapia, 1982.) Based on Cl wave functions and on reasonable approximation for the cavity radius... 

In chemical reactions, the partial molar volume of dissolved components is influenced by three factors (1) an intrinsic part of the component that is determined by a change in the Van der Waals radius, (2) by interactions between solute and solvent, oriented to electrostriction, and (3) by interaction of the component with all other dissolved components, including itself. The third factor is negligible in diluted solutions (as most fresh and high moisture foods can be considered). The intrinsic factor is supposed to be independent of solvent and concentration. In a preliminary way, total reaction volume is the addition of two parts of volume, the intrinsic part mentioned before and that of solvation, as Equation 12.14 shows ... 

For an atom in the enzyme or the substrate to interact with the solvent it must be able to form Van der Waals contact with water molecules. The accessible surface area of an atom is defined as the area on the surface of a sphere, radius R on each point of which the centre of a solvent molecule can be placed in contact with the atom without penetrating any other atoms of the molecule (Fig. 12). R is the sum of the Van der Waals radii of the atom and solvent molecule [27]. There is a linear relationship between the solubility of hydrocarbons and the surface area of the cavity they form in water [28]. It has been estimated that the hydrophobicity of residues in proteins is 100 J/mole/A of accessible surface area [29]. The surface tension of water is 72 dynes/cm so to form a free surface area of water of 1 A costs 435 J/mole/A. The implication is that the free energy of cavity formation in water to receive the hydrophobic group is offset by favourable interactions (dispersion forces) between the solute and water. 

The terms between the brackets correspond to the osmotic contribution to the Gibbs free energy (AG), and they also constitute the standard expression for AG of the Flory-Huggins theory of polymer solutions [61], where < p is the volume fraction of polymer and the ratio of the equivalent number of molecular segments of solvent to polymer (usually expressed as the ratio of molar volumes of solvent and polymer). Xap is the Flory-Huggins interaction parameter of solvent and polymer and the last term of Equation 14.1 is the interfacial free energy contribution where y is the interfacial tension, the molar volume of solvent, and r the particle radius. T is temperature in Kelvin and R is the universal gas constant. 

The Pratt-Chandler theory has been extended to consider complex molecules. For example, the hard-sphere model of -butane may have an excluded volume Av(f, X), which is a function of the torsion angle (j) and depends on the exclusion radius X of the methylene spheres. Then the part of the PMF (the potential of mean force) arising from the solute-solvent interaction can be related to the reversible work required to create a cavity with the shape and excluded volume Av((/>, X) of the -butane molecule. 

FIGURE 2.2 Different computational treatments of solute-solvent interactions, (a) Solvent treated as an ensemble of discrete molecules. In this case, solvent molecules (in tube representation) can be treated at MM level, whereas the solute (in ball-and-stick representation) is treated at QM level, (h) Treatment of the solvent as a dielectric continuum. The solute is modeled as a sphere of radius ao and dipole moment /a according to the Onsager model, (c) Same as (b) but the solute is in an ellipsoidal cavity defined by axes a, b, and c. (d) Treatment of the solute solvent interactions according to the polarization continuum model (PCM). 

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