Effective electrostatic radius

Effective Electrostatic Radius, Born Coefficient, and Solvation Energy... 

The solvation energy described by the Born equation is essentially electrostatic in nature. Born equations 8.116 and 8.120 are in fact similar to the Born-Lande equation (1.67) used to define the electrostatic potential in a crystal (see section 1.12.1). In hght of this analogy, the effective electrostatic radius of an ion in solution r j assumes the same significance as the equilibrium distance in the Born-Lande equation. We may thus expect a close analogy between the crystal radius of an ion and the effective electrostatic radius of the same ion in solution. 

Figure 6.9. (a) Values of log as a function of the dielectric constant (1/Ej.) and values of the bond strength per A (i/rM+) (b) values of log as a function of the dielectric constant (l/Sj) and the repulsive term in A (2/r/,+ ) (c) values of as a function of the effective electrostatic radius (i/Rej) and values of r j, (d) linear free energy correlations for values of logA" m+ with the aqueous-phase equihbrium association constants ATmiOHi"- (From Sverjensky, 2005.)... 

The Lewis dot formalism shows any halogen in a molecule surrounded by three electron lone pairs. An unfortunate consequence of this perspective is that it is natural to assume that these electrons are equivalent and symmetrically distributed (i.e., that the iodine is sp3 hybridized). Even simple quantum mechanical calculations, however, show that this is not the case [148]. Consider the diiodine molecule in the gas phase (Fig. 3). There is a region directly opposite the I-I sigma bond where the nucleus is poorly shielded by the atoms electron cloud. Allen described this as polar flattening , where the effective atomic radius is shorter at this point than it is perpendicular to the I-I bond [149]. Politzer and coworkers simply call it a sigma hole [150,151]. This area of positive electrostatic potential also coincides with the LUMO of the molecule (Fig. 4). 

These definitions are interpreted as follows environment atoms recognize the average weighted states of the ligands each ligand recognizes only the environment atoms and itself with the full scale for estimation of its effective Bom radius. Alternate definitions of the electrostatic solvation energy and the effective Bom radius at the intermediate states are also possible.81... 

A rather complex procedure is used to determine the Born radii a , values of which are calculated for each atom in the molecule that carries a charge or a partial charge The Born radius of an atom (more correctly considered to be an effective Born radius) corresponds to the radius that would return the electrostatic energy of the system according to the Bom equation if all other atoms in the molecule were uncharged (i.e. if tlie other atoms onl)- acted to define the dielectric boundary between the solute and the solvent). In Still s force field implementation, atomic radii from the OPTS force field are assigned to each... 

An ellipsoidal nucleus with two spherons in the inner core has major radius greater than the minor radii by the radius of a spheron. about 1.5 f, which is about 25 percent of the mean radius. The amount of deformation given by this model is accordingly in rough agreement with that observed (18). In a detailed treatment it would be necessary to take into account the effect of electrostatic repulsion in causing the helions to tend to occupy the poles of the prolate mantle, with tritons tending to the equator. 

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