Electrostatic balance terms

MEP at a grid point r on the molecular surface, and V are their average values, and n and n are the numbers of grid points with positive and negative values, v is the electrostatic balance term that reaches a maximum value of 0.25 when <5 and 0 . are equal. 

The macroscopic property of interest, e.g., heat of vaporization, is represented in terms of some subset of the computed quantities on the right side of Eq. (3.7). The latter are measures of various aspects of a molecule s interactive behavior, with all but surface area being defined in terms of the electrostatic potential computed on the molecular surface. Vs max and Fs min, the most positive and most negative values of V(r) on the surface, are site-specific they indicate the tendencies and most favorable locations for nucleophilic and electrophilic interactions. In contrast, II, a ot and v are statistically-based global quantities, which are defined in terms of the entire molecular surface. II is a measure of local polarity, °fot indicates the degree of variability of the potential on the surface, and v is a measure of the electrostatic balance between the positive and negative regions of V(r) (Murray et al. 1994 Murray and Politzer 1994). 

At the equilibrium distance r, the electrostatic attraction terms balance the repulsion terms. This equilibrium distance is identified as the bond length of the molecule and the curve is known as the potential energy diagram. If no attractive interaction is possible, then no bond formation is predicted and the potential energy curve shows no minimum. 

Early MEP-based parameters considered included surface area (A), If, and v. Flere II is a measure of local polarity, and is a measure of electrostatic interaction tendency. Larger values imply larger charge separation leading to greater electrostatic interaction. Electrostatic interactions are also described by v, which is a measure of electrostatic balance. The three charge related variables are defined in terms of the surface electrostatic potential difference, 8U at the ith point, Eq. [33],... 

Various empirical and chemical models of metal adsorption were presented and discussed. Empirical model parameters are only valid for the experimental conditions under which they were determined. Surface complexation models are chemical models that provide a molecular description of metal and metalloid adsorption reactions using an equilibrium approach. Four such models, the constant capacitance model, the diffuse layer model, the triple layer model, and the CD-MUSIC model, were described. Characteristics common to all the models are equilibrium constant expressions, mass and charge balances, and surface activity coefficient electrostatic potential terms. Various conventions for defining the standard state activity coefficients for the surface species have been... 

From one force held to the next, the balance of energy terms may be different. For example, one force held might use a strong van der Waals potential and no electrostatic interaction, while another force held uses a weaker van der Waals potential plus a charge term. Even when the same terms are present, different charge-assignment algorithms yield systematic differences in results and the van der Waals term may be different to account for this. 

The parameter redundancy is also the reason that care should be exercised when trying to decompose energy differences into individual terms. Although it may be possible to rationalize the preference of one conformation over another by for example increased steric repulsion between certain atom pairs, this is intimately related to the chosen functional form for the non-bonded energy, and the balance between this and the angle bend/torsional terms. The rotational banier in ethane, for example, may be reproduced solely by an HCCH torsional energy term, solely by an H-H van der Waals repulsion or solely by H-H electrostatic repulsion. Different force fields will have (slightly) different balances of these terms, and while one force field may contribute a conformational difference primarily to steric interactions, another may have the... 

On the basis of these comparable mechanisms, the observed regioselectivity with various 3-substituents summarized in Table I might be best interpreted in terms of the balance of three effects, namely attractive dispersion force, steric hindrance, and electrostatic repulsion which would all be operative between the 3-substituent and the ferricyanide ion in the rate-determining step. 

Some components in a gas or liquid interact with sites, termed adsorption sites, on a solid surface by virtue of van der Waals forces, electrostatic interactions, or chemical binding forces. The interaction may be selective to specific components in the fluids, depending on the characteristics of both the solid and the components, and thus the specific components are concentrated on the solid surface. It is assumed that adsorbates are reversibly adsorbed at adsorption sites with homogeneous adsorption energy, and that adsorption is under equilibrium at the fluid- adsorbent interface. Let (m" ) be the number of adsorption sites and (m 2) the number of molecules of A adsorbed at equilibrium, both per unit surface area of the adsorbent. Then, the rate of adsorption r (kmol m s ) should be proportional to the concentration of adsorbate A in the fluid phase and the number of unoccupied adsorption sites. Moreover, the rate of desorption should be proportional to the number of occupied sites per unit surface area. Here, we need not consider the effects of mass transfer, as we are discussing equilibrium conditions at the interface. At equilibrium, these two rates should balance. Thus,... 

This functional is also physically motivated as it expresses the balance of two terms a favorable (negative) solute-solvent interaction energy and an unfavorable (positive) solvent-solvent interaction. At equilibrium the second term is equal to half of the first as expected also from basic electrostatic arguments. 

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