Short-Range Electrostatic Interactions

The remainder of this section discusses several important classes of calculations in which the PB model has been, or will be, used to compute short-range electrostatic interactions. In understanding these examples, it is helpful to keep in mind the following unifying principle. Within the PB model, the electrostatic energy of a molecule or system of molecules in solution is the sum of two contributions the electrostatic interaction energy of the solute atoms, computed using Coulomb s law and the dielectric constant of the solute interior, and the electrostatic interaction between the atoms and the solvent. The first term is simple to compute and depends only on the conformation of the system under study. The second term is the one that is difficult to compute. It depends on both molecular conformation and the nature of the solvent. All the examples in this section may be viewed as varied applications of this principle. 

The results of this section may be summarized by noting that significant successes have been achieved, but further work is needed both to examine and to extend the model s range of applicability. 

Here we briefly discuss the calculation of the electrostatic energy of a molecular system from a finite difference solution of the linearized Poisson-Boltzmann equation. Calculations of the molecular electrostatic energy from grid solutions of the full nonlinear Poisson-Boltzmann equation are more involved and are discussed in detail elsewhere.  

We define a reference state in which all the charges of the molecule are infinitely separated in a medium that responds with the molecular dielectric constant e,. As described in the introduction to this section, the total elearo- 

In the linear system, the Coulombic energy of assembling the solute atoms, AGS C2n be written as  

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The purpose of this paper is to calculate the electrochemical potential and the double layer repulsion using a lattice model, applicable to hydrated ions of different sizes, that accounts for the correlation between the probabilities of occupancy of adjacent sites. As the other lattice models,4-7 this model accounts only for the steric, excluded volume effects due to ionic hydration. In feet, short-ranged electrostatic interactions between the ions and the dipoles of the water molecules, as well as the van der Waals interactions between the ions and the water molecules, are responsible for the formation of the hydrated ions. The long-ranged interactions between charges are taken into account through an electrostatic (mean field) potential. The correlation between ions is expected to be negligible for sufficiently low ionic concentrations. 

There has been far less research performed on the role of short-range electrostatic interactions such as cation- [39] and other polar- [40] effects on the reduction potential of organic cofactors. The effects of these interactions on biological systems are hard to assess mutation of charged residues near the active site perturbs multiple aspects of the catalytic process [41], whereas dipolar interactions are often subtle, and are extremely distance dependent [42]. One model study has been performed on the donor atom- interaction of electron-rich functionality with flavins [43]. These studies used a model system (Figure 11) to explore the role of this interaction... 

The electric potential resulting from any charge distribution can be represented by a convergent multicenter multipole expansion.Molecular moments of isolated molecules can be obtained experimentally, such as from the Stark effect on the microwave spectra of gas molecules. Studies of van der Waals clusters and molecular association in general require a multicenter model for short-range electrostatic interaction. Mulder and Huiszoon, for instance, found that a molecular multipole expansion was not satisfactory for the electrostatic interaction of... 

Bjerrum s concept of an ion pair and his theoretical development is the most successful treatment used in conjunction with the Debye-Hiickel theory for analysing experimental data, despite all the ambiguities in deciding at what stage to introduce the cut-off distance between ion pairs and free ions. His theory was basically a device to account for the short range electrostatic interactions not included in the Debye-Hiickel theory (see Guggenheim s treatment, Section 10.13.1). 

For electrode-solution interface problems, the treatment of Kornyshev et al. (1977) seems to be the most promising and explicit for elucidation of short-range electrostatic interaction of a charged or partially charged adsorbate with a metal-electrode surface. 

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