Classical electrostatics

Honig B and A Nicholls 1995. Classical Electrostatics in Biology and Chemistry. Science 268 1144-1149... 

Bashin A A 1990. Hydration Phenomena, Classical Electrostatics, and the Boundary Element Methoc Journal of Physical Chemistry 94 1725-1733. 

The classical electrostatic potential for q point charges is the potential energy at a position R (equation 18). 

These early results of Coulomb and his contemporaries led to the full development of classical electrostatics and electrodynamics in the nineteenth cenmry, culminating with Maxwell s equations. We do not consider electrodynamics at all in this chapter, and our discussion of electrostatics is necessarily brief. However, we need to introduce Gauss law and Poisson s equation, which are consequences of Coulomb s law. 

At long range, complex interactions having their origin in quantum mechanics are negligible, and molecular interactions can be described by classical electrostatics of nuclei and electron density. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Classical electrostatics deals with the interactions of idealized electric charges. Electrochemistry deals with real charged particles having both electrostatic and chemical properties. For a clearer distinction of these properties, let ns briefly recall some of the principles of electrostatics. 

An ideal (classical) electrostatic capacitor consists of two plane-parallel metal plates having surface areas S and a mutual distance 5, the gap being filled with air or a dielectric layer (the latter variety often is called a film capacitor). When a capacitor is charged (by applying an electrostatic potential difference A / between the two plates), electrical charges +Q m electron deficit) and Q (an efectron excess), which are equal in magnitude but opposite in sign, will accnmulate on the plates. The values of Q are proportional to the potential difference ... 

In this section we discuss the various strategies implemented in common Kohn-Sham programs to compute the classical electrostatic contribution to the electron-electron repulsion... 

Conceptually, the self-consistent reaction field (SCRF) model is the simplest method for inclusion of environment implicitly in the semi-empirical Hamiltonian24, and has been the subject of several detailed reviews24,25,66. In SCRF calculations, the QM system of interest (solute) is placed into a cavity within a polarizable medium of dielectric constant e (Fig. 2.2). For ease of computation, the cavity is assumed to be spherical and have a radius ro, although expressions similar to those outlined below have been developed for ellipsoidal cavities67. Using ideas from classical electrostatics, we can show that the interaction potential can be expressed as a function of the charge and multipole moments of the solute. For ease... 

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... 

On the basis of classical electrostatic theory, a large part of the free energy of a pair of ions depends on the dielectric constant of the medium. In a solvent of high dielectric constant, a charged object creates oriented solvent dipoles by polarization or orients existing... 

B. Honig and A. Nicholls, Classical electrostatics in biology and chemistry, Science 268 1144(1995). 

The ionic or electrostatic picture of bonding has an engaging simplicity. According to classical electrostatics, the energy of interaction (Ees) of particles with charges 0 and Qi at separation R is... 

Thus, for any fixed R classical electrostatics favors a square over a linear arrangement by 10.8%, but the only true minimum is —> 0. 

Figure 2.3 The potential-energy curve for Li+ + F ionic bond formation according to quantum mechanics (solid line) or classical electrostatics (dotted line).

Figure 2.4 Components of the Li-F potential-energy curve E R) = E (R) + E(NL>(R), showing the localized natural-Lewis-structure model energy E(L> (circles, left-hand scale) and delocalized non-Lewis correction ,(NL) (squares, right-hand scale). The classical electrostatic estimate E (dotted line) is shown for comparison.

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