Electrostatic point-charge

Figure 8,1 Structural models for H2O molecule. (A) Electrostatic point-charge model (from Eisemberg and Kauzmann, 1969 redrawn). (B) Electron density map (from Bader and Jones, 1963). (C) Formation of MOs and starting from AOs 2p and Is of oxygen and 1 of hydrogen.

The relationship describing the interaction, in terms of mutual force (F), between two electrostatic point charges F = QiQ2/(4 ned ) where <2i and Qi are the respective point charges, d is the distance separating them, and e is the permittivity of the medium. 

This model of a complex or of a crystalline salt of a metal ion in a compound such as a halide or oxide is of an electrostatic, point charge, or point dipole type. The ligands or neighbors of the metal ion are treated as structureless, orbital-less point charges, which set up an electrostatic field. The effect of this field on electrons in the d orbitals of the metal ion is then investigated. 

In 1920, two men in G.N. Lewis laboratory at Berkeley proposed the hydrogen bond (Latimer and Rodebush, 1920) using a simplified electrostatic point charge model of the water molecule. The work by Kollman (1977) indicated that the simplified model remains acceptable because of a cancellation of two other energy components. 

Aij5 Bjj and CF are constants for a given pair of atoms and qj and are atomic net charges of the atoms i and j. The first two terms correspond to the Lennard-Jones potential and the third term to the electrostatic point charge — point charge interaction. 

Figure 5.3 Schematic diagram to demonstrate the electrostatic point-charge calculation of bond dissociation energy.

Though the electrostatic point charge model is a rough approximation, it may bring some interesting informations. 

The comparison between the phenomenological parameters calculated from optical spectra and the electrostatic point charge parameters has shown that the crystal field is more different from an electrostatic one than is usual but a ligand field hypothesis seems reasonable. 

This approximation of pure electrostatic point-charge interaction between the QM and MM regions may be invalid for the interactions of near-neighbor atoms at the QM-MM border. To take into account the non-electrostatic part of the QM-MM interaction, many authors suggest to introduce an empirical term in the form of a Lenard-Jones 12-6 potential... 

The simplest model of a covalent bond is based on an electrostatic point-charge simulation of overlapping spherical valence-electron charge clouds that surround monopositive atomic cores. For a homonuclear pair of atoms with radius r and internuclear distance d, the dissociation energy D is calculated from... 

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