The point-charge model

Cohesive energies are defined as the difference between the total energy of a system and the sum of the energies of its components. If there is a rearrangement of the separate component densities when the components are brought together, this distortion must be taken into account. 

It is quite remarkable that electrostatic calculations based on a simple model of integral point charges at the nuclear positions of ionic crystals have produced good agreement with values of the cohesive energy as determined experimentally with use of the Born-Haber cycle. The point-charge model is a purely electrostatic model, which expresses the energy of a crystal relative to the assembly of isolated ions in terms of the Coulombic interactions between the ions. 

The geometry of the crystal introduces a factor multiplying the pairwise ionic interaction, which is the Madelung constant /t. It is a dimensionless constant, dependent on the geometry of the crystal under consideration. For an ionic binary crystal, consisting of N each positive and negative ions, fi is defined by 

Equation (9.12) implies the assumption that the kinetic energy and exchange-correlation terms in Eq. (9.1) are the same for the crystal and the assembly of isolated ions. 

---

In contrast to the point charge model, which needs atom-centered charges from an external source (because of the geometry dependence of the charge distribution they cannot be parameterized and are often pre-calculated by quantum mechanics), the relatively few different bond dipoles are parameterized. An elegant way to calculate charges is by the use of so-called bond increments (Eq. (26)), which are defined as the charge contribution of each atom j bound to atom i. 

VVe therefore return to the point-charge model for calculating electrostatic interactions. If sufficient point charges are used then all of the electric moments can be reproduced and the multipole interaction energy. Equation (4.30), is exactly equal to that calculated from the Coulomb summation. Equation (4.19). 

On the basis of the point-charge model formalism, applied on the experimental nuclear quadrupole splitting rationalization, I Agxp I, the results obtained were interpreted in terms of strong complex formation by either Me2Sn(OH)2 or Me3Sn(0H)(H20) with (n = 1 or 2, obtained in phosphate buffer) and... 

Kelld, V. and Sadlej, A.J. (2000) The point charge model of nuclear quadrupoles How and why does it work. Journal of Chemical Physics, 112, 522—526. 

Y2Ba4Cu7025 Nuclear quadrupole interaction at copper sites, EFG tensor at all sites is calculated using the point charge model, conclusion that holes in the Y2Ba4Cu70i5 lattice are localized predominantly at positions of chain oxygen... 

There are two main ways of representing the H2O molecule the point-charge model and molecular orbital representation. 

Figure 8.1A shows the point-charge model of Verwey (1941). Point charges... 

The approach is that adopted earlier for E b [Eq. (10.3)], using the point-charge model, which seems reasonable for describing interactions between distant atoms, at least in sigma systems. The charges and the geometries are the same as those used earlier for the total nonbonded interactions represented by Eq. (10.3). 

All symbols have their usual meaning in the c.g.s. system of units, as given in Ref. 3. The common interpretation that the central ion sees its ionic cloud at a distance k 1 away is valid for the point-charge model only. For the DH second approximation the ionic cloud can be reduced to a charge located on a spherical surface at k 1 so as to maintain a constant potential at the surface of the central ion. Therefore, it cannot be replaced by a point charge. 

The Debye-Hiickel Theory of Activity Coefficient The Point-Charge Model. The... 

In this case both e.t. processes are intramolecular, the distance between the porphyrin and the quinone being fixed by a short space. The highest rate constants of the photo-induced charge separation reach about 4 x 1011 s J and these would not be observable in a diffusion controlled intermolecular reaction. In these measurements, two solvents were used — nonpolar toluene and polar butyronitrile — and the AG values are therefore subject to the uncertainties discussed in Sect. 2.1. In particular, the Coulomb term for butyronitrile assumes the point charge model with full solvent screening, which may well underestimate the free energy values, especially in such an intramolecular system where it is clear that the solvent cannot be inserted between the chromophores. 

It is not easy to rationalize this series with the point charge model. For instance, on the basis of ionic bonding, it is difficult to see that a neutral ligand, CO, yields the largest (or at least one of the largest) A0. However, this point may be readily understood once we consider covalent bonding between the metal ion and the ligands. 

It is embarassing that the pressure experiments show the dependence of A upon the distance R between the metal and the ligand to be fairly close to that given by the point charge model. 

Dependent on the type and quality of QA, the point charge model can be used as a more or less crude approximation of the full quantum chemical calculation of (i according to Equation 6.48). As outlined below, semiempirical mapping procedures have been developed to derive QA such that Equation 6.49 yields a best fit (within the model parameters employed) to exact (experimental) dipole moments. 

Steric interaction Non-bonded or van der Waals interaction has been demonstrated to be no different from, albeit weaker than, both covalent and ionic interactions. It has in fact been demonstrated [88] that all pairwise interactions in a molecule are correctly simulated by the point-charge model of section 5.3. 

Na+.CT. According to the point charge model, the energy is described... 

In polyelectrolyte systems, the theory is adjusted either to the point charge model assuming a distribution of point charges on the polymer chain or to the dipole-ion theory considering an ion pair as a dipole. Their potential energies are expressed as... 

Brill et ah IS21 investigated the 3SC1(NQR) spectrum and used the point charge model to calculate the EFG.Semiempirical LCAO-MO calculations have also been used. An empirical Stemheimer factor of -10 for chlorine was used to explain the crystal field effects which amount to 10 % for y(35Cl) in [SnCl6]2. ... 

---