Coulomb potential Crystal lattice

Starr, T. L. and Williams, D. E. (1977 ). Coulombic nonbonded interatomic potential functions derived from crystal-lattice vibrational frequencies in hydrocarbons. Acta Crystallogr A, 33, 771-6. [153]... 

Yet another Coulomb approach was proposed by Mestechkin [208] for molecular crystals and illustrated in the case of the determination of the dressed first hyperpolarizabihty of urea and l,3,5-triamino-2,4,6-trinitiobenzene (TATB). The full crystal lattice potential was expressed in the form of Madelung sums and evaluated by using the calculated atomic charges within the Mulliken... 

T. L. Starr and D. E. Williams, Acta Crystallogr. Ser. A, A106, 771 (1977). Coulombic Non-bonded Interatomic Potential Functions Derived from Crystal-Lattice Vibrational Frequencies in Hydrocarbons. 

In an ionic crystal lattice each cation will be attracted by anions next to it and repulsed by cations near it. Consequently the coulomb potential leading to the lattice energy depends on the type of crystal. To get the total lattice energy you must sum all of the electrostatic interactions on a given ion. The general form of the electrostatic potential is... 

To subtract the cation Mg + from its lattice position in the crystal and to bring it to the surface, we must work against the static potentials (coulombic plus repulsive plus dispersive) at the Mg site. In terms of energy, this work corresponds to half the lattice contribution of Mg + (in the Mg site of interest—i.e.. Ml or M2 see section 5.2) to the bulk static energy of the phase (see also section 1.12) ... 

A similar calculation can be done for ionic crystals. In this case the Coulomb interaction is taken into account, in addition to the van der Waals attraction and the Pauli repulsion. Although the van der Waals attraction contributes little to the three-dimensional lattice energy, its contribution to the surface energy is significant and typically 20-30%. The calculated surface energy depends sensitively on the particular choice of the inter-atomic potential. 

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