Crystal energy and the Coulomb field

In the ionic model, the energy of an inorganic solid is assumed to be the sum of all the potentials, C/y, between atoms i and j. These consists of two terms, a classical electrostatic potential, C/y,eiectrostatio determined by the charges on the atoms, and a quantum mechanical term, C/,y,Fermi that includes the repulsion that prevents individual atoms from collapsing into each other as well as any residual contributions from covalent bonding (eqn (2.1))  

electrostatic Can be derived from the electrostatic fields, Ei, generated by the individual atoms, i, and these fields can in turn be represented as the sum of the three terms shown in eqn (2.2)  

In this equation ,-,mono, given by eqn (2.3), is the field generated by the point ionic charge, which is assumed to reside at the centre of the atom  

Here r is the distance from the atom centre. In this book the units are chosen so that Qi is measured in electron charges ( = valence units) and q is set equal to 1.0. According to Gauss theorem, if the electron density of the atom is spherically symmetric, fj- mono gives a fully correct description of the field generated by the atom in the region outside the atom itself, i.e. in the region where the electron density of the atom has fallen to zero. 

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