Lattice energies Some basic concepts

7 The calculation of intermolecular energies in crystals 8.7.1 Lattice energies Some basic concepts 

Consider the same N molecules at rest in a perfectly ordered infinite crystalline array with one molecule in the asymmetric unit. All molecules are equal, and surface or truncation effects are neglected, so the following discussion refers to a bulk crystal. Assuming for the moment that the intermolecular potential is pairwise additive, e.g. in the atom-atom potential approximation, the packing potential energy, PPE, or the interaction energy of any reference molecule m with the surrounding molecules n, is a sum of molecule-molecule terms, each of which is in turn a sum of atom-atom terms  

Atoms k belong to molecule m, atoms / belong to molecule n, Ru. is the interatomic distance. Writing now PPE(m) explicitly for all molecules, from equation 8.5  

Obviously U(m,n) = U(n,m), but some of the U i,j) must also be equal to some U(k, 1) due to crystal symmetry, so that equation 8.9 holds, and, as long as the crystal is infinite and perfect, the calculation of PPE is independent of the choice of the reference molecule. 

For a mole of molecules in the crystal, that is, when N equals Avogadro s number  

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