Energy packing potential

The packing potential energy is the energy released on bringing one molecule from infinity to its location in the crystal. Within the two-body atom-atom approximation, it is written as a lattice sum of all pairwise energies ... 

Fig. 12.5. A plot of the packing potential energy versus the number of carbon atoms in hydrocarbon molecules...

Braga and Grepioni have undertaken a series of analyses of the crystal structures of metal carbonyl clusters, 7t-arene complexes, mixed carbonyl n-arene complexes and some substituted derivatives [170]. Their analyses are based on examination of the packing details and motifs in the crystal structures, recognition of specific interactions, calculation of the packing potential energy for the crystal and consideration of contributions to the lattice volume. Their objective, to investigate the interplay between molecular structure and crystal structure, is very similar to the perspective in this article. 

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 ... 

Consider a crystal of a pure substance with two molecules, Ai and A2, in the asymmetric unit. The molecules are identical but become distinguishable in the solid state because of the different crystal environment. The condensation process can formally be broken down into (1) the formation of a mole of Ai A2 dimers, cohesive energy (Ai A2) and (2) the condensation of dimers into the crystal, with a packing potential energy PPE A A2), which is obtained by lattice summations in the same way as the PPE of a single molecule. If there are q molecules in the asymmetric unit (a g-mer), the same reasoning applies to the formation of q q — l)/2 dimers and to the condensation of the group of q molecules into the crystal. Then ... 

Experiment shows that heat is absorbed as iodine dissolves. The regular, ideally packed iodine crystal gives an iodine molecule a lower potential energy than does the random and loosely packed solvent environment. We see that the second factor, tendency toward minimum energy, favors precipitation and growth of the crystal. 

Only the most simple form of metallic bonding will be considered here. In its simple form a metal is a dense plasma of nearly free electrons and positive ions. The ions are condensed into close-packed 3-D face-centered arrays. Metallic bonding results from a balance between attractive potential energy and repulsive kinetic energy. 

---