The Packing Energy and its Interpretation

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  

The adjustable parameters appearing in Equation (12.6) must be carefully optimized against experimental data. These are either geometric (cell dimensions, molecular position and orientation) or energetic (sublimation enthalpies, lattice frequencies) in nature. Calculation of geometric features depends primarily on a proper balance of the attractive and repulsive parts of the potentials, not on their absolute magnitudes. Calculation of lattice energy (to be compared with sublimation enthalpies) depends primarily on the well depths of individual atom-atom interactions. Finally, lattice vibrations depend critically on the second derivative of the potential and are usually the most difficult to calculate correctly. 

The calculation of unit cell dimensions and of the optimum position and orientation of the molecules in the cell is usually carried out by relaxing the observed crystal structure under the action of the postulated potential. A reliable potential should ideally produce no displacement from the observed structure. In practice, the calculated crystal structure is already close to the observed one, i.e. attractions and repulsions are largely balanced. Improvement of the calculated positions mostly depends on improving the repulsive part of the potential, which is very steep but oth- 

The observables which are most sensitive to the choice of adjustable parameters are lattice vibration frequencies, but experimental values are sparse their calculation requires a comparatively large effort and involves approximations whose validity cannot always be taken for granted (e.g. the harmonic approximation). 

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