Energy packing

The packing energy of an organic crystal can be easily calculated by a lattice sum over pairwise interactions. The potential parameters for these calculations are summarized in Table 15. The packing energy is usually a quite accurate estimate of the crystal sublimation energy. 

As already anticipated, the molecular surface we calculate is useful in describing condensed state properties. There is a steady linear relationship between SM and packing energy for organic crystals24, and the sulphoxide and sulphone compounds make no... 

FIGURE 21. Packing energy, PE (kcal mol l at 10 A cutoff in the lattice sums), as a function of total molecular free surface, SM, in compounds 1-8. 

Experimental tilt angles have usually an accuracy of at best 3°, leading to an error of about 0.1 A in cell axes. The calculated third cell axis will show a higher deviation. If possible an internal standard should be used for calibration purposes but a higher accuracy will be obtained with a Pawley fit (e.g. fit forP CuPc in Fig. 6) from x-ray powder diffraction data [11]. Especially for packing energy minimization used for simulation methods it is essential to determine the cell parameters as precise as possible. In the case of polymorphism, it is essential to use x-ray powder diffraction to ensure that bulk and investigated nano crystals represent the same modifications. 

In the case of crystals, both intramolecular (conformational) and packing energies should be taken into account simultaneously. Such a total energy minimization method, with suitable crystallographic constraints, has been applied in different steps of the analysis of crystalline structures of three different synthetic polymers. Structures of these molecules, namely, isotactic trans-1,4-poly-penta-1,3-diene (ITPP), poly-pivalolactone (PPVL), and isotactic cis-1,4-poly(2-methyl-penta-1,3-diene)(PMPD), do not have troublesome features such as charged groups, counterions, and solvent molecules. 

It is suggested that there are two possible conformations for the bridging cyclopropyl groups the syn form (Vila) observed in the crystal and the anti form (Vllb) that appears from minimum energy calculations to be more stable in solution (100). These differences and some of the angles seem to result from crystal packing energies in the solid state versus the less constricted form in solution. 

Figure 6. Application of packing energy minimization method to poly(ethylene oxide) (16). (a) Starting model of uniform helix (b) stable crystal structure model obtained by energy minimization calculations and (c) the structure determined by x-ray analysis.

The sophistication of fiber diffraction has grown along with the development of digital computers. These techniques started with the calculation of diffraction intensities for a few proposed models for comparison with the diffraction pattern. At present, parameters of the models can be varied to produce the minimal variance for the observed and calculated diffraction intensities and simultaneously the minimal stereochemical or packing energy. 

Density of states is the number of allowed energetic states in a solid. It is a property in statistical and condensed matter physics that quantifies how closely packed energy levels are in a physical system. It is often expressed as a function g(E) of the internal energy E, or a function g(k) of the wave vector k. Most frequently density of states is used with electronic energy levels in a solid (- metals and - semiconductors). Typical values of the density of states in the conduction band of germanium are 1.04 x 1019, in the valence band 6 x 1018. With InP the respective values are 5.8 x 1017 and 1.4 x 1019. Ref [i] Memming R (2002) Semiconductor electrochemistry. Wiley-VCH, Weinheim... 

---