Polymorphism lattice energy differences

Figure 5.13. Lattice-energy differences of reolitic SiOj polymorphs, included are also stishovite (six-coordinated Si) and three ring structures. 3, contains tetrahedra constructed from threerings,...

Figures 14.2 and 14.3 show the main landscape for polymorphic pairs in organic compounds. 30% of polymorphic crystal stmcture pairs have one centrosymmetric and one non-centrosymmetric partner, and 25% of the cases show one partner with more than one molecule in the asymmetric unit. No correlation appears between crystal density differences, and either centrosymmetricity or difference in the number of molecules in the asymmetric unit. Crystal density differences range from 0 to 10%, and lattice energy differences, as computed in a preliminary way with atom-atom UNI...

Fig. 14.2. Relative lattice energy differences, AEjE, as a function of relative density difference, AD/D. 475 polymorph pairs.

An experimental study of barbituric acid found one new polymorph where molecules in the asymmetric unit adopted two different conformations [10]. The conformational aspect was investigated through the use of ab initio calculations, which permitted the deduction that the new form found would have a lower lattice energy than would the known form. It was also found that many hypothetical structures characterized by a variety of hydrogen-bonding structures were possible, and so the combined theoretical and experimental studies indicated that a search for additional polymorphs might yield new crystal structures. 

A similar success rate, four and 44 out of 50 attempts for the anatase and rutile polymorphs, respectively, was more recently found by Reinaudi et al. [68]. Their initial work differs from that of Freeman and coworkers in that the lattice energy (Eq. 2 with identical potential parameters) rather than the r12 cost function was used as the measure of quality during the SA stage. Although a better measure of quality for candidate structures that are similar to the desired structure, this definition of the cost function can be problematic, however, if there are very short interatomic distances. Thus, the benefit of using the r12 cost function, to help prevent creating candidate structures that may contain collapsed regions, is lost. 

Solution microcalorimetry is another thermal method for the determination of the difference in lattice energy of polymorphic solids. The difference in heat of solution of two polymorphs is also the difference in lattice energy (more precisely lattice enthalpy), provided of course, that both dissolution experiments are carried out in the same solvent (Guillory andErb 1985 Lindenbaum and McGraw 1985 Giron 1995). The actual value for A Hi is independent of the solvent, as demonstrated in Table 4.1 for the two polymorphs of sodium sulphathiazole. Note also that the calculated heats of transition are virtually identical in spite of the fact that the heat of solution (A//s) is endothermic in acetone and exothermic in dimethylformamide. 

In spite of these caveats, there is intense activity in the application of these methods to polymorphic systems and considerable progress has been made. Two general approaches to the use of these methods in the study of polymorphism may be distinguished. In the first, the methods are utilized to compute the energies of the known crystal structures of polymorphs to evaluate lattice energies and determine the relative stabilities of different modifications. By comparison with experimental thermodynamic data, this approach can be used to evaluate the methods and force fields employed. The ofher principal application has been in fhe generation of possible crystal structures for a substance whose crystal structure is not known, or which for experimental reasons has resisted determination. Such a process implies a certain ability to predict the crystal structure of a system. However, the intrinsically approximate energies of different polymorphs, the nature of force fields, and the inherent imprecision and inaccuracy of the computational method still limit the efificacy of such an approach (Lommerse et al. 2000). Nevertheless, in combination with other physical data, in particular the experimental X-ray powder diffraction pattern, these computational methods provide a potentially powerful approach to structure determination. The first approach is the one applicable to the study of conformational polymorphs. The second is discussed in more detail at the end of this chapter. 

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