Crystal structure calculations

In order to calculate a crystal packing, it must first be constructed from molecules of specific shape to obtain a maximum of lattice energy, resulting from molecular interactions. To date there is no analytical mathematical solution to this problem. 

In general, aU methods of global minimization foUow the same principles. In a first step, possible structures (usually several thousand structures per space group 

Generally, several hundred unique crystal packings remain after optimization. They must then be evaluated with respect to either calculated physical properties such as density and lattice energy, or by means of empirical scoring functions [44]. 

Recently, a combination of elaborated force field and quantum mechanical methods was developed which actually allows the prediction of crystal stmctures of molecules with moderate complexity [73]. By this method, the crystal stmctures of all four compounds of the 2007 blind test were correctly predicted. The geometrical accuracy is high. At present (2008) the method still requires considerably computational effort, but this will no longer be a major problem in a few years. 

8 Price, S. L., The computational prediction of pharmaceutical crystal structures and polymorphism , Adv. Drug Deliv. Rev. 2004, 56, 301-319. 

Recent refinements on the atom-atom potential method include the development of accurate anisotropic model intermolecular potentials from ab initio electron distributions of the molecules. The non-spherical features in these charge distributions reflect features of real molecules such as lone pair and 7t-electron density, and therefore are much more effective at representing key interactions such as hydrogen bonding. 

---

Any orbital-based scheme can be used for crystal-structure calculations. The trend is toward more accurate methods. Some APW and Green s function methods use empirical parameters, thus edging them toward a semiempirical classification. In order of preference, the commonly used methods are ... 

Sample surf area m /g Crystal structure calculated cell parameters ao(A) bo (A) Co (A) ... 

Crystals of stoichiometric 1 1 mixtures of compounds that can complex with each other have been shown to form preferentially to pure crystals of the individual components. In some cases these crystals may have potential non-linear optical properties. An interesting example is the 1 1 mixture of p-aminobenzoic acid and 3,5-dinitrobenzoic acid. (15) A view of the crystal structure is shown in figure 3. Examination of this figure leads one to the hypothesis that the preference for the mixed crystal may be due to a) a more stable H-bonding interaction between the different benzoic acids in the hetero-dimer than in the homo-dimer b) the ability of the mixed crystal (hetero- dimers) to H-bond between their amino and nitro groups. It is likely that both of these factors play a role in the stability of the crystal structure. Calculational modelling can aid in determining the importance of these factors. 

Figure 8.49 A typical procedure for crystal structure calculation.

Figure 8.50 A comparison of the performance of atom-atom potentials using the UNI method80 and PIXEL potentials in the description of the energy landscape for 133 naphthalene crystal structures. The experimental crystal structure is represented by a cluster of 5 points representing very similar structures with different unit cell settings. Energies are given on the abscissa in kj mol 1. The plot shows the usual way of representing the results of crystal structure calculations with the expectation that the most stable structure should be at the lowest energy and exhibit the highest density. (Reproduced with permission from The Royal Society of Chemistry).

The state of the art in crystal structure calculation is tested every few years in the crystal structure prediction blind tests organised by the Cambridge Crystallographic Data Centre (CCDC). As of the... 

Progress in crystal structure prediction has been significant in recent years with parallel synthon-based and crystal structure calculation based approaches. Calculations are now sometimes able to correctly determine crystal structure in an ab initio fashion but analysis of synthons can give significant qualitative insight. 

It is hoped that current efforts at evaluating energy parameters from crystal structure calculations will provide a basis for resolving the apparent discrepancies between charge assignments, which appear in Table 18. 

It is hoped that crystal structure calculations, now in progress, will provide a refined set of parameters for the function of eq. 13, as well as for all the other energy contributions discussed in this section (See Section VF). 

LiBr has a density of 3.464 g/caf and the NaCl crystal structure. Calculate the interionic distance and compare your answer with the value from the sum of the ionic radii found in Appendix B-1. 

Figure 6 Crystal structure, calculated band structure and Fermi surface for -(BETS)2GaCl4. (Reproduced from Figs. 10, 14 in J. Am. Chem.Soc.,...

Errors (/>(calc)-/>(expt)) in the predicted molecular crystal structures, calculated by minimizing the static lattice energy, starting from the experimental structure, for a model potential which includes a distributed multipole electrostatic model. The electrostatic term uses a DMA of a 6-31G SCF wave function, with all multipoles scaled by a factor of 0.9. The repulsion-dispersion potentials are taken from the literature (see text). The r.m.s. % error is calculated over the three cell edge lengths. Us is the calculated lattice energy, given at both the experimental and relaxed crystal structures. This can be compared with the experimental heat of sublimation AHsub (Chickos, 1987), where available. 

The carbon monoxide molecule is isoelectronic and isobaric with the nitrogen molecule, and has a very small dipole moment. The densities of the solid forms of the two are nearly the same. Assuming that they have the same crystal structure, calculate a value of the binding energy of solid carbon monoxide from that of nitrogen (Table 4.1) for comparison with the experimental value 2 09 kcal per mole. The polarizability of a CO molecule is 2-21 x 10" 40 F m2,and its ionization potential is 329 kcal per mole. 

Schmidt and Englert developed a method called CRYSCA (Crystal Structure Calculation) based on rigid body lattice energy minimization of ran-... 

Lacks, D.J. and Gordon, R.G. (1993) Crystal structure calculations with distorted ions Phys. Rev. B48, 2889-2908. 

The use of punched cards in molecular structure determinations. I. Crystal structure calculations. J. Chem. Phys. 14 (1946) 648—658. (P. A. Shaffer, Jr., Verner Schomaker, and Linus Pauling). 

As it is currently practiced, supramolecular chemistry, with its emphasis on the interactions between molecules, underpins a very wide variety of chemistry and materials science impinging on molecular host-guest chemistry, solid-state host-guest chemistry, crystal engineering and the understanding and control of the molecular solid state (including crystal structure calculation), supramolecular... 

---