Are crystal structures predictable

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As discussed in several places in this chapter, when predicting the crystal structures of flexible molecules, intra- and intermolecular energies must be optimized together. 

The influence of the solvent is also crucial in crystallization from solution, the most common crystallization technique in practice, but, as discussed in Section 13.10, there are practically no instances in the literature where this problem has appropriately been dealt with using dynamic simulation on realistic systems - not just the Lennard-Jones fluid. It is probably appropriate to say that if real progress in predicting the appearance of crystal polymorphs is desired, the current effort in improving intermolecular potentials and search algorithms for comparing static, final crystal structures should be redirected to the study of pre-crystallization states, and to the improvement of dynamic methods for the simulation of the kinetics of crystal nucleation and growth. 

Crystal structures can indeed be predicted, if the word is taken in a sensible meaning. Compare this situation with astrophysics we know mass, age, distribution, speed, and spectral properties of galaxies, although we do not (and we do not need to) know the absolute position of each star in a galaxy. In a similar fashion, computational crystallography can easily predict the essential parameters of the bulk texture of organic matter in the solid state, although it cannot tell the exact position of each atom in a crystal structure. 

648-650 de Rosier, D. J. Who needs crystals anyway Nature 1997, 386,26-27). Characteristically, fox Nature, science is mixed with tinges of journalist hype. When the results of the careful and systematic studies of ref. [9] were sent to Nature, they were considered too down to earth and boring for the readership of the journal, and rejected without even editorial consideration. 

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Gavezzotti A 1994. Are Crystal Structures Predictable Accounts of Chemical Research 27 309-314. 

Racemates, and Resolution, Krieger Publishing, Melbourne FL (b) Dunitz, J.D. (2003) Are crystal structures predictable Chemical Communications, 545—548. 

Gavezzotti A (1994) Are crystal structures predictable Acc Chem Res 27 309-314 AUinger Nl, Miller MA, Van Catledge FA, Hirsh JA (1%7) Conformational analysis.LVIl. The calculation of the conformational structures of hydrocarbons by the Westheimer-Hendrickson-Wibetg method. 1 Am Chem Soc 89 4345 357... 

Are crystal structures predictable This question is still a Holy Grail for crys-tallographers, solid-state physicists and solid-state chemists, and has been the subject of controversial discussions for more than a decade. 

As the above results show, the gross features of the cellulose I crystal structure predicted by various methods do not differ appreciably, but the accompanying deviations in the R -factors are significant. When these predictions are used to assess, for example, whether the cellulose I crystal structure is based on parallel- or antmarallel-chains, the range in the R"-factors seen for the parallel models (cf. Table II) is comparable to that between the two different polarity models. As shown in Fig. 5, the most probable parallel- and antiparallel-chain structures of cellulose I, refined by minimizing the function O, differ in R -factors by approximately the same extent as the three predictions for the parallel model shown in Fig. 4 and Table II. 

There is no doubt that a giant step forward has been made in crystal structure prediction by coupling sound theoretical means with massive computer power, but the inherent uncertainties related to randomness and to handling of temperature remain - see above improvement in force fields and in computational procedures, as results demonstrate, are very welcome but are neither indispensable nor sufficient. And there is no hope that this barrier may fall in the future, as it stems from first principles. The next step forward is the inclusion of kinetic energies and temperature in the model. This is already possible, although with great limitations, as described in Sect. 6. 

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. 

Abstract Methods, evolutionary and systematic search approaches, and applications of crystal structure prediction of closest-packed and framework materials are reviewed. Strategies include developing better cost functions, used to assess the quality of the candidate structures that are generated, and ways to reduce the set of candidate structures to be assessed. The crystallographic coordinates for new materials, available only as a powder sample, are often intractable from diffraction data alone. In recent years, steady progress has been made in the ability to solve previously unknown crystal structures of such compounds, the generation of known structures (inferring more confidence in such approaches) and the prediction of hypothetical yet-to-be-synthesised structures. 

There are two quite different approaches to crystal structure prediction, but both methods are attempts to reduce the number of candidate structures to evaluate before the desired structure is found. The first modifies a trial structure or set of structures using either a SA or a GA approach, where random ionic coordinates (unknowns, which need not include all ions within the unit cell and may also include the unit cell dimensions) are used to create the initial candidate structure(s). The second is to systematically evaluate a subset of candidate struc-... 

Before reviewing cost functions used in crystal structure prediction it is worth noting that good book keeping within a computer code can prevent many unnecessary calls to the cost-function subroutine which evaluates candidate structure . For example, consider the rock salt system used to produce Fig. 4, with Pm set such that on average only one bit per new candidate structure is mutated. After 300 cycles of a GA, if all candidates are evaluated after each cycle there will be 30,100 calls to the cost-function subroutine. Even without elitism (copying the best candidate in the current population into the new population), by evalu-... 

Since many critical physical and mechanical properties of pharmaceutical compounds are in large part dependent on crystal form, accurate prediction of crystal structure would be a highly valued tool in the pharmaceutical industry. Unfortunately, to date, reliable crystal structure prediction is only feasible for rigid, low molecular weight molecules, which do not represent the size and flexibility of pharmaceutical molecules. 

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