Crystal structure prediction thermodynamics

Both thermodynamic and kinetic factors need to be considered. Take, for instance, acetic acid. The liquid contains mostly dimer but the crystal contains the catemer and no (polymorphic) dimer crystal has ever been obtained. Various computations (R. S. Payne, R. J. Roberts, R. C. Rowe, R. Docherty, Generation of crystal structures of acetic acid and its halogenated analogs , J. Comput. Chem, 1998, 19,1-20 W. T. M. Mooij, B. P. van Eijck, S. L. Price, P. Verwer, J. Kroon, Crystal structure predictions for acetic acid , J. Comput. Chem., 1998, 19, 459-474) show the relative stability of the dimer. Perhaps the dimer is not formed in the crystal because it is 0-dimensional and as such, not able to propagate so easily to the bulk crystal as say, the 1-dimensional catemer. 

There are obvious similarities between the crystal structure prediction problem and the protein folding prediction problem. Both problems involve unsolved questions regarding the choice of force field, the existence of many almost equi-energetic minima in a multi-dimensional energy space, and the relative importance of thermodynamic and kinetic factors, including possible... 

The phenomenon of polymorphism demonstrates that metastable erystal struetures are observed, and it is not always obvious that sueh crystal structures are metastable. The energy differences between different polymorphs crystallized out of different solvent are small, and those between concomitant polymorphs presumably are very small. Kinetics must play a major role in determining which of the approximately equi-energetic hypothetical crystal structures are actually observed. How do the kinetics of nucleation and growth, and the variations with crystallization conditions, affect which thermodynamically feasible crystal structures are actually seen How can this be incorporated in the crystal structure prediction model to produce a polymorph prediction model ... 

Before embarking on a description of the computational methods involved, and how well they perform, we should address the goals of crystal structure prediction. At its most ambitious level, the aim is to start from nothing more than the structural formula of a molecule and to predict, with perfect reliability, the structure of the resulting solid, with no input from experimental observations. (Here, by structure, we mean the space group, unit cell parameters and a fiiU specification of all atomic positions.) This goal is, of course, unrealistic polymorphism in molecular crystals tells us that there is often not just one crystal structure for a molecule and we know that the crystal that is produced in an experiment depends on a variety of factors, from thermodynamic descriptors of the system (temperature and pressure) to the method of crystallization, solvent used and the presence of impurities. Without a detailed description of the crystallization conditions, prediction of the resulting structure cannot be the aim. Furthermore, many of these factors are not sufficiently well understood to be represented in a computational procedure for crystal structure prediction. 

Further applications of pattern recognition involve the determination of simple crystal structures from thermodynamic data C933, prediction of chemical reactions C77, 1143, and prediction of helical regions in proteins C653. 

Computational assessment of the likelihoods of occurrence and the relative stabilities of polymorphs is not necessarily more effective than the experimental approach. Whilst great advances have been made in the field of ab initio crystal structure prediction (CSP), as documented in five international blind tests spanning the years 1999-2010 [5], it is still not routinely possible to predict whether a molecule is likely to be polymorphic or to confirm whether the most thermodynamically stable structure has been found experimentally, especially for molecules of the complexity of a typical drug. It is possible to compute the polymorph landscape for a specific flexible molecule, but the calculations require considerable expertise, and the timescales and computing resources can render CSP impractical for application to even a limited portfolio of candidate APIs. 

It is noteworthy that as part of the same study, a crystal structure prediction of phenylethylammonium lactate was also carried out. The results were less impressive than the results obtained for pyridinium chloride the experimentally observed structure of phenylethylammonium lactate was found as the fifth crystal packing alternative, 0.24 kcal mol above the global lattice energy minimum structure. The reasons for this discrepancy are unclear. It is possible that the experimental structure of phenylethylammonium lactate is a kinetic polymorph and a thermodynamically more stable structure has not been found yet, or the known structure is stabilised by temperature effects that were not considered in the simulations, or the parameters of the dispersion correction do not transfer well from neutral systems to charged systems. Further validation work on molecular salts is required to pinpoint the reason for the inconclusive results obtained for these two compounds. 

New methods of crystalHsation that find new polymorphs are being continually developed, such as the appHcation of pressure [148], confinement in nanotubes [167], and templating with additives and surfaces, in addition to the almost infinite variations on solution crystallisation. For example, a new, more stable polymorph of dinitrobenzene [4] was found after 120 years of study, when templated by the structurally similar molecule trisinadine. Hence, there is a major role for accurate predictions of which crystal structures are thermodynamically feasible in developing our understanding of the kinetic factors that can lead to polymorphism. 

The ability to compute the relative thermodynamic stability of different crystal structures of organic molecules sufficiently reliably for crystal structure prediction and understanding polymorphism represents a major challenge to... 

Accurate prediction of materials properties and their optimization with respect to composition and structure prior to s)mthesis is a key challenge in computational materials science. Some of the main challenges for the design of new materials based on atomic scale computer simulations are the prediction of crystal structures and thermodynamic stabilities [1], and the assessment of properties at larger length and time scales than those accessible to atomic scale modeling approaches [2]. 

While we have good reason for optimism, it is worthwhile bearing in mind that at least some of the successes described here are fortuitous. The crystal structure predictions listed above were successful because the observed crystal form corresponded to the global minimum in the free energy. However, this is not always true, particularly for industrially important polymorphic molecules for which kinetic effects can be important. If we are to fully understand the interplay between kinetic and thermodynamic effects, we first need to remove any uncertainty in our ability to model molecular interactions - probably of both the intra and intermolecular types. 

Put this way, the problem of crystal structure prediction is poorly defined - in the worst sense, because any computer-generated crystal structure would be a legitimate successful prediction. The case must be reduced to a subset that, while preserving the integrity of first principles, may be meaningful and tractable in the real world and produce some results that can be comfortably checked against experiment [14]. The desirable features of a computational machine for crystal structure prediction will be now analyzed, with their thermodynamic underpinnings and practical aspects. 

It may be desirable to predict which crystal structure is most stable in order to predict the products formed under thermodynamic conditions. This is a very difficult task. As of yet, no completely automated way to try all possible crystal structures formed from a particular collection of elements (analogous to a molecular conformation search) has been devised. Even if such an effort were attempted, the amount of computer power necessary would be enormous. Such studies usually test a collection of likely structures, which is by no means infal-... 

At all temperatures above 0°K Schottky, Frenkel, and antisite point defects are present in thermodynamic equilibrium, and it will not be possible to remove them by annealing or other thermal treatments. Unfortunately, it is not possible to predict, from knowledge of crystal structure alone, which defect type will be present in any crystal. However, it is possible to say that rather close-packed compounds, such as those with the NaCl structure, tend to contain Schottky defects. The important exceptions are the silver halides. More open structures, on the other hand, will be more receptive to the presence of Frenkel defects. Semiconductor crystals are more amenable to antisite defects. 

The first is the prediction of the Habitus made from the characteristics of the crystal structure, entirely neglecting the effect of growth conditions. We will call this the structural form or abstract form. The second logical approach is to predict the Habitus thermodynamically when the crystal reaches the equilibrium state. This may be called the equilibrium form. The third is a method of analyzing the factors that may have an effect by correlating the Habitus and Tracht shown... 

The statistical thermodynamic method discussed here provides a bridge between the molecular crystal structures of Chapter 2 and the macroscopic thermodynamic properties of Chapter 4. It also affords a comprehensive means of correlation and prediction of all of the hydrate equilibrium regions of the phase diagram, without separate prediction schemes for two-, three-, and four-phase regions, inhibition, and so forth as in Chapter 4. However, for a qualitative understanding of trends and an approximation (or a check) of prediction schemes in this chapter, the previous chapter is a valuable tool. 

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