Crystal structure prediction by computer

Space group No.of raw structures First sorting Final sorting Best energy Packing coeff. 

It has been shown in the preceding section that it is very easy indeed to generate many, a great many crystal structures for a given organic compound. The Prom procedure is 

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. 

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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. 

In 2000, Theresa Beyer completed her Ph.D. thesis on the computer prediction of organic crystal structures by performing a literature survey of all the published work on crystal structure prediction by lattice energy minimisation without knowledge of the unit cell parameters. The 64 papers covered 253 searches on 189 molecules, of which 29 were known to be polymorphic. The number of studies was too small for any meaningful statistical analysis [154] but highUghted the difference between the molecules... 

This kind of crystal design is more often a failure than a success, and crystal structure prediction, particularly hard crystal structure prediction is still extremely difficult (Section 8.8). Generally, a large majority of the currently known host structures discussed in Chapter 7, for example, were discovered by accident rather than design. However, as our knowledge of the factors involved grows, in tandem with more powerful computational and modelling tools, more successes may be expected. 

The complex between ( )-37 and KPF6 was characterized by X-ray crystal-structure analysis, which confirmed the close tangential orientation of the ionophore moiety with respect to the fullerene surface, which had been predicted by computer modeling (Figure 15). 

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-... 

The so-called D-pathway in subunit I starts with a conserved aspartic acid near the iV-side, and continues into the middle of the membrane domain with a series of hydrophilic amino acids and several bound water molecules (Figure 3a). The latter were predicted by computational methods and were subsequently identified in the refined crystal structures. The D-pathway proper ends at a conserved glutamic acid residue at the bottom of a hydrophobic cavity, still some 10 A away from the site of O2 reduction (Figure 3a). Further proton conductivity to the latter site is not evident from the crystal stractures. The so-called K-pathway (mostly also in subunit I) is quite different. A conserved lysine residue either connects toward the A -side via a water molecule and a serine residue in subunit I (S255), or via a conserved glutamic acid residue (E62) in one of the membrane-spanning helices of subunit It. This pathway is lined by threonine and/or serine residues and appears to end at a key tyrosine moiety close to the O2 reduction site (Figure 3a, b). 

Crystal structure determinations either from the powder x-ray diffraction pattern or from the molecular structure are not yet routine procedures. Currently, crystal structure prediction from the molecular structure is feasible only for relatively rigid and nonionic compounds. More sophisticated criteria need to be developed to select the likely polymorphs from the predicted crystal structures. In addition, in order to estimate accurately the stability of a crystal structure, the lattice entropy needs to be taken into account as well as the lattice energy. However, no accurate method is yet available to estimate the lattice entropy. These limitations may be overcome by advances in computational chemistry and computing power. 

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. 

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