Themed issue: Solid state and cluster structure prediction

Prediction of the structures at the atomic level of molecules and materials remains one of the core challenges of chemistry. Computational chemistry and physics have given us powerful tools over the last few decades for accurate modelling of atomic level structures. But how far can we predict structures? That is, to what extent are we able, given knowledge of the chemical composition of a system, to identify reliably the thermodynamically stable structure? This issue attempts to provide at least partial answers to this question by presenting a number of recent studies of the prediction of structures of both crystals and nanoparticles.

A number of broad strategies may be adopted in structure prediction. Purely empirical methods based on comparison with and extrapolation from known structures may be employed (datamining);¹ but the majority of contemporary approaches are based on the concept of global optimisation, which involves first defining a function (commonly referred to as the “cost function”), which measures the quality of the structure. We then search the configurational space defined by the components of the structure (atoms, molecules or larger building units) to identify regions enclosing minima in the cost function. Once such regions are identified, minimisation to locate the exact minima is straightforward. The different optimisation procedures differ in the way in which they perform the search over configurational space.

All the main optimisation approaches are illustrated by articles in this volume. Several papers are based on the use of evolutionary algorithms, where different relaxed configurations, initially random stationary points on the energy hypersurface, form a population in which competition to survive and procreate is simulated.² The desired low-energy structures evolve as the probability of success of any current configuration is based on its cost function relative to the other configurations in the population. Simulated annealing provides an alternative approach in which a high-temperature simulation (using either Monte Carlo (MC) or Molecular Dynamics (MD) techniques) is used to navigate configurational space followed by simulated cooling into regions of low cost function.³Basin, or minima, hopping is another widely applied approach, where new structures, obtained by a MC move or MD from the last, are immediately quenched or relaxed to a local minimum.⁴ Here, the acceptance criterion is based on a comparison of the minimised energies. For molecular crystals, molecular packing approaches are appropriate: here the modes of packing are explored systematically followed by energy minimisation.⁵ A different approach involves the use of topological techniques—a long standing procedure in theoretical crystallography—to generate plausible networks. A significant recent development was the combination of such methods with energy evaluation in order to generate viable new hypothetical microporous structures. In this issue and elsewhere, such zeolitic framework structures are proposed for compounds that typically form dense materials,⁶ and, in the opposite direction, more porous hybrid metal-organic framework materials.⁷

Of course, it is possible to argue that with the growth of computer power, none of these methods is necessary. We can simply explore the energy surface by minimising from a series of random starting points. Indeed methods based on this simple “brute force” approach have enjoyed success. It seems likely, however, that for more complex structures, it will always be desirable and probably necessary to explore configurational space in a more systematic manner.

Last September in central London, we heard over forty oral presentations and saw many poster contributions on the topic of Structure Prediction at the annual international meeting of one of the UK’s collaborative computational projects (CCP5). We were pleased to see a wide range of applications; energy landscapes of clusters, glasses and biomolecules were discussed by David Wales, whereas Andreas Albrecht considered protein folding, Michael Deem new zeolite-like materials and Abbie Trewin porous organic polymers and networks. Moreover, a broad range of methodologies was also presented, from datamining, as applied to ternary oxides by Geoffroy Hautier, development of hypothetical AlPOs or silica frameworks resulting from topological techniques (noted above) by Alexandra Simperler, and applications of minima hopping by Stefan Goedecker and the covariance matrix adaptation evolution strategy by Christian Müller. Oral presentations were also given by many of the authors of this themed issue; and the application of MC basin hopping, simulated annealing, genetic and evolutionary algorithms, as well as the choice of cost function, were also of great interest to this community.

Many of the articles in this issue deal with crystal structure prediction of which there is a long tradition, motivated by the need to assist experimental crystal structure solution and, more ambitiously, to predict new structures with novel and improved functionalities. Although largely outside the scope of the present issue, modelling and prediction of the structures of amorphous solids is clearly of substantial value, especially in view of the difficulties in experimental structure determination of such systems. Several articles in this volume highlight the growing role of simulation in structural chemistry of nano (and sub nano) particles.^2,8 Here direct experimental determination is fraught with difficulty and simulation has a vital role to play.

Over twenty years ago, John Maddox in a celebrated ‘News and Views’ article in Nature threw down the following challenge:

“One of the continuing scandals in the physical sciences is that it remains impossible to predict the structure of even the simplest crystalline solids from a knowledge of their composition.”

To what extent has the field risen to this challenge? The present authors attempted to answer this question in a recent review⁹ as do several contributors to this volume. As two of the papers in this issue show,¹⁰ the answer is mixed. The availability of a database of molecular crystals and hypothetical framework materials has certainly advanced the progress of research, which should be emulated for other solid state materials and, in particular, for clusters. The atomic structure of clusters is certainly one area where stable and metastable structures have predicted,¹¹ and where the link to observations is via other physical and electronic properties. There has clearly been substantial progress in many areas since the “Maddox challenge”, but there is no doubt the structure prediction is still far from routine. What is certain is that the field remains exciting and stimulating with the anticipation of rapid progress in the future.

Scott M. Woodley and Richard Catlow, University College London, UK.

References

1. D. W. M. Hofmann in Data Mining in Crystallography, Springer-Verlag, Berlin, 2010, vol. 134, pp. 89–134.
2. A. Walsh and S. M. Woodley, Phys. Chem. Chem. Phys., 2010, 12, 8446–8464.
3. I. V. Pentin, J. C. Schön and M. Jansen, Phys. Chem. Chem. Phys., 2010, 12, 8491–8499.
4. M. Ji, C.-Z. Wang and K.-M. Ho, Phys. Chem. Chem. Phys., 2010, 12 10.1039/c004096g.
5. J. Moellmann and S. Grimme, Phys. Chem. Chem. Phys., 2010, 12, 8500–8504; A. Asmadi, J. Kendrick and F. J. J. Leusen, Phys. Chem. Chem. Phys., 2010, 12, 8571–8579.
6. S. M. Woodley, M. B. Watkins, A. A. Sokol, S. A. Shevlin and C. R. A. Catlow, Phys. Chem. Chem. Phys., 2009, 11, 3176–3185; W. Sangthong, J. Limtrakul, F. Illas and S. T. Bromley, Phys. Chem. Chem. Phys., 2010, 12, 8513–8520.
7. L. M. Rodriguez Albelo, A. R. Ruiz-Salvador, D. L. Lewis, A. Gómez, P. Mialane, J. Marrot, A. Dolbecq, A. Sampieri and C. Mellot-Draznieks, Phys. Chem. Chem. Phys., 2010, 12, 8632–8639.
8. S. M. Woodley, S. Hamad and C. R. A. Catlow, Phys. Chem. Chem. Phys., 2010, 12, 8454–8465; J. J. BelBruno and A. Burnin, Phys. Chem. Chem. Phys., 2010, 12, 8557–8563; R. Ismail and R. L. Johnston, Phys. Chem. Chem. Phys., 2010, 12, 8607–8619.
9. S. M. Woodley and R. Catlow, Nat. Mater., 2008, 7, 937–946.
10. M. O’Keeffe, Phys. Chem. Chem. Phys., 2010, 12, 8580–8583; A. Le Bail, Phys. Chem. Chem. Phys., 2010, 12, 8521–8530.
11. C. R. A. Catlow, S. T. Bromley, S. Hamad, M. Mora-Fonz, A. A. Sokol and S. M. Woodley, Phys. Chem. Chem. Phys., 2010, 12, 786–811.

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