Crystal structure prediction

Crystal structure prediction (CSP) is the calculation of the crystal structures of solids from first principles. Reliable methods of predicting the crystal structure of a compound, based only on its molecular structure, has been a goal of the physical sciences since the 1950s.^[1] Computational methods employed include simulated annealing, evolutionary algorithms, distributed multipole analysis, random sampling, basin hopping, data mining, density functional theory and molecular mechanics.^[2]

History

The crystal structures of simple ionic solids have long been rationalised in terms of Pauling's rules, first set out in 1929 by Linus Pauling.^[3] For metals and semiconductors one has different rules involving valence electron concentration. However, prediction and rationalization are rather different things. Most commonly, by crystal structure prediction one understands search for minimum-energy arrangement of the atoms (or, for molecular crystals, of the molecules) in space. The problem has two facets - combinatorial (the "search" problem, in practice most acute for inorganic crystals), and energetic ("ranking", most acute for molecular organic crystals). For complex non-molecular crystals ("search problem"), major recent advances have been the Martonak version of metadynamics,^[4][5] the Oganov-Glass evolutionary algorithm USPEX,.^[6] The latter is capable of solving the global optimization problem with up to a few hundred degrees of freedom, while the approach of metadynamics is to reduce all structural variables to a handful of "slow" collective variables (which often works).

Molecular crystals

Predicting organic crystal structures is important to academic and industrial science, particularly for pharmaceuticals and pigments, where understanding polymorphism is beneficial. The crystal structures of molecular substances, particularly organic compounds, are very hard to predict and rank in stability. Intermolecular interactions are relatively weak and non-directional and long range.^[7] This results in typical lattice and free energy differences between polymorphs that are often only a few kJ/mol, very rarely exceeding 10 kJ/mol.^[8] Crystal structure prediction methods often locate many possible structures within this small energy range. These small energy differences are challenging to predict reliably and with a reasonable computational effort.

Since 2007, significant progress has been made in the CSP of small organic molecules, with several different methods proving effective.^[9][10] The most widely-discussed method first ranks the energies of all possible crystal structures using a customised MM force field, and finishes by using a dispersion-corrected DFT step to estimate the lattice energy and stability of each short-listed candidate structure.^[11]

Crystal structure prediction software

The following codes can predict stable and metastable structures given chemical composition and external conditions (pressure, temperature):

• CALYPSO - The Crystal structure AnaLYsis by Particle Swarm Optimization, implementing the particle swarm optimization (PSO) algorithm to identify/determine the crystal structure. As with other codes, the knowledge of structure can be used to design the multi-functional materials (e.g.,superconductive, thermoelectric, superhard, and energetic materials,etc.). Free for academic researchers. Regularly updated.
• GASP - predicts the structure and composition of stable and metastable phases of crystals, molecules, atomic clusters and defects from first-principles. Can be interfaced to other energy codes including: VASP, LAMMPS, MOPAC, Gulp, JDFTx etc. Free to use and regularly updated.
• GRACE - for predicting molecular crystal structures, especially for the pharmaceutical industry. Based on dispersion-corrected density functional theory. Commercial software under active development.
• GULP - Monte Carlo and genetic algorithms for atomic crystals. GULP is based on classical force fields and works with many types of force fields. Free for academic researchers. Regularly updated.
• USPEX - multi-method software that includes evolutionary algorithm and other methods (random sampling, evolutionary metadynamics, improved PSO, variable-cell NEB method for phase transition mechanisms). Can be used for atomic or molecular crystals; bulk crystals, nanoparticles, polymers, surface reconstructions; can optimize the energy or other physical properties. In addition to finding the structure at given composition, can identify all stable compositions in a multicomponent variable-composition system. Free for academic researchers. Used by >2000 researchers. Regularly updated.
• XtalOpt - open source code implementing an evolutionary algorithm.

Further reading

• A. R. Oganov, ed. (2010). Modern Methods of Crystal Structure Prediction. Berlin: Wiley-VCH. ISBN 978-3-527-40939-6.

References

1. G. R. Desiraju (2002). "Cryptic crystallography". Nature Materials. 1 (2): 77–79. doi:10.1038/nmat726. PMID 12618812.
2. S. M. Woodley, R. Catlow; Catlow (2008). "Crystal structure prediction from first principles". Nature Materials. 7 (12): 937–946. Bibcode:2008NatMa...7..937W. doi:10.1038/nmat2321. PMID 19029928.
3. L. Pauling (1929). "The principles determining the structure of complex ionic crystals". Journal of the American Chemical Society. 51 (4): 1010–1026. doi:10.1021/ja01379a006.
4. Martonak R., Laio A., Parrinello M.; Schmid; Bauchinger (2003). "Predicting crystal structures: The Parrinello-Rahman method revisited". Physical Review Letters. 90 (3): 341–53. doi:10.1016/0027-5107(78)90203-8. PMID 75502.
5. Martonak R., Donadio D., Oganov A. R., Parrinello M.; Donadio; Oganov; Parrinello (2006). "Crystal structure transformations in SiO₂ from classical and ab initio metadynamics". Nature Materials. 5 (8): 623–626. Bibcode:2006NatMa...5..623M. doi:10.1038/nmat1696. PMID 16845414.
6. Oganov, A. R.; Glass, C. W. (2006). "Crystal structure prediction using ab initio evolutionary techniques: principles and applications". Journal of Chemical Physics. 124 (10): 8–13. Bibcode:2006JChPh.124x4704O. doi:10.1063/1.2210932. PMID 244704.
7. Stone, Anthony (2013). The Theory of Intermolecular Forces. Oxford University Press.
8. Nyman, Jonas; Day, Graeme M. "Static and lattice vibrational energy differences between polymorphs". CrystEngComm. 17: 5154–5165. doi:10.1039/C5CE00045A.
9. K. Sanderson (2007). "Model predicts structure of crystals". Nature. 450 (7171): 771. Bibcode:2007Natur.450..771S. doi:10.1038/450771a. PMID 18063962.
10. Day, Graeme M.; Cooper, Timothy G.; Cruz-Cabeza, Aurora J.; Hejczyk, Katarzyna E.; Ammon, Herman L.; Boerrigter, Stephan X. M.; Tan, Jeffrey S.; Della Valle, Raffaele G.; Venuti, Elisabetta; Jose, Jovan; Gadre, Shridhar R.; Desiraju, Gautam R.; Thakur, Tejender S.; Van Eijck, Bouke P.; Facelli, Julio C.; Bazterra, Victor E.; Ferraro, Marta B.; Hofmann, Detlef W. M.; Neumann, Marcus A.; Leusen, Frank J. J.; Kendrick, John; Price, Sarah L.; Misquitta, Alston J.; Karamertzanis, Panagiotis G.; Welch, Gareth W. A.; Scheraga, Harold A.; Arnautova, Yelena A.; Schmidt, Martin U.; Van De Streek, Jacco; et al. (2009). "Significant progress in predicting the crystal structures of small organic molecules – a report on the fourth blind test". Acta Crystallographica B. 65 (Pt 2): 107–125. doi:10.1107/S0108768109004066. PMID 19299868.
11. M. A. Neumann, F. J. J. Leusen, J. Kendrick; Leusen; Kendrick (2008). "A Major Advance in Crystal Structure Prediction". Angewandte Chemie International Edition. 47 (13): 2427–2430. doi:10.1002/anie.200704247. PMID 18288660.