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 composition, has been a goal of the physical sciences since the 1950s.{{cite journal | journal = Nature Materials | volume = 1 | pages = 77–79 | year = 2002 | doi = 10.1038/nmat726 | title = Cryptic crystallography | author = G. R. Desiraju | author-link = G. R. Desiraju | pmid = 12618812 | issue = 2 | bibcode = 2002NatMa...1...77D | s2cid = 6056119 }} Computational methods employed include simulated annealing, evolutionary algorithms, distributed multipole analysis, random sampling, basin-hopping, data mining, density functional theory and molecular mechanics.{{cite journal | journal = Nature Materials | volume = 7 | pages = 937–946 | year = 2008 | doi = 10.1038/nmat2321 | title = Crystal structure prediction from first principles | author = S. M. Woodley, R. Catlow | pmid = 19029928 | issue = 12 |bibcode = 2008NatMa...7..937W | last2 = Catlow }}

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.{{cite journal | author= L. Pauling | author-link= Linus Pauling | year = 1929 | title = The principles determining the structure of complex ionic crystals | journal = Journal of the American Chemical Society | volume = 51 | issue = 4 | pages= 1010–1026 | doi= 10.1021/ja01379a006 | bibcode= 1929JAChS..51.1010P }} For metals and semiconductors one has different rules involving valence electron concentration. However, prediction and rationalization are rather different things. Most commonly, the term crystal structure prediction means a search for the minimum-energy arrangement of its constituent atoms (or, for molecular crystals, of its molecules) in space. The problem has two facets: combinatorics (the "search phase space", in practice most acute for inorganic crystals), and energetics (or "stability ranking", most acute for molecular organic crystals).

For complex non-molecular crystals (where the "search problem" is most acute), major recent advances have been the development of the Martonak version of metadynamics,{{cite journal | journal = Physical Review Letters | volume = 90 | page = 75502 | issue = 3 | year = 2003 | title = Predicting crystal structures: The Parrinello-Rahman method revisited | author = Martonak R., Laio A., Parrinello M. | doi=10.1103/physrevlett.90.075503 | pmid = 12633242 | arxiv = cond-mat/0211551 | bibcode = 2003PhRvL..90g5503M | s2cid = 25238210 }}{{cite journal | journal = Nature Materials | volume = 5 | year = 2006 | pages = 623–626 | title = Crystal structure transformations in SiO₂ from classical and ab initio metadynamics | author = Martonak R., Donadio D., Oganov A. R., Parrinello M. | pmid = 16845414 | issue = 8 | doi = 10.1038/nmat1696|bibcode = 2006NatMa...5..623M | last2 = Donadio | last3 = Oganov | last4 = Parrinello | s2cid = 30791206 }} the Oganov-Glass evolutionary algorithm USPEX,{{cite journal | journal = Journal of Chemical Physics | volume = 124 | pmid = 16821993 | issue = 24| pages = 244704| year = 2006 | title = Crystal structure prediction using ab initio evolutionary techniques: principles and applications | first1 = A. R. | last1 = Oganov | first2 = C. W. | last2 = Glass | doi = 10.1063/1.2210932 |bibcode = 2006JChPh.124x4704O | arxiv = 0911.3186 | s2cid = 9688132 }} and first principles random search.{{cite journal | journal = Physical Review Letters | volume = 97 | pmid = 16907590| issue = 4| pages = 045504 | year = 2006 | title = High-Pressure Phases of Silane | first1 = C. J. | last1 = Pickard | first2 = R. J. | last2 = Needs | doi = 10.1103/PhysRevLett.97.045504 | arxiv = cond-mat/0604454 | bibcode = 2006PhRvL..97d5504P | s2cid = 36278251 }} The latter are capable of solving the global optimization problem with up to around a 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 in academic and industrial science, particularly for pharmaceuticals and pigments, where understanding polymorphism is beneficial.{{Cite journal |last=Price |first=Sarah L. |date=2014-03-10 |title=Predicting crystal structures of organic compounds |journal=Chemical Society Reviews |language=en |volume=43 |issue=7 |pages=2098–2111 |doi=10.1039/C3CS60279F |pmid=24263977 |issn=1460-4744|doi-access=free }} The crystal structures of molecular substances, particularly organic compounds, are very hard to predict and rank in order of stability. Intermolecular interactions are relatively weak and non-directional and long range.{{cite book|last1=Stone|first1=Anthony|title=The Theory of Intermolecular Forces|date=2013|publisher=Oxford University Press}} 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.{{cite journal|author1=Nyman, Jonas|author2=Day, Graeme M.|title=Static and lattice vibrational energy differences between polymorphs|journal=CrystEngComm|doi=10.1039/C5CE00045A|volume=17|issue=28|pages=5154–5165|year=2015|doi-access=free|bibcode=2015CEG....17.5154N }} Crystal structure prediction methods often locate many possible structures within this small energy range. These small energy differences are challenging to predict reliably without excessive computational effort.

Since 2007, significant progress has been made in the CSP of small organic molecules, with several different methods proving effective.{{cite journal | journal = Nature | issue = 7171| pages = 771 | year = 2007 | doi = 10.1038/450771a | title = Model predicts structure of crystals | author = K. Sanderson | pmid = 18063962 | volume = 450 |bibcode = 2007Natur.450..771S | doi-access = free }}{{cite journal | doi = 10.1107/S0108768109004066 | journal = Acta Crystallographica B | volume = 65 | issue = Pt 2 | year = 2009 | pages = 107–125 | title = Significant progress in predicting the crystal structures of small organic molecules – a report on the fourth blind test | last1 = Day | first1 = Graeme M. | last2 = Cooper | first2 = Timothy G. | last3 = Cruz-Cabeza | first3 = Aurora J. | last4 = Hejczyk | first4 = Katarzyna E. | last5 = Ammon | first5 = Herman L. | last6 = Boerrigter | first6 = Stephan X. M. | last7 = Tan | first7 = Jeffrey S. | last8 = Della Valle | first8 = Raffaele G. | last9 = Venuti | first9 = Elisabetta | last10 = Jose | first10 = Jovan | last11 = Gadre | first11 = Shridhar R. | last12 = Desiraju | first12 = Gautam R. | last13 = Thakur | first13 = Tejender S. | last14 = Van Eijck | first14 = Bouke P. | last15 = Facelli | first15 = Julio C. | last16 = Bazterra | first16 = Victor E. | last17 = Ferraro | first17 = Marta B. | last18 = Hofmann | first18 = Detlef W. M. | last19 = Neumann | first19 = Marcus A. | last20 = Leusen | first20 = Frank J. J. | last21 = Kendrick | first21 = John | last22 = Price | first22 = Sarah L. | last23 = Misquitta | first23 = Alston J. | last24 = Karamertzanis | first24 = Panagiotis G. | last25 = Welch | first25 = Gareth W. A. | last26 = Scheraga | first26 = Harold A. | last27 = Arnautova | first27 = Yelena A. | last28 = Schmidt | first28 = Martin U. | last29 = Van De Streek | first29 = Jacco | last30 = Wolf | first30 = Alexandra K. | display-authors = 29 | pmid=19299868| url = http://ri.conicet.gov.ar/bitstream/11336/66969/2/CONICET_Digital_Nro.32cd1a3a-6251-45da-ad8f-5743b58ff6eb_A.pdf | doi-access = free }} 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.{{cite journal | journal = Angewandte Chemie International Edition | volume = 47 | issue = 13 | pages = 2427–2430 | year = 2008 | title = A Major Advance in Crystal Structure Prediction | author = M. A. Neumann, F. J. J. Leusen, J. Kendrick | doi = 10.1002/anie.200704247 | pmid = 18288660 | last2 = Leusen | last3 = Kendrick | arxiv = 1506.05421 }} More recent efforts to predict crystal structures have focused on estimating crystal free energy by including the effects of temperature and entropy in organic crystals using vibrational analysis or molecular dynamics.{{cite journal | journal = Acta Crystallographica B | volume = 72 | issue = 4 | pages = 439–459 | year = 2016 | title = Report on the sixth blind test of organic crystal structure prediction methods | last1 = Reilly | first1 = Anthony M. | last2 = Cooper | first2 = Richard I. | last3 = Adjiman | first3 = Claire S. |authorlink3=Claire Adjiman| last4 = Bhattacharya | first4 = Saswata | last5 = Boese | first5 = A. 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