The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation

Abstract

A genetic algorithm has been used to generate plausible crystal structures from the knowledge of only the unit cell dimensions and constituent elements. We successfully generate 38 known binary oxides and various known ternary oxides with the Perovskite, Pyrochlore and Spinel structures, from starting configurations which include no knowledge of the atomic arrangement in the unit cell. The quality of the structures is initially assessed using a cost function which is based on the bond valence model with a number of refinements. The lattice energy, based on the Born model of a solid, is minimised using a local optimiser for the more plausible candidate structures. The method has been implemented within the computational package GULP. An extensive collection of Buckingham potential parameters for use in such simulations on metal oxides is also tabulated.

References

1. For example, R. G. Bell, R. A. Jackson and C. R. A. Catlow, J. Chem. Soc., Chem. Commun., 1990, 782.
2. M. D. Shannon, J. L. Casci, P. A. Cox and S. J. Andrews, Nature (London), 1991, 353, 417.
3. J. Maddox, Nature (London), 1988, 335, 201.
4. J. D. Gale, J. Chem. Soc., Faraday Trans., 1997, 93, 629.
5. M. C. Payne, M. P. Teter, D. C. Allan, A. T. Arias and J. D. Joannopoulos, Rev. Mod. Phys., 1992, 64, 1045.
6. F. C. Hawthorne, Nature (London), 1990, 345, 297.
7. C. R. A. Catlow, A. N. Cormack and F. Theobald, Acta Crystallogr., 1984, B40, 195.
8. S. M. Tomlinson, R. A. Jackson and C. R. A. Catlow, J. Chem. Soc., Chem. Commun., 1990, 813.
9. Computer Modelling in Inorganic Crystallography, ed. C. R. A. Catlow, Academic Press, 1997.
10. C. M. Freeman and C. R. A. Catlow, J. Chem. Soc., Chem. Commun., 1992, 89.
11. C. M. Freeman, J. M. Newman, S. M. Levine and C. R. A. Catlow, J. Mater. Chem., 1993, 3, 531.
12. D. S. Coombes, G. K. Nagi and S. L. Price, Chem. Phys. Lett., 1997, 265, 532.
13. M. U. Schmidt and U. Englert, J. Chem. Soc., Dalton Trans., 1996, 2077.
14. J. R. Holden, Z. Du and H. L. Ammon, J. Comput. Chem., 1993, 14, 422.
15. A. Gavezzotti and G. Filippini, J. Am. Chem. Soc., 1996, 118, 7153.
16. B. P. Van Eijck and J. Kroon, J. Comput. Chem., 1997, 18, 1036.
17. T. Hirano, S. Tsuzuki, K. Tanabe and N. Tajima, Chem. Lett., 1995, 1073.
18. D. W. M. Hofmann and T. Lengauer, Acta Crystallogr., 1997, A53, 225.
19. R. J. Wawak, K. D. Gibson, A. Liwo and H. A. Scheraga, Proc. Natl. Acad. Sci. USA, 1996, 93, 1743.
20. R. J. Wawak, J. Pillardy, A. Liwo, K. D. Gibson and H. A. Scheraga, J. Phys. Chem., 1998, A102, 2904.
21. H. Putz, J. C. Schön and M. Jansan, Ber. Bunsen-Ges. Phys. Chem., 1995, 99, 1148.
22. R. J. Gdanitz, Chem. Phys. Lett., 1992, 190, 391.
23. H. R. Karfunkel and R. J. Gdanitz, J. Comput. Chem., 1992, 13, 1171.
24. W. I. F. David, K. Shankland and N. Shankland, Chem. Commun., 1998, 931.
25. J. Pannetier, J. Bassas-Alsina, J. Rodriguez-Carvajal and V. Caignaert, Nature (London), 1990, 346, 343.
26. Y. G. Andreev and P. G. Bruce, J. Chem. Soc., Dalton Trans., 1998, 24, 4071.
27. B. M. Kariuki, H. Serrano-Gonzalez, R. L. Johnston and K. D. M. Harris, Chem. Phys. Lett., 1997, 280, 189.
28. K. D. M. Harris, R. L. Johnston, B. M. Kariuki and M. Tremayne, J. Chem. Res. (S), 1998, 390.
29. K. D. M. Harris, Int. Union Crystallogr. Newsl., 1998, 20, 1.
30. K. D. M. Harris, R. L. Johnston and B. M. Kariuki, Acta Crystallogr., 1998, A54, 632.
31. T. S. Bush, C. R. A. Catlow and P. D. Battle, J. Mater. Chem., 1995, 5, 1269.
32. M. W. Deem and J. M. Newsam, Nature (London), 1989, 342, 260.
33. N. W. Deem and J. M. Newsam, J. Am. Chem. Soc., 1992, 114, 7189.
34. W. M. Meier and H. Villiger, Z. Kristallogr., 1969, 129, 503.
35. C. R. A. Catlow and A. N. Cormack, Int. Rev. Phys. Chem., 1987, 6, 227.
36. Computer Simulation of Solids, ed. C. R. A. Catlow and W. C. Mackrodt, Lecture Notes in Physics, Springer, Berlin, vol. 166, 1982.
37. S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Science, 1983, 220, 671.
38. I. D. Brown, Acta Crystallogr., 1992, B48, 553.
39. I. D. Brown, Acta Crystallogr., 1988, B44, 545.
40. More precisely, the required structure is defined as that which would be obtained if the observed crystal structure which we are trying to generate has had its lattice energy minimised, thus eliminating any lattice energy discrepancy due to the chosen potential parameters that are used in stage 2.
41. M. P. Tosi, Solid State Phys., 1964, 16, 1.
42. C. R. A. Catlow and M. J. Norgett, UKAEA Report AERE-M2936, United Kingdom Atomic Energy Authority, 1978.
43. The Rietveld Method, ed. R. A. Young, Oxford University Press, 1993.
44. J. D. Gale, Philos. Mag., 1996, B73, 3.
45. M. Cherry, M. S. Islam and C. R. A. Catlow, J. Solid State Chem., 1995, 118, 125.
46. D. R. Collins and C. R. A. Catlow, Am. Mineral., 1992, 77, 1172.
47. T. S. Bush, J. D. Gale, C. R. A. Catlow and P. D. Battle, J. Mater. Chem., 1994, 4, 831.
48. As explained in Bush et al.³¹ rather than fixing one point at the beginning of the parent's DNA and randomly choosing just one point along the parent's DNA, two points are randomly chosen along a parent's DNA and the middle section swapped when crossing to produce children DNA.
49. A. A. Bolzan, C. Fong, B. J. Kennedy and C. J. Howard, Aust. J. Chem., 1993, 46, 939.
50. O. Greis, R. Ziel, B. Breidenstein, A. Haase and T. Petzel, J. Alloys Compd., 1994, 216, 255.
51. M. J. Sanders, M. J. Leslie and C. R. A. Catlow, J. Chem. Soc., Chem. Commun., 1984, 1271.
52. L. Reinaudi, R. E. Carbonio and E. P. M. Leiva, J. Chem. Soc., Chem. Commum., 1998, 255.
53. R. W. G. Wyckoff, Crystal Structures, J. Wiley & sons, 2nd edn., New York, 1964, vol. 2.
54. M. Marezio and P. D. Dernier, Mater. Res. Bull., 1971, 6, 23.
55. M. A. Subramanian, B. H. Toby, A. P. Ramirez, W. J. Marshall, A. W. Sleight and G. H. Kwei, Science, 1996, 273, 81.