The Prediction of Inorganic Crystal Structures
using a Genetic Algorithm and Energy Minimisation.


Dr. S. M. Woodley and Prof. C. R. A. Catlow, The Royal Institution of Great Britain,
Dr. J. D. Gale, Imperial College and Dr. P. D. Battle, University of Oxford.

Is it possible to predict inorganic crystal structures from little or no initial knowledge of the atomic co-ordinates? The minimum requirement for such a task is the knowledge of the lattice parameters and chemical composition which are available from the method of synthesis and the X-ray powder diffraction pattern. We have developed a general and robust procedure which predicts the crystal structure from this minimum data and random initial crystallographic co-ordinates. This has been incorporated into the General Utility Lattice Package, GULP [1,2], for ease of use. It should be noted that GULP already had the capability of fitting interatomic potentials, locally minimising the lattice energy (under the Born model of a solid) by optimising the approximate crystallographic co-ordinates and cell parameters and calculating various properties (elastic constants etc.) of the optimised crystal.

Our technique consists of three stages based on that developed by Bush et al. [3] who successfully predicted the previously unknown structure of Li3RuO4. To allow a more efficient global optimisation of the crystallographic co-ordinates two quality measures are used: the first (known as the cost function) is based upon the Bond Valence Model and Coulombic interaction energy, and the second is the crystal lattice energy. The cost function is a robust measure of geometry violation and is faster to evaluate than the lattice energy. However, when the structure has reasonable bond lengths, the final crystallographic co-ordinates are less accurate than those produced by minimising the lattice energy. In stage 1 of our procedure we use a genetic algorithm (GA) to produce plausible candidate structures by 'breeding' configurations such that good quality structures 'evolve'. The GA needs to evaluate the quality of many candidates; thus we use our cost function throughout this initial stage. Then, in stage 2, the co-ordinates of the plausible approximate models are locally optimised such that the lattice energy (a better measure of quality) is minimised. Only at this stage, when the prediction is complete, is it necessary to compare generated and observed diffraction patterns in order to determine which candidate structure is correct. This third stage could also be extended to include a refinement of the co-ordinates of the best candidates to improve the fit between the observed and predicted X-ray diffraction patterns.

Ultimately we have created a 'user friendly' version of the crystal prediction method of Bush et al. with many improvements and changes which gives the user more control options. The parameters for the Bond Valence Model [4,5] are already encoded within GULP and a collection of published interatomic potential parameters that can be used in stage 2 can be easily down-loaded from the web, "http://www.ri.ac.uk/Potentials/". So far we have generated a wide range of known binary and ternary oxides (including various polymorphs of TiO2, -quartz, perovskites, spinel and pyrochlore structures) using our enhanced version of GULP [6].


  1. J. D. Gale, J.Chem.Soc., Faraday Trans., 1997, 93, 629.
  2. J. D. Gale, Phil. Mag., 1996, B73, 3.
  3. T. S. Bush, C. R. A. Catlow and P. D. Battle, J.Mater.Chem., 1995, 5, 1269.
  4. I. D. Brown, Acta Crystallogr., 1992, B48, 553.
  5. I. D. Brown, Acta Crystallogr., 1988, B44, 545.
  6. P. D. Battle, C. R. A. Catlow, J. D. Gale and S. M. Woodley, in preparation.

    General Utility Lattice Program (GULP)

    This is a program for the simulation of solids, molecules and defects using interatomic potential models. Originally designed for the modelling of ionic materials and incorporating the shell model for ionic polarisation, GULP now contains all the functionality required to treat more general systems such as biological molecules and metals. A particular feature of the program is the use of space group symmetry both to build structures and to accelerate the calculation.

    The following is a brief summary of program features :

    • Geometry optimisation
    • Location of transition states with eigenvector following
    • Property calculation including elastic, dielectric and piezoelectric constants
    • Phonon calculations including density of states and dispersion curves
    • Calculation of defect energies
    • Free energy minimisation for thermal expansion calculations
    • Derivation of potential parameters by empirical fitting or from QM energy surfaces
    • Interface to Cerius2 modelling environment (available from MSI)

    System requirements :

    The code is written in Fortran77 with non-standard extensions and is supported for all standard Unix/Linux platforms. An MPI version will also soon be available for parallel execution of energy and force evaluations during optimisation and molecular dynamics.


    Availability :

    The program is available to academics working in Universities at no charge for non-commercial research by contacting the author by email: [email protected]
    All other users should contact Molecular Simulations Inc.


    Further information :

    More details about the program, including a copy of the manual can be obtained from the following web site :


    http://www.ch.ic.ac.uk/gale/Research/gulp.html

    Julian Gale,
    Imperial College, London

    Page last updated 12 Mar 1999

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