An Evolutionary Algorithm for
Crystal Structure Prediction
Researcher: James Atkinson | Supervisors: M S Leeson, K K Mallick
Background
 Significant progress has been
made with crystal structure
prediction in recent years.
[3]
The ability to predict the structures of crystals based solely on the knowledge of their
chemical composition was dismissed in relatively recent times as fundamentally
unpredictable by Maddox in 1988 [1]. Despite this claim, significant progress has been
made with crystal structure prediction in recent years, particularly by Oganov et al. at
Stony Brook University [2]. The ability to predict the crystal structure of a material before
it has been synthesised has led to the discovery of new materials and the ability to design
specific materials for particular uses, prior to manufacture. Additionally, the ability to
analyse the crystal structure under defined or extreme environmental conditions allows for the collection of data that
may not be experimentally possible. These factors provide the aspiration that drives research in this field.
 Machine learning provides an
efficient way to intelligently search
the characteristic energy
landscape of a crystal.
 An ab initio evolutionary algorithm
was developed to calculate and
search for the minimal free energy
of ionic compounds.
Machine Learning - Evolutionary Algorithms
Solution & Future Development
Machine learning involves recognising patterns and learning from data to
produce an intelligent system that is able to construct solutions that are selfimproving. Recent advances in processing power in computer technology has
increased the suitability of machine learning as a tool for crystal structure
prediction.
In this project, an ab initio evolutionary algorithm
was developed to calculate and search for the
minimal free energy of ionic compounds. The
evolutionary algorithm uses the most significant
features of natural biological evolution for global
optimisation. These processes include:
recombination, mutation, selection, and survival
of the fittest [9].
A crystal structure is considered stable where the constituent atoms are
arranged such that they have minimal free energy. An algorithm can search
through the characteristic energy landscape to find the structure with the
least free energy. Evolutionary algorithms prove to provide an efficient way to
intelligently search this landscape and return
an optimum solution. Where possible, it is
[4]
often beneficial to provide a known starting
structure and use
neighbourhood
search methods to
predict new
structures [2].
A common problem associated with optimisation algorithms is their tendency
to converge to local minima. The energy landscape consists of many local
minima and getting stuck in one will prevent the whole energy landscape from
being analysed. There are a number of methods to prevent this to create a
more efficient algorithm. The developed method of calculating crystal
structure gives an accurate 3D graphical representation of the crystal structure
as an output, as well as data on the efficiency of the evolutionary algorithm.
This method could be developed further to calculate properties such as
hardness and density, at a range of pressure-temperature conditions.
Crystal Lattice Energy
Using energy formulas will only provide an
[8]
estimate for the crystal lattice energies of ionic
crystals; the classical Born-Meyer formula shows
good agreement with experimental values.
Alternatively, the simple and convenient formulas
of Kapustinskii and Yatsimirskii can be used [5, 6].
The crystal becomes increasingly stable as the
cohesive/binding energy is minimised (the difference between the total
energy of the created structure and the total energy of the free atoms). There
are several methods that are used in crystal structure prediction, including:
simulated annealing, genetic algorithms, basin (or minima) hopping, particle
swarm optimisation and random structure searches [7].
References
[1] J. Maddox, “Crystals from first principles,” Nature, vol. 355, no. 201, 1988.
[2] A. R. Oganov et al, “Evolutionary metadynamics: a novel method to predict crystal structures,” CrystEngComm, vol. 14, pp. 3596-3601, 2012.
[3] Wikimedia Commons. “Nacl-structure,” wikimedia.org. [Online]. Available: http://upload.wikimedia.org/wikipedia/commons/d/de/Nacl-structure.jpg
[Accessed: Nov. 5, 2013].
[4] Shark Machine Learning Library. “EALib Documentation,” shark-project.sourceforge.net. [Online]. Available: http://shark-project.sourceforge.net/EALib/index.html
[Accessed: Nov. 5, 2013].
[5] L. Glasser, “Lattice Energies of Crystals with Multiple Ions: A Generalized Kapustinskii Equation,” Inorganic Chemistry, vol. 34, pp. 4935-4936, 1995.
Researcher Contact Information
Supervisor Contact Information
[6] A. Kolezynski et al, “Effective Cystal Potential from Electronegativity Viewpoint,” International Journal of Quantum Chemistry, vol. 91, no. 3, pp. 311-316, 2002.

James Atkinson - Email: [email protected]

Dr Mark Leeson - Email: [email protected]
[7] S. Q. Wu et al, “Adaptive Genetic Algorithm for Crystal Structure Prediction,” 2013. [Online]. Available: http://arxiv.org/abs/1309.4742 [Accessed: Oct. 14, 2013].

School of Engineering, University of Warwick, Coventry, CV4 7AL

Dr Kajal Mallick - Email: [email protected]
[8] A. R. Oganov et al, “Evolutionary crystal structure prediction and novel high-pressure phases,” High-pressure crystallography, pp. 293-325, 2010.
[9] S. Bahmann and J. Kortus, “EVO - Evolutionary algorithm for crystal structure prediction,” Computer Physics Communications, vol. 184, no. 6, pp. 1618-1625, 2013.
November 2013