Predicting Crystal Structures with Data Mining of Quantum Calculations

Predicting and characterizing the crystal structure of materials is a key problem in materials research and development. It is typically addressed with highly accurate quantum mechanical computations on a small set of candidate structures, or with empirical rules that have been extracted from a large amount of experimental information, but have limited predictive power. In this Letter, we transfer the concept of heuristic rule extraction to a large library of ab initio calculated information, and we demonstrate that this can be developed into a tool for crystal structure prediction.

Figure 1

The rms error as a function of the number of principal components. The solid lines show results for the libraries containing 35, 45, and 55 alloys. The dashed line shows results for the 55-alloy library where the energies for each alloy have been randomly permuted.

Figure 2

The number of calculations as a function of the percentage of ground states predicted correctly, with the DMQC method (solid line) and with random structure selection (dashed line). 90% accuracy can be achieved with DMQC with 26 calculations, many fewer than the 98 calculations necessary for random structure selection.

Figure 3

The average number of calculations needed to obtain a given accuracy of predicted crystal structures, as a function of the number of structures in the library. Results are given for 80%, 85%, 90%, and 95% accuracies. The number of calculations increases less than linearly with the number of structures in the database, demonstrating that efficiency increases as the library grows.