Data-Mining-Driven Quantum Mechanics for the Prediction of Structure
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Introduction Over the last 40 years, ab initio methods have become ubiquitous tools in chemistry, physics, and materials science. Ab initio methods, which accurately solve the fundamental quantum mechanical equations (Schrödinger or Dirac) for the electrons of a system, hold the promise of virtual materials research, that is, learning the properties of materials completely by computation, before experimental synthesis and testing. In the last decade, significant advances in solid-state physics, fundamental materials science, and advanced computing have brought us closer to that objective, and accurate ab initio approaches now exist for many properties (e.g., diffusion, thermodynamic quantities, ferroelectricity, lattice parameters, elastic constants, etc.). The September 2006 issue of MRS Bulletin on density functional theory (guest-edited by J. Hafner, C. Wolverton, and G. Ceder) highlights some of the successes of ab initio methods in a variety of materials research areas. Ab initio studies are still primarily used to further the understanding and rationalize the properties of well-known materials. Studies of this type bypass the problem of predicting the structure of a material, as it is usually known from experiment. If we peek into the future and
imagine true virtual materials design, our efforts will need to extend beyond property prediction and address the problem of structure prediction. Most materials properties, from bandgaps to brittle fracture, melting temperature to magnetism, depend strongly on the structure of the materials involved, and without knowledge of the crystal structure, ab initio computations easily become irrelevant. Hence, the full power of ab initio calculations for materials design will only be unlocked if we address the problem of structure prediction. In this article, we focus on equilibrium crystal structure prediction, setting aside the even more difficult problem of predicting amorphous and metastable structures.
Data Mining Structure Prediction Predicting the stable crystal structure of a material in essence requires one to find the atomic arrangement with lowest free energy (at non-zero temperature), or with lowest energy (at zero temperature and pressure). We only focus here on the zerotemperature, zero-pressure ground-state search, as it is also a key component of any finite-temperature, finite-pressure study. Models to construct the free energy of a given structure or class of structures
MRS BULLETIN • VOLUME 31 • DECEMBER 2006 • www/mrs.org/bulletin
(e.g., those on a fixed topology) are well developed and have led to a large number of successful phase diagram computations.1–5 Both an accurate description of the energetics of a material as well as a strategy to search through the almost infinite space of possible structures are needed to find the most stable structure. Decades of work with ab initio methods studying specific systems and/or properties, typically using the local density approximation (LDA) or generalized gradient approximation (GGA) to density functional th
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