This formulation of crystal structure prediction establishes a connection to the theory of algorithms and provides the absolute energetic status of observed or predicted materials. A single subsequent local minimization of the resulting atom allocations then reaches the correct structures of key inorganic materials directly, proving their energetic optimality under clear assumptions. We encode the combinatorial task of finding the lowest energy periodic allocation of all atoms on a lattice as a mathematical optimization problem of integer programming 6, 7, enabling guaranteed identification of the global optimum using well-developed algorithms.
Here we show that the structure of a crystalline material can be predicted with energy guarantees by an algorithm that finds all the unknown atomic positions within a unit cell by combining combinatorial and continuous optimization. Although these methods can often access all configurations in principle, there is no guarantee that the lowest energy structure has been found. Researchers have developed efficient heuristics to identify structural minima on the potential energy surface 3, 4, 5.
Crystal structure prediction can thus play a central part in the design of new functional materials 1, 2. Crystalline materials enable essential technologies, and their properties are determined by their structures.
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