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arXiv · 1910.12026

On the Hardness of Energy Minimisation for Crystal Structure Prediction

Duncan Adamson·Argyrios Deligkas·Vladimir Gusev·Igor Potapov
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Abstract

Crystal Structure Prediction (csp) is one of the central and most challenging problems in materials science and computational chemistry. In csp, the goal is to find a configuration of ions in 3D space that yields the lowest potential energy. Finding an efficient procedure to solve this complex optimisation question is a well known open problem. Due to the exponentially large search space, the problem has been referred in several materials-science papers as "NP-Hard and very challenging" without a formal proof. This paper fills a gap in the literature providing the first set of formally proven NP-Hardness results for a variant of csp with various realistic constraints. In particular, we focus on the problem of removal: the goal is to find a substructure with minimal potential energy, by removing a subset of the ions. Our main contributions are NP-Hardness results for the csp removal problem, new embeddings of combinatorial graph problems into geometrical settings, and a more systematic exploration of the energy function to reveal the complexity of csp. In a wider context, our results contribute to the analysis of computational problems for weighted graphs embedded into the three-dimensional Euclidean space.

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Duncan Adamson, Argyrios Deligkas, Vladimir Gusev, Igor Potapov. 2019-10-26. On the Hardness of Energy Minimisation for Crystal Structure Prediction. https://arxiv.org/abs/1910.12026

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