The ability to predict crystal structures is a key part of the design of new materials. New research shows that a mathematical algorithm can guarantee to predict the structure of any material just based on knowledge of the atoms that make it up. More specifically, the chemists and computer scientists 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.”

This work could signal a step change in the quest to design the new materials that are needed to meet the challenge of net zero and a sustainable future.

This work is published in the journal Nature, in the paper, “Optimality Guarantees for Crystal Structure Prediction.

Developed by an interdisciplinary team of researchers from the University of Liverpool’s Departments of Chemistry and Computer Science, the algorithm systematically evaluates entire sets of possible structures at once, rather than considering them one at a time, to accelerate identification of the correct solution.

This makes it possible to identify those materials that can be made and to predict their properties. The new method was demonstrated on quantum computers that have the potential to solve many problems faster than classical computers and can therefore speed up the calculations even further.

“Having certainty in the prediction of crystal structures now offers the opportunity to identify from the whole of the space of chemistry exactly which materials can be synthesized and the structures that they will adopt,” noted Matt Rosseinsky, DPhil, professor of chemistry at the University of Liverpool, “giving us for the first time the ability to define the platform for future technologies.”

“With this new tool,” he continued, “we will be able to define how to use those chemical elements that are widely available and begin to create materials to replace those based on scarce or toxic elements, as well as to find materials that outperform those we rely on today, meeting the future challenges of a sustainable society.”

New materials are needed to meet the challenge of net zero, from batteries and solar absorbers for clean power to providing low-energy computing and the catalysts that will make the clean polymers and chemicals for our sustainable future.

Typically, this search is slow and difficult because there are so many ways that atoms could be combined to make materials, and in particular so many structures that could form. In addition, materials with transformative properties are likely to have structures that are different from those that are known today, and predicting a structure that nothing is known about is a tremendous scientific challenge.

“We managed to provide a general algorithm for crystal structure prediction that can be applied to a diversity of structures,” noted Paul Spirakis, PhD, professor in computer science in Liverpool. “Coupling local minimization to integer programming allowed us to explore the unknown atomic positions in the continuous space using strong optimization methods in a discrete space. Our aim is to explore and use more algorithmic ideas in the nice adventure of discovering new and useful materials. Joining efforts of chemists and computer scientists was the key to this success.”

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