Optimality guarantees for crystal structure prediction

Area of Science:

• Materials Science
• Computational Chemistry
• Crystallography

Background:

• Crystalline materials are vital for modern technologies, with properties dictated by their atomic structures.
• Crystal structure prediction is key for designing novel functional materials.
• Current heuristic methods for structure prediction lack guarantees of finding the lowest energy configuration.

Purpose of the Study:

• To develop a method for crystal structure prediction with guaranteed energy optimality.
• To establish a connection between crystal structure prediction and algorithmic theory.
• To provide a definitive energetic status for predicted or observed material structures.

Main Methods:

• Formulating crystal structure prediction as an integer programming problem to find the global optimum.
• Combining combinatorial and continuous optimization techniques.
• Utilizing subsequent local minimization to determine final atomic positions within the unit cell.

Main Results:

• Guaranteed identification of the lowest energy periodic atomic arrangements on a lattice.
• Direct determination of correct structures for key inorganic materials with proven energetic optimality.
• Establishment of a connection to the theory of algorithms for crystal structure prediction.

Conclusions:

• The developed algorithm provides a method for crystal structure prediction with energy guarantees.
• This approach offers the ground truth for existing and future structure prediction methodologies.
• The formulation is suitable for quantum annealers, addressing the combinatorial complexity of atomic configurations.