Finding well-optimized special quasirandom structures with decision diagram

TL;DR

This paper introduces a ZDD-based algorithm for efficiently finding optimized special quasirandom structures (SQSs) that closely mimic random substitutional structures, outperforming existing methods in structure optimization.

Contribution

The paper presents a novel ZDD-based algorithm that efficiently extracts and optimizes SQSs from an enormous set of structures, improving upon previous approaches.

Findings

Successfully extracted a tiny number of highly optimized SQSs from over 10^12 structures.

Found SQSs that outperform those proposed in previous literature.

Demonstrated the algorithm's potential for broader structure enumeration problems.

Abstract

The advanced data structure of the zero-suppressed binary decision diagram (ZDD) enables us to efficiently enumerate nonequivalent substitutional structures. Not only can the ZDD store a vast number of structures in a compressed manner, but also can a set of structures satisfying given constraints be extracted from the ZDD efficiently. Here, we present a ZDD-based efficient algorithm for exhaustively searching for special quasirandom structures (SQSs) that mimic the perfectly random substitutional structure. We demonstrate that the current approach can extract only a tiny number of SQSs from a ZDD composed of many substitutional structures (>$10^{12}$). As a result, we find SQSs that are optimized better than those proposed in the literature. A series of SQSs should be helpful for estimating the properties of substitutional solid solutions. Furthermore, the present ZDD-based algorithm should be useful for applying the ZDD to the other structure enumeration problems.