Symmetry-Driven Generation of Crystal Structures from Composition

TL;DR

This paper introduces a symmetry-driven generative framework using language models and heuristic algorithms to predict crystal structures directly from composition, overcoming previous limitations and enabling discovery of new materials.

Contribution

It presents a novel approach combining language models, heuristic search, and diffusion models to generate physically valid crystal structures from composition without relying on known templates.

Findings

Achieves state-of-the-art performance on stability, uniqueness, and novelty benchmarks.

Effectively generates new crystal structures with no prior structural knowledge.

Demonstrates superior matching performance compared to existing methods.

Abstract

Crystal structure prediction (CSP), which aims to predict the three-dimensional atomic arrangement of a crystal from its composition, is central to materials discovery and mechanistic understanding. However, given the composition in a unit cell, existing methods struggle with the NP-hard combinatorial challenge of rigorous symmetry enforcement or rely on retrieving known templates, which inherently limits both physical fidelity and the ability to discover genuinely new materials. To solve this, we propose a symmetry-driven generative framework. Our approach leverages large language models to encode chemical semantics and directly generate fine-grained Wyckoff patterns from atomic stoichiometry, effectively circumventing the limitations inherent to database lookups. Crucially, to overcome the exponentially complex problem of combinatorial site assignments, we incorporate domain knowledge through an efficient, linear-complexity heuristic beam search algorithm that rigorously enforces algebraic consistency between site multiplicities and atomic stoichiometry. By integrating this symmetry-consistent template into a diffusion backbone, our approach constrains the stochastic generative trajectory to a physically valid geometric manifold. This framework achieves state-of-the-art performance across stability, uniqueness, and novelty (SUN) benchmarks, alongside superior matching performance, thereby establishing a new paradigm for the rigorous exploration of targeted crystallographic space which can be previously uncharted, with no reliance on a priori structural knowledge.