NextCrystal: a Symmetry-Driven Generative Framework for Crystal Structure Prediction

Crystal structure prediction (CSP), which aims to predict the 3D atomic arrangement of a crystal from its composition, is central to materials discovery and mechanistic understanding. Crystal symmetry plays a crucial role in CSP, but given the composition in a unit cell, existing methods either struggle with the NP-hard combinatorial challenge of enforcing symmetry rigorously or rely on retrieving known templates, inherently limiting both physical fidelity and the discovery of genuinely new materials. To address this challenge, we introduce NextCrystal, a symmetry-driven generative framework that employs language models to encode chemical semantics and directly generate fine-grained Wyckoff site patterns from atomic stoichiometry, without retrieving pre-existing structural templates at inference. To overcome the combinatorial complexity of site assignments, we incorporate domain knowledge via an efficient, linear-complexity heuristic beam search, rigorously enforcing algebraic consistency between site multiplicities and atomic stoichiometry. By integrating this symmetry-consistent template into a diffusion backbone, the framework constrains the stochastic generative trajectory to a physically plausible geometric manifold. NextCrystal achieves state-of-the-art performance on stability, uniqueness, and novelty (SUN) benchmarks, as well as superior structural matching, establishing a paradigm for exploring previously unexplored crystallographic space without relying on prior structural templates. As a blind-rediscovery case study, NextCrystal recovers the known low-energy antipolar oV Pnma polymorph of HfO₂, which is absent from the training dataset, without retrieving a structural prototype during inference. Standardized structure matching after a common first-principles relaxation confirms its equivalence to the published oV/a62 structure and its distinction from the conventional high-pressure cotunnite/oII Pnma phase.