Chemical-space completeness: a new strategy for crystalline materials exploration

Abstract: The emergence of deep learning has brought the long-standing goal of comprehensively understanding and exploring crystalline materials closer to reality. Yet, universal exploration across all elements remains hindered by the combinatorial explosion of possible chemical environments, making it difficult to balance accuracy and efficiency. Crucially, within any finite set of elements, the diversity of short-range bonding types and local geometric motifs is inherently limited. Guided by this chemical intuition, we propose a chemical-system-centric strategy for crystalline materials exploration. In this framework, generative models are coupled with machine-learned force fields as fast energy evaluators, and both are iteratively refined in a closed-loop cycle of generation, evaluation, and fine-tuning. Using the Li-P-S ternary system as a case study, we show that this approach captures the diversity of local environments with minimal additional first-principles data while maintaining structural creativity, achieving closed-loop convergence toward chemical completeness within a bounded chemical space. We further demonstrate downstream applications, including phase-diagram construction, ionic-diffusivity screening, and electronic-structure prediction. Together, this strategy provides a systematic and data-efficient framework for modeling both atomistic and electronic structures within defined chemical spaces, bridging accuracy and efficiency, and paving the way toward scalable, AI-driven discovery of crystalline materials with human-level creativity and first-principles fidelity.