LLM-driven discovery for carbon allotropes with bond-network entropy

The discovery of novel carbon allotropes with tailored thermal and mechanical properties is critical for advanced thermal management. However, exploring the vast configurational space of carbon using ab initio calculations remains computationally prohibitive. Driven by the rich topological landscape of carbon, where the competition between sp, sp2, and sp3 hybridization states dictates material performance, we establish a closed-loop artificial intelligence (AI) framework to explore this complex configurational space. We introduce a hybridization entropy descriptor to guide the search beyond conventional forms. Here, we establish a closed-loop AI framework that synergizes a Large Language Model (LLM) for structural generation with a Machine Learning Potential (MLP) for accelerated evaluation. Leveraging CrystaLLM to generate candidates and an iteratively refined MLP for high-fidelity validation, we screened thousands of structures to identify several stable allotropes with exotic properties. Specifically, we report “yne-diamond C12” and “yne-hex-diamond C8,” which exhibit extreme thermal anisotropy and ultralow in-plane shear stiffness arising from their mixed sp–sp3 hybridization. Furthermore, we discovered a complex sp–sp2–sp3 hybridized C12 phase that combines metallic conductivity with an anomalous negative Poisson's ratio. Notably, we identified a superhard phase (C16_3) possessing a calculated Vickers hardness (103.3 GPa) exceeding that of diamond {96 GPa [R. A. Andrievski, Int. J. Refract. Met. Hard Mater. 19, 447–452 (2001)]}. Microscopic analysis reveals that thermal transport in these materials is governed by the interplay between rigid frameworks and flexible linkers. This work expands the known carbon phase space and demonstrates the efficacy of coupling generative AI with MLPs for the accelerated inverse design of functional materials.