[Paper Review] LLM-driven discovery for carbon allotropes with bond-network entropy

Yuzhou Hao, Yujie Liu+5 more|arXiv (Cornell University)|Feb 26, 2026

Machine Learning in Materials Science0 citations

TL;DR

The paper develops a closed-loop AI framework that combines an LLM-based generative model with a machine-learning potential to discover thermodynamically stable carbon allotropes, guided by bond-network entropy, and reports several exotic phases with unique thermal, mechanical, and electronic properties.

ABSTRACT

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 extit{ab initio} calculations remains computationally prohibitive. Driven by the rich topological landscape of carbon, where the competition between $sp, sp^2,$ and $sp^3$ hybridization states dictates material performance, we establish a closed-loop 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 C$_{12}$'' and ``yne-hex-diamond C$_{8}$'', which exhibit extreme thermal anisotropy and ultralow in-plane shear stiffness arising from their mixed $sp$-$sp^3$ hybridization. Furthermore, we discovered a complex $sp$-$sp^2$-$sp^3$ hybridized C$_{12}$ 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). 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 machine learning potentials for the accelerated inverse design of functional materials.

Motivation & Objective

• Motivate the need to explore the vast configurational space of carbon beyond conventional sp3 networks for tailored thermal and mechanical properties.
• Develop a dual-loop active-learning framework that integrates LLM-based structure generation with rapid, high-fidelity MLP validation.
• Introduce a hybridization entropy descriptor to guide inverse design toward mixed-hybridization carbon networks.
• Demonstrate the framework by discovering stable, high-performance carbon allotropes with anomalous thermal and mechanical behaviors.

Proposed method

• Use CrystaLLM to generate candidate carbon structures (C1–C100) and screen them for dynamical stability and preliminary lattice thermal conductivity.
• Iteratively train and refine a universal NEP-based Machine Learning Potential (MLP) to achieve DFT-level accuracy across diverse sp-hybridization environments.
• Evaluate stability and properties with phonon calculations (Phonopy), MD simulations (GPUMD/LAMMPS), and Boltzmann Transport Equation analyses (HNEMD, 3ph/4ph scattering).
• Apply active learning to target high-uncertainty configurations and expand the training set to cover ultra-high pressures and mixed-hybridization networks.
• Quantify structural complexity via hybridization Shannon entropy and connect it to thermal transport and mechanical properties.
• Validate predictions against DFT benchmarks and hybrid functional band structures (HSE06) to assess electronic nature (insulator/semiconductor/metal).

Experimental results

Research questions

• RQ1 Can an LLM-driven generative loop efficiently explore the carbon configurational space to identify dynamically stable, thermodynamically competitive allotropes?
• RQ2 Does coupling CrystaLLM with an actively trained NEP-based ML potential enable accurate prediction of phonon spectra, thermal conductivity, and mechanical properties across diverse sp-hybridization environments?
• RQ3 How does bond-network entropy correlate with thermal transport and mechanical performance in newly discovered carbon allotropes?
• RQ4 What novel carbon topologies (e.g., mixed sp/sp2/sp3 networks) yield extreme properties such as superhardness, auxeticity, or highly anisotropic thermal conduction?
• RQ5 Are the discovered phases thermodynamically accessible under experimental synthesis conditions?

Key findings

• Identified several dynamically stable carbon allotropes, including yne-diamond C12, yne-hex-diamond C8, and an sp–sp2–sp3 hybrid C12 with metallic conductivity and auxetic behavior.
• Discovered a high-density superhard phase, C16_3, with a calculated Vickers hardness of 103.3 GPa, exceeding the Diamond benchmark within the Chen model framework.
• Demonstrated extreme thermal anisotropy and ultralow in-plane shear stiffness in mixed-hybridization networks due to decoupled rigid backbones and flexible linkers.
• Showed that NEP generalizes across sp, sp2, and sp3 bonding environments with high fidelity to DFT, reproducing phonon dispersions and virial stresses over wide ranges (including high pressures).
• Revealed that heat transport is dominated by particle-like phonons with four-phonon effects becoming relevant only along certain axes; MFP analysis indicates dominant heat carriers in the 10–100 nm range.
• Mapped discovered phases in a multi-dimensional property landscape linking structural complexity (hybridization entropy) to lattice thermal conductivity anisotropy, supporting bond-network entropy as a predictive descriptor.