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Iterative learning scheme for crystal structure prediction with anharmonic lattice dynamics

Hao Gao1,2, Yue-Wen Fang1,*, and Ion Errea1,2,3,†

  • *Contact author: yuewen.fang@ehu.eus
  • †Contact author: ion.errea@ehu.eus
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Phys. Rev. B 113, 134113 – Published 15 April, 2026

DOI: https://doi.org/10.1103/fcrd-8zzf

Abstract

First-principles based crystal structure prediction (CSP) methods have proved to be an essential tool for the discovery of new materials. However, in solids close to displacive phase transitions, which are common in ferroelectrics, thermoelectrics, charge-density wave systems, or superconducting hydrides, the ionic contribution to the free energy and lattice anharmonicity become significant, limiting the capacity of CSP techniques to determine the thermodynamic stability of competing phases. While variational methods like the stochastic self-consistent harmonic approximation (SSCHA) accurately account for anharmonic lattice dynamics ab initio, their high computational cost makes them impractical for CSP. Machine-learning interatomic potentials offer accelerated sampling of the energy landscape compared to purely first-principles approaches, but their reliance on extensive training data and limited generalization restricts practical applications. Here, we propose an iterative learning framework combining evolutionary algorithms, atomic foundation models, and SSCHA to enable CSP with anharmonic lattice dynamics. Foundation models enable robust relaxations of random structures, drastically reducing the required training data. Applied to the highly anharmonic H3S system, our framework achieves good agreement with benchmarks based on density functional theory, accurately predicting phase stability and vibrational properties from 50 to 200 GPa. In PdH, our method is capable of revealing that the true ground state of the system is the rock-salt structure even if classical crystal structure predictions favor the zincblende structure. Importantly, we find that the statistical averaging in the SSCHA reduces the error in the free energy evaluation, avoiding the need for extremely high accuracy of machine-learning potentials. This approach bridges the gap between data efficiency and predictive power, establishing a practical pathway for CSP with anharmonic lattice dynamics.

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Phys. Rev. B 113, 134113– Published 15 April, 2026
  • Received 23 December 2025
  • Revised 12 March 2026
  • Accepted 30 March 2026
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