Iterative learning scheme for crystal structure prediction with anharmonic lattice dynamics

TL;DR

The paper tackles the challenge of crystal structure prediction in the presence of strong anharmonic lattice dynamics by introducing an iterative learning pipeline that merges evolutionary algorithms, foundation-model interatomic potentials, and the stochastic self-consistent harmonic approximation (SSCHA). The approach achieves data-efficient, anharmonic CSP, demonstrated on the highly anharmonic H3S system under high pressure, with good agreement to DFT benchmarks across 50–200 GPa. A key insight is that ensemble averaging in SSCHA significantly mitigates MLIP inaccuracies, enabling reliable thermodynamic predictions even with moderate potential quality. This work provides a practical pathway to incorporate quantum and thermal lattice effects into CSP workflows, with implications for discovering high Tc hydrides and other anharmonic materials.

Abstract

First-principles based crystal structure prediction (CSP) methods have revealed 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 essential, limiting the capacity of CSP techniques to determine the thermodynamical stability of competing phases. While variational methods like the stochastic self-consistent harmonic approximation (SSCHA) accurately account for anharmonic lattice dynamics \emph{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 required training data. Applied to the highly anharmonic H$_3$S system, our framework achieves good agreement with the benchmarks based on density functional theory, accurately predicting phase stability and vibrational properties from 50 to 200 GPa. 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.

Figures (8)

• Figure 1: Iterative learning (a) and SSCHA-assisted searching (b) workflows in this work.
• Figure 2: The enthalpy–volume plots for H$_3$S phases predicted by the pretrained MatterSim foundation model at 150 GPa.
• Figure 3: Parity plots of energy (upper) and forces (lower) comparing finetuned MatterSim predictions and DFT reference data for H$_3$S.
• Figure 4: (a) Squared frequency of the $T_{1u}$ mode at $\Gamma$ point of H$_3$S $I\bar{m}3m$ phase, as a function of the pressure, predicted by the finetuned MatterSim and PBE with HA and SSCHA. The grey dashed lines represent pressures for generating datasets. (b) Anharmonic (at 0 K) phonon dispersions from free-energy Hessian matrices for H$_3$S computed by PBE and the finetuned MatterSim under 60 GPa. The imaginary mode at $\Gamma$ is the $T_{1u}$ mode.
• Figure 5: Relative enthalpy at the classical BO level without considering anharmonic effects of H$_3$S phases, as a function of the pressure, predicted by the finetuned MatterSim. The $I\bar{m}3m$ phase is set as the reference system.