Iterative learning scheme for crystal structure prediction with anharmonic lattice dynamics
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.
Summary
This paper addresses the challenge of accurately predicting crystal structures (CSP) for materials exhibiting significant anharmonic lattice dynamics, a common issue in ferroelectrics, thermoelectrics, and superconducting hydrides. Traditional CSP methods, which rely on static enthalpy calculations, fail to capture the thermodynamic stability of phases stabilized by quantum and thermal ionic fluctuations. While methods like the stochastic self-consistent harmonic approximation (SSCHA) accurately account for anharmonicity, their computational cost makes them impractical for CSP. The authors propose an iterative learning framework that combines evolutionary algorithms (EA), atomic foundation models (specifically MatterSim), and SSCHA relaxations. The key innovation is the use of foundation models to provide robust relaxations of random structures, drastically reducing the required amount of training data for machine-learning interatomic potentials (MLIPs). The framework starts with randomly generated structures relaxed using the MatterSim foundation model. Selected low-enthalpy structures undergo DFT calculations, and this data is used to iteratively finetune the MatterSim model. Simultaneously, new structures are generated using EA and relaxed with the finetuned MLIP. The finetuned MLIP is then used in extensive CSP searches, and the lowest-enthalpy structures are subjected to SSCHA relaxations to determine their free energies and relative stabilities. Applied to the highly anharmonic H3S system, the framework achieves good agreement with DFT benchmarks, accurately predicting phase stability and vibrational properties from 50 to 200 GPa. A significant finding is that the statistical averaging in SSCHA reduces the sensitivity to MLIP errors, avoiding the need for extremely high-accuracy potentials. This approach bridges the gap between data efficiency and predictive power, establishing a practical pathway for CSP with anharmonic lattice dynamics.
Key Insights
- •An iterative learning scheme combining evolutionary algorithms, atomic foundation models (MatterSim), and SSCHA relaxations is proposed for crystal structure prediction with anharmonic lattice dynamics.
- •Atomic foundation models enable robust relaxations of random structures, significantly reducing the required training data size for MLIPs.
- •Applied to H3S, the finetuned MatterSim potential achieves energy RMSEs of ~6 meV/atom, allowing accurate identification of stable phases.
- •The framework accurately predicts phase stability and vibrational properties of H3S from 50 to 200 GPa, demonstrating its ability to handle highly anharmonic systems.
- •Statistical averaging in SSCHA reduces the error in free energy evaluation, relaxing the accuracy requirements for MLIPs compared to standard BO-PES calculations. For example, for cubic Im-3m H3S at 60 GPa, the RMSE of atomic forces is 128 meV/Å, but the RMSE of the SSCHA free-energy gradient decreases drastically to only 4.5 meV/Å.
- •Anharmonic effects primarily affect the stability ranking of configurations with low formation enthalpies (below 50 meV/atom), simplifying CSP with thermal and quantum fluctuations.
- •Limitations include the fact that the performance at finite temperatures has not yet been tested, and the method's robustness across a broader range of materials needs further evaluation.
Practical Implications
- •The proposed framework enables the prediction of crystal structures for materials with significant anharmonic lattice dynamics, which is critical for the discovery of new ferroelectrics, thermoelectrics, and superconducting hydrides.
- •Materials scientists and engineers can use this approach to identify thermodynamically stable phases that are missed by traditional CSP methods, accelerating the discovery of novel materials with desired properties.
- •The framework can be used to perform finite-temperature crystal structure predictions by incorporating SSCHA calculations at any temperature.
- •The insight that SSCHA reduces the accuracy requirements for MLIPs can guide the development of more efficient and cost-effective MLIPs for materials simulations.
- •Future research directions include further reducing computational costs, enhancing the robustness of the approach for a broader range of materials, and extending the framework to finite temperatures.