SSCHA-based evolutionary crystal structure prediction at finite temperatures with account for quantum nuclear motion

TL;DR

This work presents a quantum-accurate crystal structure prediction workflow that integrates SSCHA with MLIPs within an evolutionary CSP framework to account for quantum anharmonicity at finite temperature. By evaluating $LaH_{10}$ at 150 GPa and 300 K, the authors compare lightweight AL-MLIPs and universal MLIPs (Matbench) for CSP: AL-MLIPs require thermodynamic perturbation corrections to align free-energy rankings, while Mattersim-5m, a large uMLIP, enables near-training-free CSP with robust ranking near the global minimum. The study demonstrates that quantum anharmonicity significantly simplifies the finite-temperature landscape by reducing viable polymorphs and is essential for correct stability ordering, particularly for high-temperature phases that may be missed by 0 K CSP. Overall, the approach extends CSP to strongly anharmonic, quantum-dominated systems such as superconducting hydrides, enabling more efficient discovery and ranking of finite-temperature phases. Future work should aim to further improve uMLIP accuracy for high-pressure systems and integrate automated fine-tuning within the CSP pipeline.

Abstract

Accurate crystal structure prediction (CSP) at finite temperatures with quantum anharmonic effects remains challenging but very prominent in systems with lightweight atoms such as superconducting hydrides. In this work, we integrate machine-learned interatomic potentials (MLIPs) with the stochastic self-consistent harmonic approximation (SSCHA) to enable evolutionary CSP on the quantum anharmonic free-energy landscape. Using LaH$_{10}$ at 150 GPa and 300 K as a test case, we compare two approaches for SSCHA-based CSP: using light-weight active-learning MLIPs (AL-MLIPs) trained on-the-fly from scratch, and foundation models or universal MLIPs (uMLIPs) from the Matbench project. We demonstrate that AL-MLIPs allow to correctly predict the experimentally known cubic Fm$\bar{3}$m phase as the most stable polymorph at 150 GPa but require corrections within the thermodynamic perturbation theory to get consistent results. The uMLIP Mattersim-5m allow to conduct SSCHA-based CSP without requiring per-structure training and even get correct structure ranking near the global minimum, though fine-tuning may be needed for higher accuracy. Our results show that including quantum anharmonicity simplifies the free-energy landscape and is essential for correct stability rankings, that is especially important for high-temperature phases that could be missed in classical 0 K CSP. The proposed approach extends the reach of CSP to systems where quantum nuclear motion and anharmonicity dominate.

Figures (4)

• Figure 1: Three LaH$_{10}$ polymorphs with $\mathrm{Fm}\bar{3}\mathrm{m}$, $\mathrm{Cmmm}$, and $\mathrm{P}6/\mathrm{mmm}$ spacegroups predicted on the anharmonic free energy landscape at 300 K and 150 GPa with AL-MLIPs trained from scratch for each structure. The values of the free energy, $G$, are with respect to the ground state structure, $\mathrm{Fm}\bar{3}\mathrm{m}$. The visualizations of crystal structures were prepared with STMng program Valle2005.
• Figure 2: Harmonic and anharmonic phonon dispersion curves at 150 GPa for cubic LaH$_{10}$ with $\mathrm{Fm}\bar{3}\mathrm{m}$ symmetry group, orthorhombic LaH$_{10}$ with $\mathrm{Cmmm}$ symmetry group, and hexagonal LaH$_{10}$ with $\mathrm{P}6/\mathrm{mmm}$ symmetry group.
• Figure 3: A comparison of energy landscapes showing the reduction in number of LaH$_{10}$ polymorphs at 150 GPa when quantum anharmonicity is considered. The quantum anharmonic free-energy landscape at 300 K exhibits a simpler configuration space than the classical 0 K landscape. Both landscapes were generated using the dimensionality reduction method for fingerprint space implemented in STMng Valle2005. Although the projections are dataset-specific, they highlight the critical role of anharmonic effects in narrowing the search space during structural relaxation and ranking.
• Figure 4: A common scheme of structure optimization within the SSCHA using active-learning MLIP.