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

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.