Path-integral molecular dynamics with actively-trained and universal machine learning force fields

Accounting for nuclear quantum effects (NQEs) can significantly alter material properties at finite temperatures. Atomic modeling using the path-integral molecular dynamics (PIMD) method can fully account for such effects, but requires computationally efficient and accurate models of interatomic interactions. Empirical potentials are fast but may lack sufficient accuracy, whereas quantum-mechanical calculations are highly accurate but computationally expensive. Machine-learned interatomic potentials offer a solution to this challenge, providing near-quantum-mechanical accuracy while maintaining high computational efficiency compared to density functional theory (DFT) calculations. In this context, an interface was developed to integrate moment tensor potentials (MTPs) from the MLIP-2 software package into PIMD calculations using the i-PI software package (the MTP-PIMD approach). This interface was then applied to active learning of potentials and to investigate the influence of NQEs on material properties, namely the temperature dependence of lattice parameters and linear lattice thermal expansion (LTE) coefficients, as well as radial distribution functions, for lithium hydride (LiH) and silicon (Si) systems. The dependencies of the linear LTE on temperature for LiH and Si obtained with MTPs are in a good agreement with available experimental dependencies and with the ones calculated with the MatterSim universal machine learning force field and with the quasi-harmonic approximation. The MTP-PIMD approach thus proves to be highly accurate and effective.