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

TL;DR

This work addresses the computational challenge of incorporating nuclear quantum effects in materials modeling by combining path-integral molecular dynamics with fast, accurate Moment Tensor Potentials via an active-learning MLIP-2 interface to i-PI. The authors demonstrate that MTP-PIMD can reproduce lattice parameters, thermal expansion, and radial distribution functions for LiH and Si with high fidelity, closely matching experimental data and quasi-harmonic predictions while offering substantial computational savings over DFT-based PIMD. A key contribution is the development of an active-learning loop and a scalable i-PI interface that enables efficient on-the-fly training of interatomic potentials during PIMD. The findings highlight the significance of NQEs in LTE behavior and RDF broadening, including a negative LTE in Si, and establish a practical, scalable framework for quantum-aware simulations of complex materials.

Abstract

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. 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 thermal expansion coefficients, as well as radial distribution functions, for lithium hydride (LiH) and silicon (Si) systems. The results were compared with experimental data, quasi-harmonic approximation calculations, and predictions from the universal machine learning force field MatterSim. These comparisons demonstrated the high accuracy and effectiveness of the MTP-PIMD approach.

Figures (6)

• Figure 1: The flowchart describes the general process of potential fitting and its subsequent use in calculating thermal properties using the PIMD method. The upper part of the figure illustrates the fitting of the initial potential. The middle part demonstrates the active learning procedure using the interface between i-PI and MLIP-2. The lower part shows the usage of the fitted potential: the MTP-PIMD calculation with the fitted potential is performed, and the obtained trajectory is used for subsequent processing.
• Figure 2: Comparison of DFT-calculated and MTP-calculated energies (on the left) and forces (in the middle) of structures from the training set, as well as phonon band structures (on the right) for the LiH and Si systems.
• Figure 3: The dependence of the lattice parameter $a$ on temperature for different values of the parameter $P$ (number of copies of the system) for the LiH system. The $P_{\rm T}$ curve corresponds to the value of the number of replicas of the system $P = 1.7 \cdot \hbar \omega_{\rm max} /k_B T$.
• Figure 4: Partial lithium-lithium, lithium-hydrogen, and hydrogen-hydrogen radial distribution functions for the LiH system at 50 K for a different number of replicas of the system. The dashed line corresponds to the optimal beads number $P$ for the chosen temperature.
• Figure 5: The dependence of the linear LTE coefficient $\alpha_{\rm L}$ for the LiH system on temperature for the cases of classical MD (red squares) and PIMD (green circles) using MTP (on the left) and MS (on the right), QHA (yellow triangles), and the experimental data obtained in the article LiHLTE (blue dashed line).