Symmetry-restricted energy landscapes as a benchmark for machine learned interatomic potentials

TL;DR

This work introduces symmetry-constrained two-dimensional PES (s2DPES) as a visualization-based benchmark to assess pretrained interatomic potentials (uMLIPs) against DFT references. By sampling Wyckoff symmetry-allowed degrees of freedom, the authors generate 2D energy landscapes for multiple materials and model families (MACE variants, ORB v2, CHGNet, SevenNet) to probe local minima, saddles, and PES topology. The results reveal both strengths and limitations of current uMLIPs: near-equilibrium regions are typically well-captured, but artifacts and spurious minima can arise far from minima or due to training data bias, with newer models (e.g., MACE_OMAT-0) showing improved fidelity. The s2DPES workflow provides a robust platform for model evaluation, active learning, and targeted improvements in PES realism, with implications for reliable structure prediction and materials discovery.

Abstract

Machine learned interatomic potentials (MLIPs) are becoming a standard method for DFT-level accurate molecular dynamics simulation and large-scale studies of crystal energetics. Increasingly popular are universal pre-trained potentials, also called foundation models, based one, e.g. the MACE, CHGNet, M3GNet, ORB, and SevenNet architectures. While there are many benchmarks of these models using validation errors and materials discovery tasks, their fidelity in reproducing the detailed features of potential energy surfaces (PES) is not understood to the same degree. We evaluate the accuracy of these potentials by systematically probing their predicted energy landscapes. Two-dimensional slices of the potential energy surface are constructed where the atomic positions are varied along selected Wyckoff degrees of freedom within a fixed crystal symmetry. This approach enables a direct, visual comparison of the interatomic potentials and DFT-calculated surfaces which reveals potential artifacts e.g., arising from unique local environments. Our analysis highlights the strengths and limitations of different potentials in capturing local minima, saddle points, and overall PES topology, offering insights into the physical accuracy of current pre-trained IAPs and providing benchmarks for future model development.

Figures (4)

• Figure 1: Illustration of the workflow. A toy crystal structure with three atom types is depicted: blue atoms remain fixed by symmetry, while green and red atoms (each with multiplicity 2) can vary within $[0,1]$. In the workflow, the user can selectively freeze or free these Wyckoff degrees of freedom. Here, the workflow produces a 2D meshgrid $\{(x_i, y_j) \mid x_i, y_j \in [0,1]\}$ that enumerates possible configurations in some discrete step size. Each point on the meshgrid corresponds to a distinct crystal structure, and we calculate the energy of that structure using any interatomic potential that provides an ASE calculator interface. The resulting 2D energy slice shows how displacements of these atoms affect the total energy of the system.
• Figure 2: Two-dimensional energy landscape for $\mathrm{W}_2\mathrm{N}_3$ generated by varying the x and z Wyckoff degrees of freedom of tungsten atoms (indicated with blue colour in the crystal structure figure) in the protostructure A3B2_oP20_62_3c_2c:N-W. The distance cost is calculated with a minimum interatomic distance of 1.1115 Å for N–N pairs, 1.647 Å for N–W pairs, and 2.1825 Å for W–W pairs. Energy values are presented in eV/atom.
• Figure 3: Energy landscapes for $\mathrm{Al}\mathrm{Ti}\mathrm{N}_{3}$ from $x$-direction mutations of two N atoms in AB3C_tP40_135_f_3g_h:Al-N-Ti, which was examined after inconsistent outputs between MACE_MPA-0 and other MACE models. Minimum interatomic distances used for the distance cost are 1.98 Å (Ti–Ti), 1.55 Å (Ti–N), 2.04 Å (Ti–Al), 1.112 Å (N–N), 1.61 Å (N–Al), and 2.10 Å (Al–Al). Energies are in eV/atom.
• Figure 4: Energy landscapes of $\mathrm{Cu_2O_8S_4}$ with protostructure label A4B2C_hP14_187_g_in_gh:Cu-O-S along two different degrees of freedom. (a) Two degrees of freedom along x and z of Oxygen at Wyckoff position n, (b) Oxygen in Wyckoff position n and Sulfur in Wyckoff position g perturbed along z.