MACE-MP-0: ML Potential for Atomistic Simulations

• MACE-MP-0 is a machine-learned interatomic potential that employs multilayer equivariant message-passing with tensor product representations to capture invariant atomic environments.
• It achieves high predictive accuracy with MAEs near 20 meV/atom for energies and correctly models phase transitions, such as quartz-to-coesite at ~3.5 GPa.
• Its scalable design and transferability across 89 elements support high-throughput simulations and fine-tuning for specialized systems like MOFs and ionic liquids.

MACE-MP-0 is a machine-learned interatomic potential (ML-IP) founded on the MACE (Multilayer Atomic Cluster Expansion) framework, distinguished by its ability to accurately model energies, forces, and material properties for a chemically diverse range of systems. Designed as a "foundation model" for atomistic simulation, MACE-MP-0 leverages symmetry-preserving message-passing neural networks built atop tensor product representations from ACE, yielding a flexible, transferable potential applicable throughout the periodic table and in complex, physically relevant environments.

1. Architectural Foundations and Theoretical Framework

MACE-MP-0 is constructed within the MACE architecture—a multilayer equivariant message-passing graph neural network built upon the ACE formalism. Each local atomic environment is initially mapped to a set of symmetrized tensor product basis functions that rigorously enforce rotational and permutation invariance:

$$B_i^{(p)} = \sum_{\alpha_1,\ldots,\alpha_p} c_{\alpha_1 \cdots \alpha_p} \ \phi_{\alpha_1}(\mathbf{r}_{i1}) \cdots \phi_{\alpha_p}(\mathbf{r}_{ip}),$$

where $p$ is the body order (commonly up to 4), $\phi_{\alpha_k}$ are radial/angular basis functions (with Bessel functions for radial expansion), and $c_{\alpha_1 \cdots \alpha_p}$ are learnable coefficients.

These basis features form the input for a message-passing graph neural network. One step of the message-passing update is:

$$\mathbf{h}_i^{(\ell + 1)} = \mathcal{F}\left(\mathbf{h}_i^{(\ell)}, \sum_{j \in \mathcal{N}(i)} \mathcal{M}(\mathbf{h}_i^{(\ell)}, \mathbf{h}_j^{(\ell)}, \vec{r}_{ij})\right),$$

where $\mathbf{h}_i^{(\ell)}$ are atomic features at layer $\ell$, $\mathcal{M}$ is a symmetry-respecting message function (supporting angular components up to $l=2$), and $\mathcal{F}$ is an MLP node update.

The total energy readout is computed as:

$$E = \sum_i \mathrm{MLP}_{\mathrm{read}}(\mathbf{h}_i^{(L)}),$$

where $L$ is the final GNN layer.

A typical MACE-MP-0 implementation uses a radial cutoff of 6–12 Å, with 10 Bessel radial functions and two message-passing layers. This design balances representability (through nonlinear neural components and high body order) with computational tractability (notably suitable for GPU acceleration).

2. Transferability and Universal Coverage

Unlike classical empirical potentials constrained to fixed analytic forms and typically parameterized for a small chemical domain (e.g., Buckingham, Born-Huggins-Mayer), MACE-MP-0 is parameterized on a large, chemically diverse database (the Materials Project). As a result, MACE-MP-0 demonstrates transferability and stability across 89 elements and complex chemical environments, achieving mean absolute errors (MAE) near 20 meV/atom for energy and 45 meV/Å for forces in validation tests (Bernstein, 8 Oct 2024).

This foundation model is "off-the-shelf" and directly applicable to atomistic simulations of inorganic crystals, molten salts, and silicates, among others, without requiring system-specific refitting.

3. Thermochemical and Structural Accuracy

MACE-MP-0 has been benchmarked for the computation of framework energies (e.g., energy differences between zeolite structures and silica polymorphs), phase stability, and high-pressure transitions (Nasir et al., 1 Nov 2024). For example, the energy difference

$\Delta E = E_\text{cristobalite} - E_\text{quartz}$

is predicted at 2.5 kJ/mol by MACE-MP-0, consistent with the experimental range (1.88–2.64 kJ/mol). Simulations of phase transitions, such as quartz-to-coesite ($\sim$3.5 GPa) and coesite-to-stishovite ($\sim$9 GPa), closely match laboratory measurements.

For molten salts, MACE-MP-0 recovers the melting temperature of LiF (1121–1143 K) with high fidelity simply by heating a crystal lattice—a performance not matched by classical potentials, whose melting points are offset by $\sim$300 K (Devereux et al., 31 Oct 2024). This concordance enables physically accurate predictions of transport coefficients, such as viscosity, computed via the Green–Kubo formalism:

$$\eta = \frac{V}{k_B T} \int_0^\infty \langle \sigma_{xy}(t) \sigma_{xy}(0) \rangle dt,$$

where $\sigma_{xy}$ is the off-diagonal stress tensor component.

4. Enhanced Description of Many-Body Dynamics

The MACE message-passing architecture naturally encodes many-body and higher-order effects. Atomistic simulations reveal that MACE-MP-0 captures velocity autocorrelation functions and radial distribution functions indicating a broader, more realistic coordination environment and more solid-like dynamic character (deeper minima, pronounced oscillations) than classical models. This enhanced fidelity suggests accurate representation of energy barriers and interatomic stiffness—critical for diffusive phenomena and vibrational dynamics (Devereux et al., 31 Oct 2024, Nasir et al., 1 Nov 2024).

For dynamic properties in ionic liquids, such as diffusion coefficients,

$$D = \frac{1}{6N} \lim_{t \rightarrow \infty} \frac{d}{dt} \sum_{i=1}^N \langle |\mathbf{r}_i(t) - \mathbf{r}_i(0)|^2 \rangle,$$

fine-tuned implementations of MACE outperform DPMD and MACE-MP-0 foundational models in reproducing experimental trends and molecular conformations (Park et al., 24 Mar 2025).

5. Role in High-Throughput and Phonon Calculations

While MACE-MP-0 excels for equilibrium structural prediction and thermodynamics, unmodified versions display limitations for high-fidelity phonon properties in MOFs, notably generating spurious imaginary vibrational modes and inaccurate thermal expansion coefficients. Fine-tuned derivatives (e.g., MACE-MP-MOF0) remedy these issues by retraining on chemically diverse MOF datasets, weighting force/stress loss, and removing unwanted artifacts, enabling accurate calculations within the quasi-harmonic approximation: $$F(V, T) = E_0(V) + \frac{1}{2}\sum_n \hbar \omega_n(V) + k_B T \sum_n \ln\left[1 - e^{-\hbar \omega_n(V) / k_B T}\right],$$ where $E_0(V)$ is the static energy at volume $V$, and $\omega_n(V)$ are phonon frequencies (Elena et al., 3 Dec 2024).

This adaptation supports high-throughput calculation of mechanical properties (e.g., bulk moduli, thermal expansion), guiding material design in energy storage and thermoelectrics.

6. Fine-Tuning and Dataset Requirements

High-fidelity predictive results in specialized systems (e.g., ionic liquids, MOFs) require fine-tuning of MACE-MP-0 on curated datasets—including both equilibrated and non-equilibrated configurations to thoroughly sample the PES. Studies highlight the necessity for tailored two-stage loss weighting (energy vs. force) and farthest point sampling to ensure robust coverage and convergence (Park et al., 24 Mar 2025, Elena et al., 3 Dec 2024).

Empirically, foundational models may reproduce generic benchmarks at high accuracy (above 98% without fine-tuning), but fine-tuning is critical for resolving subtle conformational features, correct density, and dynamic properties encountered in experimental measurements or polarizable force fields.

7. Implications and Future Prospects

MACE-MP-0 advances computational materials science by approximating DFT-level accuracy at reduced computational cost and extending the limits of empirical force fields. Applications span:

• Accurate prediction of phase stability, framework energies, and pressure-induced transitions in silicates and zeolites.
• Reliable computation of transport and thermodynamic properties in molten salts and ionic liquids, with correct melting points and viscosity.
• Enabling high-throughput screening of MOFs for energy storage, thermal management, and mechanical stability (when fine-tuned).
• Offering a scalable surrogate to DFT in large-scale simulations, thereby accelerating materials discovery.

Continued development centers on improved handling of environmental effects (e.g., fluoride stabilization), robust extrapolation to complex molecular systems, task-specific fine-tuning, and expansion to broader inorganic and hybrid materials domains. The synergy with DFT enables rapid iteration between quantum-informed accuracy and simulation performance, positioning MACE-MP-0 and its derivatives as pivotal components of modern atomistic modeling workflows.