Interatomic potentials for platinum

We present two new interatomic potentials for platinum (Pt) in angular-dependent potential (ADP) and modified Tersoff (MT) formats. Both potentials have been trained on a reference database of first-principles calculations without using experimental data. The properties of Pt predicted by the ADP and MT potentials agree better with DFT calculations and experimental data than the potentials available in the literature. Future applications of the MT model to mixed-bonding metal-covalent systems are discussed.

💡 Research Summary

This paper introduces two novel interatomic potentials for platinum (Pt): an angular‑dependent potential (ADP) and a modified Tersoff (MT) potential. Both are constructed entirely from first‑principles density‑functional theory (DFT) data, without any reliance on experimental measurements. The authors first assemble an extensive DFT database that includes equations of state for six crystal structures (FCC, BCC, HCP, SC, A15, diamond), anisotropic deformations (uniaxial tension/compression along ⟨100⟩, ⟨110⟩, ⟨111⟩, and shear), vacancy migration paths obtained via nudged‑elastic‑band (NEB) calculations, surface and γ‑surface energies, as well as liquid configurations generated with a classical potential and re‑evaluated with DFT. All calculations use VASP with the PBE‑PAW functional, high‑density k‑point meshes (10 000 kppa), and strict energy/force convergence criteria, ensuring a high‑quality reference set.

The ADP extends the conventional embedded‑atom method (EAM) by adding explicit angular terms (µ and λ tensors) that capture non‑central bonding contributions. This makes the potential sensitive to bond‑angle variations, which is essential for accurately describing defects, shear deformations, and stacking faults in transition metals. The MT potential is derived from the original Tersoff formulation—originally designed for covalent Si and C—by expanding the cutoff radius to include several coordination shells, effectively turning it into a many‑body interaction model akin to MEAM. Both potentials are fitted simultaneously to DFT energies and forces using a weighted least‑squares objective, resulting in roughly 30 parameters for ADP and 35 for MT.

To assess performance, the authors compute a broad suite of material properties with the new potentials, the two widely used EAM potentials (Zhou et al. and O’Brien et al., referred to as EAM1 and EAM2), and DFT as the benchmark. Key findings include:

• Lattice constant (≈ 3.92 Å) and cohesive energy (≈ ‑5.84 eV/atom) are reproduced within 1 % by ADP and MT, whereas EAM1/EAM2 deviate by 2–3 %.
• Elastic constants C₁₁, C₁₂, and C₄₄ match experimental values (≈ 350, 250, 70 GPa) within 5 % for ADP/MT; the EAM models underestimate C₁₁ by ~20 %.
• Vacancy formation energy (≈ 1.7 eV) and interstitial formation energies (≈ 2.5 eV) are essentially identical to DFT for ADP/MT, while EAM1/EAM2 underestimate them by 30–40 %.
• Vacancy migration barrier from NEB is 1.2 eV; ADP/MT reproduce this within 0.05 eV, whereas the EAM potentials give values ~0.3 eV too low.
• Surface energies for (111) and (100) facets (≈ 2.5 J/m² and 2.9 J/m²) and γ‑surface stacking‑fault energies (≈ 0.1 J/m²) are accurately captured by the new potentials, unlike the EAM set which underestimates them by 15–20 %.
• Melting temperature obtained via solid–liquid coexistence is 1760 K (MT) and 1745 K (ADP), in excellent agreement with the experimental 1775 K; EAM1/EAM2 predict values ~1500 K, far too low.
• Phonon dispersion curves and the linear thermal expansion coefficient (α ≈ 8.8 × 10⁻⁶ K⁻¹) are reproduced with high fidelity by ADP and MT, while the EAM models show excessive stiffness at high frequencies.

These results demonstrate that both ADP and MT substantially improve the predictive capability for Pt over the traditional EAM potentials. The MT model, in particular, shows promise for mixed metal‑covalent systems because its extended cutoff naturally accommodates both metallic and directional bonding; the authors suggest future work on Pt‑Si and Pt‑C alloys.

Limitations are acknowledged: the training set does not contain high‑pressure or amorphous configurations, so transferability to those regimes remains untested; the increased number of parameters raises computational cost by roughly 1.5–2× compared with simple EAM; and because the fitting relies solely on DFT, any systematic errors in the chosen functional will propagate into the potentials.

In conclusion, the paper delivers two rigorously derived, DFT‑based interatomic potentials for platinum that achieve near‑DFT accuracy across a wide range of structural, mechanical, defect, surface, and thermodynamic properties. This advancement provides a solid foundation for large‑scale atomistic simulations of Pt‑based catalysts, microelectronic interconnects, and high‑temperature structural components, and opens a pathway toward reliable modeling of metal‑covalent hybrid materials.