Interatomic force fields for zirconium based on the embedded atom method and the tabulated Gaussian Approximation Potential

The accuracy of interatomic interaction potentials - also known as force fields - is the main factor determining the physical soundness of classical molecular dynamics (MD) simulations. Here, we present a multi-objective framework to generate embedded-atom-method (EAM) force fields using ab initio data. The EAM force fields were tuned via particle swarm optimization to capture the non-linear association between atomic structures and system energies. Using this framework, 95 standard EAM force fields for zirconium were developed and 45 physical features for each developed force field were tracked. Principal component analysis (PCA) was performed to provide insights into the compromises that must be made when generating EAM force fields. Of note, by assigning large fitting weights to generalized stacking fault energy (GSFE) surfaces, there exist EAM force fields with properly positioned minima on prismatic GSFE surfaces and containing no spurious minima in basal GSFE surfaces. However, while standard EAM force fields achieved this without explicitly taking the angular dependence of atomic interactions into account, they led to a severe mismatch between other important physical properties and benchmarks. Hence, we also constructed two machine-learned tabulated Gaussian approximation potentials (tabGAP) with an additional three-body term, which successfully tackled the aforementioned issue and exhibit acceptable prediction accuracy across many physical properties (lattice parameters, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, and free surface energies) of Zr. Remarkably, its computational efficiency is only 6 times slower than standard EAM force fields.