First-principles interatomic potentials for ten elemental metals via compressed sensing

Interatomic potentials have been widely used in atomistic simulations such as molecular dynamics. Recently, frameworks to construct accurate interatomic potentials that combine a set of density functional theory (DFT) calculations with machine learning techniques have been proposed. One of these methods is to use compressed sensing to derive a sparse representation for the interatomic potential. This facilitates the control of the accuracy of interatomic potentials. In this study, we demonstrate the applicability of compressed sensing to deriving the interatomic potential of ten elemental metals, namely, Ag, Al, Au, Ca, Cu, Ga, In, K, Li, and Zn. For each elemental metal, the interatomic potential is obtained from DFT calculations using elastic net regression. The interatomic potentials are found to have prediction errors of less than 3.5 meV/atom, 0.03 eV/Å, and 0.15 GPa for the energy, force, and the stress tensor, respectively, which enable the accurate prediction of physical properties such as lattice constants and the phonon dispersion relationship.

Figure 1

Relationship between total energy and crystal structure.

Figure 2

Cutoff radius dependence of RMSE of linear ridge PES.

Figure 3

Dependence of RMSE of linear ridge PES on the number of basis functions for (a) cosine and (b) MMW types. Max. stands for the maximum value of the arithmetic sequence of the internal parameter.

Figure 4

Dependence of RMSEs for the energy and the stress tensor of elastic net PES ($\alpha =1$, LASSO) on the number of the basis functions for ten elemental metals. RMSEs for the energy and the stress tensor are shown by orange open circles and blue open squares, respectively.

Figure 5

Comparison of the energies predicted by the elastic net PES and DFT for (a) Al and (b) Zn, measured from the energy of the most stable structure among the bcc, fcc, hcp, sc, $\omega$ and $\beta$-tin structures.

Figure 6

Phonon dispersion relationships for ten elemental metals with (a) fcc and (b) bcc structures. Phonon dispersion curves obtained by the elastic net PES and DFT are shown by blue solid and orange broken lines, respectively. Negative values indicate imaginary modes.