EpNet-Si: Atomic Form Factors Learned from Band Structures

Abstract

The empirical pseudopotential method (EPM) computes band structures with one diagonalization per $k$ point and no self-consistency, but its fixed atomic form factors do not transfer between crystal structures. To address this limitation, we introduce EpNet-Si, an EPM for silicon in which an equivariant network predicts each atom's plane-wave form factor from its local environment: a species potential plus monopole, dipole and quadrupole corrections, mixed by a learned router over atomic densities, together with an $s/p$ nonlocal projector. With 6{,}195 parameters, the model is trained through the eigensolver on reference density functional theory (DFT) band energies of only 77 cells. Among 231 distortions of the trained structure types, the 142 gapped cells have mean band and gap errors of 15 and 8\,meV; among 192 unseen structures, the 165 gapped cells have mean errors of 38 and 49\,meV. Physical properties derived from EpNet-Si, including effective masses, gap pressure coefficients, deformation potentials and the density of states at the Fermi level, agree with those obtained from the reference DFT calculations. These results suggest that the classical EPM, fitted to a small set of reference data, can be extended into a fast alternative for modern electronic band-structure calculations.