  Many computational models have been developed to predict the rates of atomic
displacements in two-dimensional (2D) materials under electron beam
irradiation. However, these models often drastically underestimate the
displacement rates in 2D insulators, in which beam-induced electronic
excitations can reduce the binding energies of the irradiated atoms. This bond
softening leads to a qualitative disagreement between theory and experiment, in
that substantial sputtering is experimentally observed at beam energies deemed
far to small to drive atomic dislocation by many current models. To address
these theoretical shortcomings, this paper develops a first-principles method
to calculate the probability of beam-induced electronic excitations by coupling
quantum electrodynamics (QED) scattering amplitudes to density functional
theory (DFT) single-particle orbitals. The presented theory then explicitly
considers the effect of these electronic excitations on the sputtering cross
section. Applying this method to 2D hexagonal BN and MoS$_2$ significantly
increases their calculated sputtering cross sections and correctly yields
appreciable sputtering rates at beam energies previously predicted to leave the
crystals intact. The proposed QED-DFT approach can be easily extended to
describe a rich variety of beam-driven phenomena in any crystalline material.
