▎ 摘　　要

The theoretical scattering cross section of electron energy loss spectroscopy (EELS) is essentially given by -Im epsilon-1(k, omega) with the energy loss h over bar omega and the momentum transfer h over bar k. The macroscopic dielectric function epsilon(k, omega) can be calculated from first principles using time-dependent density-functional theory. However, exper-imental EELS measurements have a finite k resolution or, when operated in spatial resolution mode, yield a k-integrated loss spectrum, which deviates significantly from EEL spectra calculated for specific k momenta. On the other hand, integrating the theoretical spectra over k is complicated by the fact that the integrand varies over several (typically six) orders of magnitude around k = 0. In this article, we present a stable technique for integrating EEL spectra over an adjustable range of momentum transfers. The important region around k = 0, where the integrand is nearly divergent, is treated partially analytically, allowing an analytic integration of the near divergence. The scheme is applied to three prototypical two-dimensional systems: monolayers of MoS2 (semiconductor), hexagonal BN (insulator), and graphene (semimetal). Here, we are confronted with the added difficulty that the long-range Coulomb interaction leads to a very slow supercell (vacuum size) convergence. We address this difficulty by employing an extrapolation scheme, enabling an efficient reduction of the supercell size and thus a considerable speedup in computation time. The calculated k-integrated spectra are in very favorable agreement with experimental EEL spectra.