First-principles average electronic stopping power calculations: Trajectory selection based on electronic density

The electronic stopping of an ion in a material is at the heart of many application-relevant phenomena. For those applications, a calculation of the average electronic stopping power of the ion in the material of interest is often necessary. Computing such average values with first-principles simulations is not an easy task, especially for materials having ionic and/or covalent bonding, for which simple descriptors like the impact parameter or the nearest-neighbor distance are not representative of the electronic stopping power along a projectile trajectory. In this article, we present a method which can be applied to all kinds of materials to calculate average electronic stopping powers with real-time time-dependent density functional theory simulations (rt-TDDFT). By selecting initial projectile directions inside the crystal based on the material's ground state electronic density the projectile samples along its path, we are able to identify a priori $80\phantom{\rule{0.28em}{0ex}}\AA{}$ long trajectories suitable for average stopping power simulations. The method is validated on Si with protons and neutral Si projectiles by comparison to SRIM and experiments. Results with protons are in very good agreement with SRIM/experiments on a wide energy range and show excellent precision. With Si projectiles, calculated stopping powers are also in very good agreement with experiments below a few MeV. At higher energies, the rt-TDDFT methodology we employ fails to reproduce experimental stopping powers of Si projectiles into Si. Finally, although the results with Si projectiles show more deviations than with proton projectiles, the precision of our results is again very satisfactory compared to the existing deviations between different experiments and/or SRIM.