The electronic stopping power is an observable that quantifies the ability of swift ions penetrating matter to transfer energy to the electron cloud. The recent literature has proven the value of Real-Time Time-Dependent Density Functional Theory to accurately evaluate this property from firstprinciples but questions remain regarding the capability of computer codes relying on atom-centered basis functions to capture the physics at play. In this article, we draw attention to the fact that irradiation by swift ions triggers electron emission into the continuum, especially at the Bragg peak. We investigate the ability of Gaussian atomic orbitals (AOC), that were fitted to mimic continuum wave functions, in improving electronic stopping power predictions. AOC are added to standard correlationconsistent basis sets or STO minimal basis sets. Our benchmarks on water irradiation by fast protons clearly advocate for the use of AOC, especially near the Bragg peak. We show that AOC only need to be placed on the molecules struck by the ion. The number of AOC that are added to the usual basis set is relatively small compared to the total number of atomic orbitals, making the use of such basis set an excellent choice from a computational cost point of view. The optimum basis set combination is applied for the calculation of stopping power of a proton in water with encouraging agreement with experimental data.