Fully ab-initio all-electron calculation of dark matter--electron scattering in crystals with evaluation of systematic uncertainties

We calculate target-material responses for dark matter--electron scattering at the \textit{ab-initio} all-electron level using atom-centered gaussian basis sets. The all-electron effects enhance the material response at high momentum transfers from dark matter to electrons, $q\gtrsim \mathcal{O}\left({10\ \alpha m_e}\right)$, compared to calculations using conventional plane wave methods, including those used in QEDark; this enhances the expected event rates at energy transfers $E \gtrsim 10$~eV, especially when scattering through heavy mediators. We carefully test a range of systematic uncertainties in the theory calculation, including those arising from the choice of basis set, exchange-correlation functional, number of unit cells in the Bloch sum, $\mathbf{k}$-mesh, and neglect of scatters with very high momentum transfers. We provide state-of-the-art crystal form factors, focusing on silicon and germanium. Our code and results are made publicly available as a new tool, called Quantum Chemistry Dark (``QCDark'').