We extend the calculation of dark matter direct detection rates via electronic transitions in general dielectric crystal targets, combining state-of-the-art density functional theory calculations of electronic band structures and wave functions near the band gap, with semi-analytic approximations to include additional states farther away from the band gap. We show, in particular, the importance of all-electron reconstruction for recovering large momentum components of electronic wave functions, which, together with the inclusion of additional states, has a significant impact on direct detection rates, especially for heavy mediator models and at $mathcal{O}(10,text{eV})$ and higher energy depositions. Applying our framework to silicon and germanium (that have been established already as sensitive dark matter detectors), we find that our extended calculations can appreciably change the detection prospects. Our calculational framework is implemented in an open-source program $texttt{EXCEED-DM}$ (EXtended Calculation of Electronic Excitations for Direct detection of Dark Matter), to be released in an upcoming publication.
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