  Dark matter (DM) detectors employing a Spherical Proportional Counter (SPC)
have demonstrated a single-electron detection threshold and are projected to
have small background rates. We explore the sensitivity to DM-electron
scattering with SPC detectors in the context of DarkSphere, a proposal for a
300 cm diameter fully-electroformed SPC. SPCs can run with different gases, so
we investigate the sensitivity for five targets: helium, neon, xenon, methane,
and isobutane. We use tools from quantum chemistry to model the atomic and
molecular systems, and calculate the expected DM induced event rates. We find
that DarkSphere has the potential to improve current exclusion limits on DM
masses above 4 MeV by up to five orders of magnitude. Neon is the best
all-round gas target and provides good sensitivity to scenarios with both light
and heavy mediators. Gas mixtures, where methane or isobutane is added to a
noble gas, can extend the sensitivity at lower masses. Our study highlights the
currently untapped potential of SPCs to search for DM-electron scattering in
the MeV-to-GeV DM mass range.
