  Impacts may have had a significant effect on the atmospheric chemistry of the
early Earth. Reduced phases in the impactor (e.g., metallic iron) can reduce
the planet's H$_2$O inventory to produce massive atmospheres rich in H$_2$.
Whilst previous studies have focused on the interactions between the impactor
and atmosphere in such scenarios, we investigate two further effects, 1) the
distribution of the impactor's iron inventory during impact between the target
interior, target atmosphere, and escaping the target, and 2) interactions
between the post-impact atmosphere and the impact-generated melt phase. We find
that these two effects can potentially counterbalance each other, with the
melt-atmosphere interactions acting to restore reducing power to the atmosphere
that was initially accreted by the melt phase. For a $\sim10^{22}\,\mathrm{kg}$
impactor, when the iron accreted by the melt phase is fully available to reduce
this melt, we find an equilibrium atmosphere with H$_2$ column density
$\sim10^4\,\mathrm{moles\,cm^{-2}}$
($p\mathrm{H2}\sim120\,\mathrm{bars}\mathrm{,}~X_\mathrm{H2}\sim0.77$),
consistent with previous estimates. However, when the iron is not available to
reduce the melt (e.g., sinking out in large diameter blobs), we find
significantly less H$_2$ ($7\times10^2-5\times10^3\,\mathrm{moles\,cm^{-2}}$,
$p\mathrm{H2}\lesssim60\,\mathrm{bars}\mathrm{,}~X_\mathrm{H2}\lesssim0.41$).
These lower H$_2$ abundances are sufficiently high that species important to
prebiotic chemistry can form (e.g., NH3, HCN), but sufficiently low that the
greenhouse heating effects associated with highly reducing atmospheres, which
are problematic to such chemistry, are suppressed. The manner in which iron is
accreted by the impact-generated melt phase is critical in determining the
reducing power of the atmosphere and re-solidified melt pool in the aftermath
of impact.
