  Recent experimental work has realized a new insulating state of samarium
nickelate (SmNiO$_3$), accessible in a reversible manner via high-density
electron doping. To elucidate this behavior, we use the first-principles
density functional theory (DFT) + U method to study the effect of added
electrons on the crystal and electronic structure of SmNiO$_3$. First, we track
the changes in the crystal and electronic structure with added electrons
compensated by a uniform positive background charge at concentrations of
$\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, and 1 electrons per Ni. The change
in electron concentration does not rigidly shift the Fermi energy; rather, the
added electrons localize on NiO$_6$ octahedra causing an on-site Mott
transition and a change in the density of states resulting in a large gap
between the occupied and unoccupied Ni $e_g$ orbitals at full doping. This
evolution of the density of states is essentially unchanged when the added
electrons are introduced by doping with interstitial H or Li ions.
