  Surface state localization and hybridization on B, Mg, and Li terminated
MgB_2(0001) surfaces are studied within density functional theory (DFT). For
the B terminated surface we find a low energy B {\sigma}_1 surface state, a spz
surface state, and B {\sigma}_2 and {\sigma}_3 quantum well states, which are
90% localized in the topmost B layer. Our results demonstrate that by charging
the B atomic layer, either by changing the surface termination or through
electro-chemical doping, the B {\sigma} surface states are shifted down in
energy, filled, and delocalize through hybridization as they cross the bulk
MgB_2 bulk bands. On the other hand, the spz surface state should be shifted up
in energy, emptied, and gain an increasingly metallic s character by adding a
Mg, Mg^{+1}, or Li terminating atomic layer. These results clearly show both
the robust nature of MgB_2(0001) surface states, and how their localization and
energy range may be tuned by surface termination and charging, with
implications for the superconducting and plasmonic behaviour of MgB_2.
