  Stoichiometric LiFeAs at ambient pressure is an 18 K superconductor while
isoelectronic MgFeGe is not, despite their extremely similar electronic
structures. To investigate possible sources of this distinctively different
superconducting behavior, we quantify the differences using first principles
density functional theory, establishing first that the Fe total 3d occupations
are identical in the two compounds. Individual 3d orbital occupations also
differ very little ($\sim 0.01$). The differences in Fermi surfaces (FSs) do
not seem significant; however a redistribution of bands just above the Fermi
level does represent a possibly significant distinction. Because the bands and
FSs of LiFeAs are less in agreement with experiment than for other
iron-pnictides, we study the effects of additional exchange-correlations
effects beyond GGA (the generalized gradient approximation) by applying the
modified Becke-Johnson potential (mBJ) exchange potential, which gives much
improved bandgaps in insulators compared to GGA and might be useful for
semimetals such as the Fe-based superconductors. Overall, we conclude that the
mBJ corrections do not improve the description of LiFeAs as compared to
experiment.
