  Ab initio calculations predict a metal-insulator transition at zero
temperature to occur in La$_4$Ni$_3$O$_8$ at moderate pressures as a result of
a pressure-induced spin-state transition. The spin-state transition that is
seen at 105 K at ambient pressure from a low-temperature high-spin state to a
high-temperature low-spin state has been observed to be shifted to lower
temperatures as pressure is applied. From our calculations we find that a
smaller unit cell volume favors the metallic low-spin state, which becomes more
stable at 5 GPa. Similar physics should take place in the related compound
La$_3$Ni$_2$O$_6$, but on a different energy scale, which may account for why
the transition has not been observed in this material.
