  Superionic states are phases of matters that can simultaneously exhibit some
of the properties of a fluid and of a solid. Superionic states of ice,
H$_{3}$O, He-H$_{2}$O or He-NH$_{3}$ compounds have been reported in previous
works. Silicon, sodium, and hydrogen are abundant elements inside the earth.
Here, we use ab initio calculations to show that, at extreme conditions inside
the earth, Na, Si, and H can form many hypervalent compounds that some of them
can exist every close to ambient pressure, and surprisingly a previously
unknown type of superionic state of $P\overline3m1 - $Na$_{2}$SiH$_{6}$ can
form as well. Our work focused on new superionic state of Na$_{2}$SiH$_{6}$,
and the results also reveal several different hypervalent Si-H anions
discovered, which are different from individual SiH$_{5}^{\,-}$ and octahedral
SiH$_{6}^{\,2-}$ in previous research of ternary alkali hypervalent silicon
hydrides. Our work provides some advice on further investigations on potential
ternary hydrides inside the earth.
