  According to previous interpretations of experimental data, sodium-scandium
double-cation borohydride NaSc(BH$_4$)$_4$ crystallizes in the crystallographic
space group $Cmcm$ where each sodium (scandium) atom is surrounded by six
scandium (sodium) atoms. A careful investigation of this phase based on
\textit{ab initio} calculations indicates that the structure is dynamically
unstable and gives rise to an energetically and dynamically more favorable
phase with $C222_1$ symmetry and nearly identical x-ray diffraction pattern. By
additionally performing extensive structural searches with the minima-hopping
method we discover a class of new low-energy structures exhibiting a novel
structural motif in which each sodium (scandium) atom is surrounded by four
scandium (sodium) atoms arranged at the corners of either a rectangle with
nearly equal sides or a tetrahedron. These new phases are all predicted to be
insulators with band gaps of $7.9-8.2$ eV. Finally, we estimate the influence
of these structures on the hydrogen-storage performance of NaSc(BH$_4$)$_4$.
