Jahn-Teller distortion, octahedra rotations and orbital ordering in perovskites: KScF 3 $$ {}_3 $$ as a model system.

The KScF 3 $$ {}_3 $$ perovskite has been used as a model for investigating the relative importance of the Jahn-Teller (JT) lift of degeneracy, the ScF 6 $$ {}_6 $$ octahedra rotation (OR), and the quadrupole-quadrupole interaction linked to different occupancy of the Sc t 2 g $$ {}_{2g} $$ subshell in various sites of the unit cell (orbital ordering, OO). The group-subgroup sequence P m 3 ¯ m $$ Pm\overline{3}m $$ , P 4 m m m $$ P\frac{4}{m} mm $$ , P 4 m b m $$ P\frac{4}{m} bm $$ , and P n m a $$ Pnma $$ , supplemented by C m m m $$ Cmmm $$ and I 4 m c m $$ I\frac{4}{m} cm $$ , has been explored by using an all electron $$ \mathrm{all}\ \mathrm{electron} $$ Gaussian type basis set, hybrid functionals, and the CRYSTAL17 code. The JT lift of degeneracy provides a stabilization about 5 times larger than the sum of the OO and OR effects. The energy gained in the transition from P 4 m m m $$ P\frac{4}{m} mm $$ to P 4 m b m $$ P\frac{4}{m} bm $$ , consisting in a rotation of the octahedra around the c $$ c $$ axis, is 1077 μ $$ \mu $$ E h $$ {}_h $$ . From P 4 m b m $$ P\frac{4}{m} bm $$ to P n m a $$ Pnma $$ , additional rotations around the a $$ a $$ and b $$ b $$ axes are possible, and the d $$ d $$ Sc electron can occupy a different t 2 g $$ {}_{2g} $$ orbital, with a total energy reduction of 2318 μ $$ \mu $$ E h $$ {}_h $$ . The rotation of the octahedra reduces the strength of superexchange: in going from P 4 m m m $$ P\frac{4}{m} mm $$ to P n m a $$ Pnma $$ the G-AFM stabilization with respect to FM shrinks by a factor 4.