Table I.

Atomic displacements corresponding to unit amplitude of the ${\text{t}}_{1\text{u}}^{(1)}(z)$ degree of freedom for the TiO6 cluster in a perovskite titanate. Entries that are zero are left blank. The unit-amplitude ${\text{t}}_{1\text{u}}^{(1)}(x)$ and ${\text{t}}_{1\text{u}}^{(1)}(y)$ displacement patterns can be found be cyclic permutation and by replacing the z direction 5-atom primitive perovskite cell lattice paramter c with the corresponding lattice parameter in the x or y direction. Atomic displacement patterns for the other TiO₆ cluster degrees of freedom can be found in the Table S1 of the Supplemental Material[19].

Ti

O+x

O−x

O+y

O−y

O+z

O−z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

$(2/\sqrt{6})c$

$(-1/\sqrt{6})c$

$(-1/\sqrt{6})c$