Group Theory Solutions: #3

3.* (1997 1 6) Aluminum (III) hexafluoride anion, AlF₆^3-, has an octahedral structure in which the Al³⁺ cation is located at the center and the six F- anions are located at the mid points of the six faces of a cube:

Fill in the following table with information about the structure of AlF₆^3-. To receive partial credit describe the symmetry elements you have found.

Symmetry element	How many?
C₂ axes	9 (6 C₂ axes and 3 C₄² axes)
C₃ axes	4
C₄axes	3
C₆axes	0
S₃axes	0
S₄axes	3
S₆axes	4
inversion center?	yes

Is this molecule polar? Chiral?

No, no. Anything with an inversion center is both nonpolar (because the dipole moments cancel out) and achiral (because the inversion center is equivalent to a second order improper rotation axis (S₂).