- Point group
- Td — The full symmetry of a regular tetrahedron: four C3 axes, three C2 axes (each also an S4 axis) and six dihedral mirror planes. There is no centre of inversion.
- Order
- 24
- Operations
- E, 8C₃, 3C₂, 6S₄, 6σd
- Shape
- Tetrahedral
- Atoms
- 5 (Mn, O × 4)
Symmetry elements of MnO₄⁻
- C₃ (1) — along one Mn–O bond
- C₃ (2) — along one Mn–O bond
- C₃ (3) — along one Mn–O bond
- C₃ (4) — along one Mn–O bond
- C₂ (x) — bisects two bond angles; also an S₄ axis
- C₂ (y) — bisects two bond angles; also an S₄ axis
- C₂ (z) — bisects two bond angles; also an S₄ axis
- S₄ (x) — rotate 90°, then reflect
- S₄ (y) — rotate 90°, then reflect
- S₄ (z) — rotate 90°, then reflect
- σd (1) — contains Mn and two ligands
- σd (2) — contains Mn and two ligands
- σd (3) — contains Mn and two ligands
- σd (4) — contains Mn and two ligands
- σd (5) — contains Mn and two ligands
- σd (6) — contains Mn and two ligands
Structure
- Mn–O 1.63 Å (all equal)
- O–Mn–O 109.5°
- Mn(VII); the deep purple colour is a charge-transfer band
