1. Lecture 9 THE SYMMETRY POINT GROUPS
1) Point Groups with improper axes
S2n (n ≥ 2)
1,3,5,7-tetrafluorocycloocta-1,3,5,7-tetraene (S4), [6.5]-coronane (S6)
Symmetry elements: E, S4, C2
Special cases: S1 = s, S2 = i
E, C3, i, S6

2. 2) Point Groups of high symmetry (cubic groups)
In contrast to groups C, D, and S, cubic symmetry groups are characterized by the presence of several rotational axes of high order (≥ 3).
Cases of regular polyhedra:
Td (tetrahedral) BF4‑ , CH4
Symmetry elements: E, 4C3, 3C2, 3S4, 6sd
Symmetry operations: E, 8C3, 3C2, 6S4, 6sd
If all planes of symmetry and i are missing, the point group is T (pure rotational group, very rare);
If all dihedral planes are removed but 3 sh remain, the point group is Th ( [Fe(py)6]2+ )

3. 3) Point Groups of high symmetry
Oh (octahedral) TiF62‑, cubane C8H8
Symmetry elements: E, i, 4S6, 4C3, 3S4, 3C4, 6C2, 3 C2, 3sh, 6sd
Symmetry operations: E, i, 8S6, 8C3, 6S4, 6C4, 6C2, 3 C2, 3sh, 6sd
Pure rotational analogue is the point group O (no mirror planes and no Sn; very rare)

4. 4) Point Groups of high symmetry
Th group (symmetry elements: E, i, 4S6, 4C3, 3C2, 3sh) can also be considered as a result of reducing Oh group symmetry (E, i, 4S6, 4C3, 3S4, 3C4, 6C2, 3 C2, 3sh, 6sd )
by eliminating C4, S4 and some C2 axes and sd planes

5. 5) Point Groups of high symmetry
Ih (icosahedral) B12H122‑, C20
Symmetry elements: E, i, 6S10, 6C5, 10S6, 10C3, 15C2, 15s
Pure rotation analogue is the point group I (no mirror planes and thus no Sn, very rare)

6. 6) Systematic Symmetry Classification of molecules

7. 7) Systematic Symmetry Classification of molecules
Some very useful information related to symmetry point groups + examples: