Week 4 W - Characteris* Point Group Comments C1 E,C1 Cs...

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Characteris*c symmetry elements of some important classes Point Group Characteris1c symmetry elements Comments C 1 E, C 1 C s E, one σ plane C i E, inversion centre C n E, one principal n‐fold axis S n Only S n (n even, n≠2) C nv E, one principal n‐fold axis, n σ v planes C nh E, one principal n‐fold axis, one σ h plane and one S n ‐fold axis, coincident with the C n axis. The S n axis necessarily follows from the C n axis and σ h plane. For n=2, 4 or 6 there is also a centre of inversion D nh E, one principal n‐fold axis, n C 2 axes, one σ h plane, n σ v planes and one S n ‐fold axis. The S n axis necessarily follows from the C n axis and σ h plane. For n=2, 4 or 6 there is also a centre of inversion D nd E, one principal n‐fold axis, n C 2 axes, n σ v planes and one S 2n ‐fold axis. For n=3 or 5 there is also a centre of inversion T d tetrahedral O h octahedral I h Icosahedral
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Examples of molecules belonging to D nh point groups: D 2h D 3h D 3h D 3h D 4h D 4h D 5h D 5h C 2 C 3 C 3 C 3 C 4 C 4 C 5 C 5
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Characteris*c symmetry elements of some important classes Point Group Characteris1c symmetry elements Comments C 1 E, C 1 C s E, one σ plane C i E, inversion centre C n E, one principal n‐fold axis S n Only S n (n even, n≠2) C nv E, one principal n‐fold axis, n σ v planes C nh E, one principal n‐fold axis, one σ h plane and one S n
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