1. Lecture 34: Symmetry Elements The material in this lecture covers the following in Atkins. 15 Molecular Symmetry The symmetry elements of objects 15.1 Operations and symmetry elements 15.2 Symmetry classification of molecules (a) The groups C 1,C i, and C s (b) The groups C n,C nv, and C nh (c) The groups D n,D nh, and D nd Lecture on-line Symmetry Elements (PowerPoint) Symmetry Elements (PDF) Handout for this lecture

2. Some of the symmetry elements of a cube. The twofold, threefold, and fourfold axes are labelled with the conventional symbols.

3. (b) an H 2 O molecule has a twofold (C 2 ) axis. Both have other symmetry elements too. (a) An NH 3 molecule has a threefold (C 3 ) axis

6. (b) an H2O molecule has a twofold (C2) axis.

9. A regular octahedron has a centre of inversion (i).

10. (a). A CH 4 molecule has a fourfold improper rotation axis (S 4 ): the molecule is indistinguishable after a 90° rotation followed by a reflection across the horizontal plane, but neither operation alone is a symmetry operation.

11. (b) The staggered form of ethane has an S 6 axis composed of a 60° rotation followed by a reflection.

17. The presence of a twofold axis and a horizontal mirror plane jointly imply the presence of a centre of inversion in the molecule.

18. A molecule with n twofold rotation axes perpendicular to an n-fold rotation axis belongs to the group Dn.

20. A molecule with a Mirror plane perpendicular to a C n axis, and with n twofold axes in the plane, belongs to the group D nh.

25. 1. Given a molecule, you should be able to identify the different symmetry elements (C n,  v,  h,  d,i,S n, etc. ) 2. Having identified the symmetry elements of a molecule, you should be able to establish the point group to which the molecule belong