2. Symmetry Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology

3. 10/13/2015 Symmetry Effects Simplifies the amount of work needed to solve a problem reduces it by a factor of 2, 3 or more.

4. 10/13/2015 Symmetry Effects Symmetric atoms in a molecule are energetically equivalent. - cyclopentadienide ion C 5 H 5 - Simplifies the appearance of spectra (the symmetric bonds absorb energy at identical energies): nmr, ir, etc. Simplifies crystallography (fewer unique atoms have to be located). Simplifies chemistry (symmetric atoms in a molecule react the same way).

5. 10/13/2015 Elements of Symmetry Look at diagrams or models of the following molecules What is symmetric about each? Are they symmetric in the same way? Are some more symmetric than others? H2OH2O HCN HCCH CH 2 Cl 2 NH 3 BF 3 C6H6C6H6 PtCl 4 2-

6. 10/13/2015 Rotational Symmetry O H H How many equivalent positions are there? C2C2 What is the rotational order for each molecule? Rotation about an axis produces two or more equivalent structures. H2OH2O HCN HCCH CH 2 Cl 2 NH 3 BF 3 C6H6C6H6 PtCl 4 2-

7. 10/13/2015 Rotational Symmetry Can a molecule have more than one rotation axis? Rotation about an axis produces two or more equivalent structures. H2OH2O HCN HCCH CH 2 Cl 2 NH 3 BF 3 C6H6C6H6 PtCl 4 2-

8. 10/13/2015 Rotational Symmetry HCCH Can a molecule have more than one rotation axis? Rotation about an axis produces two or more equivalent structures. C6C6 C2C2 C2’C2’ ∞C 2  C∞C∞

9. 10/13/2015 Reflection Symmetry O H H How many mirror planes are there? vv How many mirror planes does each molecule have? A mirror plane reflects one half of a molecule into the other half of the molecule. v’v’ H2OH2O HCN HCCH CH 2 Cl 2 NH 3 BF 3 C6H6C6H6 PtCl 4 2-

10. 10/13/2015 vv Reflection Symmetry How many of each type of mirror plane are there? Are there different kinds of mirror planes? v’v’

11. 10/13/2015 Reflection Symmetry How many mirror planes are there? Are there different kinds of mirror planes? hh Which of these molecules have different types of mirror planes? H2OH2O HCN HCCH CH 2 Cl 2 NH 3 BF 3 C6H6C6H6 PtCl 4 2-

12. 10/13/2015 Alternate Diagram of Atom Positions atom above the plane atom below the plane atom on the plane CH 4 What is the order of the major rotation axis? Where are the mirror planes? Are there C 2  axes?

13. 10/13/2015 Inversion Symmetry Which of these molecules has a center of inversion? Every position in a molecule can pass through the center of the molecule to give an equivalent position. trans-dibromodichlorocuprate(II) ion Cu Cl Br 2- H2OH2O HCN HCCH CH 2 Cl 2 NH 3 BF 3 C6H6C6H6 PtCl 4 2- i

14. 10/13/2015 Improper Rotation Symmetry Rotation about an n-fold (improper axis) followed by reflection through a perpendicular plane gives an equivalent structure. CH 4 S4S4 atom above the plane atom below the plane atom on the plane

15. 10/13/2015 Improper Rotation Symmetry Rotation about an n-fold (improper axis) followed by reflection through a perpendicular plane gives an equivalent structure. C 6 H 12 (chair) S8S8 C 2 H 6 (staggered) What is the order of the improper rotation axis in each of these molecules?

16. Combination of Symmetry Operations The combination of a two-fold rotation followed by a horizontal reflection is equivalent to what symmetry operation? hh C2C2

18. 10/13/2015