1. Reflectional Symmetry (Bilateral Symmetry) The mirror line runs from the tip of the head to the toes. The human body does not have perfect symmetry ( internal organs)

2. More examples Top: tree of life Bottom: waterbuffalo

3. Asymmetric molecules are denoted as L- and R-forms L-amino-acids and R-sugars in life forms Antibiotics (contain R-amino-acids) Artificial sweetners? (use L-sugars) Phenylketonuria: metabolic disease caused by ingestion of the wrong type of phenyl- alanine. Bonding of enzymes to proteins.

4. Rotational Symmetry Record the highest degree rotational symmetry. Both examples have 5- fold rotational symmetry.

5. Chemistry How do we know what molecules look like, and what properties they have? DNA helix Alzheimer and Prion diseases caused by incorrectly folded molecules? Plaque formation in AD and gingivitis.

6. Laue X-rays Determine the crystallographic structure using X-rays

7. Symmetry groups in two dimensions We record the symmetries for a geometric shape. E (the existence of the rectangle) Reflection over a vertical line: M1 Reflections over a horizontal line: M2 2-fold rotation R G={E,M1,M2,R}

8. Classifying the groups If there is reflectional symmetry -> D If there is no reflectional symmetry -> C Record the largest possible degree of rotational symmetry. For the rectangle we get: D2

9. Identifying symmetry groups What is the symmetry group for the geranium? What is the symmetry group for the celtic knot?

10. Groups and subgroups A group is a collection of objects which has the property that any combination of the elements will give you another element of the group. Some groups contain smaller units, the so called subgroups. For example {E,R} in the symmetry group for the rectangle.

11. Three dimensional shapes Here are 2 water molecules. H 2 O How do we know water molecules look like this? Is the geometric structure of molecules important?

13. Two questions How do we know what these molecules look like? What information do we get from the geometric structure of molecules?

14. Geometric structure of molecules “ Detective work”: General knowledge Optical properties Laue X-Rays Spectroscopy (microwave, laser, photoelectric)

15. 3-D symmetry groups Find rotation. Axis of rotation is called the vertical axis. Water has a C 2V symmetry group [there are no C 2 axes perp. to axis of rotation, hence a C group and not D. There is 2-fold rotation, and there are vertical mirror planes.]

16. Benzene = (CH) 6 6-fold rotation There are 2 fold rotations perpendicular to the main axis. So the group has to belong to the D 6 - types There is a horizontal reflection, so this is a D 6H

17. Applications Molecular Orbital Theory Transition Theory