SB Lecture 3 Flashcards
Describe σd mirror plane (Benzene, C6H6)
- Both σv and σ mirror planes can be collinear with the principal axis…
- BUT it is only possible to have a dihedral mirror plane in a molecule in which EITHER the principal axis Cn
OR an improper rotation axis Sn is 3-fold or larger (n ≥ 3)
- In a molecule that has both σv and an σd mirror planes, the σv planes bisect as many atoms as possible and the σd planes bisect as many bonds as possible.
What are the σd mirror plane rules?
- Some molecules only have σd planes
- These are molecules in which there is an S2n improper rotation collinear with a unique principal Cn axis
- Molecules belonging to the point group Dnd have only σd planes.
- Molecules belonging to the point group Oh have σh & σd planes.
- Molecules belonging to the point group Td have only σd planes.
- σd planes are possible in molecules with multiple principal axes; but if there is a unique principal axis, the σd planes are always collinear this axis.
- NOTE: σv planes do NOT exist in molecules with more than one principal axis. (e.g., Oh and Td)
What is an improper rotation?
Give examples
Improper rotation, Sn (an axis, a line)
An improper rotation consists of a rotation followed by a reflection in the plane perpendicular to the rotation axis.
Methane, CH4: S4
Note: Neither C4 nor the σ perpendicular is a symmetry operator of methane but their product C4 x σ perp is (i.e., S4)
What is S1?
What is S2?
S1= reflection - its just a reflection (mirror plane)
S2 = i - isn’t an S2 its an inversion
What is inversion center, i?
Give an example.
- A center of inversion is a point in the middle of the molecule (object). If you take each atom and move it through that point from its original position to the same distance on the other side of the center of inversion, the molecule appears unchanged.
- Hexafluoroantimonate SbF6- : i
- Tetrahedral molecules do not have an inversion factor
- Water does not have a center of inversion
- Must appear unchanged in space, push atoms through the center and swap them. If there’s nothing there; no center of inversion
What are the point groups?
- Whether or not a molecule has all or some of these symmetry elements can easily be classified by assigning a label.
- This label identifies the POINT GROUP of the molecule.
- Common point groups:
- C2v (which describes water, H2O)
- C3v (which describes ammonia, NH3)
- Td (tetrahedral, which describes methane CH4)
- D2h (which describes ethylene, H2CCH2)
- Oh (octahedral, which describes sulfur hexafluoride, SF6)
Decision Tree For Assigning Point Groups
For knowledge
Summary of the truth table:
How many linear groups are there?
What happens if there are multiple Cn axes where n > 2
What is the difference between D & C
For D groups…