SB Lecture 3

Question 1

Describe σ_d mirror plane (Benzene, C₆H₆)

Answer 1

• Both σ_v 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 C_n

OR an improper rotation axis S_n is 3-fold or larger (n ≥ 3)

• In a molecule that has both σ_v and an σ_d mirror planes, the σ_v planes bisect as many atoms as possible and the σ_d planes bisect as many bonds as possible.

Question 2

What are the σ_d mirror plane rules?

Answer 2

• Some molecules only have σ_d planes
• These are molecules in which there is an S_2n improper rotation collinear with a unique principal C_n axis
• Molecules belonging to the point group D_nd have only σ_d planes.
• Molecules belonging to the point group O_h have σ_h & σ_d planes.
• Molecules belonging to the point group T_d have only σ_d planes.
• σ_d planes are possible in molecules with multiple principal axes; but if there is a unique principal axis, the σ_d planes are always collinear this axis.
• NOTE: σ_v planes do NOT exist in molecules with more than one principal axis. (e.g., O_h and T_d)

Question 3

What is an improper rotation?

Give examples

Answer 3

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)

Question 4

What is S₁?

What is S₂?

Answer 4

S₁= reflection - its just a reflection (mirror plane)

S₂ = i - isn’t an S₂ its an inversion

Question 5

What is inversion center, i?

Give an example.

Answer 5

• 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 SbF_6^- : 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

Question 6

What are the point groups?

Answer 6

• 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:
  
  • C_2v (which describes water, H₂O)
  • C_3v (which describes ammonia, NH₃)
  • T_d (tetrahedral, which describes methane CH₄)
  • D_2h (which describes ethylene, H₂CCH₂)
  • O_h (octahedral, which describes sulfur hexafluoride, SF₆)

Question 7

Decision Tree For Assigning Point Groups

For knowledge

Answer 7

Question 8

Summary of the truth table:

How many linear groups are there?

What happens if there are multiple C_n axes where n > 2

What is the difference between D & C

For D groups…

Answer 8