Inorg. Exam 1

What is the symbol of the symmetry operation for nothing

E

• In everything

• Also the result of a completed symmetry operation (ex. rotating smth on its C3 axis, 3 times)

What is the symbol of the symmetry operation for horizontal plane

σh

• horizontal mirror plane

• sits perpendicular to molecule’s principal rotation axis

What is the symbol of the symmetry operation for vertical plane

σv

• vertical mirror plane

• contains principle rot. axis

• bisects atoms

What is the symbol of the symmetry operation for dihedral plane

σd

• special type of vertical mirror plane

• contains principle rot. axis

• bisects conjugate C’2 axes (so typically, bisects molecular bonds)

What is the difference between C2 & C’2 axes?

• A C₂ axis is a principal 180° rotational symmetry axis of a molecule

• A C₂' axis is a secondary 180° rotational axis perpendicular to the principal axis

what is the inversion operation?

i

• atoms move through inversion center i (green dot) from (x, y, z) to (-x, -y, -z)

• if result is indistinguishable from initial molecule, inversion exists

what is the proper axis of rotation

Cn

• rotating a molecule 360°/n about a rotation axis of the order n gives an indistinguishable result

How many operations does the C3 axis give and why?

C3 gives 2 unique operations:

• C3 #1 = 120° rot.

• C3 #2 = 240° rot. (looks like 120° “backwards”)

• C3 #3* = 360° rot. (ALL atoms in original spot; nothing happened, so = E)

What is the improper axis of rotation

Sn

• rotate molecule 360°/n on n-order rot. axis, THEN reflect atom over plane ⟂ to rot. axis

• (In image, n = 6)

How many unique operations does S6 have and why?

S6 has 2 unique operations: S6¹ & S6⁵, also known as S6(-1).

S6², S6³, S6⁴, and S6⁶ all correspond to other symmetry operations

How many unique operations does S10 have and why?

S10 has 4 unique operations: S10¹, S10³, S10⁷, and S10⁹

S10², S10⁴, S10⁵, S10⁶, and S10⁸ all correspond to other symmetry operations

Definition of chirality relative to molecular symmetry

• molecules w/o Sn (improper rot. axis)

• C1, Cn, Dn

Where do polar molecules belong, symmetrically?

• Polar molecules can’t have an inversion center

• No polar molecules in D, T, O, or I point groups

Difference between symmetry element and symmetry operation

Element = C₂ axis

Operation = rotating 180° around the axis