Chapter 4 - Symmetry and Group Theory

Question 1

symmetry elements

Answer 1

mirror planes, axes of rotation, inversion centers, etc

Question 2

symmetry opration

Answer 2

the actual reflection/rotation/inversion operation

Question 3

Identity operation

Answer 3

E, no change in molecule

Question 4

Rotation operation

Answer 4

Cn, rotation through 360º/n

Question 5

Reflection operation

Answer 5

σ, reflection through mirror plane

Question 6

Inversion operation

Answer 6

i, each point moves through the center of the molecule to a position opposite the original position and as far from the central point as where it started

Question 7

Rotation-reflection operation

Answer 7

Sn, aka improper rotation: rotation of 360º/n followed by reflection through a plane perpendicular to a axis of rotation

Question 8

E

Answer 8

Identity operation, no change

Question 9

Cn

Answer 9

Rotation operation, 360/nº each time

Question 10

σ

Answer 10

Reflection operation through mirror plane

Question 11

σh

Answer 11

Horizontal reflection operation when the plane is perpendicular to the principal axis of rotation

Question 12

σv/σd

Answer 12

Vertical reflection operation when the plane contains the principal axis of rotation

σ_d: Dihedral passes through fewer atoms (dihedral to the angle of the bonds). Dihedral, same plane as v but related by half a rotation of the principle axis

σ_v: Vertical, parallel to/passing through the principal axis (primary rotation axis)

Question 13

i

Answer 13

Inversion, each point moves through the center of the molecule to a position opposite the original position and as far from the central point as where it started

Question 14

Sn

Answer 14

Rotation-reflection/improper-rotation operation, rotation of 360º/n followed by reflection through a plane perpendicular to a axis of rotation

Question 15

Principal axis

Answer 15

The Cn axis with the largest value of n

Question 16

Point group

Answer 16

a set of symmetry operations that best describes the molecule’s overall symmetry

Question 17

Groups of low symmetry

Answer 17

C₁ - no symmetry other than the identity operation

Cs - only one mirror plane

C_i - only an inversion center

Question 18

Groups of high symmetry

Answer 18

C_∞v - Linear molecule with an infinite number of rotations and an infinte number of reflection planes containing the rotation axis (e.g. H-Cl). Do not have a center of inversion.

D_∞h - Linear molecule with an infinite number of rotations and an infinite number of reflection planes containing the rotation axis.

Question 19

Answer 19

d orbital: z²

Question 20

Answer 20

d orbital x²-y²

Question 21

Answer 21

d_xy

Question 22

Answer 22

d_yz

Question 23

Answer 23

d_xz

Question 24

σ-bond

Answer 24

orbitals are symmetric to rotation about the line connecting the nuclei

no nodes that include the line between nuclei

Question 25

π-bond

Answer 25

a change in sign in the wave function with C₂ rotation about the bond axis

one node including the line between nuclei

Question 26

δ-bond

Answer 26

change in sign on C₄ rotation about the bond axis

two nodes including the line between nuclei

Question 28

Identify rotation axes

Answer 28

Question 29

What is the difference between dihedral and vertical mirror planes?

Answer 29

σ_d: Dihedral passes through fewer atoms (dihedral to the angle of the bonds). Dihedral, same plane as v but related by half a rotation of the principle axis

σ_v: Vertical, parallel to/passing through the principal axis (primary rotation axis)