Character Table COPY Flashcards

1
Q

“Mulliken Symbol​”

Meaning: Designates symmetry with respect to inversion center

A

Gerade (symmetric)

Ungerade (Antisymmetric)

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2
Q

“Mulliken Symbol​”

In D Point Groups:

Meaning: Designate symmetry with respect to ⊥C2​

A

Subscript 1 (Symmetric)

Subscript 2 (Antisymmetric)

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3
Q

“Mulliken Symbol​”

In C Point Groups:

Meaning: Designate symmetry with respect to σ<span>v</span>

A

Subscript 1 (Symmetric)

Subscript 2 (Antisymmetric)

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4
Q

Properties of Multiplication Tables

A symmetric multiplication table of a finite group implies the group is _____.

A

An Abelian Group

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5
Q

Properties of Multiplication Tables

Every row and column contains each element exactly once.

True or False

A

True

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6
Q

A group whose elements are all members of another higher order group, both being subject to the same operations.

A

Subgroup

(Practical use: Building correlation diagrams)

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7
Q

Properties of the Character Table

The square of any irreducible representation will include the_____.

A

Totally symmetric irreducible representation

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8
Q

Around the Character Table

Identify the highlighted property of the character table below.

A

Totally symmetric irreducible representation

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9
Q

Around the Character Table

Identify the highlighted property of the character table below.

A

Mulliken Notation

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10
Q

Around the Character Table

Identify the highlighted property of the character table below.

A

Dimensions

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11
Q

Around the Character Table

What is the symmetry of a rotation along the x-axis in a D3h symmetric molecule?

A

E’‘

( x and y rotations are degenerate in this case)

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12
Q

The D4h molecule [PtCl4]2- has a b1g bending mode:

Applying the the project operator for b1g yields with θ1 as the basis:

Pb1g1)=N(θ1 + θ3- θ2 - θ4)

What does the bending motion look like?

A
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13
Q

The facial isomer of MCl3(CO)3 has Cl streching modes with the irreducible representations of:

Γ​=A1+E

How many Cl streching modes are there in MCl3(CO)3

A

3 Cl streching modes

A1 (1 mode)

E (2 degenerate modes)

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14
Q

What is the subgroup(s) of C3V based on the multiplication table below?

A

C3 (in purple)

Cs (in orange)

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15
Q

To have a subgroup g in a higher order group G, the divisor of the orders must be an integral value (e.g h/g )

True or False

A

True

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16
Q

Use the multiplication table below:

C4x= ?

A

σd

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17
Q

A group whose group operation between two elements does not depend on the order in which they are written.

A

Abelian Group

18
Q

If a multiplication table’s values are symmetric along its diagonal axis, then that is an _______.

A

Abelian Group

19
Q

Around the Character Table

What is the symmetry of the dipole moment along the z-axis in a D3h symmetric molecule?

A

A2’‘

20
Q

Around the Character Table

The highlighted operations are ordered in what way?

A

Classes of Operations

21
Q

Properties of Irreducible Representations

Each irreduible representation is _______ to all other irreducible representation of that group.

A

Orthogonal

22
Q

Properties of Irreducible Representations

The number of irreducible representations of the group equals____.

A

The number of classes in a group

23
Q

The characters of all operations in the same class.

A

Identical

24
Q

Representations that are the combinations of irreducible representations.

A

Reducible Representations

25
Q

A fundamental representation of a operator’s matrix that cannot be reduced further.

A

Irreducible Representations

26
Q

What are the characters of the direct product of

(A1‘)x(A2”) ?

A

{1,1,-1,-1,-1,1}

Therefore, the direct product A2

(Note: Anything direct producted with the symmetric irreducible representation is itself.)

27
Q

What is direct product of

(E”)x(E’) irreducible representations

in the D3h point group?

(Note: Will involve a reduction to a sum of irreducible representations)

A

A1“+A2“+E”

28
Q

What is direct product of

(A2‘)x(A1“)x(A2”) irreducible representations

in the D3h point group?

A

A1

29
Q

Inspect the multiplication table for C3v, is this an Abelian group?

A

Yes

(Symmetric along the diagonal)

30
Q

What is the order of D3h?

A

h=12

31
Q

Total number of symmetry operations in the group

A

Group Order

32
Q

Elements related by a similarity transform_____.

A

belong to the same class of elements

33
Q

A, B, and X are elements of a group. What does the following operation represent?

X*A*X-1= B

A

Similarity Transform

(“ B is the similarity transform of A and X”)

34
Q

“Mulliken Symbol​”

Meaning: Designate symmetry with respect to σh

A

Primes (symmetric)

Double Primes (antisymmetric)

35
Q

“Mulliken Symbol​”

Meaning: Dimension 3

(Triply Degenerate)

A

T

36
Q

“Mulliken Symbol​”

Meaning: Dimension 2

(Doubly Degenerate)

A

E

37
Q

“Mulliken Symbol​”

Meaning: Dimension One

A

A or B

38
Q

Every element of the group must have a reciprocal which is also an element of the group

A*(B*C)=(A*B)*C

A

Reciprocity

39
Q

The result of an expression is independent of the grouping of the terms

A*(B*C)=(A*B)*C

A

Associativity

40
Q

One element of the group must, when multiplied in either direction, leave the other elements unchanged.

A

Identity

41
Q

The product of any two elements of the group or the square any elements, is a member of the group.

A

Closure

42
Q

A collection of elements that obey the following:

Closure

Contains an Idenitiy

Associativity

Reciprocity

A

Group