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Core 4b > Symmetry and Group Theory > Flashcards

Symmetry and Group Theory Flashcards

1
Q

What does the symbol Cn mean?

A

A rotational axis of order n, where a rotation of 360/n leaves the object unchanged

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2
Q

What is C1?

A

E - the indentity - everything has this

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3
Q

What directions are rotations?

A

Clockwise

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4
Q

What is the principal axis?

A

The axis of the highest rotational symmetry

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5
Q

What is the coincident of a C4 axis?

A

A C2 axis (if it has a C4 it has a C2)

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6
Q

What is an improper operation?

A

An operation that you cannot physically perform

Represented by Sn

It is a rotation of Cn, followed by a reflection in the plane PERPENDICULAR to that Cn axis.

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7
Q

What is S1?

A

A rotation of 360 followed by a reflection - so just a reflection

Represented by σ

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8
Q

What is σv?

A

the vertical reflection

contains principal axis

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9
Q

What is σd?

A

The dihedral reflection, bisects 2 C2 axes (C2, C2’)

Contains Principal axis

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10
Q

What is σh?

A

The horizontal reflection (PERPENDICULAR to principal axis)

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11
Q

What is coincident of a C6 axis?

A

A C2 and a C3

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12
Q

What is S2?

A

A rotation of 180, and a reflection in the perpendicular plane

Also known as an inversion (i)

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13
Q

How do you check if the centre of an object is an inversion centre?

A

Take each point of the object through the inversion centre to the equivalent point on the other side, and if the object remains unchanged, there is an inversion centre.

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14
Q

What is the relation of gerade and ungerade have to do with inversion centres?

A

When an object has an inversion centre, orbitals can be labelled g or u,

If no inversion centre, no orbitals are g or u

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15
Q

What is ungerade?

A

Charge inverts

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16
Q

What is gerade?

A

Charge retained

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17
Q

What is an S4 operation?

A

Rotation of 90 followed by reflection in the perpendicular axis

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18
Q

How do you find the point group?

A

Find all the symmetry elements of the object, determine the number of proper vs improper operations.

They should be the same, if the object has both proper + improper operations

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19
Q

What is a point group?

A

A group of symmetry operations which form a closed set

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20
Q

What is a closed set?

A

A set of symmetry operations such that successive applications of the operations is equivalent to another operation which is also a property of the object

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21
Q

What does a proper operation followed by a proper operation give?

A

A proper operation

22
Q

What does an improper operation followed by an improper operation give?

A

A proper operation

23
Q

What does an improper operation followed by a proper operation (and vice versa)?

A

An improper operation

24
Q

Where can you find the point groups?

A

In the data book

25
Q

Where can you find the flow chart for point groups?

A

in the data book

26
Q

Are chiral objects symmetrical?

A

No they are dissymetric, the chiral carbon is asymmeric

27
Q

Can chiral objects have improper operations?

A

NO, only proper operations

28
Q

How can you determine what the mirror plane means (e.g. xz, yz)?

A

Draw a 3D axis with x y and z

29
Q

In a character table for a point group what do the 2 far right column show?

A

1st - The p oribitals and the rotations
2nd - d orbitals

30
Q

What does an irreducible representation describe?

A

The symmetry of a particular property of the point group of intererest

31
Q

What is an E irreducible?

A

A doubly degenerate irreducible

Represents a pair of properties that are symmetry indistinguishable

32
Q

What does the label A mean ?

A

Singly degenerate and totally symmetric (1) about the principle axis

33
Q

What does the label B mean?

A

Singly degenerate and antisymmetric (-1) about the principle axis

34
Q

What does the label T mean?

A

Triply degenerate

35
Q

What is C2’ mean?

A

Perpendicular to the principal axis

36
Q

What does subscipt 1 mean

A

The property is symmetric under C2’

37
Q

What does subscript 2 mean<

A

Antisymmetric under C2’

38
Q

What does superscript ‘ mean?

A

Symmetric under σh

No inversion centre

39
Q

What does superscript ‘’ mean?

A

unsymmetric under σh

No inversion centre

40
Q

What does subscript g mean?

A

symmetric under i (inversion)

41
Q

What does subscript u mean?

A

unsymmetric under i (inversion)

42
Q

What is a degenerate property?

A

When two group properties (can be orbitals) are interconverted by a symmetry element in the point group, they are regarded as degenerate and must be treated together

43
Q

What is the trace?

A

the diagonal of a matrix, can give the eigen value (add it up)

44
Q

where can u find the formula for the reducible representations? and what will your answer be?

A

data book - answer will always be an integer

45
Q

What is LCAO?

A

Linear Combination of Atomic Orbitals

46
Q

What do you need to do for an LCAO (linear combination of atomic orbitals) ?

A

Determine symmetry of orbitals on central atom and on the ligated groups

47
Q

Can atomic orbitals of DIFFERENT symmetries overlap?

A

NO

48
Q

What does + mean in an LCAO symmetric representatin?

A

IN phase with

49
Q

What does - mean in LCAO symmetric representation?

A

Out of phase with

50
Q

what can mix on a molecular orbital diagram?

A

Orbitals of the same symmetry

51
Q

How do you know which MO atom shoukd be lower on the diagram?

A

The highest electronegative atom is lower

52
Q

What is the equation for bond order ?

A

no. of bonding e- - no. of antibonding e- /2.

should be the same as the no of bonds

Core 4b (4 decks)

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