Symmetry and Group Theory

Question 1

What does the symbol Cn mean?

Answer 1

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

Question 2

What is C1?

Answer 2

E - the indentity - everything has this

Question 3

What directions are rotations?

Answer 3

Clockwise

Question 4

What is the principal axis?

Answer 4

The axis of the highest rotational symmetry

Question 5

What is the coincident of a C4 axis?

Answer 5

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

Question 6

What is an improper operation?

Answer 6

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.

Question 7

What is S1?

Answer 7

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

Represented by σ

Question 8

What is σv?

Answer 8

the vertical reflection

contains principal axis

Question 9

What is σd?

Answer 9

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

Contains Principal axis

Question 10

What is σh?

Answer 10

The horizontal reflection (PERPENDICULAR to principal axis)

Question 11

What is coincident of a C6 axis?

Answer 11

A C2 and a C3

Question 12

What is S2?

Answer 12

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

Also known as an inversion (i)

Question 13

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

Answer 13

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.

Question 14

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

Answer 14

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

If no inversion centre, no orbitals are g or u

Question 15

What is ungerade?

Answer 15

Charge inverts

Question 16

What is gerade?

Answer 16

Charge retained

Question 17

What is an S4 operation?

Answer 17

Rotation of 90 followed by reflection in the perpendicular axis

Question 18

How do you find the point group?

Answer 18

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

Question 19

What is a point group?

Answer 19

A group of symmetry operations which form a closed set

Question 20

What is a closed set?

Answer 20

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

Question 21

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

Answer 21

A proper operation

Question 22

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

Answer 22

A proper operation

Question 23

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

Answer 23

An improper operation

Question 24

Where can you find the point groups?

Answer 24

In the data book

Question 25

Where can you find the flow chart for point groups?

Answer 25

in the data book

Question 26

Are chiral objects symmetrical?

Answer 26

No they are dissymetric, the chiral carbon is asymmeric

Question 27

Can chiral objects have improper operations?

Answer 27

NO, only proper operations

Question 28

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

Answer 28

Draw a 3D axis with x y and z

Question 29

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

Answer 29

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

Question 30

What does an irreducible representation describe?

Answer 30

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

Question 31

What is an E irreducible?

Answer 31

A doubly degenerate irreducible Represents a pair of properties that are symmetry indistinguishable

Question 32

What does the label A mean ?

Answer 32

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

Question 33

What does the label B mean?

Answer 33

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

Question 34

What does the label T mean?

Answer 34

Triply degenerate

Question 35

What is C2’ mean?

Answer 35

Perpendicular to the principal axis

Question 36

What does subscipt 1 mean

Answer 36

The property is symmetric under C2’

Question 37

What does subscript 2 mean<

Answer 37

Antisymmetric under C2’

Question 38

What does superscript ‘ mean?

Answer 38

Symmetric under σh No inversion centre

Question 39

What does superscript ‘’ mean?

Answer 39

unsymmetric under σh No inversion centre

Question 40

What does subscript g mean?

Answer 40

symmetric under i (inversion)

Question 41

What does subscript u mean?

Answer 41

unsymmetric under i (inversion)

Question 42

What is a degenerate property?

Answer 42

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

Question 43

What is the trace?

Answer 43

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

Question 44

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

Answer 44

data book - answer will always be an integer

Question 45

What is LCAO?

Answer 45

Linear Combination of Atomic Orbitals

Question 46

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

Answer 46

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

Question 47

Can atomic orbitals of DIFFERENT symmetries overlap?

Answer 47

NO

Question 48

What does + mean in an LCAO symmetric representatin?

Answer 48

IN phase with

Question 49

What does - mean in LCAO symmetric representation?

Answer 49

Out of phase with

Question 50

what can mix on a molecular orbital diagram?

Answer 50

Orbitals of the same symmetry

Question 51

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

Answer 51

The highest electronegative atom is lower

Question 52

What is the equation for bond order ?

Answer 52

no. of bonding e- - no. of antibonding e- /2. should be the same as the no of bonds