Chapter 4

Question 1

E

Answer 1

Identity; unchanged molecule

Question 2

Cn

Answer 2

n-fold rotation; C2=180º, C3=120º (Cn has to be perpendicular to the other Cn in the molecule)

Question 3

Sn

Answer 3

n-fold rotation-reflection (360º/n); perpendicular to rotation axis

Question 4

sigma

Answer 4

planes

Question 5

i

Answer 5

inversion center

Question 6

What is the difference between a C2 and a C3?

Answer 6

A C2 is parallel to the plane (z-axis) while a C3 is perpendicular to it (goes through; x or y axis)

Question 7

The C2v group is closed.

Answer 7

True

Question 8

What makes a group Abelian?

Answer 8

When two operators commute (AC=CA)

Question 9

Multiplying an operator by the identity gives:

Answer 9

The operator (AE=EA=A)

Question 10

Group D3 is Non-Abelian.

Answer 10

True

Question 11

Associative operations are done right to left.

Answer 11

True (C2 sigmav) sigmav’ = C2(sigmav sigmav’)

Question 12

What are the ways to find the order of the group, h?

Answer 12

1. Adding the squares of the values in the first column (E)
2. Adding the coefficients of the operators at the top
3. Multiplying the coefficient times the square value of any row (just has to be that same row consistently) and adding them up.

Question 13

The number of irreducible representations is the same as the number of classes.

Answer 13

True

Question 14

How can you tell if two representations are orthogonal?

Answer 14

You multiply the two values, then multiply the result by the coefficient of the column, and add each of them up. You should get a zero.

Question 15

What are the rules for reducible representations?

Answer 15

1. If the AO is unchanged, you have a +1
2. If the AO changes position in space, you have a 0
3. If the AO changes position but doesn’t move in space, you have a -1

Question 16

How do you find which representations are used in the reducible representations?

Answer 16

You multiply every value by the reducible value corresponding to that column, and then multiply by the coefficient of that column. Then you add up the answers per row and divide each by the group order.
*Remember: the number of representations involved must add up to the reducible value. If it’s a 4 and you found out that the ones involved are A1 and T2 then you know that it’s 1A1 and 3T2 (there can only be one A1 because it’s perfectly symmetrical).

Therefore, if you can apply the orbitals relative to each representation you can find the hybridization. In this case A1 is s and T2 is p, so you can sp3.

Question 17

You need a Cn or an Sn with n equal or greater than 4 to have a sigma-d.

Answer 17

True
(It is pretty much the same as sigma-v planes – Difference is that sigma-v ‘slices’ atoms and sigma-d is in between atoms)

Question 18

There are two types of s orbitals in water from the hydrogen, the symmetric (from A1) and the antisymmetric (from B1)

Answer 18

True

1s + 1s and 1s - 1s respectively.

Question 19

Besides the 1s orbital in oxygen, which other orbital binds to the hydrogen?

Answer 19

The pz orbital because we find that it also has an A1 symmetry.