sym 3

Question 1

when is the symmetry plane given sigma h

Answer 1

when its perpendicular to the principal axis.

Question 1

when does a symmetry point group occur

Answer 1

when molecules can undergo the exact set of operations

aka they all only undergo the same 5 operations

Question 2

what must apply for a set of operations to form a proper group

Answer 2

• make sure the group is closed aka u cannot genberate a new symmetry operation by combining ones in the group,, if u combine operations, the result must also be in the group.
• u must remember to write the identity operation as all objects have one!! E
• every memeber // operation of the group must also have an inverse operation that gives u E. aka NH3: C1/3 inverse is C2/3 as them added gives C3/3 which is E.

Question 3

inverse operation of sigmav

Answer 3

sigma v

bc doing it twice gets u back to E

Question 4

inverse of C1/3

Answer 4

C2/3

bc doing both of them gets u back to E.

Question 5

how to check the group is closed

Answer 5

make sure the product of 2 operations gives the same result as a single operator from the group.

lecture 3 slide 5

Question 6

when do operations commute with one another

Answer 6

when the pair can be carried out in any order

Question 7

when doing all the operations,, what should u include on the atoms to see how theyre changing

Answer 7

number the atoms if theyre the same but also draw an arrow perpendicular to the plane of the molecule to see how it changes with rotations and mirrors etc.

Question 8

where do u draw sigma d’s

Answer 8

between C2s!!

Question 9

do all operations commute aka can all operations be done in any order and give the same result

Answer 9

nope!! some operations just dont commute and wont give us the same final orientation.

Question 10

point group shorthand notation: belonging in the C2v group explanation

Answer 10

C: only one axis present
2: principal axis has an order of 2
V: there are 2 vertical planes of symmetry

Question 11

point group shorthand notation: C3v group explanation

Answer 11

C: principal axis is the only axis
3: the order of the principal axis = 3
V = there are 3 vertical planes of symmetry.

Question 12

sigma h

Answer 12

has no z character
look for principal axis!!!

Question 13

sigma v’

Answer 13

has z character
look for principal axis

Question 14

point group subscript D3h explanation

Answer 14

D: there are multiple rotational axis present,, not just the principal axis

3: order of the principal axis

h: bc it has a horizontal plane of symmetry.

Question 15

subscript d is used whennn

Answer 15

there are only dihedral planes,, no vertical ones

Question 16

what is the idea of point group theory

Answer 16

every molecule will conform to one of the point groups that help describe their symmetry properties

C2v D3h etccc

Question 17

example of point groups

Answer 17

C2v D3h D3d

these are important and we should assign a molecule to these to help us with group theory problems

Question 18

closed point group meaning

Answer 18

that the product of any 2 operations will equal another single operation in the group,, if the group is closed.

Question 19

sub group meaning

Answer 19

complex groups have subgroups of operations.

D3 is the rotational subgroup of D3h and D3d.

theyre just easier to work with.

Question 20

product of 2 operations meaning

Answer 20

doing one operation after another.

sigmav C2 means do a C2 rotation and then reflect in the sigma v plane!!!

bc theyre written the wrong way around.

Question 21

commute

Answer 21

when the product of operations depends on the order of operations!!

they are said to commute when the order doesnt matter.

if the order does matter they dont commute.