sym 4

Question 1

point group examples and their meanings

Answer 1

C2v: principal axis is the only rotational axis,, order of principal axis =2,, 2 vertical mirror planes so v (no horizontal plane)

D3h: principal axis is not the only axis,, order of principal axis = 3,, there is a horizontal plane of symmetry.

aswer the flow chart questions to see which point group its in

Question 2

what can u get from the point group

Answer 2

u get a lovely little chart.

this chart is super helpful and gives u all the operations of that point group as characters and its written at the top,, like the title

Question 3

point groups focus on the effect of symmetry operations onnnn

Answer 3

the position of the atom

Question 4

what else do we need to think about when symmetry operations occur

Answer 4

the position of the atom
any changes in the atomic orbital!!

Question 5

same set of symmetry operations means they will be in the sameee

Answer 5

point group

Question 6

if the operation changes the s/p orbital we give it the number

Answer 6

-1,, bc we inverted the phase of the orbital

Question 7

if the operation doesnt change the orbital ,, we give it the number

Answer 7

1 bc it stayed the same

Question 8

the s orbital remains unchanged and we therefore call it

Answer 8

A1

A 1 for only 1,, aka bc no operation chnages the orbital orientation. the orbitals dont get reversed.

Question 9

orbital is reversed by the operation,, we give it the number

Answer 9

-1

Question 9

orbital remains unchanged after the operation,, we give it the number

Answer 9

1

Question 10

characters of the operation areee

Answer 10

the numbers that show if the orbital was unaffected or reversed

-1/1

Question 11

the set of characters in the rows of the tables are

Answer 11

representations
the things going down on the lhs

Question 12

px follows what representation

Answer 12

B1

Question 13

py follows what representation

Answer 13

B2

Question 14

pz follows what representation

Answer 14

A1

Question 15

A2 is the representation of which orbital

Answer 15

the dxy orbital

think of a 4 petal flower

Question 16

when we think of dxy what should be think about

Answer 16

think a 4 petal flower

and think that we are looking down the Cn main axis!! so like birds eye view

Question 17

dxy is a function!! its the product of what?? and what does this mean

Answer 17

x and y

if X follows B1
and Y follows B2
and Z follows A1

the direct product can help us get the xy representation

so u do B1 x B2,, the characters// numbers.

B1 x B2 gives A2.

Question 18

top left of the table

Answer 18

point group symbol

Question 19

top bit of the table

Answer 19

classes

Question 20

h of the group =

Answer 20

total number of unique operations!!

u just add the amount of classes u have including the big number

Question 21

left row of the table

Answer 21

irreducible representations
symmetry labels for each row of characters in the table.

Question 22

why is E = 2

Answer 22

it refers to doubly degenerate objects.

it means that 2 vibrations have the same frequency.

it also means that 2 orbitals have the same energy.

Question 23

characters in the table

Answer 23

these are the numbers

how objects in the irreducible representations are transformed by the operation in each class.

Question 24

table hasss

Answer 24

point group

irreducable representations

classes

characters (-1/ 1)

Question 25

xyz indicate
R indicates
products : x2, xy etc

Answer 25

XYZ indicate:
transiton dipole moments
that its IR active
symmetry of p orbitals.

R indicates: rotation around that axiss - its microwave spec active.

products: raman spec // d orbitals

Question 26

if ‘operation b’ x ‘operation m’ is the same as operation ‘g’ what does this mean

Answer 26

that their characters should also multiply to give the same type vibe.

aka 1 x 1 = 1

Question 27

multiplication table: anything multiplied by E gives

Answer 27

the original thing.

Question 28

when finding the product of operations,, what should be do

Answer 28

draw it out and do one after the other and see which operation can be used to get from the beginning to now 💗

sounds hard but youve got it.
remmeber that u should read right to left.

Question 29

if we use the axis system,, what does this mean

Answer 29

the principal = z
and then a cross made up of x and y

when we rotate by doing Cn,, we move the xx and yy to give
x-> -y
and y-> -x

we can uses matrixes and [ x] -> [ -y] to show what happened after the transformation.

we do this bc using the character multiplication table loses some info. if 2 operations are -1,, we cant tell which one the product refers to .

Question 30

matrix multiplication numbers meaning

Answer 30

-1 = reversed vector
0 = changed to someplace else
1 = unchanged vector

Question 30

x’ y’ z’ meansss

Answer 30

the new version

Question 31

x y z means

Answer 31

old version

Question 32

how do we set the matrix up to multiply

Answer 32

|x’| |0 -1 0 | |x|
|y’| = |1 0 0 | |y|
|z’| |0 0 1 | |z|

u go across then down
new x (x’) = -y (reverse y)
new y (y’) = x (old x)
new z (z’) = z (old z)

Question 33

characters

Answer 33

numbers that show how orbitals // vibrations respond to an operation.

1 = no change
-1 = reverse
0 = change

the amount of original orbital still present after the operation.

Question 34

basis means

Answer 34

set of orbitals// vibrations or other molecular properties used to understand what happens when a symmetry operation is used

Question 35

h =

Answer 35

sum of headings (make sure u include the big number in front of them)

Question 36

matric representation

Answer 36

complex representation of an operation which describes the result of the operation for several members of the basis together.

the numbers = the characters for the operation

Question 37

in the matrix representation,, what do the characters mean

Answer 37

0 = moved
1 = not moved

matrix goes: x, y, z

if for the y’ (new y) there is a 1 in the ‘x’ column,, y’ = x

if for the x’ (new x) column,, there is a -1 in the y column,, x’ = -y