sym 5

Question 1

in the D4h,, operations mix x and y but leave z

Answer 1

independent

so we can do a seperate x and y matrix,, and treat them separately to the z matrix

bc z’ normally = z bc its the principal so rotating it kinda just makes it stay in its place.

for D4h

Question 2

so by splitting the xy from the z matrix we go from a 3x3 matrix to a

Answer 2

2x2 + 1x1 matrix

2x2 being xy
1x1 being z

for D4h

Question 3

3x3 matrix can be simplified due to z’ being z,, and so it called a

Answer 3

reducible representation

for D4h

Question 4

the 2x2 + 1x1 representation is therefore called the

Answer 4

irreducible representation

bc u cannot simplify the relationship between them any more.

for D4h

Question 5

in Dh4,, the x and y vectors are

Answer 5

degenerate

theyre both in the same chemical environment

operations cause them to interchange

the px and py orbitals have the same energy

a vibration changing the x dipole moment has the same frequerncy as the one changing the y dipole moment

Question 6

Eu meaning

Answer 6

ungerade

inversion // i does reverse the vectors!!!

Question 7

Eg meaning

Answer 7

gerade// inversion // i doesnt change the vectors

Question 8

the x and y orbitals in D4h belong to XXXX bc what

Answer 8

they belong to Eu

an irreducible representation

Eu bc inversion reverses both of them!!

from x –> -x
from y –> -y

Question 9

what do matrixes help us do

Answer 9

they help us realise how much of the original vector is present in the new one

when the character chnages its 0

but then like the one where it says -1 is the new vector.

Question 10

how do we find gamma // r // the reproducible representation

r for reproducible representation

Answer 10

we draw an arrow at each atom around the central atom and see how these chnage with the operation:

for E in ammonia,, its 3,, bc when u do the identity operation all the arrows stay in the same place (they dont change so 1 + 1 + 1 bc theres 3 arrows)

for the 2C3 its 0,, bc they all change,, so 0 + 0 + 0 = 0

for 3sigmav (plane running through each NH bond) when u do it only one think stays the same (the bond ur going through) so u get 0 + 0 + 1 = 1

remmeber if it chnages its 0 and if it doesnt change its 1

Question 11

how to remmeber when we use 0 and when we use 1

Answer 11

1 will stay where it is bc its standing up and straight

0 will roll away bc its curved so it will move

Question 12

how do we know if what weve foun usung ‘r’ is reducble

Answer 12

bc it doesnt match any of the standard irriducible representations

Question 13

group theory and reducible representation exppp

Answer 13

group theory says that any reducible representation can be broken down into a sum of standard irreducible representations

these will give the labels for the representations of the fundamental vibrations we need to predict the lines that should be seen in ir and raman spec.

Question 14

h =

Answer 14

order of the group

total number of operations in the group (add the big numbers of the clases up)

Question 15

what is the gc of a class

Answer 15

the big number of the classss

Question 16

what is the gc of the operation 2C3

Answer 16

the gc would be 2

the large number

Question 17

finding the order of a column,, the order of A1

Answer 17

sum of (gc) (xi ^2)

(u do big number x character^2) + (big number x character^2) across the whole row (each class) then add the numbers together and this gives u the order,, h

Question 18

rows are the

Answer 18

bits on the lhs,, Xi

Question 19

columns are the ones that

Answer 19

fall down,, like groups in a periodic table

C

Question 20

2 different irreducible representations are

Answer 20

orthogonal (at right angles to eachother)

sum of: gc X xi X xj = 0

Question 21

h =

Answer 21

sum of : gc x xi^2

xi = the characters for the irreducible representations

gc = the stoichiometry of the class/column

Question 22

we only square the xi value when

Answer 22

were looking for the order!!

we then multiply this by gc and do this for every one.

Question 23

when making the multiplication matrix,, where do u write the 0s and 1s

Answer 23

u put the 1 where the think moved to

aka u put a 1 in the atoms new position!!

then u put 0 where the atom didnt go

Question 24

what do u do to the matrix characters to get a character

Answer 24

u add them together!!

if the matrix is:
|0 1|
|-1 0|
the character would be
1+(-1) = 0

Question 25

Xi means we need to use the characters in what row

Answer 25

we use the characters in the E irreducible row 💗

Ei

Question 26

Xj means we use characters in which row

Answer 26

the A1 irreducible row

AJ

Question 27

to see if irreducible reps are orthogonal,, what equation do we do and what do we do

Answer 27

we use the sum: gc Xi Xj formula

u should get 0 if theyre orthogonal.

aka u use the big stoichiometry number (gc) X the character for the A1 X character for E

and then add the answers uppp!!!

if theyre orthogonal,, youll get a 0 💗

Question 28

what do we use the reduction formula for

Answer 28

to go from the reproducible rep to the irreducible rep

Question 29

what is the reduction formula

Answer 29

its given in the booklet and in exams

Question 30

what is h

Answer 30

the order

gc X xi^2

remember xi = E

Question 31

what is gc

Answer 31

gc is the large number,, the stoichiometry if the class

Question 32

what is xr

Answer 32

r is gamma

this is where we use the arrows to see if they change (0) or stay the same (1) or are reversed (-1) when the operation its under is done.

Question 33

what is Xi

Answer 33

Xi is the E!!

Question 34

how can x,y,z be split

Answer 34

x,y = doubly degenerate bc they kind just move into each others area!! theyre Eu

z is A2u

it tells u this in the table tho!!

Question 35

when we have r, A2u and Eu,, whats special about them

Answer 35

the irreducible representation characters sum to those for the reducible ones for every class.

r = Eu + A2u

Question 36

for r,, u do the operation for

Answer 36

for every axis

then u see where the x, y and z went etccc

then u see what numbers they give: 1 for no change,, 0 for change,, -1 for reverse

Question 37

what else does it mean when things are ungerade

Answer 37

they reverse when theyre inverted

Question 38

when analysing vibrational modes,, what does the irreducible representations tell us

Answer 38

tell us the symmetry of each fundamental mode,, the table then identifies which modes are Ir and raman active

helps us predict the number of bands seen in spectra for a given set of vibrations.

Question 39

if character tables are square,, this means

Answer 39

the number of irreducible representations = number of classes!!

Question 40

how many operations are there in a 3C2 class

Answer 40

3!!

Question 41

will h and the sum thing always be the same

Answer 41

im guessing nope

bc its 1/h x sum

so i fear not,, or else it would always be 1.

Question 42

when do we do the thing where we add an arrow to the atom

Answer 42

planar molecules!! to see if the arrow changes direction during the operation.