sym 4 /5

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

if a molecule has the same set of symmetry operations,, it 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

Question 38

note down all the symmegtry operations for BF3 - and its point group symbol. then describe why the operations have the stoichiometry they have

Answer 38

E 2C3 3C2 sigma h 3 sigma v 2S3 draw out the moelcule including the numbered atoms and the arrow for each of the operations. then see which ones are the same. the number of unique operations = the stoich number bc some operations will give the same result as another. if a S3 operation is equal to a C3 operation, we ignore that S3 operation and take the C3 one into account!!. basically the Cprincipal and the sigmas kinda hold priority, so if a S3 matches one of these, u keep them and say the S3 isnt a unique operation.

Question 39

odd number of S

Answer 39

u dont get the correct orientation back . u get the atoms in the righ place but the arrow will be pointing in the opposite way

Question 40

even number of S

Answer 40

gives u the identical orientation. the atoms and arrow will be in the someplace. do the clap thing with ur hands, do it even and odd and youll clock why

Question 41

D3 is like a subgroup of what

Answer 41

subgroup of D3h and D3d D3 is in both of them

Question 42

in a newman projection the C2 and sigma d are where

Answer 42

the C2 are between the Hs // groups and the sigma d are on the H's // groups

Question 43

if the pointgroup has a small d,, aka D3 d ,, what does that usually tell us

Answer 43

thats the molecule is in a staggered position

Question 44

if smt is octahedral,, what does this mean

Answer 44

that the thing has 6 bonds, but all the bonds have the same distance.

Question 45

if smt is tetrahedral,, what does this mea n

Answer 45

they have 4 bonds and the bond lengths are identical

Question 46

tip for seeing if smt is octagedral or tetrahedral

Answer 46

the thing will have either 6 or 4 bonds but they will be bonded to the same atom.. CH4 = tetrahedral CH3Cl = not tetrahedral bc the bond lengths are different.

Question 47

how do we find the point group of a molecule and alllllll its symmetry operations

Answer 47

- we use the flow chart!! - remember that n for principal axis = n for all the other q's!! - use symmetry otterbein to help with the axis counting etc!! - find the point group - go to the graph + youll have alllll the symmetry operations that molecule should have - remember the big number before the operation = the number of unique operations of that operation!!!

Question 48

when will there be an S6 operation

Answer 48

if u have a sigma h and a C6 axis

Question 49

when will u have an S3 operation

Answer 49

when u have a sigma h and a C3 axis

Question 50

when will the S operation be seen

Answer 50

when u have an axis 'C' and a sigma h the n of the axis = the n of the S C2 = S2 axis! if u also have sigma h (rememeber that sigma h = perpendicular to the principal axis)

Question 51

sigma d's are always

Answer 51

between C2 axis

Question 52

okay wait how can we tell which orbital on our molecule corresponds to the A1 A2 B1 B2 etc orbitals on the character tables.

Answer 52

okay so lets say u have H2O: u can have 3 different p orbitals in ten: py, px, pz. if we draw H2O and label the principal axis as Z,, then y will be the one going left to right. and x will be the one going in and out so the p orbital we have in H2O will be a py orbital. bc its laying on the y axis. no u do all the symmetry operations of that point group and see if it alters the phasing of the orbital we have drawn. 1 for unchanged -1 for reversed. and note these down under the operation. then we look at the point group character table. we know which orbital we have (Y) and we know what characetrs we got for each operation. we then look at the characters for each orbital row (a1, a2, b1, b2 etc) and see which one has the same correspondong character for each operation!!! so in H2O,, Py is a B2 orbital.

Question 53

z axis

Answer 53

= up and down

Question 54

y axis

Answer 54

left and right

Question 55

x axis

Answer 55

in and out

Question 56

in character tales: what does R mean

Answer 56

rotation around that axis: shows what irriducible rep is microwave // rotational spec active

Question 57

in character tables: what does x, y , z mean

Answer 57

its the symmetry of the p orbital shows transition dipole moments. tells us what is IR active

Question 58

in character tables: what do products: (x^2, xy etc) mean

Answer 58

tells us what is raman active // symmetry of d orbitals

Question 59

dxy has the same characters as what

Answer 59

the characters corresponding to the irriducible representation of the px orbital X the irriducible representation characters corresponding to the py orbital. aka in C2v,, px =B1 and py = B2 so dxy = B1 x B2 numbers

Question 60

when we have C3 as a principal,, why does the character table usually have 2C3 written

Answer 60

bc theres C1/3, C2/3 and C3/3 and C3/3 = E so theres 2 unique C3 operations. thats why we write 2C3

Question 61

h =

Answer 61

total number of unique operations in a point group. u add all the numbers of the operations up,, not the characters.

Question 62

whats on the lhs of a character table .. under the point group

Answer 62

these are irreducible representations,, they cant be made any smaller

Question 63

(x,y) meaning in character table + what we do about it

Answer 63

x and y orbitals are interchangable. they have the same energy theyre degenerate they have the same vibrational frequency: bc energy is proportional to freq,, v. that means for the row where theyre doubley degenerate,, the irriducible representation row. u see how each operation effects the px and py orbital individually by drawing it out and giving either a -1, 1 and then u add the x and y values for that operation to give u the correct characters for that row. (x,y) seen, doubly degenerate. how does each operation effect those p orbitals separately. add the characters we found using the effects of the operation and thats ur answerrrr.

Question 64

okay so how do we find out what the character means for the Cn rotation when we have (x,y)

Answer 64

we need to figure out how the rotation effects each of the px and py orbitals separately. so draw them out and do the rotation. the H's // atoms will rotate as normal when u do C1/n etc and continue going and the orbital must have the same relationship to all of the H's each time. so for the px in ammonia, itll be on the bond,, so when u rotate the orbital remains on the bond. the pz in ammonia is perpendicular to one of the H's,, so when we rotate, the orbital must remain that way. the orbitals havent stayed in the same place,, but also havent reversed,, so what character do we assign them? we do cos( the angle we rotated it by) then add them together. the angle we rotated them by can be found by 360/n where n = Cn

Question 65

how can we tell a group is closed with characters + what is the problem with multiplying characters.

Answer 65

multiplying the characters together will give u the character of the product!! aka 1x1 = 1 but sometimes its hard to differentiate what product it is based on characters,, bc different operations can have the same character