Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

physical - yr2, s1 > sym 4 /5 > Flashcards

sym 4 /5 Flashcards

1
Q

point group examples and their meanings

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

what can u get from the point group

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

point groups focus on the effect of symmetry operations onnnn

A

the position of the atom

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

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

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

if a molecule has the same set of symmetry operations,, it means they will be in the sameee

A

point group

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

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

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

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

A

1 bc it stayed the same

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

the s orbital remains unchanged and we therefore call it

A

A1

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

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

A

-1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

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

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

characters of the operation areee

A

the numbers that show if the orbital was unaffected or reversed

-1/1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

the set of characters in the rows of the tables are

A

representations
the things going down on the lhs

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

px follows what representation

A

B1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

py follows what representation

A

B2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

pz follows what representation

A

A1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

A2 is the representation of which orbital

A

the dxy orbital

think of a 4 petal flower

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

when we think of dxy what should be think about

A

think a 4 petal flower

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

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

A

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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

top left of the table

A

point group symbol

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

top bit of the table

A

classes

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

h of the group =

A

total number of unique operations!!

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

left row of the table

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

why is E = 2

A

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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

characters in the table

A

these are the numbers

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

table hasss

A

point group

irreducable representations

classes

characters (-1/ 1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

xyz indicate
R indicates
products : x2, xy etc

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

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

A

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

aka 1 x 1 = 1

27
Q

multiplication table: anything multiplied by E gives

A

the original thing.

28
Q

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

A

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.

29
Q

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

A

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 .

30
Q

matrix multiplication numbers meaning

A

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

30
Q

x’ y’ z’ meansss

A

the new version

31
Q

x y z means

A

old version

32
Q

how do we set the matrix up to multiply

A

|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)

33
Q

characters

A

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.

34
Q

basis means

A

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

35
Q

h =

A

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

36
Q

matric representation

A

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

37
Q

in the matrix representation,, what do the characters mean

A

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

38
Q

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

A

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.

39
Q

odd number of S

A

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

40
Q

even number of S

A

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

41
Q

D3 is like a subgroup of what

A

subgroup of D3h and D3d

D3 is in both of them

42
Q

in a newman projection the C2 and sigma d are where

A

the C2 are between the Hs // groups

and the sigma d are on the H’s // groups

43
Q

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

A

thats the molecule is in a staggered position

44
Q

if smt is octahedral,, what does this mean

A

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

45
Q

if smt is tetrahedral,, what does this mea n

A

they have 4 bonds

and the bond lengths are identical

46
Q

tip for seeing if smt is octagedral or tetrahedral

A

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.

47
Q

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

A
  • 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!!!
48
Q

when will there be an S6 operation

A

if u have a sigma h
and a C6 axis

49
Q

when will u have an S3 operation

A

when u have a sigma h
and a C3 axis

50
Q

when will the S operation be seen

A

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)

51
Q

sigma d’s are always

A

between C2 axis

52
Q

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

A

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.

53
Q

z axis

A

= up and down

54
Q

y axis

A

left and right

55
Q

x axis

A

in and out

56
Q

in character tales: what does R mean

A

rotation around that axis:

shows what irriducible rep is microwave // rotational spec active

57
Q

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

A

its the symmetry of the p orbital

shows transition dipole moments.

tells us what is IR active

58
Q

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

A

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

59
Q

dxy has the same characters as what

A

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

60
Q

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

A

bc theres C1/3, C2/3 and C3/3

and C3/3 = E

so theres 2 unique C3 operations.

thats why we write 2C3

61
Q

h =

A

total number of unique operations in a point group.

u add all the numbers of the operations up,, not the characters.

62
Q

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

A

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

63
Q

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

A

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.

64
Q

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

A

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

65
Q

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

A

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

physical - yr2, s1 (17 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions