sym 4 /5 Flashcards
point group examples and their meanings
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
what can u get from the point group
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
point groups focus on the effect of symmetry operations onnnn
the position of the atom
what else do we need to think about when symmetry operations occur
the position of the atom
any changes in the atomic orbital!!
if a molecule has the same set of symmetry operations,, it means they will be in the sameee
point group
if the operation changes the s/p orbital we give it the number
-1,, bc we inverted the phase of the orbital
if the operation doesnt change the orbital ,, we give it the number
1 bc it stayed the same
the s orbital remains unchanged and we therefore call it
A1
A 1 for only 1,, aka bc no operation chnages the orbital orientation. the orbitals dont get reversed.
orbital is reversed by the operation,, we give it the number
-1
orbital remains unchanged after the operation,, we give it the number
1
characters of the operation areee
the numbers that show if the orbital was unaffected or reversed
-1/1
the set of characters in the rows of the tables are
representations
the things going down on the lhs
px follows what representation
B1
py follows what representation
B2
pz follows what representation
A1
A2 is the representation of which orbital
the dxy orbital
think of a 4 petal flower
when we think of dxy what should be think about
think a 4 petal flower
and think that we are looking down the Cn main axis!! so like birds eye view
dxy is a function!! its the product of what?? and what does this mean
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.
top left of the table
point group symbol
top bit of the table
classes
h of the group =
total number of unique operations!!
u just add the amount of classes u have including the big number
left row of the table
irreducible representations
symmetry labels for each row of characters in the table.
why is E = 2
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.
characters in the table
these are the numbers
how objects in the irreducible representations are transformed by the operation in each class.
table hasss
point group
irreducable representations
classes
characters (-1/ 1)
xyz indicate
R indicates
products : x2, xy etc
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
if ‘operation b’ x ‘operation m’ is the same as operation ‘g’ what does this mean
that their characters should also multiply to give the same type vibe.
aka 1 x 1 = 1
multiplication table: anything multiplied by E gives
the original thing.
when finding the product of operations,, what should be do
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.
if we use the axis system,, what does this mean
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 .
matrix multiplication numbers meaning
-1 = reversed vector
0 = changed to someplace else
1 = unchanged vector
x’ y’ z’ meansss
the new version
x y z means
old version
how do we set the matrix up to multiply
|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)
characters
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.
basis means
set of orbitals// vibrations or other molecular properties used to understand what happens when a symmetry operation is used
h =
sum of headings (make sure u include the big number in front of them)
matric representation
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
in the matrix representation,, what do the characters mean
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
note down all the symmegtry operations for BF3 - and its point group symbol. then describe why the operations have the stoichiometry they have
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.
odd number of S
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
even number of S
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
D3 is like a subgroup of what
subgroup of D3h and D3d
D3 is in both of them
in a newman projection the C2 and sigma d are where
the C2 are between the Hs // groups
and the sigma d are on the H’s // groups
if the pointgroup has a small d,, aka D3 d ,, what does that usually tell us
thats the molecule is in a staggered position
if smt is octahedral,, what does this mean
that the thing has 6 bonds, but all the bonds have the same distance.
if smt is tetrahedral,, what does this mea n
they have 4 bonds
and the bond lengths are identical
tip for seeing if smt is octagedral or tetrahedral
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.
how do we find the point group of a molecule and alllllll its symmetry operations
- 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!!!
when will there be an S6 operation
if u have a sigma h
and a C6 axis
when will u have an S3 operation
when u have a sigma h
and a C3 axis
when will the S operation be seen
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)
sigma d’s are always
between C2 axis
okay wait how can we tell which orbital on our molecule corresponds to the A1 A2 B1 B2 etc orbitals on the character tables.
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.
z axis
= up and down
y axis
left and right
x axis
in and out
in character tales: what does R mean
rotation around that axis:
shows what irriducible rep is microwave // rotational spec active
in character tables: what does x, y , z mean
its the symmetry of the p orbital
shows transition dipole moments.
tells us what is IR active
in character tables: what do products: (x^2, xy etc) mean
tells us what is raman active // symmetry of d orbitals
dxy has the same characters as what
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
when we have C3 as a principal,, why does the character table usually have 2C3 written
bc theres C1/3, C2/3 and C3/3
and C3/3 = E
so theres 2 unique C3 operations.
thats why we write 2C3
h =
total number of unique operations in a point group.
u add all the numbers of the operations up,, not the characters.
whats on the lhs of a character table .. under the point group
these are irreducible representations,, they cant be made any smaller
(x,y) meaning in character table + what we do about it
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.
okay so how do we find out what the character means for the Cn rotation when we have (x,y)
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
how can we tell a group is closed with characters + what is the problem with multiplying characters.
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
