Semester 2 Flashcards
(131 cards)
1
Q
What is Cn rotation?
A
Rotation by (360/n) clockwise
2
Q
What is Cn^-1 rotation?
A
Anti-clockwise rotation by 360/n
3
Q
What is Cn ^2 rotation?
A
Clockwise rotation by 360/n, performed twice
4
Q
What is the identity operation?
A
E, the equivalent of doing nothing to the molecule = Cn ^n
DONT mistake for inversion, which is i
5
Q
How do you represent a plane of symmetry perpendicular to the page?
A
Hatched line, draw as if cutting back through the shape
6
Q
What is a plane of symmetry perpendicular to the page?
A
Sigma v plane, = at 90 to the page, represents a mirror plane/reflection line, intersects at the Cn axis and is perpendicular to the sigma h plane
7
Q
What is a plane of symmetry perpendicular to the axis? How is it represented?
A
Sigma h, represented by a box around the shape (only if it is planar), because is perpendicular to the central axis (90)
Remember there must be a central axis of inversion otherwise there is nothing to be perpendicular to and the axis is sigma v instead
8
Q
What is inversion?
A
The swapping of bond positions through the centre of symmetry in the plane of the molecule
Found by checking if can draw a straight line with a pair of the same atoms on both sides of the straight line, if so the centre of the line is the inversion centre
Number atoms to make this easier
Represented by i
9
Q
Improper rotation Allene can do?
A
S4
10
Q
What is an improper rotation?
A
1) proper rotation
2) reflection across the plane perpendicular to the Cn axis (reflection across sigma h)
11
Q
What is S4 rotation?
A
C4 rotation (comes from the 4 in S4) Followed by reflection across sigma h
12
Q
What improper axis is a mirror plane equivalent to?
A
S1
13
Q
What improper axis is an inversion centre equivalent to?
A
S2
14
Q
How does chirality depend on improper axes?
A
If there is an improper axis (including S1 and S2), it cannot be chiral
15
Q
what is the first question in the point group assignment chart?
A
is the molecule linear
16
Q
what is the point group if a molecule is linear and CAN undergo inversion?
A
D infinity h
17
Q
what is the point group if a molecule is linear and CANNOT undergo inversion?
A
C infinity v
18
Q
What is the point group if a molecule is non-linear, has two or more Cn with n>2, and CANNOT be inverted?
A
Td (for all tetrahedral shapes)
19
Q
What are the two point group possibilities if a molecule is non-linear, has two or more Cn with n>2, and can undergo inversion?
A
If it is C5 then Ih (not L)
if it is not C5 then Oh (for all octahedral shapes)
20
Q
What is the point group when the molecule is
- non-linear
- doesn’t have 2 or more Cn with n>2
- has a Cn
- the highest order Cn has a C2 perpendicular to it
-and it has sigma h
?
A
Dnh
21
Q
- non-linear
- doesn’t have 2 or more Cn with n>2
- has a Cn
- the highest order Cn has a C2 perpendicular to it
- doesn’t have sigma h
-has more than one sigma d
?
A
Dnd
22
Q
- non-linear
- doesn’t have 2 or more Cn with n>2
- has a Cn
- the highest order Cn has a C2 perpendicular to it
- doesn’t have sigma h
- and doesn’t have more than one sigma d
?
A
Dn
23
Q
- non-linear
- doesn’t have 2 or more Cn with n>2
- has a Cn
- the highest order Cn doesn’t have a C2 perpendicular to it
-and it has sigma h
?
A
Cnh
24
Q
- non-linear
- doesn’t have 2 or more Cn with n>2
- has a Cn
- the highest order Cn doesn’t have a C2 perpendicular to it
-it doesn’t have sigma h
-and it has more than one sigma v
?
A
Cnv
25
- non-linear
- doesn’t have 2 or more Cn with n>2
- has a Cn
- the highest order Cn doesn’t have a C2 perpendicular to it
-it doesn’t have sigma h
-it doesn’t have more than one sigma v
-it has an S2n
?
S2n
26
- non-linear
- doesn’t have 2 or more Cn with n>2
- has a Cn
- the highest order Cn doesn’t have a C2 perpendicular to it
-it doesn’t have sigma h
-it doesn’t have more than one sigma v
-it doesn’t have an S2n
?
Cn
27
- non-linear
- doesn’t have 2 or more Cn with n>2
- doesn’t have a Cn
-it has sigma h
?
Cs
28
- non-linear
- doesn’t have 2 or more Cn with n>2
- doesn’t have a Cn
- doesn’t have sigma h
- can be inverted
?
Ci
29
- non-linear
- doesn’t have 2 or more Cn with n>2
- doesn’t have a Cn
-it doesn’t have sigma h
-it can’t be inverted
?
C1
30
In a point group what does the n stand for if it’s there? e.g. Dnh
the highest order rotation axis, e.g. D3h
31
What is the sigma d mirror plane?
dihedral, goes between the bond angles, goes inbetween two parallel C2 axes
32
What are the symmetry operations for C1?
E
33
What are the symmetry operations for Cs?
E and sigma (h)
34
What are the symmetry operations for Ci?
E and i
35
What are the symmetry operations for Cn?
E and Cn (can be more than one Cn but the point group is the highest order Cn)
36
What are the symmetry operations for Cnv?
E, Cn, and n sigma v
37
What are the symmetry operations for Dn?
E, Cn, and nC2 (perpendicular)
38
What are the symmetry operations for Dnh?
E, Cn, nC2 (perpendicular), and sigma h
Higher order Cn also have Sn and sigma_v and sigma_d
39
What are the symmetry operations for Dnd?
E, Cn, nC2 perpendicular, sigma d, also S2n (2 x the n of the Cn), e.g. C5 = S10
40
What are the symmetry operations for Td?
E, 8 x C3, 3C2, 6S4, 6 sigma d
41
What are the symmetry operations for Oh?
E, 8C3, 6C2, 6C4, 3C2, i, 6S4, 8S6, 3sigma_h, 6sigma_d
42
How do you combine symmetry operations for a point group?
make a table with all of the operations along the top and along the side (don’t forget to separate sigma v for example into sigma v(xz ) and sigma v(yz)
multiply them by performing the top operation then the side operation to give the result
An operation multiplied by itself = E
draw the axes out so you can see what happens to them when the operations are performed
the order of operations is important as the axes will move in different ways
43
how are the sigma v reflections different depending on the axes in the brackets?
whatever axis isn’t in the brackets is the one reflected
e.g. sigma v (xz) = y is reflected (gives -y)
44
How are symmetry operations of a point group represented numerically?
The number 1 is used in place of a molecule/axes so when reflected becomes -1
45
What does the A1 irrep represent?
Total symmetry (nothing changes when any symmetry operations occur)
46
What does the A irrep represent?
Symmetry to C2 (a symmetric stretch so bonds stretch in and out in the same direction)
47
What does the B irrep represent?
Antisymmetry to C2 (an asymmetric stretch so bonds stretch in opposite directions)
48
What does the ^1 irrep represent?
Symmetry to sigma v
49
What does the ^2 irrep represent?
Antisymmetry to sigma v
50
What does Tx, Ty, Tz represent?
Translation along x,y, z
51
What does Rx, Ry, Rz represent?
Rotation about x, y, z
52
What are irreps? Their labels?
Irreducible representations
A1, A2, B1, B2
53
What does it mean that irreps are orthogonal?
If 2 irreps are multiplied together the sum is zero
E.g. A1 x A2 = zero
54
What does the square of an irrep equal?
The order of the group (number of operations)
E.g. for C2v :
B2 x B2 = 4
And there are 4 symmetry operations
55
When writing a Gamma point group representation what do you do?
Make a table of symmetry elements along the top vs the Gamma(atoms) on the side
E.g. Gamma_HH for H2O
For each atom that has the same position after the symmetry operation, use a number 1
E.g, in a 4 atom molecule E representation will = 4 bc all 4 atoms have stayed in the same place
If an atom changes position use zero (IF FOR P ORBITALS DO MINUS IF THE ORBITAL HAS BEEN MADE NEGATIVE
Add all of the numbers in the row together, if it equals zero is an irrep, if not it is reducible
56
How do you reduce a representation?
Do (1/ order of the group) x sum of (irrep row x symmetry operation gamma of the point group representation )
= (1/order of the group) x (table of numerical point group representation x irrep row of character table)
with the two separate tables
If the symmetry operation is not singular, multiply the irrep by this number as well
E.g. 2C3 multiply the irrep by 2 AND by the symmetry operation number)
The representation is then equal to the number outcome of the equation, x the irrep label) and all of these added together equalling Gamma
E.g. Gamma = 3A1 + 2B1 +B2
Obviously anything with zero isn’t included
57
What does E mean in reduced representations?
Double degeneracy = the stretches have the same energy (if there is more than one)
58
What is a reducible representation?
A sum of irreps
59
What is the order of the group for reducible representations?
The number of operations in the group (NOT necessarily the number of columns)
60
What is the normal vibration equal to?
The sum of the normal modes (which behave as irreps of the point group)
61
What is the whole molecule method for reducing representations?
If asked to do the reduced representation of Gamma_all
+1 for each axis that remains unchanged
-1 for each axis that becomes negative
0 for each axis that moves
Also multiply by the character for each operation before adding to the representation table (e.g. using the cos equation for Cn, (sigma)v character= +1for each atom in the (sigma)v plane
62
What is Gamma_all made up of?
Gamma_vib + Gamma_rot + Gamma_trans
63
What is Gamma_ vib made up of?
Gamma_str + Gamma_bend
64
How do you determine symmetries of vibrations?
Subtract the translations (Tx, Ty, Tz) and rotations (Rx, Ry, Rz) from the point group’s character table from Gamma_all
So for Gamma_trans = sum of the irreps from the table which have Tx,Ty,Tz next to the row
For Gamma_rot = sum of the irreps with Rx,Ry,Rz next to them
Then do the total of Gamma_trans + Gamma_rot and minus from Gamma_all to give Gamma_vib
65
How do you calculate Gamma_str?
By reducing the representation of the bond using the normal (NOT WHOLE MOLECULE) method
66
How do you work out Gamma_bend?
Doing Gamma_vib minus Gamma_str
67
What is the formula for normal modes of a linear molecule?
3N - 5
N =number of atoms in the molecule
68
What is the formula for the number of normal modes in a non-linear molecule?
3N - 6
N = number of atoms in the molecule
69
What are the normal modes?
Stretching and bending
70
When is a normal mode IR active?
If it has the same symmetry label as x,y or z (Tx, Ty, Tz)
So in the group theory table, if the irrep has x,y or z next to it, it is IR active
71
What are Tx, Ty and Tz also known as?
Simply x, y and z
72
When is a vibration Raman active?
If it has the same symmetry label as x^2, y^2, z^2, xy, xz, or yz
73
What is the exclusion rule?
If a molecule has an inversion centre then none of its normal modes can be both IR and Raman active
74
What does X refer to?
```
The character (from the character tables)
Meaning the sum of the diagonal elements in the matrix
```
75
How do you make the matrix representation of a symmetry operation?
Draw out the axes and perform the operation to see how their positions change
If an axis is the same then we use 1
If an axis is reversed/negative we use -1
Write the original matrix in the form [x, y, z] but in a column
And do the same after but with the new signs of the axes after the operation
Now do a 3x3 grid of numbers in a matrix format
The first COLUMN of the grid represents x, the second y, third z
The first ROW of the grid represents x, the second y, third z,
So the numbers should be placed diagonally if in the order x, y, z
Fill in the numbers of the 1 and -1s and use 0 for anything else
E.g. if x goes to -x then you put -1 in the top left column
However if x goes to -y then you put the -1 in the second column, top row (the x row bc was originally x, but the second column bc is now y)
76
What does the character (X) equal when rotated by theta about the z axis?
X = 2 cos (theta) +1
Remember theta is just the angle of rotation used
77
What is the general rule for matrix representations and the character?
X = 1 for each atom within the mirror plane
| So only applies to sigma v
78
How do you calculate the character for the identity operation?
= the number of atoms in the molecule, multiplied by the number of axis (usually 3 bc x,y,z)
Therefore X = 3 for each atom in the molecule
79
What does SALCs stand for and mean?
Symmetry Adapted Linear Combinations
Means the combinations of the in-phase and out of phase stretching modes of individual bond stretches
80
How do you work out SALCs?
- label the bonds as r1, r2, r3, etc, these are referred to as vectors (this is similar to how you would label atoms a,b,c,d but that is less clear)
- write out the symmetry operations table for the molecule, with the operations fully expanded e.g. C2x C2y C2z if there are 3C2, C3+/C3- (clockwise/anti),  (sigma)a/b/c
- choose one of the vectors and perform the symmetry operations on it in the table, (treat it like the axis so r1 could form r2 or r3 etc)
- add rows for the stretching modes/irreps below that of the row for r (e.g. A1, B2 etc)
- you should have the numbers for these rows from character tables
- multiply each of the numbers from each of the irreps by the r row, giving only values for r
- simplify your result (e.g. if 2r1 + 2r2 simplify to r1+r2)
- keep the result for each stretching mode row separate, so you will have a result for each stretching mode
- normalise your values and check they are orthogonal
81
How do you normalise values for SALCs?
The sum of the squares should be equal to one so you need to multiply the r values by a fraction so when they are squared they give one r value
e.g. (1/root 2) x (r1 + r2) = ( 1/2) x r1 + r2
So as a general rule put the number of r values you have on the bottom of the fraction and root it, so when squared will give 1/ the number of values
Remember that if a value has a coefficient in front of it that you need to square it before adding to the number of values to put on the bottom of the fraction
82
When calculating SALCs what does it mean if something is positive or negative (from multiplying by the -1)?
That it is stretching in the opposite phase to the positive ones
All negative values are in the same phase as each other, stretching into the centre (contracting)
All positive values are in the same phase as each other, stretching away from the centre (expanding)
draw the orbitals with shading if positive and without shading if negative
83
What does it mean if stretching modes are in phase?
They’re expanding and contracting in phase, at the same time
84
How do you check that your SALC values are orthogonal for doubly degenerate SALCs?
When multiplied together they should equal zero
They will have the same normalisation factor so these multiplied will just remove the root on the bottom and leave one fraction
Multiply each of the same values by each other, e.g. r1 x r1, r2 x r2 etc, no need to intermultiply, only multiply by values of the same
The number of r values should equal zero, if this is not the case they’re not orthogonal
85
How to obtain an orthogonal SALC if not initially found?
Use the vector r_o which will be orthogonal to r1 because r_o = r3-r2
r_o literally means r orthogonal
Write this in the table as r3-r2 (these values will change depending on the number of bonds you have, could be r4-r3-r2 because that would be equal to r1
Multiply as you usually do for calculating SALCs and check that they’re orthogonal
86
When can atomic orbitals interact to form molecular orbitals?
when they belong to the same irrep of the molecule's point group (they have the same symmetry)
87
How do you determine the symmetry labels of valence orbitals?
Write out the orbitals e.g. 2s, 2p(x), 2p(y), 2p(z) - even if not containing electrons write all the orbitals in the set out
use the point group table to read off what symmetry label each orbital belongs to (where the x etc is on the left)
s orbitals will always have the symmetry label at the top of the table
88
When determining symmetry labels of valence orbitals why does the s orbital always have the symmetry label at the top of the table?
s = spherically symmetric, so must belong to the totally symmetric reducible representation = the top line of the table
89
How do you determine valence orbital interactions?
Determine the symmetry labels of each of the atoms orbitals (e.g. in water, the orbitals of H and O separately) - by doing a reduced representation for whatever isn't in the centre of the molecule (for the ones that can't be done with the table)
work out the linear combinations of orbitals to determine in phase/out of phase options
compare symmetry labels, the orbitals with the same symmetry labels will interact, make a table with the symmetry label and the orbitals which will interact
if there are any orbitals that can't interact with anything then it must be a non-bonding orbital (e.g. lone pair)
90
When drawing the molecules resulting from SALCs, what do you do if an orbital has a SALC with a different number in front of it, e.g. (2a + b)?
The orbital will be that order of magnitude larger than the other orbitals, e.g. draw the a orbital twice as big as the b orbital
91
Is a shaded orbital positive or negative?
Positive
92
Is an unshaded orbital positive or negative?
Negative
93
When doing SALCs why do you often need to do a second linear combination?
There must be a doubly degenerate combination for all orbitals so you need to do a second combination orthogonal to the axis used initially.
e.g. y axis is orthogonal to x axis so use those orbitals in a second combination
94
What is d(z^2) an abbreviation for?
d(2z^2-x^2-y^2)
95
What does T2g mean in terms of degeneracy?
triply degenerate, 3 orbitals with the same energy
96
What does Eg mean in terms of degeneracy?
Doubly degenerate, 2 orbitals with the same energy
97
When is the g label used for symmetry labels of d orbitals?
d orbitals always have a g label when there's a centre of symmetry
98
What point group is square planar always if all ligands are the same?
D4h
99
What point group is cis square planar always?
C2v
100
What point group is trans square planar always?
D2h
101
What does crystal field theory treat ligands as?
Point negative charges
102
What are all of the labels for d orbitals?
d(xy), d(xz), d(yz), d(z^2), d(x^2-y^2)
103
In an octahedral complex where are the 6C2? How does this affect the representation?
6C2 going in-between the bonds, all ligands move so representation = 0
104
In an octahedral complex where are the 3(sigma)h? How does this affect the representation for SIGMA bonding?
4 bonds in the plane of the reflection so don't move and the representation = 4
105
In an octahedral complex where are the 6(sigma)d? How does this affect the representation for SIGMA bonding?
bisecting the bond angles/going through the centre, two ligands therefore don't move so the representation = 2
106
In an MO diagram, which side do the metal and ligand electrons go on?
Metal on the left, ligand on the right
107
Where do the ligand lone pairs occupy in MO diagrams?
all the bonding orbitals
108
Where do metal d-electrons occupy in MO diagrams?
non-bonding T2g and anti-bonding Eg* orbitals
109
For reduced representations, is it +1 or 0 for if the orbital moves?
0 if it moves
| 1 if it DOESN'T move
110
What type of ligand are halides?
pi-donor ligand
111
What type of ligand is CO?
pi-acid ligand
112
What type of ligand is CN^-1?
pi-acid ligand
113
Why are halides the ligand type that they are?
they have full p orbitals (pi-donor ligand)
114
What type of ligand is PR3?
pi-acid ligand
115
Why are CO, CN^-1, and PR3 the ligand type that they are?
they have vacant pi anti-bonding orbitals (pi-acid ligands)
116
How are p orbitals positioned relative to the M-L bond?
the p orbitals are perpendicular to the axis of the M-L bond
117
What is an S6 symmetry element?
rotation by 60 degrees followed by a reflection across the perpendicular plane
118
In an octahedral complex where are the 3C2? How does this affect the representation for SIGMA bonding?
3C2 about the C4 rotation axis, there are two ligands along each rotation axis, so these 2 ligands don't move and the representation = 2
119
In an octahedral complex where are the 6C4? How does this affect the representation for SIGMA bonding?
Through the bonds so there are two ligands along each rotation axis which don't move, so the representation = 2
120
In an octahedral complex how is the representation for 3C2 for PI bonding different to that for sigma bonding?
for pi bonding the representation of 3C2 = -4 bc each orbital becomes minus of itself
121
In an octahedral complex how is the representation for 6C4 for PI bonding different to that for sigma bonding?
= 0
122
In an octahedral complex how is the representation for 3(sigma)h for PI bonding different to that for sigma bonding?
there are 4 ligands within the plane = +4 but the orbitals perpendicular to the plane are minused so the representation = zero
123
In an octahedral complex how is the representation for 6(sigma)d for PI bonding different to that for sigma bonding?
the planes bisect the ligands so all of the orbitals move and the representation = zero
124
Why do sigma bonding and pi bonding give different representations?
Sigma only involves the changes of the s orbitals, pi-bonding involves the changes of the p orbitals, which can become negative and cancel out any positives (positive still means where the orbital has remained unchanged)
125
How do pi-donor ligands affect delta oct? Why?
reduce delta oct bc weak field ligands
126
How do pi-acceptor ligands affect delta oct? Why?
increase delta oct bc strong field ligands
127
What metal orbitals can ligands form pi bonds with? why?
T2g, they have the correct symmetry
128
How do you label the sigma which goes around the molecule like a box from the axis?
Whatever the axis are, label with those (not the one perpendicular to the page), ie, if the axes are normal x,y, the box is labelled (sigma)(xy)
129
How do you find gamma all?
Do the whole molecule method to reduce the representation
130
What is an infinite rotation axis?
If the molecule is cylindrical (linear)
131
What shape is a tetrahedron?
four-sided triangle based pyramid
