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1
Crystal field theory
Molecular orbital theory
Density function theory
Look at crystal field theory first
http://www.tcd.ie/Chemistry/Under/ch3018.html
Huheey, Ch. 11; Carter, Chapter 7
How do we take interactions with ligands into account?
Andrei N. Vedernikov -- University of Maryland http://www.chem.umd.edu/groups/vedernikov/VGroup_Teaching-601.htm
2
Transition Metals -- Bonding and Spectroscopy
Hybrid orbitals and valence bond theoryIncludes crystal field theory for transition metal complexes (Ch 11, pp 387 - 413 Huheey; Ch 7 Carter)
Molecular orbital theoryIncludes MO theory for transition metal complexes(Ch 11, pp 413 - 433 Huheey; Ch 7 Carter)
3
H = E
= Hfree atom
Free Atoms Molecular Complexes Solids
4
Atkins/Shriver
Free Atom States --- Term Symbols
2
5
Free Atom States -- Term Symbols
6
Lifting of energy degeneracies in ad2 gaseous atom
HFree atom contributions
7
electron
configuration
spin states and
terms from sisj
and lilj couplingmultiplets from
lisi coupling
Experimental
Lifting of energy degeneracies in a d2 gaseous atom
8
Crystal field theory
Molecular orbital theory
Density function theory
Look at crystal field theory first
http://www.tcd.ie/Chemistry/Under/ch3018.html
Huheey, Ch. 11; Carter, Chapter 7
How do we take interactions with ligands into account?
Andrei N. Vedernikov -- University of Maryland http://www.chem.umd.edu/groups/vedernikov/VGroup_Teaching-601.htm
3
9
H = E
Three cases
• Ligands don t a ect outer valence electrons- lanthanides
• Ligands weakly affect outer valence electrons---many 3d complexesWeak Field case
• Ligands strongly affect outer valence electrons--Strong Field case
The electronic effects of adding ligands to the free atom
10
Electronic structure of Coordination CompoundsCrystal Field Theory
• Considers only electrostatic interactions between theligands and the metal ion.
Oh octahedral
Main steps to estimate the relative energies of d-orbitalsin a field of a particular symmetry
1) An isolated metal ion. Five d-orbitals are degenerate
2) A metal ion in an averaged ligand field. The orbitalenergy increases due to electron (metal) – electron(ligands) repulsions.
3) A metal ion in a ligand field of certain symmetry. d-energy levels may become split into several sublevels.
Some of d-orbitals become stabilized, some become lessstable. The total orbital energy gain due to thestabilization is equal to the total orbital energy loss.
Ligands are considered as point charges creating an
electrostatic field of a particular symmetry
•
11
Interactions of d-orbitals with octahedral ligand field
12
Characters, Characters, [R], for operations in[R], for operations in spherical symmetry (groupspherical symmetry (group
RR33) as a function) as a function of the angular momentum quantum number, j,of the angular momentum quantum number, j,
of the wave function are given by:of the wave function are given by:
These relations can be used with
any point group, since all are
subgroups of the spherical
group, R3
Carter, page 205
for d orbitals or D term symbol!!
Symmetry and the atom ...reducible representations basedon angular momentum
4
13
d-Orbital splitting in the fields of various symmetries
• The d-orbital splittings presented on diagramcorrespond to the cases of cubic shape MX8(Oh), tetrahedral shape MX4 (Td), icosahedralshape MX12 (Ih), octahedral shape MX6 (Oh) andsquare planar shape MX4 (D4h).
…
(xz, yz)Eg
xyB2g
x2-y2B1g
x2+y2, z2A1g
D4h
(2z2-x2-y2, x2-y2, xy, xz, yz)Hg
Ih
free ion
IhOh Td OhD4h
MX8
MX4
MX4
MX6
MX12
t2g
eg
e
t2
eg
t2g
b1g
b2g
a1g
eg
dxy
dyz
dz2
dx2-y2
dxz
dyzdxz
dz2
dx2-y2
dyzdxz
dz2
dx2-y2
dz2
dx2-y2
dxy
dxy
dxy
dyzdxz
averagedligandfield
hg
E
(xy, xz, yz)T2
(2z2-x2-y2, x2-y2)E
Td
14
Octahedral field. ML6 complexes
• In the field of Oh symmetry five degenerate d-orbitals will be split into two sets, t2g andeg orbitals (check the Oh point group character table)
• Three t2g orbitals be stabilized by 0.4 o and two eg orbitals will be destabilized by 0.6 o
x
y
z1
2
34
x
y
z1
2
3
4
dz2=0.5(dz2-y2+dz2-x2)
x
y
z1
2
34
dyz
x
y
z
12
3
4
dx2-y2
eg
t2g
dz2-x2dz2-y2
…
(xz, yz, xy)T2g
…
(2z2-x2-y2, x2-y2)Eg
…
Oh
the ion in an averaged ligand field
x
y
the ion in an octahedralligand field
2x = 3y
x = 0.6 o
y = 0.4 o
x + y = o
L LLL
L
L
eg
t2g
15
d orbitals
spectrochemical series
3rd row > 2nd row > 1st row transition metal atoms
higher charge TM > smaller charge
How does an octahedral array of ligands affect the d orbitals?eg
t2g
16
strong field d4
t2g2
t2g3
t2g4
t2g3 eg
1
t2g
eg
low spin
high spinif weak field
configurations
5
17
Ligand-field splitting parameters O of ML6 complexes
• values are in multiples of 1000 cm-1
• entries in parentheses are for low-spin complexes
Shriver, Table 7.3
18
Factors affecting the magnitude of • Higher oxidation states of the metal atom correspond to larger :
=10,200 cm-1 for [CoII(NH3)6]2+ and 22,870 cm-1 for [CoIII(NH3)6]3+
=32,200 cm-1 for [FeII(CN)6]4- and 35,000 cm-1 for [FeIII(CN)6]3-
• In groups heavier analogues have larger . For hexaammine complexes[MIII(NH3)6]3+: = 22,870 cm-1 (Co)
34,100 cm-1 (Rh)41,200 cm-1 (Ir)
• Geometry of the metal coordination unit affects greatly. For example, tetrahedralcomplexes ML4 have smaller than octahedral ones ML6:
= 10,200 cm-1 for [CoII(NH3)6]2+
5,900 cm-1 for [CoII(NH3)4]2+
• Ligands can be arranged in a spectrochemical series according to their ability toincrease at a given metal center:
I- < Br- < Cl- < F- , OH- < H2O < NH3 < NO2- < Me- < CN- < CO
For [CoIIIL6] we have , cm-1: 13,100 (F), 20,760 (H2O), 22,870 (NH3)
For [CrIIIL6] we have , cm-1: 15,060 (F), 17,400 (H2O), 26,600 (CN)
19
Some consequences of d-orbital splitting• Magnetism. In the case of large we observe
low-spin, while for small high-spincomplexes (d4-d7 configurations).
• Energy. If the occupancy (x) of the orbitalsstabilized by a ligand field is more than that ofthe destabilized orbitals (y), the complexbecomes more stable by the Crystal FieldStabilization Energy (CFSE )which is (0.4y-0.6x) for octahedral species.
• For d0, d5 (high-spin) and d10 complexes CFSE isalways zero.
• Redox potentials. Some oxidation states maybecome more stable when stabilized orbitals arefully occupied. So, d6 configuration becomesmore stable than d7 as o increases.
CoL62+ = CoL6
3+ + e-
E0= -1.8 (L=H2O) … +0.8 V (L=CN-)
• M-L bond lengths and Ionic radii of Mn+ aresmaller for low-spin complexes and have aminimum for d6 configuration (low spin).
R, Å, of M3+: 0.87 (Sc), 0.81 (Ti), 0.78 (V), 0.74(Cr), 0.72 (Mn), 0.69 (Fe), 0.67 (Co), 0.71 (Ni),… 0.78 (Ga)
Oh
MX6
eg
t2g
dyzdxz
dz2
dx2-y2
dxy
eg
t2g
low spin d6 high spin d6
large o small o
E
20
Calculating CFSE for Octahedral species
CFSE = [0.4 x #t2g electrons – 0.6 x # eg electrons)
the ion in an averaged ligand field
x
y
the ion in an octahedralligand field
2x = 3y
x = 0.6 o
y = 0.4 o
x + y = o
L LLL
L
L
eg
t2g
t
t2g3 eg
1For
(0.4 x 3 - 0.6 x 1)
= 0.6
Note:
= 10Dq
6
21
Lattice energies of the divalent metal halides of the firsttransition series
Huheey, Fig 11.14 22
Radii of some trivalent ionsas a function of the number of d electrons
Huheey, Fig 11.15
low spin -- solid circles
23
Crystal-field stabilization energies
• N is the number of unpaired electrons
• CFSE is in units of O for octahedra or T for tetrahedra
• the calculated relation is T (4/9) O
Shriver, Table 7.3
C C
24
High and low spin complexes of various geometries
• d-d Electron-electron repulsions in d4-d7 metal complexes (3d) correspond tothe energy of 14000-25000 cm-1. If > 14000-25000 cm-1, the complex is lowspin.
• For octahedral complexes o ranges from 9000 to 45000 cm-1. It is thereforecommon to observe both high and low spin octahedral species.
• For tetrahedral complexes t = (4/9) o ranges from 4000 to 16000 cm-1. Lowspin tetrahedral complexes are very rare.
• For square planar complexes is very large. Even with weak field ligandshigh-spin d8 complexes are unknown (but known for d6).
• Sometimes complexes of different configuration and magnetic propertiescoexist in equilibrium in solution. For the Ni(II) complexes shown below µ=0
M (R = Me; square planar); 3.3 (R = tBu; tetrahedral) and 0-3.3 (R = iPr; both)
O
N
R
Ni
R
O
N
O
N
R
Ni
R
O
N
µ = 3.3 Mµ = 0 M
TdD4h
MX4MX4
e
t2
b1g
b2g
a1g
eg
dyzdxz
dz2
dx2-y2
dz2
dx2-y2
dxy
dxy
dyzdxz
tetrahedral
square-planar
Nr =Co
IV
Nr
NrNr
Nr
d5
µ=1.8 M
7
25
How do we determine the magnitude of the crystal field?Magnetism of octahedral transition metal complexes
• The number of unpaired electrons n in a metal complex can be derived from theexperimentally determined magnetic susceptibility M.
• M is related to magnetic moment µ 2.84( MT)1/2 (Bohr magnetons)
• µ is related to n: µ [n(n+2)]1/2.
• Calculated magnetic moments for octahedral 3d metal complexes, ML6:
1.73
0
1.73
2.83
µ, M
1.73(tg)2 (tg)2 (tg)2 (eg)2 (eg)11 (d9)Cu2+
2.83(tg)2 (tg)2 (tg)2 (eg)1 (eg)12 (d8)Ni2+
(tg)2 (tg)2 (tg)2 (eg)11 (d7)3.87(tg)2 (tg)2 (tg)1 (eg)1 (eg)13 (d7)Co2+, Ni3+
(tg)2 (tg)2 (tg)20 (d6)4.90(tg)2 (tg)1 (tg)1 (eg)1 (eg)14 (d6)Fe2+, Co3+
(tg)2 (tg)2 (tg)11 (d5)5.92(tg)1 (tg)1 (tg)1 (eg)1 (eg)15 (d5)Mn2+, Fe3+
(tg)2 (tg)1 (tg)12 (d4)4.90(tg)1 (tg)1 (tg)1 (eg)14 (d4)Cr2+, Mn3+
3.87(tg)1 (tg)1(tg)13 (d3)V2+, Cr3+
2.83(tg)1 (tg)12 (d2)V3+
1.73(tg)11 (d1)Ti3+, V4+
# of unp. e’sµ, M# of unp. e’s
Low spin complexesHigh spin complexesM
26
Ti(H2O)63+
d1 configuration
500nm
How do we determine the Crystal Field Splitting?(from an electron configuration perspective)
measure optical absorption...
27
Why multiple peaks?
d3
Why the increasing absorption at 200 nm?
What is the electronic structure of the chromium atom?What are the magnetic properties?
A more complicated problem
28
What is it?
How do you use it?
Tanabe Sugano Diagram
A good guide---
8
29
1. number of maxima (observed absorption peaks)
What are the electronic states of the complex?
Absorption maxima in a visible spectrum have threeimportant characteristics
2. position (what wavelength/energy)
What is the ligand field splitting parameter, e.g., oct or tet, and the
degree of inter-electron repulsion?
3. intensity
What is the "allowedness" of the transitions as described by selection
rules
30
ground state
(note labels)
Instead of electron configurations-- look at how the free atom states
are affected
Answer to these questions--
d2 correlation
diagram
Oh
weak field
31
Can do the same for other Can do the same for other orbitals orbitals and/orand/or terms asterms as wellwell
Carter, page 205
For F ground state term (j = 3)
F = A2g + T1g + T2g
Symmetry and the atom... reducible representations based
on angular momentum
32
d2 correlation
weak field
Note non-crossing rule:
States with the same
symmetry and
multiplicity do not cross
Example 3F state from d2 configuration withweak ligand field
9
33
Summary of splitting of states for dn configurations in anoctahedral (Oh) field
34
d2 correlation
Work out strong field side
by starting with
hypothetical configurations
For t2g2 get reducible
representation by taking
direct product t2g x t2g
(t(t2g2g))22 = A = A1g1g + + EEgg + T+ T1g1g + + TT2g2g
see Carter, page 239
What happens if the ligand field is strong?
strong field
35
Summary - d2 Correlation Diagram
Energy states!
36
Why multiple peaks?
d3
Now ready to begin interpreting optical spectra andmagnetic properties of transition metal complexes
Why the increasing absorption at 200 nm?
What is the electronic structure of the chromium atom?What are the magnetic properties?
10
37
What is it?
How do you use it?
Tanabe Sugano Diagram
A good guide---
Ground State38
R O Y G B I VUVIR
600 nmWavelength
500 nm 400 nm
E = h = hc/
650 nm 600nm
800nm560 nm400 nm
430 nm 490 nm
If a substanceabsorbs here...
It appears
as this color
If an object is black it absorbs all colors of light
The color spectrum -- a review Sir Isaac Newton
An object is white if it reflects all colors of light
An object is orange if it reflects only this color and absorbs all others
An object is also orange if it reflects all the colors except blue,the complementary color of orange
39
//www.cs.rit.edu/~ncs/color/a_chroma.html
Chromaticity
3 “virtual”
colors, which
when added
together give
all other
colors
40
molecular rotations
lower energy
(0.01 - 1 kJ mol-1)
microwave radiation
electron transitions
higher energy
(100 - 104 kJ mol-1)visible and UV radiation
molecular vibrationsmedium energy
(1 - 120 kJ mol-1)
IR radiation
Ground State
Excited State
During an electronic transition
the complex absorbs energy
complex changes energy states
redistributes the electronic charge
http://www.tcd.ie/Chemistry/Under/ch3018.html
Energy of transitionsEnergy of transitions
11
41
• Values of are easily obtained from absorption spectra of d1 transitionmetal complexes
• In the d1 metal complex [Ti(H2O)6]3+ max = 500 nm, so that
= = 1/ max = 1/(5.00 10-5cm)= 20000 cm-1
Estimating from electronic absorption spectra of d1 species
d1
2Eg
2T2g
2Eg
2T2g
=
max
42
Why multiple peaks?
d3
Now ready to begin interpreting optical spectra andmagnetic properties of transition metal complexes
Why the increasing absorption at 200 nm?
What is the electronic structure of the chromium atom?What are the magnetic properties?
43
Free Atom States -- Term Symbols
44
d1 d9
move hole
behaves like behaves like
Close relationships between dn electronic properties- electrons and holes--
S = 1/2
S = 4
2S + 1 = 2
2S + 1 = 5
12
45
move hole
behaves like
Putting this in the context of term symbols states…
ML6
d1
2D
M
Oh
2Eg
2T2g
ML6
d5+1
5D
M
Oh
5Eg
5T2g
(not a single term)
ML6M
d10-1
2D
Oh
2Eg
2T2g
ML6
d5-1
5D
M
(not a single term)
Oh
5Eg
5T2g
behaves like
46
Relationships for octahedral and tetrahedral
ML6
d1
2D
M
Oh
2Eg
2T2g
Td
ML4
2E
d1
2D
M
t
2T2
Td
ML4
2Ed10-1
2D
M
t
2T2
The term sequence is the opposite for octahedral and tetrahedral
complexes of the same configuration
The term sequence is in the same order for dn octahedral and d10-n
tetrahedral complexes.
47
d1 d6 d4 d9Summarize with Orgel Diagram
48
A
/ cm-1-
30 00020 00010 000
[Ti(OH2)6]3+
E
LF strength
Orgel diagram for d1, d4, d6, d9
0
D
d4, d9 tetrahedral
T2g or T2
T2g or T2
d4, d9 octahedral
Eg or E
d1, d6 tetrahedral
Eg or E
d1, d6 octahedral
2Eg 2T2g
2Eg
2T2g
2D
d1 octahdral
13
49
F
P
Ligand field strength (Dq)
Energy
A2 or A2g
T1 or T1g
T2 or T2g
A2 or A2g
T2 or T2g
T1 or T1g
T1 or T1g
T1 or T1g
Quantum Mixing
d2, d7 tetrahedral d2, d7 octahedral
d3, d8 octahedral d3, d8 tetrahedral
0
Orgel diagram for d2, d3, d7, d8 ions
50
Couple of things missing: spin multiplicties and electron-electron repulsion (Racah Parameters B and C)
Use Tanabe Sugano DiagramsUse Tanabe Sugano Diagrams
51
What is it?
How do you use it?
Tanabe Sugano Diagram
A good guide---
Ground State52
Spin Selection Rule
S = 0
There must be no change in spin multiplicity during an electronic transition
Laporte Selection Rule
l = ± 1
There must be a change in parity during an electronic transition
Selection rules determine the intensity of electronic transitions
g u
Selection Rules
14
53
Transitions may occur only between energy states with the
same spin multiplicity.
S = 0
violated by spin orbit or jj coupling
Selection Rules for optical transitions -- Spin Selection Rule
54
A transition matrix element of the form , where O is the operator of
interaction, can be used to calculate the intensity of a transition according to
M = f O i
I f O i2
Such integrals of the type are only non-zero if the function is
symmetric with respect to all symmetry operations of the group, i.e. if it forms the basis for
the totally symmetric irreducible representation of the group.
M = f O i fO i
Consider the irreducible representation of the direct product
where is the operator of an electric dipole
transition. This operator transforms as the irreducible
representation of the cartesian coordinates.
M = f µ i
In a centrosymmetric point group, must be an odd (u) function
f and i must be of opposite parity (u g or g u)
This means that d p, s p, . . . are allowed, but
d d, s d, . . . are not
LaPorte’s Rule 10,000
5 - 100
Selection Rules for optical transitions ---LaPorte’s Rule
55
Vibronic Mechanism
For a centrosymmetric structure (e.g. Oh ) vibrations
of odd parity (e.g. T1u) distorts the octahedron,
which partially relaxes LaPorte’s rule, so get a small
absorption, 5 - 100
Tetrahedral (Td), noncentrosymmetric, complexes
have d d transition intensities greater than those for
octahedral (Oh) 100 - 200 since no g or u symmetry
Selection Rules for optical transitions ---LaPorte’s Rule
56
/ cm-1-
2Eg
2T2g
2D
E
oct
[Ti(OH2)6]3+, d1, Oh field
10 000 20 000 30 000
0.01
0.02
0.03
Spin allowed
Laporte forbidden
Transition between d orbitals
Selection Rules andIntensity for d-d transitions
note size of
15
57
F
P
Dq
A2g
T2g
T1g
T1
T2
A2
T1 T1g
d7 tetrahedral d2 octahedral0
10 00030 000 / cm-1
[V(H2O)6]3+, d2 Oh10
20 000
5
4T1g
4T2g
4T1g
4A2g
25 000 20 000 15 000 10 000 5 000v / cm-1
[CoCl4]2-, d7 Td
3T1
3T2
3A2
3T1
600
400
200
Spin allowed; Laporte forbidden
58
Octahedral complex
Centrosymmetric
Laporte rule applies
Tetrahedral complex
Non-centrosymmetric
Laporte rule relaxed
inversion
centre
Orbital mixing:Oh complex d eg and t2g p t1u
Td complex d e and t2 p t2
In tetrahedral complexes, d-orbitals have some p character
Relaxation of the Laporte Selection Rule for Tetrahedral Complexes
59
6S
10 000
20 000
30 000
40 000
50 000
4G
4P
4D
4F
Dq (cm-1)
500 1000
Energy (cm-1)
4E(g)4T2(g)4E(g),
4A1(g)
4T2(g)
4T1(g)
6A1(g)
4T2(g)
4T1(g)
4A2(g)
4T1(g)
Laporte forbidden
Spin forbidden
Weak transitions occur due to: Unsymmetrical Vibrations (vibronic transitions)
Spin-orbit Coupling
Intenstity of transitions in d5 complexes
60
d5 octahedral complex
[Mn(H2O)6]2+
v / cm-1
20 000 25 000 30 000
Multiple absorption bands
Very weak intensity
4T2g (D)
4Eg (D)4T1g(G)
4Eg (G)
4A1g (G)
4T2g (G)0.01
0.02
0.03
Transitions are forbidden
Ground State6A1g
Spin forbidden transitions
16
61
Transition complexes
Spin forbidden 10-3 – 1 Many d5 Oh
Laporte forbidden [Mn(OH2)6]2+
Spin allowed
Laporte forbidden 1 – 10 Many Oh
[Ni(OH2)6]2+
10 – 100 Some square planar [PdCl4]
2-
100 – 1000 6-coordinate complexes of low symmetry, many square planar particularly with
organic ligands
Spin allowed 102 – 103 Some MLCT bands in complexes with
unsaturated ligands
Laporte allowed102 – 104 Acentric complexes with ligands such as acac,
or with P donor atoms
103 – 106 Many CT bands, transitions in organic species
Selection rules and observed intensitiesSelection rules and observed intensities
62
What is it?
How do you use it?
Tanabe Sugano Diagram
A good guide---
Ground State
63
Why multiple peaks?Why the increasing absorption at 200 nm?What is the electronic structure of the Chromium?What are the magnetic properties?
Understanding Cr3+
64
Understanding Cr(NH3)63+ --- Tanabe Sugano Diagram
Expect two main d-d transition bands
Measure energies accurately
is at 21550 cm-1
is at 28500 cm-1
28500/21550 = 1.32
is ~ 15400 cm-1 = 650nmNote: slope = 1
g
g
g
g
g
g
g
gg
17
65
E/B
/B
[Cr(NH3)6]3+: Three spin allowed transitions
1 = 21550 cm-1 visible
2 = 28500 cm-1 visible
3 = obscured by CT transition
/B = 32.8
3 = 2.2 x 1 = 2.2 x 21500
3 = 47300 cm-1 ~ 211nm
= 32.8
Tanabe-Sugano diagram interpretation
One spin forbidden transition
4 = 15400 cm-1 visible
285002
1=
21550= 1.32
154004
1=
21550= 0.72
E/B =
32.8
cm-1
66
E/B
/B
1 = 21550 cm-1
2 = 28500 cm-1
= 32.8
E/B = 43 cm-1
E/B = 32.8 cm-1
When 1 = E =21550 cm-1
E/B = 32.8
so B = 657 cm-1
If /B = 32.8
= 32.8 x 657 = 21550 cm-1
Determining and B for [Cr(NH3)6]3+
/B = 20.8
For spin forbidden transition
B = 740 cm-1
4 = 15400 cm-1 visible
67
4A2g
4T1g
4T2g
4T1g
10 Dq
2 Dq
6 Dq
x
x
15 B'
For Oh d3, o = 1 = 21550 cm-1
o / B = 32.8
B = 657 cm-1
1 = 21550 cm-1 visible
2 = 28500 cm-1 visible
3 = obscured by CT
transition
Energy diagram for octahedral d3 complex
E
68
Why multiple peaks?Why the increasing absorption at 200 nm?What is the electronic structure of the Chromium?What are the magnetic properties?
Understanding Cr3+
18
69
E/B
/B
[Cr(H2O)6]3+: Three spin allowed transitions
1 = 17 400 cm-1 visible
2 = 24 500 cm-1 visible
3 = obscured by CT transition
24 500 = 1.41
17 400
/B = 24
3 = 2.1 x 1 = 2.1 x 17400
3 = 36 500 cm-1
= 24
Tanabe-Sugano diagram for weaker field d3 ions
E/B =
24
cm-1
70
E/B
/B
1 = 17 400 cm-1
2 = 24 500 cm-1
= 24
E/B = 34 cm-1
E/B = 24 cm-1
When 1 = E =17 400 cm-1
E/B = 24
so B = 725 cm-1
When 2 = E =24 500 cm-1
E/B = 34
so B = 725 cm-1
If /B = 24
= 24 x 725 = 17 400 cm-1
Determining and B
71
4A2g
4T1g
4T2g
4T1g
10 Dq
2 Dq
6 Dq
x
x
15 B'
For Oh d3, o = 1 = 17 400 cm-1
o / B = 24
B = 725 cm-1
1 = 17 400 cm-1 visible
2 = 24 500 cm-1 visible
3 = obscured by CT
transition
Energy diagram for octahedral d3 complex
72
650 nm 600nm
800nm560 nm400 nm
430 nm 490 nm
If a substanceabsorbs here...
It appearsas this color
What color is this Cr3+ complex?
19
73
E/B
/B
[V(H2O)6]3+: Three spin allowed transitions
1 = 17 800 cm-1 visible
2 = 25 700 cm-1 visible
3 = obscured by CT transition in
UV
10 00030 000 / cm-1
10
20 000
5
25 700 = 1.44
17 800
/B = 32
3 = 2.1 1 = 2.1 x 17 800
3 = 37 000 cm-1
= 32
Tanabe-Sugano diagram for d2 ions
74
E/B
/B = 32
1 = 17 800 cm-1
2 = 25 700 cm-1
1
2E/B = 43 cm-1
E/B = 30 cm-1
E/B = 43 cm-1 E = 25 700 cm-1
B = 600 cm-1
o / B = 32
o = 19 200 cm-1
Getting spectrochemical parameters for a d2 configuration
75
P
F
15 B'15 B
x
x
10 Dq
6 Dq
2 Dq
T1(g)
T1(g)
A2(g)
T2(g)
1: x + 8 Dq
2: 2 x + 6 Dq + 15 B'
3: x + 18 Dq
1
2
3
1: T2(g) T1(g)
2: T1(g)(P) T1(g)
3: A2(g) T1(g)
Energy level diagram for oct d2, d7, tet d3, d8
76Ruby - Cr3+ in Al2O3
second
lifetime
627 nm
1st laser in 1960
Phosphorescence ---radiative decay from an excited state of different
spin multiplicity than ground state (generally slow!)
20
77
Fluorescence --- radiative decay from an excited state of the same
spin multiplicity as the ground state
Half-life of the order of nanoseconds or less
Phosphorescencee -- radiative decay from a state of different
spin multiplicity from the ground state (spin forbidden
transition)
Half-life of the order of microseconds or more
Emission Spectra
78
d7 tetrahedral complex
15 B' = 10 900 cm-1
B' = 727 cm-1
[CoCl4]2-[Co(H2O)6]2+
d7 octahedral complex
15 B' = 13 800 cm-1
B' = 920 cm-1
Free ion [Co2+]: B = 971 cm-1
B' = 0.95
B
B' = 0.75
B
Nephelauxetic ratio,
is a measure of the decrease in electron-electron repulsion on complexation
Racah Parameters
=
79
- some covalency in M-L bonds – M and L share electrons
-effective size of metal orbitals increases
-electron-electron repulsion decreases
Nephelauxetic series of ligands
F- < H2O < NH3 < en < [oxalate]2- < [NCS]- < Cl- < Br- < I-
Nephelauxetic series of metal ions
Mn(II) < Ni(II) Co(II) < Mo(II) > Re (IV) < Fe(III) < Ir(III) < Co(III) < Mn(IV)
cloud expandingThe Nephelauxetic Effect
80
4Eg, 4A1g
6S
10 000
20 000
30 000
40 000
50 000
4G
4P
4D
4F
Dq (cm-1)
500 1000
Energy (cm-1)
4T2g
4T2g
4T1g
6A1g
4T2g
4T1g
4A2g
4T1g
v / cm-1
20 000 25 000 30 000
0.01
0.02
0.03
1. Molecular vibration4T2g (D)
4Eg (D)4T1g(G)
4Eg (G)
4A1g (G)
4T2g (G)
4Eg
4Eg
4T2g
4T1g
6A1g
E
Dq
Why are some lines broader than others?
21
81
2. Spin-Orbit Coupling
Coupling between an allowed
and forbidden transition which
are very close in energy
MS- MS > ML - MS > ML - MS
A
14 000 50 00025 000
[Ni(H2O)6]2+, d8
10
/ cm-1-
[Ni(H2O)6]2+, d8
3F
1D
3A2g
3T2g
1Eg
3T1g
Dq/B
E/B
3T1g 3A2g
spin forbidden transition
Why are some lines broader than others?
A
/ cm-1-30 00020 00010 000
[Ti(H2O)6]3+, d1
2T2g
2Eg
2B1g
2A1g
d3 4A2g
d5 (high spin) 6A1g
d6 (low spin) 1A1g
d8 3A2g
Degenerate electronic ground state: T or E
Non-degenerate ground state: A
3. The Jahn-Teller Theorem
Any non-linear molecule in a degenerate electronic state will undergo distortion
to lower it's symmetry and lift the degeneracy
83
eg
t 2g
eg
t 2g
weak field ligands
e.g. H2O
high spin complexes
strong field ligands
e.g. CN-
low spin complexes
I- < Br- < S2- < SCN- < Cl-< NO3- < F- < OH- < ox2-
< H2O < NCS- < CH3CN < NH3 < en < bpy
< phen < NO2- < phosph < CN- < CO
Spin Transition?
Crystal fields and magnetism --- high spin versus low spin
Spectrochemical series
84
E/B
/B
2T2g
4A1g, 4E
4T2g
4T1g
4T2g
4T1g
2A1g
4T2g
2T2g
6A1g
2Eg
4A2g, 2T1g
2T1g
2A1g
4EgAll terms included
Ground state assigned to E = 0
Higher levels drawn relative to GS
Energy in terms of B
High-spin and low-spin configurations
Critical value of
d5
WEAK FIELD STRONG FIELD
Weak field - strong field transitions and Tanabe Sugano diagrams
22
85
More Tanabe Sugano - d6, d7, d8
86
More Tanabe Sugano - d2, d3, d4,d5
87
Weak and strong fields as described by the MO’s ofCoordination Compounds MLx (x = 4,6)
1) Octahedral complexes with M-L -bonds only
Consider an example of an octahedralcomplex ML6 where metal and ligandsare -bound.
• Group orbitals of 6 L’s suitable for -bonding transform as a1g, eg and t1u
M 6 L GO's
d
t2g
t1u
s
p
a1g
egeg
a1g
t1u
2t1u
1t1u
2a1g
1a1g
1eg
2eg
t2g
88
2) Octahedral complexes with M-L -bonds. -Donating ligands
T2u
(x,y,z)T1u
(xz, yz, xy)T2g
(Rx,Ry,Rz)T1g
(2z2-x2-y2, x2-y2)Eg
x2+y2+z2A1g
Oh
M 6 L -GO's
t2g
eg
t2g
eg
1t2g
2t2g
The symmetry of metal and ligand group orbitals suitablefor M-L -bonding in octahedral complexes can befound using group theory: r( ) = T1g + T2g + T1u +T2u
• Transition metal atom has orbitals of the t2g (dxy, dyz,dxz) and t1u (px, py, pz) symmetry and no orbitals of thet1g or t2u symmetry (see the character table below).
• Metal orbitals of the t1u symmetry are alreadyinvolved in -bonding with 6 L’s (see the previousdiagram).
• Therefore, -bonding is only possible between metaland ligand orbitals of the t2g symmetry.
Consider the case of the ligand-to-metal -donation whenthe ligands t2g orbitals are completely filled (and of lowenergy) while the metal t2g orbitals are not completelyfilled.
• We will get two new t2g-MO’s, 1t2g and 2t2g.• The energy gap between the partially filled 2t2g and eg
MO’s and thus o are now smaller.• So -donating ligands are weak field ligands (halogeno
ligands, OH-, H2O etc).
23
89
3) Octahedral complexes with M-L -bonds. -Accepting ligands
M 6 L -GO's
t2g
eg
t2g
eg
1t2g
2t2g
• In the case of -accepting ligands likeCO, CN- etc. the ligands group orbitalsof t2g symmetry are empty and higher inenergy than corresponding t2g metalorbitals.
• The metal-ligand -bonding stabilizesthe metal complex and increases o.
• Therefore the ability of a ligand to be a-acceptor makes the ligand a strongerfield ligand.
• Increased o prevents the eg level frombeing filled and the metal valence shellto be “overfilled” and helps it obey the“18 electron rule”.
90
TiF4 d0 ion
TiCl4 d0 ion
TiBr4 d0 ion
TiI4 d0 ion
d0 and d10 ion have no d-d transitions
[MnO4]- Mn(VII) d0 ion
[Cr2O7]- Cr(VI) d0 ion
[Cu(MeCN)4]+ Cu(I) d10 ion
[Cu(phen)2]+ Cu(I) d10 ion
Zn2+ d10 ion
extremely purple
bright orange
white
white
orange
dark brown
colourless
dark orange
white
Charge Transfer Transitions
91
Charge Transfer Transitions
Ligand-to-metal charge transfer
LMCT transitions
Metal-to-ligand charge transfer
MLCT transitions
M d
L
L
L
t2g*
eg*
d-d transitions
Charge Transfer Transitions
92
t2*
a1*
a1
t2
t2*
t2
t2a1 ,
et1,t2t1
t2
a1
t2
nd
( )
( )
(n+1)s
(n+1)p
t
Ligand to Metal Charge Transfer (LMCT)
24
93
CT transitions are spin allowed and Laporte allowed
Transitions occur from a
singlet GS to a singlet ES
S = 0
Transitions occur between
metal based orbitals with d-
character and ligand based
orbitals with p-character
l = ± 1
CT transitions are therefore much more intense than d-d transitions!!
Charge Transfer Selection Rules
94
spin-allowed; Laporte allowed
Cr
NH3
NH3H3N
H3N
H3N
2+
Cl
log
(/L
mo
l-1 c
m-1
)
/ nm600
(17 000 cm-1)
3
4
1
2
200
(50 000 cm-1)
400
(25 000 cm-1)
LMCT
d-d d-d
Identifying charge transfer transitions
Intensity
Solvatochromism - variation in absorption wavelength with solvent
[CrCl(NH3)5]2+, Cr(III), d3
Ligand to Metal Charge Transfer (LMCT) Transitions
95
Why multiple peaks?Why the increasing absorption at 200 nm?What is the electronic structure of the Chromium?What are the magnetic properties?
Understanding Cr3+
96
[MnO4]-, dark purple
e- poor metal (electropositive), high charge
Cr(III), d3 ion, Mn(VII), d0 ion
LMCT = ligand to metal charge transfer
e- rich ligand
O2-, Cl-, Br-, I-
spin-allowed; Laporte allowed
O
Mn
OO
O
-
LMCT Transitions
25
97
nd
(n+1)p
a1 ,t2
t2
a1
e, t2t1 ,t2
M 4LML4
t
L(t1) M(e) 17 700 cm-1
L(t1) M(t2*) 29 500 cm-1
L(t2) M(e) 30 300 cm-1
L(t2) M(t2*) 44 400 cm-1
(n+1)s
a1
t2
t2
t1
e
t2*
a1*
t*
MO diagram of MnO4-
98
Metal Ligand Charge Transfer (MLCT)
99
[Cu(phen)2]+, dark orange
e- rich metal, low charge, lower OS
Cu(I), d10 ion
MLCT = metal to ligand charge transfer
-acceptor ligand with low-lying * orbitals
1,10-phenanthroline
/ nm400 500 600
300
400
500
100
200
max = 458 nm
spin-allowed; Laporte allowed
N
N
N
NCu
+
Charge-Transfer Transitions: MLCT
100
[Ru(bpy)3]2+, bright orange
e- rich metal, low charge, lower OS
Ru(II), d6 ion, low spin
MLCT = metal to ligand charge transfer
-acceptor ligand with low-lying * orbitals
2,2'-bipyridine
/ nm300 500
max = 452 nm
MLCT
spin-allowed; Laporte allowed
200 400
- *
Ru
N
NNN
N
N
2+
Charge-Transfer Transitions: MLCT
26
101
YAl3(BO3)4
Yttrium aluminium borate
Second harmonic generation
Converts near IR laser emission
at 1060 nm to 530 nm
Dope with Pr3+ which emits
at 1060 nm to make a self-
doubling laser
D3 site symmetry
1 mm
Rare Earth Complexes --- Some special features
102
Why rare earth?? [Xe]4fN5s25p6
N electrons in the outer shell are not the most outer ones
Shielded by 5s25p6
Result: Energy levels are not affected as much by
surroundings. Get very sharp absorption and emission lines
Can determine energy levels of a rare earth ion in a crystalin a crystal
to a good accuracy from a total free ion Hamiltonian
HF = Ho + HC + HSO
Rare EarthRare Earth Complexes --- Some special featuresComplexes --- Some special features
103
HF = Ho + HC + HSO
For rare earth ions HC HSO
For Pr3+ configuration is [Xe]4fN5s25p6
Term symbols are worked out as we did for d2
1I, 3P, 1D, 1G, 3F, 3H
Rare EarthRare Earth Complexes --- Some special featuresComplexes --- Some special features
104Free ion withFree ion with spin orbitspin orbit crystal field
27
105
(full line) (dashed line)
Polarized absorption spectra of Pr3+ in YAB
106
polarizer crystal detector
107
z
From irreducible representations, E irreducible rep will transmit
light with electric field vector in the x,y plane; A2 in z direction
Which bands will be polarized?
108
Photon is a particle with spin 1, has spin angular momentum
http://www-structure.llnl.gov/cd/cdtutorial.htm
Linear polarized light can be viewed as a superposition ofopposite circular polarized light of equal amplitude andphase. A projection of the combined amplitudesperpendicular to the propagation direction thus yields a line
left helicity
right helicity
Circular dichroism
28
109http://www-structure.llnl.gov/cd/cdtutorial.htm
Recall: Molecule is not chiral (achiral) if itpossesses an Sn improper rotation axis(includes i and ) Absorption spectra
Chiral molecules exist as two (left - right)
enantiomers.
Circular Dichroism (CD) Spectra
of two optical isomers of
Circular dichroism
Recall: Molecule is not chiral (is achiral) if
it posseses an Sn improper rotation axis(includes i and )
They have different absorption coefficients
for left and right circularly polarized light
[Co(en)3]3+
[Co(en)3]3+
[Co(en)3]3+
[Co(en)3]3+
110http://www-structure.llnl.gov/cd/cdtutorial.htm
Absorption spectra
Circular Dichroism (CD) Spectra
new band-really D3
Circular dichroism
Looks like Oh
111http://www-structure.llnl.gov/cd/cdtutorial.htm
Assign geometrical
configurations by
comparison with
known CD and
configuration for
Circular dichroism
112
Optical Isomer Resolution