The document discusses several theories for how transition metals form complexes and interact with ligands, including crystal field theory, molecular orbital theory, and density functional theory. It recommends first looking at crystal field theory, as described in chapters 11 of Huheey and chapter 7 of Carter. Crystal field theory models the electronic effects of ligands on a metal atom by considering the electrostatic interactions between ligand point charges and the metal's d-orbitals. This splitting of d-orbital energies depends on the symmetry of the ligand field. An octahedral field splits the five d-orbitals into a lower-energy t2g set and higher-energy eg set.

1. How do we take interactions with ligands into account? Transition Metals -- Bonding and Spectroscopy
Crystal field theory
Molecular orbital theory
Hybrid orbitals and valence bond theory
Includes crystal field theory for transition metal complexes
Density function theory
(Ch 11, pp 387 - 413 Huheey; Ch 7 Carter)
Look at crystal field theory first
Molecular orbital theory
Huheey, Ch. 11; Carter, Chapter 7 Includes MO theory for transition metal complexes
(Ch 11, pp 413 - 433 Huheey; Ch 7 Carter)
Andrei N. Vedernikov -- University of Maryland
http://www.chem.umd.edu/groups/vedernikov/VGroup_Teaching-601.htm
http://www.tcd.ie/Chemistry/Under/ch3018.html
1 2
Free Atom States --- Term Symbols
Free Atoms Molecular Complexes Solids
H = E
Atkins/Shriver
= Hfree atom
3 4
1

2. HFree atom contributions
Free Atom States -- Term Symbols
Lifting of energy degeneracies in a
d2 gaseous atom
5 6
Lifting of energy degeneracies in a d2 gaseous atom
How do we take interactions with ligands into account?
Crystal field theory
Molecular orbital theory
Density function theory
Look at crystal field theory first
electron Huheey, Ch. 11; Carter, Chapter 7
configuration
Andrei N. Vedernikov -- University of Maryland
http://www.chem.umd.edu/groups/vedernikov/VGroup_Teaching-601.htm
spin states and
terms from sisj multiplets from Experimental
http://www.tcd.ie/Chemistry/Under/ch3018.html
7 8
and li lj coupling lisi coupling
2

3. The electronic effects of adding ligands to the free atom Electronic structure of Coordination Compounds
H = E Crystal Field Theory
• Considers only electrostatic interactions between the
ligands and the metal ion.
• Ligands are considered as point charges creating an
electrostatic field of a particular symmetry
Main steps to estimate the relative energies of d-orbitals
in a field of a particular symmetry
Three cases
1) An isolated metal ion. Five d-orbitals are degenerate
• Ligands don t a ect outer valence electrons- lanthanides
2) A metal ion in an averaged ligand field. The orbital
energy increases due to electron (metal) – electron
(ligands) repulsions. Oh octahedral
• Ligands weakly affect outer valence electrons---many 3d complexes
Weak Field case 3) A metal ion in a ligand field of certain symmetry. d-
energy levels may become split into several sublevels.
• Ligands strongly affect outer valence electrons--
Some of d-orbitals become stabilized, some become less
Strong Field case
stable. The total orbital energy gain due to the
9 stabilization is equal to the total orbital energy loss. 10
Symmetry and the atom ...reducible representations based
Interactions of d-orbitals with octahedral ligand field
on angular momentum
Characters, [R], for operations in spherical symmetry (group
R3) as a function of the angular momentum quantum number, j,
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
for d orbitals or D term symbol!!
11 12
Carter, page 205
3

4. d-Orbital splitting in the fields of various symmetries Octahedral field. ML6 complexes
MX4
• The d-orbital splittings presented on diagram E dx2-y2
correspond to the cases of cubic shape MX8 b1g • In the field of Oh symmetry five degenerate d-orbitals will be split into two sets, t2g and
(Oh ), tetrahedral shape MX4 (Td), icosahedral eg orbitals (check the Oh point group character table)
shape MX12 (Ih), octahedral shape MX6 (Oh) and
square planar shape MX4 (D4h).
Oh Td Ih Oh D4h
• Three t2g orbitals be stabilized by 0.4 o and two e g orbitals will be destabilized by 0.6 o
MX6
Td L eg
1
z dz2=0.5(dz2-y2+dz2-x2) z
dx2-y2
z
L L 1
L L
E (2z2-x2-y2 , x2-y2) MX8
dz2 4 4
dx2-y2 L
T2 (xy, xz, yz) eg 2x = 3y 4 3 2
eg 1
x+y= o y y y
MX4
x
dyz 3 3
Ih dxz t2g
x = 0.6 o 2
dz2-y2
2
dz2-x2
dxy dxy y x x x
MX12 t2g y = 0.4
Hg (2z2-x2-y2 , x2-y2, xy, xz, yz) free ion dyz
b2g
the ion in an
o
dxz t2 averaged the ion in an
dxy ligand field octahedral
dyz
D4h ligand field
1
z
averaged hg t2g
A1g x2+y2, z2 ligand Oh
field
e
B1g x2-y2 a1g … 4 3
dz2 y
B2g xy dz2
dz2 Eg (2z2-x2 -y2, x2-y2)
dx2-y2
dx2-y2 dyz …
Eg (xz, yz) eg dyz eg dxz x 2
dxz t2g 13 T2g (xz, yz, xy) 14
… dxy
…
How does an octahedral array of ligands affect the d orbitals? eg
configurations
eg t2g2
t2g
d orbitals
t2g t2g3
spectrochemical series
t2g4 low spin
3rd row > 2nd row > 1st row transition metal atoms
higher charge TM > smaller charge strong field d4 if weak field t2g3 eg1 high spin
15 16
4

5. Factors affecting the magnitude of
Ligand-field splitting parameters O of ML6 complexes • 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-
• values are in multiples of 1000 cm-1
• entries in parentheses are for low-spin complexes • 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, tetrahedral
complexes 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 to
increase at a given metal center:
I- < Br- < Cl- < F- , OH- < H2O < NH3 < NO2- < Me- < CN- < CO
For [CoIIIL 6 ] we have , cm-1: 13,100 (F), 20,760 (H 2 O), 22,870 (NH3)
Shriver, Table 7.3 For [CrIIIL 6] we have , cm-1: 15,060 (F), 17,400 (H 2O),
17 26,600 (CN) 18
Some consequences of d-orbital splitting Calculating CFSE for Octahedral species
• Magnetism. In the case of large we observe
low-spin, while for small high-spin
complexes (d4-d7 configurations). E low spin d6 high spin d6
CFSE = [0.4 x #t2g electrons – 0.6 x # eg electrons)
• Energy. If the occupancy (x) of the orbitals eg
stabilized by a ligand field is more than that of L
t 3 e1
the destabilized orbitals (y), the complex Oh dx2-y2
becomes more stable by the Crystal Field L L For
Stabilization Energy (CFSE )which is (0.4y-
0.6x) for octahedral species.
MX6
dz2
L L 2g g
eg L
• For d0, d5 (high-spin) and d10 complexes CFSE is
always zero. 2xt = 3y (0.4 x 3 - 0.6 x 1)
large small
eg x+y=
o o
o
• Redox potentials. Some oxidation states may
become more stable when stabilized orbitals are x = 0.6
fully occupied. So, d6 configuration becomes
more stable than d 7 as o increases.
CoL62+ = CoL63+ + e - x = 0.6 o
t2g y
E0= -1.8 (L=H2O) … +0.8 V (L=CN- ) y = 0.4 Note:
t2g o
the ion in an
• M-L bond lengths and Ionic radii of M n+ are averaged
smaller for low-spin complexes and have a the ion in an = 10Dq
minimum for d6 configuration (low spin). ligand field octahedral
t2g
R, Å, of M3+: 0.87 (Sc), 0.81 (Ti), 0.78 (V), 0.74 ligand field
(Cr), 0.72 (Mn), 0.69 (Fe), 0.67 (Co), 0.71 (Ni),
… 0.78 (Ga) dxy dxz dyz 19 20
5

6. Lattice energies of the divalent metal halides of the first Radii of some trivalent ions
transition series as a function of the number of d electrons
low spin -- solid circles
Huheey, Fig 11.15
Huheey, Fig 11.14 21 22
Crystal-field stabilization energies High and low spin complexes of various geometries
• d-d Electron-electron repulsions in d4-d7 metal complexes (3d) correspond to
• N is the number of unpaired electrons the energy of 14000-25000 cm-1. If > 14000-25000 cm-1, the complex is low dx2-y2
b1g
• CFSE is in units of O for octahedra or for tetrahedra spin.
T
• the calculated relation is T (4/9) O • For octahedral complexes o ranges from 9000 to 45000 cm -1. It is therefore
common to observe both high and low spin octahedral species.
tetrahedral
MX4 MX4
• For tetrahedral complexes t = (4/9) o ranges from 4000 to 16000 cm-1. Low
C C Td D4h
spin tetrahedral complexes are very rare.
square-planar
Nr
Nr = d5
IV
Nr Co Nr
µ=1.8 M
Nr
• For square planar complexes is very large. Even with weak field ligands
high-spin d8 complexes are unknown (but known for d6). dxy
b2g
dyz
dxz t2
• Sometimes complexes of different configuration and magnetic properties dxy
coexist in equilibrium in solution. For the Ni(II) complexes shown below µ=0
t i
M (R = Me; square planar); 3.3 (R = Bu; tetrahedral) and 0-3.3 (R = Pr; both)
e
R a1g
R
O N dz2
N dz2
Ni O
Ni dx2-y2
N O N dyz
23 R
R O 24 eg dxz
Shriver, Table 7.3 µ=0 M
µ = 3.3 M
6

7. How do we determine the magnitude of the crystal field? How do we determine the Crystal Field Splitting?
Magnetism of octahedral transition metal complexes (from an electron configuration perspective)
• The number of unpaired electrons n in a metal complex can be derived from the measure optical absorption... d1 configuration
experimentally determined magnetic susceptibility M .
• M is related to magnetic moment µ 2.84( M T)
1/2 (Bohr magnetons)
• µ is related to n: µ [n(n+2)]1/2.
• Calculated magnetic moments for octahedral 3d metal complexes, ML6:
M High spin complexes Low spin complexes
# of unp. e’s µ, M # of unp. e’s µ, M
Ti3+, V4+ 1 (d1) (tg ) 1 1.73
V3+ 2 (d2) (tg ) 1 (tg)1 2.83 500nm
V2+, Cr3+ 3 (d3) (tg ) 1 (tg)1(tg ) 1 3.87
Cr2+, Mn3+ 4 (d4) (tg ) 1 (tg)1 (tg)1 (eg) 1 4.90 2 (d4) (tg ) 2 (tg)1 (tg)1 2.83
Mn2+, Fe3+ 5 (d5) (tg ) 1 (tg)1 (tg)1 (eg) 1 (eg)1 5.92 1 (d5) (tg ) 2 (tg)2 (tg)1 1.73
Fe2+, Co3+ 4 (d6) (tg ) 2 (tg)1 (tg)1 (eg) 1 (eg)1 4.90 0 (d6) (tg ) 2 (tg)2 (tg)2 0
Co2+, Ni3+ 3 (d7) (tg ) 2 (tg)2 (tg)1 (eg) 1 (eg)1 3.87 1 (d7) (tg ) 2 (tg)2 (tg)2 (eg) 1 1.73
Ni2+ 2 (d8) (tg ) 2 (tg)2 (tg)2 (eg) 1 (eg)1 2.83
Ti(H2O)63+
25 26
Cu2+ 1 (d9) (tg ) 2 (tg)2 (tg)2 (eg) 2 (eg)1 1.73
A good guide---
A more complicated problem Tanabe Sugano Diagram
d3
What is it?
How do you use it?
Why multiple peaks?
Why the increasing absorption at 200 nm?
What is the electronic structure of the chromium atom?
What are the magnetic properties? 27 28
7

8. Answer to these questions-- Instead of electron configurations
Absorption maxima in a visible spectrum have three -- look at how the free atom states
important characteristics Oh
are affected
d2 correlation
1. number of maxima (observed absorption peaks) diagram
(note labels)
What are the electronic states of the complex?
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
ground state
29 30
weak field
Symmetry and the atom... reducible representations based weak field Example 3F state from d2 configuration with
on angular momentum weak ligand field
Can do the same for other orbitals and/or terms as well d2 correlation
Note non-crossing rule:
For F ground state term (j = 3)
States with the same
symmetry and
multiplicity do not cross
F = A2g + T1g + T2g 31 32
Carter, page 205
8

9. Summary of splitting of states for dn configurations in an d2 correlation What happens if the ligand field is strong?
octahedral (Oh) field Work out strong field side
by starting with
hypothetical configurations
For t2g2 get reducible
strong field representation by taking
direct product t2g x t2g
(t2g)2 = A1g + Eg + T1g + T2g
see Carter, page 239
33 34
Now ready to begin interpreting optical spectra and
Summary - d2 Correlation Diagram
magnetic properties of transition metal complexes
d3
Energy states!
Why multiple peaks?
Why the increasing absorption at 200 nm?
What is the electronic structure of the chromium atom?
35 What are the magnetic properties? 36
9

10. A good guide--- The color spectrum -- a review Sir Isaac Newton
R O Y G B I V
Tanabe Sugano Diagram IR UV
600 nm 500 nm 400 nm
Wavelength
E = h = hc/
If a substance
absorbs here... 650 nm 600nm
What is it?
How do you use it?
800nm
400 nm 560 nm
It appears
430 nm 490 nm
as this color
If an object is black it absorbs all colors of light
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
Ground State An object is also orange if it reflects all the colors except blue,
37 the complementary color of orange 38
Energy of transitions
Excited State
Chromaticity
molecular rotations
lower energy
3 “virtual”
(0.01 - 1 kJ mol-1)
colors, which microwave radiation
when added
electron transitions
together give higher energy
all other (100 - 104 kJ mol-1) Ground State
colors visible and UV radiation
molecular vibrations
medium energy
(1 - 120 kJ mol-1)
IR radiation
During an electronic transition
the complex absorbs energy
complex changes energy states http://www.tcd.ie/Chemistry/Under
39 /ch3018.html 40
redistributes the electronic charge
//www.cs.rit.edu/~ncs/color/a_chroma.html
10

11. Now ready to begin interpreting optical spectra and
Estimating from electronic absorption spectra of d1 species
magnetic properties of transition metal complexes
• Values of are easily obtained from absorption spectra of d1 transition
metal complexes
d3
• In the d1 metal complex [Ti(H2O)6]3+ max = 500 nm, so that
= = 1/ max = 1/(5.00 10-5cm)= 20000 cm-1
1
d 2
max
Eg 2
Eg
=
Why multiple peaks?
Why the increasing absorption at 200 nm?
2
T2g 2
T2g What is the electronic structure of the chromium atom?
41 What are the magnetic properties? 42
Close relationships between dn electronic properties
Free Atom States -- Term Symbols - electrons and holes-- move hole
d1 d9
S = 1/2
2S + 1 = 2
behaves like behaves like
S=4
2S + 1 = 5
43 44
11

12. Putting this in the context of term symbols states… move hole
Oh
Relationships for octahedral and tetrahedral
Oh 10-1
1 d
d 2
2 T2g Oh Td Td
d1
Eg
2
d1 2
T2 d10-1 2E
2
D
Eg
2
D
2 2 2
T2g Eg 2 D
D 2
D t t
M ML6 M ML6
behaves like behaves like 2 2E 2
T2g T2
Oh 5-1 Oh M ML4 M ML4
5+1 d M ML6
d 5
T2g
5
Eg
The term sequence is the opposite for octahedral and tetrahedral
complexes of the same configuration
5
D 5
D
(not a single term)
(not a single term)
5 5
Eg The term sequence is in the same order for dn octahedral and d 10-n
T2g tetrahedral complexes.
M ML6 M ML6
45 46
Summarize with Orgel Diagram d1 d6 d4 d9 d1 octahdral A [Ti(OH2)6]3+
2E
g
2E 2T
g 2g
2D
2T
2g
10 000 20 000 30 000
- / cm-1
Orgel diagram for d1, d 4, d6, d 9
E Eg or E
T2g or T2
D
T 2g or T2
Eg or E
d1, d6 tetrahedral 0 d1, d6 octahedral
d4, d9 octahedral d4, d9 tetrahedral
47 LF strength 48
12

13. Orgel diagram for d2, d3, d7, d8 ions Quantum Mixing
Energy
A2 or A2g
Couple of things missing: spin multiplicties and electron-
T1 or T1g
electron repulsion (Racah Parameters B and C)
P T1 or T1g
T1 or T1g T2 or T2g
F Use Tanabe Sugano Diagrams
T2 or T2g
T1 or T1g
A2 or A2g
d2, d 7 tetrahedral 0 d2, d 7 octahedral
d3, d 8 octahedral d3, d 8 tetrahedral 49 50
Ligand field strength (Dq)
A good guide--- Selection Rules Spin Selection Rule
Tanabe Sugano Diagram
S=0
There must be no change in spin multiplicity during an electronic transition
What is it?
How do you use it?
Laporte Selection Rule
l=±1
There must be a change in parity during an electronic transition
g u
Ground State Selection rules determine the intensity of electronic transitions
51 52
13

14. Selection Rules for optical transitions -- Spin Selection Rule Selection Rules for optical transitions ---LaPorte’s Rule
A transition matrix element of the form , M = f O i where O is the operator of
2
interaction, can be used to calculate the intensity of a transition according to I f O i
Transitions may occur only between energy states with the
same spin multiplicity. Such integrals of the type M = f O i are only non-zero if the function fO i 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.
S=0
Consider the irreducible representation of the direct product
M = f µ i where is the operator of an electric dipole
violated by spin orbit or jj coupling transition. This operator transforms as the irreducible
representation of the cartesian coordinates.
In a centrosymmetric point group, must be an odd (u) function
f and i must be of opposite parity (u g or g u)
LaPorte’s Rule
10,000
This means that d p, s p, . . . are allowed, but
d d, s d, . . . are not 5 - 100
53 54
Selection Rules for optical transitions ---LaPorte’s Rule Selection Rules and note size of
Intensity for d-d transitions
0.03
Vibronic Mechanism
For a centrosymmetric structure (e.g. Oh ) vibrations [Ti(OH2)6]3+ , d1, Oh field 0.02
of odd parity (e.g. T1u) distorts the octahedron,
0.01
which partially relaxes LaPorte’s rule, so get a small
Spin allowed
absorption, 5 - 100 - / cm-1
Laporte forbidden 10 000 20 000 30 000
Transition between d orbitals
Tetrahedral (Td), noncentrosymmetric, complexes
2E
have d d transition intensities greater than those for E g
octahedral (Oh) 100 - 200 since no g or u symmetry
2D
2T
2g
55 oct 56
14

15. Relaxation of the Laporte Selection Rule for Tetrahedral Complexes
[V(H2O)6 ]3+, d2 Oh
600 [CoCl4 ]2-, d7 Td 10
Octahedral complex Tetrahedral complex
400
Centrosymmetric Non-centrosymmetric
5
200 Laporte rule applies Laporte rule relaxed
v / cm -1
25 000 20 000 15 000 10 000 5 000 / cm-1
30 000 20 000 10 000
Spin allowed; Laporte forbidden
4A
A2g 2g
inversion
3T 4T
1 T1 1g centre
P T1g
T1 T2g 4T
3T 2g
1
T2 F
3T
2 Oh complex d eg and t2g p t1u
T1g 4T Orbital mixing:
1g
3A
A2 Td complex d e and t2 p t2
2
d7 tetrahedral d2 octahedral
0 57 58
Dq In tetrahedral complexes, d-orbitals have some p character
Intenstity of transitions in d5 complexes
Laporte forbidden Spin forbidden transitions d5 octahedral complex
Energy (cm-1)
Spin forbidden Multiple absorption bands
4T [Mn(H2O)6 ]2+
50 000 2(g)
4T Very weak intensity
4F 1(g)
4A
40 000 2(g)
4T
4D 1(g)
30 000 4E
4P 4T
(g) Transitions are forbidden
2(g) 4E (G)
4G g
4E , 4A
(g) 1(g) 4A
20 000 0.03 1g (G)
4T
2(g)
4T (D)
4T 2g
10 000 1(g)
4E
Ground State
0.02 4T (D)
1g (G) g 6A
1g
6S 4T
500 1000
6A
1(g) 2g (G)
0.01
Dq (cm-1)
v / cm-1
Weak transitions occur due to: Unsymmetrical Vibrations (vibronic transitions) 20 000 25 000 30 000
Spin-orbit Coupling 59 60
15

16. Selection rules and observed intensities A good guide---
Tanabe Sugano Diagram
Transition complexes
Spin forbidden 10-3 – 1 Many d5 Oh
Laporte forbidden [Mn(OH2 )6]2+
Spin allowed
Laporte forbidden 1 – 10 Many Oh What is it?
[Ni(OH2 )6]2+ How do you use it?
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 allowed
102 – 104 Acentric complexes with ligands such as acac,
or with P donor atoms
Ground State
103 – 106 61
Many CT bands, transitions in organic species 62
Understanding Cr3+ Understanding Cr(NH3)63+ --- Tanabe Sugano Diagram
g g Expect two main d-d transition bands
g
g
g
g
g
g
Measure energies accurately
is at 21550 cm-1
Why multiple peaks? g
is at 28500 cm-1
Why the increasing absorption at 200 nm? 28500/21550 = 1.32
What is the electronic structure of the Chromium? Note: slope = 1 is ~ 15400 cm-1 = 650nm
What are the magnetic properties? 63 64
16

17. Tanabe-Sugano diagram interpretation Determining and B for [Cr(NH3)6]3+
1 = 21550 cm-1
[Cr(NH3) 6]3+: Three spin allowed transitions = 21550 cm-1 visible
1
2 = 28500 cm-1
2 = 28500 cm-1 visible
E/B
3 = obscured by CT transition
When 1 = E =21550 cm-1
2 28500
= = 1.32 E/B = 32.8
E/B 1 21550
so B = 657 cm-1
/B = 32.8
E/B = 43 cm-1
3 = 2.2 x 1 = 2.2 x 21500
E/B = 3 = 47300 cm-1 ~ 211nm E/B = 32.8 cm-1
32.8 If /B = 32.8
cm-1 = 32.8 x 657 = 21550 cm-1
One spin forbidden transition
4 = 15400 cm-1 visible For spin forbidden transition
4 15400 /B = 20.8
= = 0.72
1 21550 = 15400 cm-1 visible
/B = 32.8 65 4 66
/B = 32.8
B = 740 cm-1
Energy diagram for octahedral d3 complex Understanding Cr3+
4T 1 = 21550 cm-1 visible
1g
x 2 = 28500 cm-1 visible
3 = obscured by CT
transition
15 B'
x For Oh d3, o = 1 = 21550 cm-1
E 4T
1g 6 Dq
2 Dq o / B = 32.8
4T
2g
10 Dq B = 657 cm-1 Why multiple peaks?
4A
2g
Why the increasing absorption at 200 nm?
What is the electronic structure of the Chromium?
67
What are the magnetic properties? 68
17

18. Tanabe-Sugano diagram for weaker field d3 ions Determining and B
1 = 17 400 cm-1
[Cr(H2O)6]3+: Three spin allowed transitions
1 = 17 400 cm-1 visible 2 = 24 500 cm-1
2 = 24 500 cm-1 visible
E/B E/B When = E =17 400 cm-1
3 = obscured by CT transition 1
E/B = 24
24 500 = 1.41
so B = 725 cm-1
17 400
/B = 24
When 2 = E =24 500 cm-1
E/B = 34
3 = 2.1 x 1 = 2.1 x 17400
so B = 725 cm-1
E/B = 34 cm-1
3 = 36 500 cm-1
E/B = E/B = 24 cm-1
24 If /B = 24
cm-1 = 24 x 725 = 17 400 cm-1
69 70
/B = 24 /B = 24
Energy diagram for octahedral d3 complex What color is this Cr3+ complex?
If a substance
absorbs here... 650 nm 600nm
1 = 17 400 cm-1 visible
4T 800nm
1g 560 nm
= 24 500 cm-1 visible 400 nm
x 2
3 = obscured by CT It appears
430 nm 490 nm
as this color
transition
15 B'
x For Oh d3, o = 1= 17 400 cm-1
4T
1g 6 Dq
o / B = 24
2 Dq
4T
2g
B = 725 cm-1
10 Dq
4A
2g
71 72
18

19. Tanabe-Sugano diagram for d2 ions 10 Getting spectrochemical parameters for a d2 configuration
E/B
[V(H2O)6]3+: Three spin allowed transitions
5
E/B 1 = 17 800 cm-1
2 = 25 700 cm-1
30 000 20 000 10 000
/ cm-1
2
E/B = 43 cm-1
1 = 17 800 cm-1 visible
2 = 25 700 cm-1 visible
E/B = 30 cm-1 1
3 = obscured by CT transition in
UV
E/B = 43 cm-1 E = 25 700 cm-1
25 700 = 1.44 /B = 32
17 800 B = 600 cm-1
o /B = 32
o = 19 200 cm-1 /B = 32
3 = 2.1 1 = 2.1 x 17 800
3 = 37 000 cm-1
73 74
/B = 32
Energy level diagram for oct d 2, d7, tet d3, d8 Phosphorescence ---radiative decay from an excited state of different
1: x + 8 Dq spin multiplicity than ground state (generally slow!)
2: 2 x + 6 Dq + 15 B'
A2(g)
3: x + 18 Dq
3
T1(g)
2 x 10 Dq 1: T2(g) T1(g)
P
2: T1(g)(P) T1(g)
second
3: A2(g) T1(g)
lifetime
15 B 15 B'
T2(g)
F 1 2 Dq
6 Dq
T1(g) x 627 nm
75 Ruby - Cr3+ in Al2O3 76
1st laser in 1960
19