Crystal field theory11 21

1

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


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



10

37

What is it?

How do you use it?


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


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



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?


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?


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


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


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


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



3 = obscured by CT

transition

Energy diagram for octahedral d3 complex

E

68


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


Ligand-to-metal charge transfer

LMCT transitions

Metal-to-ligand charge transfer

MLCT transitions

M d

L

L

L

t2g*

eg*

d-d 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


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-


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


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


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+


Absorption spectra

Circular Dichroism (CD) Spectra

new band-really D3

Circular dichroism

Looks like Oh


Assign geometrical

configurations by

comparison with

known CD and

configuration for

Circular dichroism

112

Optical Isomer Resolution

Technology

Crystal field theory11 21