1. semester 2 Lecture note 1 Crystal Field Theory
Dr.Sadeem M.Al-Barody

2. Crystal-Field Theory
Model explaining bonding for transition metal complexes
• Originally developed to explain properties for crystalline material
• Basic idea:
Electrostatic interaction between lone-pair electrons result in coordination.

3. Energetics CFT - Electrostatic between metal ion and donor atom i
i) Separate metal and ligand high energy
ii) Coordinated Metal - ligand stabilized
iii) Destabilization due to ligand -d electron repulsion
iv) Splitting due to octahedral field. ii iv
iii

4. Ligand-Metal Interaction
Crystal Field Theory - Describes bonding in Metal Complexes
Basic Assumption in CFT:
Electrostatic interaction between ligand and metal
d-orbitals align along the octahedral axis will be affected the most.
More directly the ligand attacks the metal orbital, the higher the the energy of the d-orbital.
In an octahedral field the degeneracy of the five d-orbitals is lifted

5. d-Orbitals and Ligand Interaction (Octahedral Field)
Ligands approach metal
d-orbitals pointing directly at axis are affected most by electrostatic interaction
d-orbitals not pointing directly at axis are least affected (stabilized) by electrostatic interaction

6. Splitting of the d-Orbitals
Octahedral field Splitting Pattern:
The energy gap is referred to as (10 Dq) , the crystal field splitting energy.
The dz2 and dx2-y2 orbitals lie on the same axes as negative charges.
Therefore, there is a large, unfavorable interaction between ligand (-) orbitals.
These orbitals form the degenerate high energy pair of energy levels.
The dxy , dyx and dxz orbitals bisect the negative charges.
Therefore, there is a smaller repulsion between ligand & metal for these orbitals.
These orbitals form the degenerate low energy set of energy levels.

7. Magnitude of CF Splitting ( or 10Dq)
Color of the Complex depends on magnitude of 
1. Metal: Larger metal  larger 
Higher Oxidation State  larger 
2. Ligand: Spectrochemical series
Cl- < F- < H2O < NH3 < en < NO2- < (N-bonded) < CN-
Weak field Ligand: Low electrostatic interaction: small CF splitting.
High field Ligand: High electrostatic interaction: large CF splitting.
Spectrochemical series: Increasing 

8. Electron Configuration in Octahedral Field
Electron configuration of metal ion:
s-electrons are lost first.
Ti3+ is a d1, V3+ is d2 , and Cr3+ is d3
Hund's rule:
First three electrons are in separate d orbitals with their spins parallel.
Fourth e- has choice:
Higher orbital if  is small; High spin
Lower orbital if  is large: Low spin.
Weak field ligands
Small  , High spin complex
Strong field Ligands
Large  , Low spin complex

9. High Spin Vs. Low Spin (d1 to d10)
Electron Configuration for Octahedral complexes of metal ion having d1 to d10 configuration [M(H2O)6]+n.
Only the d4 through d7 cases have both high-spin and low spin configuration.
Electron configurations for octahedral complexes of metal ions having from d1 to d10 configurations. Only the d4 through d7 cases have both high-spin and low-spin configurations.

10. Color Absorption of Co3+ Complexes
The Colors of Some Complexes of the Co3+ Ion
Complex Ion Wavelength of Color of Light Color of Complex
light absorbed Absorbed
[CoF6] (nm) Red Green
[Co(C2O4)3] , 420 Yellow, violet Dark green
[Co(H2O)6] , 400 Yellow, violet Blue-green
[Co(NH3)6] , 340 Blue, violet Yellow-orange
[Co(en)3] , 340 Blue, ultraviolet Yellow-orange
[Co(CN)6] Ultraviolet Pale Yellow
The complex with fluoride ion, [CoF6]3+ , is high spin and has one absorption band. The other complexes are low spin and have two absorption bands. In all but one case, one of these absorptionsis in the visible region of the spectrum. The wavelengths refer to the center of that absorption band.

11. Colors & How We Perceive it
Artist color wheel
showing the colors
Which are complementary
to one another and
the wavelength
range of each color.

12. Black & White When a sample absorbs light, what we see is the sum
of the remaining colors that strikes our eyes.
If a sample absorbs all wavelength of visible light, none reaches our eyes from that sample. Consequently, it appears black.
If the sample absorbs no
visible light, it is white
or colorless.

13. Absorption and Reflection
If the sample absorbs
all but orange, the
sample appears orange.
750
430
650
580
560
490
400
Further, we also perceive orange color when visible light of all colors except blue strikes our eyes. In a complementary fashion, if the sample absorbed only orange, it would appear blue; blue and orange are said to be complementary colors.

14. Why Titanium (III) ion is violet ?
Transition Metals (d block elements) – Coloured Complexes
Why transition metals ion complexes have different colour?
Why Titanium (III) ion is violet ?
Taken from:

15. Transition Metals (d block elements) – Coloured Complexes
Colour formation due to splitting of 3d orbitals of metal ion by ligands
Absence of ligands
3d orbitals same energy level
five 3d orbitals are equal in energy
Presence of ligands
3d orbitals split
five 3d orbitals unequal in energy
Five 3d orbitals
Five 3d orbitals
Splitting 3d orbitals
Why Titanium (III) ion solution is violet ?
violet
No ligands
No splitting of 3d orbitals
3d orbitals equal energy
With ligands
Splitting of 3d orbitals
3d orbitals unequal energy
Splitting 3d orbitals
3d orbitals split into different energy level
Electronic transition possible
Photon of light absorbed to excite electrons

16. Ti3+ transmit blue/violet region BUT absorb green/yellow/red
Transition Metals (d block elements) – Coloured Complexes
Why Titanium (III) ion solution is violet ?
Ti3+ transmit blue/violet region BUT absorb green/yellow/red
Light in vis region
Ti3+ transmit
blue/violet region
Electron excited
Ground state Ti3+ (3d1)
Ti3+ absorb green/yellow/red photons
to excite electrons to higher level

17. Transition Metals (d block elements) – Coloured Complexes
Why Copper (II) ion solution is blue ?
Cu2+ transmit blue/violet BUT absorb /orange/red region
Light in vis region
Cu2+ transmit
blue/violet region
Electron excited
Ground state Cu2+ (3d9)
Cu2+ absorb orange/red photons
to excite electrons to higher level
Cu2+ appears blue
Complementary colour (Red/Orange) are absorbed to excite electron
Blue colour is transmitted

18. Transition Metals (d block elements) – Coloured Complexes
Transition metal have different colours due to
splitting of 3d orbitals by ligands
partially filled 3d orbitals for electron transition
Why some are colourless ?
Cu2+ anhydrous – colourless
Cu1+ hydrous – colourless
Zn2+ hydrous – colourless
Sc3+ hydrous – colourless
CuSO4 (anhydrous) without ligands - Colourless
NO Colour
No ligands
No splitting of 3d orbitals
No electron transition
No colour
CuSO4 (hydrous) with H2O ligands – Blue Colour
Colour
Ground state Cu2+ (3d9)
Electron transition from
lower to higher level by
absorbing ∆E
Ligands split the 3d orbitals
[Cu(H2O)6]2+ SO4 – splitting 3d orbitals by ligand – Blue colour

19. Sc 3+ ion with ligands - Colourless Zn2+ ion with ligands - Colourless
Transition Metals (d block elements) – Coloured Complexes
Sc 3+ ion with ligands - Colourless
[Sc(H2O)6]3+ CI3
Empty 3d orbitals
No colour
NO Colour
No electrons in 3d orbital
No electron transition
Ground state Sc3+ (3d0)
Ligands split the 3d orbitals
[Zn(H2O)6]2+ SO4
Filled 3d orbitals
No colour
Zn2+ ion with ligands - Colourless
NO Colour
Fully filled in 3d orbital
No electron transition
Ground state Zn2+ (3d10)
Ligands split the 3d orbitals

20. Transition Metals (d block elements) – Coloured Complexes
[Cu(H2O)6]1+ CI
Filled 3d orbitals
No colour
Cu1+ ion with H2O ligands - Colourless
NO Colour
Fully filled in 3d orbital
No electron transition
Ground state Cu2+ (3d10)
Ligands split the 3d orbitals
Cu2+ ion without H2O ligands – Colourless
NO Colour
No ligands
No splitting of 3d orbitals
No electron transition
No colour
Cu2+ ion with H2O ligands – Blue Colour
Colour
Ground state Cu2+ (3d9)
Electron transition from
lower to higher level by
absorbing ∆E
Ligands split the 3d orbitals
[Cu(H2O)6]2+ SO4 – splitting 3d orbitals by ligand – Blue colour

21. Octahedral, Tetrahedral & Square Planar
CF Splitting pattern for various molecular geometry
dz2
dx2-y2
dxz
dxy
dyz
dxz
dz2
dx2-y2
dxy
dyz
dx2-y2
dz2
dxz
dxy
dyz
Octahedral
Tetrahedral
Square planar
Mostly d8
(Majority Low spin)
Strong field ligands
i.e., Pd2+, Pt2+, Ir+, Au3+
Pairing energy Vs. 
Weak field  < Pe
Strong field  > Pe
Small   High Spin

22. Summary
Crystal Field Theory provides a basis for explaining many features of transition-metal complexes. Examples include why transition metal complexes are highly colored, and why some are paramagnetic while others are diamagnetic. The spectrochemical series for ligands explains nicely the origin of color and magnetism for these compounds. There is evidence to suggest that the metal-ligand bond has covalent character which explains why these complexes are very stable. Molecular Orbital Theory can also be used to describe the bonding scheme in these complexes. A more in depth analysis is required however.