Crystal Field Theory
400
500
600
•The
relationship
between colors
and complex
metal ions
800
Crystal Field Model
A purely ionic model for transition metal complexes.
Ligands are considered as point charge.
Predicts the pattern of splitting of d-orbitals.
Used to rationalize spectroscopic and magnetic
properties.
Salient features of CFT
The interaction between the metal ion and the ligand is electrostatic
one i.e ionic.
The metal ion the ligands are considered as point charges.
The negative ligands are regarded as negative point charges and the
neutral ligands are regarded as diploes. The negative end of the
ligand dipole is oriented towards the metal ion.
The central metal ion is surrounded by ligands that contain one or
more lone pair of electrons.
The lignand electron pairs can’t enter into the metal orbitals. Thus
there is no orbital overlap between the metal and the ligand.
Number and the nature of lignds and their arrangement around the
central metal ion will determine the crystal field
Different crystal field will have different effects on the relative
energies of the five d orbitals.
The electrons of the central metal ion and those of the ligands have
repulsive effect. This causes the splitting of the degenerate d orbitals
into two groups- namely t2g and eg. It is called crystal field splitting.
d-orbitals: look attentively along the axis
Linear combination of
dz2-dx2 and dz2-dy2
d2z2-x2-y2
Octahedral Field
19.3
Crystal Field Theory: Splitting of the 5 d orbitals
Consider the response of the energy of the d
orbitals to the approach of 6 negatively
charged ligands (a “crystal field”) along the
x, y and z axes of the metal
The two d orbitals (dx2-y2 and dz2) that are
directed along the x, y and z axes are
affected more than the other three d orbitals
(dxy, dxz and dyz)
eg orbitals
crystal
field
energy
splitting
The result is that the dx2-y2 and dz2
orbital increase in energy relative to the
dxy, dxz and dyz orbitals (D0 is called the
“crystal field energy splitting”
t2g orbitals
7
Crystal field splitting of the 5 d orbitals by the “crystal field” of 6 ligands
eg orbitals
Crystal field
splitting
t2g orbitals
Orbitals “on axis”: “energy increases”
Orbitals “off axis”: “energy decreases”
8
Crystal Field Splitting Energy (CFSE)
• In Octahedral field, configuration is: t2gx egy
• Net energy of the configuration relative to the
average energy of the orbitals is:
= (-0.4x + 0.6y)O
O = 10 Dq
BEYOND d3
• In weak field: O  P, => t2g3eg1
• In strong field O  P, => t2g4
• P - paring energy
The Spectrochemical Series
Based on measurements for a given
metal ion, the following series has been
developed:
I-<Br-<S2-<Cl-<NO3-<N3-<F-<OH-<C2O42-<H2O
<NCS-<CH3CN<pyridine<NH3<en<bipy<phen
<NO2-<PPh3<CN-<CO
The Spectrochemical Series
The complexes of
cobalt (III) show the
shift in color due to the
ligand.
(a) CN–, (b) NO2–, (c)
phen, (d) en, (e) NH3,
(f) gly, (g) H2O, (h) ox2–
, (i) CO3 2–.
Tetrahedral Complexes
Square Planar Complexes
Ligand Field Strength Observations
1. ∆o increases with increasing oxidation
number on the metal.
Mn+2<Ni+2<Co+2<Fe+2<V+2<Fe+3<Co+3
<Mn+4<Mo+3<Rh+3<Ru+3<Pd+4<Ir+3<Pt+4
2. ∆o increases with increases going down a
group of metals.
Magnitude of 
Oxidation state of the metal ion
[Ru(H2O)6]2+
19800 cm-1
[Ru(H2O)6]3+
28600 cm-1
Ground-state Electronic Configuration,
Magnetic Properties and Colour
When the 4th electron is assigned it will either go into the higher
energy eg orbital at an energy cost of o or be paired at an energy
cost of P, the pairing energy.
d4
Strong field =
Low spin
(2 unpaired)
P < o
P > o
Coulombic repulsion energy and exchange energy
Weak field =
High spin
(4 unpaired)
Ground-state Electronic Configuration,
Magnetic Properties and Colour
[Mn(H2O)6]3+
Weak Field Complex
the total spin is 4  ½ = 2
High Spin Complex
[Mn(CN)6]3Strong field Complex
total spin is 2  ½ = 1
Low Spin Complex
What is the CFSE of [Fe(CN)6]3-?
C.N. = 6  Oh
Fe(III)  d5
3-
CN
NC
CN- = s.f.l.
h.s.
l.s.
eg
CN
eg
+ 0.6 oct
Fe
CN
NC
CN
- 0.4 oct
t2g
t2g
CFSE = 5 x - 0.4 oct + 2P = - 2.0 oct + 2P
If the CFSE of [Co(H2O)6]2+ is -0.8 oct, what spin state is it in?
C.N. = 6  Oh
Co(II)  d7
2+
OH 2
H 2O
h.s.
l.s.
eg
eg
+ 0.6 oct
OH 2
Co
OH 2
H 2O
OH 2
t2g
CFSE = (5 x - 0.4 oct)
+ (2 x 0.6 oct) +2P = - 0.8 oct+2P
t2g
- 0.4 oct
CFSE = (6 x - 0.4 oct)
+ (0.6 oct) + 3P= - 1.8 oct + P
The origin of the color of the transition
metal compounds
E2
E
h
E1
E = E2 – E1 = h
Ligands influence O, therefore the colour
The colour can change depending on a number of factors
e.g.
1. Metal charge
2. Ligand strength
The optical absorption spectrum of [Ti(H2O)6]3+
Assigned transition:
eg
t2g
This corresponds to
the energy gap
O = 243 kJ mol-1
absorbed
color
observed
color
• Spectrochemical Series: An order of ligand
field strength based on experiment:
Weak Field I-  Br- S2- SCN- Cl-
NO3- F-  C2O42- H2O NCS-
CH3CN NH3 en  bipy phen
NO2- PPh3 CN- CO Strong Field
H2 N
NH2
N
N
N
N
Ethylenediamine (en)
2,2'-bipyridine (bipy)
1.10 - penanthroline (phen)
[CrF6]3-
[Cr(H2O)6]3+
[Cr(NH3)6]3+ [Cr(CN)6]3-
As Cr3+ goes from being attached to a weak field
ligand to a strong field ligand,  increases and the
color of the complex changes from green to yellow.
Limitations of CFT
Considers Ligand as Point charge/dipole only
Does not take into account of the overlap of ligand and
metal orbitals
Consequence
e.g. Fails to explain why CO is stronger ligand than CN- in
complexes having metal in low oxidation state