Crystal field theory

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Bonding and Spectroscopic Properties of
Transition Metal Complexes
Dr. Christoph Sontag, Phayao University Aug.2012
This tutorial was published on the web site:
http://www.chem.shef.ac.uk/level-4/cha99kw/index.html
by the University of Sheffield, but is no longer available online.
A copy of the online version is available at my website: http://myphayao.com
1. Bonding
1.1 Crystal Field Theory
1.2 Factors affecting the size of Δo and Δt
1.3 Jahn-Teller Effect
1.4 Hard and Soft Acids and Bases
2. Spectroscopic Properties
1.1 Crystal Field Theory
 Introduction to crystal field theory
 Octahedral crystal field
 Tetrahedral crystal field
 Square planar crystal field
 Crystal field splitting parameters
 CFSE

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Introduction
The bonding of transition metal complexes can be explained by two approaches:
crystal field theory and molecular orbital theory.
Molecular orbital theory takes a covalent approach, and considers the overlap of
d-orbitals with orbitals on the ligands to form molecular orbitals; this is not
covered on this site.
Crystal field theory takes the ionic approach and considers the ligands as point
charges around a central metal positive ion, ignoring any covalent interactions.
The negative charge on the ligands is repelled by electrons in the d-orbitals of
the metal. The orientation of the d-orbitals with respect to the ligands around
the central metal ion is important, and can be used to explain why the five d-
orbitals are not degenerate (= at the same energy). Whether the d-orbitals point
along or in between the cartesian axes determines how the orbitals are split into
groups of different energies. We shall examine the splitting of d-orbitals for
octahedral, square planar and tetrahedral ligand geometries.
First let us look at the shapes and
relative orientations of them:

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The Octahedral Crystal Field
Consider an octahedral arrangement of ligands around
the metal. The lone pair of electrons on each of the six
ligands is treated as a negative point charge. The
ligands are centered on the cartesian axes.
There are 2 forces:
(1) electrostatic attraction between each of the ligands
and the positive metal ion
(2) electrostatic repulsion between the ligands and electrons in the d-orbitals.
Question 1.1.1
Which of the d-orbitals point directly towards the ligands?
d xy d xz d yz d z2 d x2-y2
There is repulsion between the electrons in the d-orbitals and the lone pairs on
the ligands. This has a destabilizing effect on the d-orbitals. In a spherical field
all five d-orbitals would be raised in energy by the same amount. However,
electrons in the orbitals pointing towards the ligands are repelled by the ligand
lone pair to a greater extent than those pointing in between the ligands, because
they are closer. Hence, the dz
2
and dx
2
-y
2
orbitals are destabilized to a greater
extent than the dxy, dxz and dyz orbitals, and the degeneracy is removed.
We can now construct the d-orbital splitting diagram for an octahedral field.
The d-orbitals for an octahedral complex are split as shown in the diagram
below.

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The two sets of orbitals are labelled eg and t2g and the separation between these
two sets is called the ligand field splitting parameter, o. The subscript o is used
to signify an octahedral crystal field. o will be discussed in more detail later.
Next we will consider a tetrahedral crystal field.
The Tetrahedral Crystal Field
Consider a tetrahedral arrangement of ligands
around the central metal ion. The best way to
picture this arrangement is to have the ligands at
opposite corners of a cube. As with octahedral
complexes there is an electrostatic attraction
between each of the ligands and the positive

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metal ion, and there is electrostatic repulsion between the ligands and electrons
in the d-orbitals.
None of the d-orbitals point directly at the ligands as they did with the
octahedral geometry. However some orbitals come closer to the ligands than
others.
Question 1.1.2
Draw the tetrahedral configuration looking down the z-axis and draw the d-
orbitals to find those with the biggest interaction:
We can now construct the d-
orbital splitting diagram for a
tetrahedral complex.
The d-orbital splitting diagram
is the inverse of that for an
octahedral complex.

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The two sets of orbitals are labeled e and t2. The subscript g is not needed here,
it is only used for systems that possess a centre of symmetry (tetrahedral systems
do not have a centre of symmetry). The separation between the two sets of
orbitals is Δt (the subscript t signifies a tetrahedral crystal field). It should be
noted that Δt is smaller than Δo;
Δt ≈ 4
⁄9Δo
The reason for this will be discussed later.
Next we will consider a square planar crystal field.
The Square Planar Crystal Field
If we consider an octahedral complex, with six
ligands centered on the cartesian axes, then remove
two trans- ligands (the two ligands centered on the
z-axis) we arrive at a square planar arrangement of
ligands around the central metal ion.
Removing these two ligands has the effect of stabilizing the orbitals which point
directly or partially along the z-axis. That is, the dz
2
, dyz and dxz orbitals are
stabilized. Electrons in these orbitals suffer less repulsion than in an octahedral
field, and so are lowered in energy. As the dz
2
orbital points directly along the z-
axis it is stabilized to a greater extent than the dyz and dxz orbitals, which point
in between the z-axis.

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Crystal Field Splitting Parameters
In an octahedral or a tetrahedral crystal field, the d-orbitals are split into two
sets. The energy separation between them is called the crystal field splitting
parameter. It is given the symbol Δo (for an octahedral crystal field) or Δt (for a
tetrahedral crystal field).
In both cases the overall stabilization of one set of orbitals equals the overall
destabilization of the other set. In the octahedral crystal field the overall
stabilization of the t2g set equals the overall destabilization of the eg set. If the eg
set is raised by two units, the t2g set is lowered by three units to achieve this
energy balance. Therefore, the eg set is raised by 0.6Δo and the t2g set is lowered
by 0.4Δo. Note that some texts will use 10Dq instead of Δo, these are equivalent.

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In the tetrahedral crystal field the overall
stabilization of the e set equals the
overall destabilisation of the t2 set. Thus,
the e set is lowered by 0.6Δt and the t2
set are raised by 0.4Δt.
If all other things are equal, then Δt is smaller than Δo. Δt ≈ 4
⁄9Δo ≈ 1
⁄2Δo
“Bary Center”

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Crystal Field Stabilization Energy (CFSE)
Octahedral Complexes
Consider a dn configuration. As the d-orbitals are not degenerate, the way in
which the electrons are arranged in the orbitals is important. For a d1
system,
the electron will go into the lowest available orbital. This corresponds to
configuration t2g
1
, and there is a stabilization energy of -0.4Δo with respect to
the average energy. This is called the crystal field stabilization energy, CFSE.
For the general configuration t2g
x
eg
y
the CFSE is
CFSE = (-0.4x + 0.6y)Δo
For a d4
system it is clear that there are two possibilities. The fourth electron can
go into the t2g set or into the eg set, corresponding to configurations t2g
4
eg
0
(low
spin arrangement) and t2g
3
eg
1
(high spin arrangement), respectively.
If the fourth electron goes into the t2g set there would be an energy penalty
associated with the pairing of electrons. This is called the pairing energy, P. The
CFSEs are then -1.6Δo + P (for the low spin case) and -0.6Δo (for the high spin
case). Both low and high spin arrangements arise in practice, and which
configuration is adopted depends on the size of Δo.

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For large values of Δo: Δo > P
⇒ complex will be low spin
For small values of Δo: Δo < P
⇒ complex will be high spin
Question 1.1.3
Which of the following compounds has a CFSE of 0.0Δo associated with it?
[PtF6]
[Fe(CN)6]3-
[Mn(OH2)6]2+
Pairing energy - example:
from:
http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Crystal_Field_Theory/Virtual%3a_Electronic
_Structure/Ligand_Properties
The Fe2+
ion is d6
and has a pairing energy of approximately 17000 cm-1
(this is 2.1
eV or 200 kJ mol-1
). (The pairing energy varies somewhat with the coordination
environment.) For [Fe(H2O)6]2+
, Δo = 10000 cm-1
.
Because P > Δo, [Fe(H2O)6]2+
is a high-spin complex. The electron configuration is
(π*)4
(σ*)2
and the total spin is 2. (Note that water is a weak π-donor ligand.) On
the other hand, for [Fe(CN)6]4-
Δo = 33800 cm-1
, and this complex is low-spin (P <
Δo). All six d electrons reside in the low lying (π) orbitals (cyanide is an excellent
π-acceptor ligand), leading to a total spin of zero.

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Tetrahedral Complexes
The procedure for working out the CFSEs for tetrahedral complexes is the same
as that for octahedral complexes. However, as the energies of the two set of
orbitals are reversed (the e set is lower in energy than the t2 set) the CFSE for a
t2
x
ey
configuration is now:
CFSE = (-0.6y + 0.4x)Δt
As Δt is less than half the size of Δo, then normally all tetrahedral complexes are
high spin. This is because the pairing energy P is almost always larger than the
splitting between the two energy levels.
Question 1.1.4: Calculate the CFSE of the following molecules - do you expect
high- or low spin configuration ?
[CoCl4]2-
[ReO4]-
[FeCl4]-
1.2 Factors Affecting the Size of Δo
The size of the energy gap between the t2g and eg levels, Δo, depends on 3
factors:
 Oxidation state of the transition metal
 Row of the transition metal
 Ligand

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Oxidation State of the Transition Metal
As the oxidation state of the transition metal (effectively the charge on the
metal) is increased, the surrounding ligands are attracted more closely to the
metal centre. The orbitals on the ligands interact more strongly with the d-
orbitals and Δo increases.
Question 1.2.1
Which of the following two complexes would have the smallest value of Δo?
A. [Fe(OH2)6]3+
B. [Fe(OH2)6]2+
Row of the Transition Metal
On going from the first to the second row of a transition metal triad, there is
approximately a 50% increase in the size of Δo, and another 50% increase on going
from the second row to the third row. This is due to the fact that as you descend
a transition metal triad the size of the d-orbitals increases (3d < 4d < 5d). The
larger d-orbitals interact more with the orbitals on the ligands, hence Δo is
larger. It should also be noted that the pairing energies for the larger d-orbitals
are smaller, which means that low spin configurations are favoured.
Question 1.2.2
Which of the following would have the smallest value of Δo?
A. [Os(OH2)6]3+
B. [Fe(OH2)6]3+
C. [Ru(OH2)6]3+

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Ligand
The size of Δo depends on the ligand(s) present according to the spectrochemical
series, which is a list of ligands in order of decreasing crystal field strength.
CN-
= CO = C2H4 > PR3 > NO2
-
= phen > bipy > SO3
2-
> en = py = NH3 > edta4-
> NCS-
> H2O > C2O4
2-
> ONO2
-
> OSO3
2-
> OH-
= ONO-
> F-
> Cl-
= SCN-
> Br-
> I-
Weak field ligands, such as Cl-
and SCN-
, give rise to small values for Δo, while
strong field ligands, such as CN-
and CO, give rise to large values for Δo.
It is also possible to arrange the metals according to a spectrochemical series as
well. The approximate order is:
Mn2+
< Ni2+
< Fe2+
< V2+
< Fe3+
< Co3+
< Mn3+
< Mo3+
< Rh3+
< Ru3+
< Pd4+
< Ir3+
< Pt4+
Question 1.2.3
Which of the following would have the largest value of Δo?
A. [Cr(OH2)6]3+
B. [CrF6]3-
C. [Cr(NH3)6]3+
D. [Cr(NH3)6]2+
That concludes the section on factors affecting the size of Δo.

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Sigma Bonding Interactions
From:
http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Crystal_Field_Theory/Virtual%3a_Electronic
_Structure/Ligand_Properties
The essential feature of a coordination compound is the donation of a pair of
electrons by the ligand to form a coordinate covalent bond with the metal.
This interaction is illustrated in the following energy diagram for an octahedral
complex. (The six ligand donor orbitals are grouped into two sets, one of which
has appropriate symmetry for interacting with the metal dz
2
orbital and the other
with appropriate symmetry for interacting with the metal dx
2
-y
2
orbital)
The Lewis acid-base reaction between the metal and the ligand results in a set of
low energy, fully
occupied (because
the original ligand
donor orbitals were
fully occupied) σ
bonding orbitals that
are primarily
localized on the
ligand and a set of
high energy σ*
orbitals that are
primarily localized on
the metal. Three of the metal orbitals (dxy, dxz, and dyz) do not interact with the
ligand orbitals and remain as nonbonding orbitals completely centered on the
metal.

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The d-orbital splitting, Δo, arises from the increase in energy of the σ* orbitals
relative to the nonbonding orbitals. The stronger the bonding interaction, the
higher the σ* energy and the greater Δo. A strong σ bonding interaction requires a
good energy match between the metal and the ligand. Empirically, there is a
correlation between Δo and the basicity of the ligand. A ligand that is a good
Brønsted (or Lewis) base tends to form strong σ bonds with metals and thus
produces a relatively large Δo.
Pi Bonding Interactions
Some ligands are capable of π bonding interactions, either by acting as a π
acceptor ([Cr(CO)], for example) or a π donor ([Cr(F)]2+
, for example). The energy
diagram shown below illustrates the behavior of a π donor ligand on Δo.

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1.3 The Jahn-Teller Effect
This section will include:
 Jahn-Teller theorem
 Example of complexes
 Nature of the distortion
 Explanation of why it occurs
Jahn-Teller Theorem
In 1937 H.A. Jahn and E. Teller put forward a theorem which explained some of
the distortions observed in transition metal complexes. This became known as
the Jahn-Teller theorem. It states:
"For any non-linear molecule in an electronically degenerate state, distortion
must occur to lower the symmetry, remove the degeneracy and lower the
energy."
These distortions are called Jahn-Teller distortions. But how are the molecules
distorted, and how does the distortion occur? This section aims to describe what
is meant by an electronically degenerate state and explain how Jahn-Teller
distortions can lower the energy of molecules in such states.
Examples of distorted complexes
There are some complexes which might at first be expected to be octahedral, but
which are in fact distorted from the ideal octahedron. These distortions are
called Jahn-Teller distortions. One notable example is the complex ion
[Cu(OH2)6]2+
, shown below. Two of the metal-ligand bonds are longer than the
other four. This type of distortion is called a tetragonal elongation.

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Another example is KCrF3. In this compound Cr is in oxidation state II and is high
spin d4
. There are four long Cr-F bonds and two short Cr-F bonds. This type of
distortion is called a tetragonal compression.

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For comparison, below is the [Ni(OH2)6]2+
complex ion, which is symmetrical and
undistorted:
Explanation
The existence of distorted complexes, such as [Cu(OH2)6]2+
and KCrF3 (shown on
the previous page), can be explained by considering their electronic structure.
Consider the complex ion [Cu(OH2)6]2+
, which is a tetragonally elongated
octahedron. Cu(II) is d9
and the population of the d orbitals is t2g
6
eg
3
. The third
electron in the eg set may occupy either the dz
2
orbital or the dx
2
-y
2
orbital, as
they are equal in energy. This is what is meant by an electronically degenerate
state.
Which orbital will the ninth electron go into?

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If the electron goes into the dz
2
orbital there will be a greater amount of charge
density along the z axis. This means that the ligands along the z axis cannot
approach as closely as when the dz
2
orbital is singly occupied, as there will be
more repulsion between the electrons in the dz
2
orbital and the ligand lone pair.
The ligands which lie on the z-axis move out a bit and the other ligands move in a
bit, as they now suffer less repulsion - the complex ion will be tetragonally
elongated. The ligands along the z axis are further away from the metal, which
means the energy of the dz
2
orbital is lowered with respect to the dx
2
-y
2
orbital.
The energy of t2g set is also affected, but to a lesser extent. The dxz and dyz
orbitals (which have components along the z axis) interact less with the z axis
charges and are lowered in energy relative to the dxy orbital. The degeneracy of
the orbitals is lifted and the overall energy of the complex is lowered, as stated
by the Jahn-Teller theorem.
Question 1.3.1
Which of the d-orbitals are raised in energy as a result of a tetragonal elongation?

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If the electron goes into the dx
2
-y
2
orbital there will be a greater amount of charge
density along the x and y axes. Ligands along the x and y axes cannot approach as
closely as when the dx
2
-y
2
orbital is singly occupied, which results in the ligands
centered on the x and y axes being further away from the metal. The bond
lengths along the z axis will be shorter than those on the x and y axes. This
distortion is called a tetragonal compression. The energies of the orbitals with
components in the x-y plane are stabilized relative to the other orbitals. The dx
2
-y
2
orbital is stabilized to a greater extent than the dxy orbital since it points more
directly towards the ligands. Again the degeneracy is lifted and the overall
energy is lowered.
Question 1.3.2
Which of the d-orbitals are raised in energy as a result of a tetragonal
compression?

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Elongation results in a greater stabilization than compression; this explains why
the [Cu(OH2)6]2+
ion is tetragonally elongated.
Jahn-Teller distortions will occur for any electronically degenerate configuration,
not just for d9
. If there is a choice of where to put the electrons in a complex,
then there will be a Jahn-Teller distortion to remove this choice.
Example: [Ti(OH2)6]3+
: Ti is in oxidation state III. Ti is d1
, and the electron can
occupy the dxz, dyz or the dxy orbital.
The complex will undergo a Jahn-Teller distortion to remove this choice.
Tetragonal compression is likely because only one d-orbital has lowest energy !

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1.4 Hard and Soft Acids and Bases
 Introduction
 Irving-Williams series
 Classification of acids and bases
Introduction
First, the distinction between Brønstead acids and bases and Lewis acids and
bases should be made clear:
A Brønstead acid is a proton donor
A Brønstead base is a proton acceptor
A Lewis acid is an electron pair acceptor
A Lewis base is an electron pair donor
Consider a simple transition metal complex, MLn. The central metal ion (a Lewis
acid) accepts an electron pair from each of the ligands (Lewis bases).
Irving-Williams Series
In 1953 Irving and Williams attempted to correlate stability constant data for the
group 2 metals. They looked at the stability constants for the M2+
ions of group 2
and some of the first transition series. They found that, for a given ligand (Lewis
base), the stability constants for the metal ion (Lewis acid) generally followed
the same sequence. This sequence became known as the Irving-Williams series.
The Irving-Williams series is:
Ba2+
< Sr2+
< Ca2+
< Mg2+
< Mn2+
< Fe2+
< Co2+
< Ni2+
< Cu2+
> Zn2+

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Crystal Field Theory (see Section 1.1) assumes that the interaction between
metal ions and surrounding ligands is completely electrostatic. Metal ions with
high charge densities interact strongly with the surrounding ligands, so it is
expected that the smaller metal ions form more stable complexes than the larger
metal ions. Copper is considered out of line with predictions based on Crystal
Field Theory. This is probably a consequence of the tendency for Cu(II) to form
distorted octahedral complexes.
The electrostatic argument would also predict the stability constants for M3+
to
be greater than those for M2+
, due to increasing charge density. This is generally
the case.
Classification of Acids and Bases
In 1963 Pearson suggested that class a metal ions should be termed hard and
those of class b should be termed soft. This was extended to include ligands, so
that Lewis acids and bases can be classified as hard, soft or borderline. The term
borderline is introduced as the terms hard and soft are not absolute. There are
some species which fall in the middle, which will be classified as borderline.
Hard Acid small, not polarisable, highly charged
Soft Acid larger, more polarisable
Borderline Acid medium size, medium charge
Hard Base small, not highly polarisable, not highly charged
Soft Base larger, more polarisable
Borderline Base medium size, medium polarisability

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Examples of hard, soft and borderline acids and bases
The element highlighted in bold is that which is directly coordinated to the
metal
Hard Borderline Soft
Acids
H+
, Sc3+
, Ti4+
, Cr2+
, Cr3+
,
Mn+
, Mn7+
, Fe3+
, Co3+
Fe2+
, Co2+
, Ni2+
,
Cu2+
, Zn2+
, Ru3+
,
Ir3+
Cu+
, Ag+
, Au+
, Hg+
, Hg2+
, Pt2+
,
Pd2+
, all d-block metals in
zero oxidation state
Bases
NH3, NH2R, OH2, OH-
, O2-
, OR-
, OR2, CO3
2-
,SO4
2-
,
Cl-
, F-
, NO3
-
, PO4
3-
NH2Ph, N2, NO2
-
,
SO3
2-
, Br-
, SCN-
H-
, R-
, C2H4, C6H6, CN-
, CO,
SCN-
, PR3, P(OR)3, SR2, SHR,
SR-
, I-
The HSAB Principle
Pearson also stated that "hard acids prefer to coordinate to hard bases, and soft
acids to soft bases". This statement is still used today and is known as the HSAB
Principle. The word “prefer” is used as there are many examples of strong bonds
between mismatched pairs of acids and bases. This is due to the fact that there
are other factors (in addition to matching hard and soft acids and bases) that
affect the strength of bonds.
Question 1.4.1
What is a Lewis acid?
A. An electron acceptor
B. An electron donor

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2. UV-visible absorption spectroscopy
 Example spectra
 Explanation of key features of the
spectra
 Using spectra to calculate values of Δo
 Selection rules
How we see colours
White light (simplified by showing only green, red, and blue) is shown through a
solution. The solution absorbs the red and green wavelengths, however the blue
light is reflected and passes through, so we see the solution as being blue:
Absorption Spectra of Transition Metal Complexes
Solutions of transition metal complexes come in a variety of colours. For
example, a solution of [Cu(OH2)6]2+
is blue, a solution of [MnO4]-
is an intense
purple, and a solution of [Co(OH2)6]2+
in water is pink. In contrast, [Zn(OH2)6]2+
is
colourless. What is responsible for the difference in colour?
Complexes are coloured because they absorb light in the visible region. The
colour observed (or transmitted) is complementary to the colour of the light
absorbed. If light from the yellow-green part of the spectrum is absorbed, the
colour observed will be white light with yellow-green subtracted out, that is,
violet.
Wavelengths of colours
and complementary colours

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Colour of light
absorbed
Wavelength
ranges / nm
Colour of light
transmitted
Red 700-620 Green
Orange 620-580 Blue
Yellow 580-560 Violet
Green 560-490 Red
Blue 490-430 Orange
Violet 430-380 Yellow
Absorption spectra of transition metal complexes
The absorption bands in spectra are a result of HOMO-LUMO transitions. The
HOMO and LUMO of an octahedral complex are mostly d-orbital in character (the
separation between the two is characterised by the size of Δo), so these
transitions are called d-d transitions. It is these electronic transitions that are
responsible for the colour of complexes.
The pages that follow use the complex [Ti(OH2)6]3+
to demonstrate how the value
of Δo for a complex can be calculated from its absorption spectrum. The selection
rules for electronic d-d transitions are also considered.
UV-Visible Spectrum of
[Ti(OH2)6]3+
Ti is in oxidation state III and
is d1
. The metal has the
electronic configuration
t2g
1
eg
0
.
A d-d transition takes place
(t2g
0
eg
1
← t2g
1
eg
0
) which is

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attributable to the absorption band at 493 nm. This absorption band is in the
visible region of the electromagnetic spectrum, so the complex is coloured.
Question
What colour will the complex be?
Calculation of Δo
If the wavelength of the light absorbed is known, the value of Δo can be
calculated by converting from wavelength to energy. The following two equations
are used:
 E = hν
where E is energy, h is Plank's constant and ν is frequency
 c = λν
where c is the speed of light, λ is the wavelength and ν is the frequency
Combining these equations:
E = hc/λ
Therefore,
E = 6.626 x 10-34
x 2.998 x 108
/ 493 x 10-9
Js ms-1
/ m
E = 4.029 x 10-19
J
This is the value of Δo for one molecule of the complex. The value for one mole
can be calculated by multiplying by Avogadro's number, 6.022 x 1023
mol-1
.
This gives Δo = 242.6 kJmol-1
.

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Another common way to express the CFSE is in cm-1
(1 kJ/mol = 84 cm-1
),
in this example about 20.400 cm-1
which corresponds to a wavelength of 490 nm.
You should be familiar with energy conversions (convert between kJ and kJ/mol
and cm-1 and wavelength in nm) !
Additional features of the UV-visible spectrum of [Ti(OH2)6]3+
The absorption band for the d-d transition has a shoulder
This is due to Jahn-Teller distortion, a tetragonal compression. The splitting
diagram for a tetragonal compression below, shows that there are two possible d-
d transitions from the t2g to the eg. This means that light of two different
wavelengths is absorbed and there are two different absorption peaks. The two
peaks are close together and one appears as a shoulder on the other.

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The absorption band for the d-d transition is broad
This is due to the fact that molecules are not static. The [Ti(OH2)6]3+
molecule is
continually vibrating and the Ti-O bond lengths are continually changing. The size
of Δo depends on the Ti-O bond length. If the Ti-O bonds are longer there is less
repulsion between the ligand lone pairs and the d-electrons, so Δo will be
smaller. At any one instant, there will be a range of Ti-O bond lengths in solution
and a range of Δo values. Hence the absorption band is broad.
There is a strong absorption in the UV region (to the left of the graph)
This is due to charge transfer transitions. This type of transition involves
electrons moving from orbitals which are essentially ligand in character to
orbitals which are essentially metal in character. This means charge transfer
from one part of the molecule to another takes place. This type of absorption
tends to be intense as there are no selection rules governing the transition.
(Explanation about metal- and ligand-character of orbitals will follow in another
part about Ligand-Field Theory or MO-Theory !)
Charge transfer transitions can also take place in the visible region of the
electromagnetic spectrum. When this happens, the complex is usually intensely
coloured. For example, the complex KMnO4 is a deep purple colour because
charge transfer transitions take place between O2-
ligands and the Mn metal
centre (ligand → metal charge transfer). Metal → ligand charge transfer is also
possible.

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Selection rules
Electronic transitions are subject to selection rules. These selection rules are
statements about whether a given transition is allowed or forbidden. If the
transition obeys a given set of rules it is said to be allowed, if it does not follow
the rules it is said to be forbidden.
1. Spin selection rule
The electromagnetic field of the incident radiation cannot change the relative
orientations of the spins of the electrons in a complex. That is, the electrons
must have the same orientation of spin in the excited state as in the ground
state.
Although transitions involving a change of spin are formally forbidden, they do
occur in some 4d and 5d complexes. This is known as the heavy-atom effect. The
intensities of such transitions, however, will be less than those for spin-allowed
transitions.

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2. Laporte selection rule
Terminology:
Gerade (g)
An orbital which possesses a centre of symmetry
Ungerade (u)
An orbital which does not possess a centre of symmetry
The subscript g in the t2g and eg indicates that the orbitals have a centre of
symmetry in an octahedral field. In a tetrahedral field there is no centre of
symmetry, so the subscript g's are removed.
The Laporte selection rule (also known as the symmetry selection rule) states
that for a complex that contains a centre of symmetry only transitions which
involve a change in parity are allowed. That is, only transitions between g and u
orbitals are allowed.
gerade-ungerade gerade-gerade ungerade-ungerade
Allowed Forbidden Forbidden
Therefore, in a symmetrical complex (e.g. an octahedral complex) d-d transitions
are formally forbidden as these are g-g transitions. However, the Laporte
selection rule can be relaxed if the complex is slightly distorted, for example if
Jahn-Teller distortions occur. The intensity is weaker than that for symmetry-
allowed transitions, but it is usually more intense than spin-forbidden transition.
Tetrahedral complexes do not have a centre of symmetry, so the Laporte
selection rule no longer applies. Therefore, d-d transitions are not forbidden in
tetrahedral complexes.

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Calculation example for Ruby (Cr3+)
From:
http://chemwiki.ucdavis.edu/Inorganic_
Chemistry/Crystal_Field_Theory/Virtual%
3a_Electronic_Structure/Energy_Level_S
plitting
Cr3+
ground-state electron
configuration
in octahedral environment:
For this particular ruby the lowest energy
transition is centered at λ= 561 nm.
The splitting energy is therefore
Δo = h c/λ = 3.54 x 10-19
J = 213 kJ/mol = 2.21 eV
Wavenumber υ = 1/λ = 17800 cm-1
h = 6.62608 x 10-34
J sec
c = 3 x 108
m/sec
In most compounds, there are large gaps in energies between the bonding
orbitals (which are typically filled with electrons) and the antibonding orbitals
(which are typically empty). Promotion of an electron from an occupied bonding
orbital to an unoccupied antibonding orbital (a π → π* transition) usually requires
6 eV or more energy. Such light falls in the ultraviolet region, which the human
eye cannot detect, and the substance is colorless. Nonbonding orbitals (which are
usually occupied) lie between the bonding and antibonding orbitals and thus give
rise to lower energy transitions. These n → π* transitions are usually 3.5 eV or
greater, which still corresponds which light in the ultraviolet region (near
ultraviolet light).

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In order to have color, a substance must have an electronic transition whose
energy change is between 1.8 and 3.1 eV, which corresponds with light in the
visible range (about 400 to 700 nm). Such low energy transitions require closely
spaced energy levels, some of which contain electrons and some of which do not.
Many dyes are large organic molecules with extended π bonding, which gives rise
to closely spaced occupied π and unoccupied π* orbitals. Transition metal
complexes are often colored, because the crystal field splitting gives rise to
closely spaced, partially filled d orbitals.
For the Inorganic Chemistry Exam, please study especially the chapters about
Crystal Field Theory and CFSE as well as UV/VIS spectroscopy.
The HSAB principle, Jahn-Teller Effect and Spin-selection rules are more
advanced subjects and will be covered later in more detail.
For questions please contact AJ. Christoph at SC 2201 or email
c.sontag@web.de / my web site is: http://myphayao.com

Crystal field theory

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