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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 dz2 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 dz2, 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 dz2 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 t2g1, 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 t2gxeg

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 t2g4eg

0 (low

spin arrangement) and t2g3eg

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

t2xey 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 > C2O42- > ONO2

- > OSO32- > 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 dz2 orbital and the other

with appropriate symmetry for interacting with the metal dx2-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 t2g6eg

3. The third

electron in the eg set may occupy either the dz2 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 dz2 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 dz2 orbital is singly occupied, as there will be

more repulsion between the electrons in the dz2 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 dz2 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?

d xy d xz d yz d z2 d x2-y2

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If the electron goes into the dx2-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 dx2-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 dx2-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?

d xy d xz d yz d z2 d x2-y2

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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

This section will include:

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, CO32-,SO4

2-,

Cl-, F-, NO3-, PO4

3-

NH2Ph, N2, NO2-,

SO32-, 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

This section will include:

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

t2g1eg

0.

A d-d transition takes place

(t2g0eg

1 ← t2g1eg

0) which is

Page 27 of 33

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.

Page 28 of 33

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.

Page 31 of 33

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.

Page 32 of 33

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).

Page 33 of 33

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