Coordination complex, Lecture notes of Chemistry

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Structure, Properties and Reactivity of Transition

Metal Complexes

Assoc. Prof. Lisa Martin

[email protected]

Rm 1 57 , 1 7 Rainforest Walk

CHM 2911 Inorganic - Coordination Chemistry

Topics covered:

Week 1

Electron configurations

The eighteen electron rule

Crystal Field Stabilisation Energy

Coordination number

Week 2

Jahn Teller stabilisation

Chelate and macrocyclic effects

Ligand Field Stabilisation

Week 3

Formation constants

Irving Williams Series

Use of electrode potentials

Effects of complexation

Additional sources of information:

Inorganic Chemistry 7

th

Ed; Weller, Overton, Rourke and Armstrong,

2018 , Oxford University Press

The Eighteen Electron Rule

One of the first approaches to bonding in transition metal complexes was to regard the

bonding as that between a Lewis acid (the metal ion) and Lewis bases (the ligands). This

model produced the 18-electron rule or the effective atomic number (EAN) rule which states

that a complex is stable if there are eighteen electrons around the metal. For example,

[Cr(CO) 6 ] Cr(0) electron configuration [Ar]3d

6

So we have 6 electrons from Cr, 12 electrons from 6 x CO = 18 electrons

This model works for many metal compounds in which the metal is in a low oxidation state,

especially carbonyl complexes. But it does not work for most compounds, nor does it explain

the colour or paramagnetism of many transition metal compounds.

Self-Test 3: Show that the following complexes obey the 18-electron rule:

(a) [ Ni(CO) 4 ] (b) [Mn(CO) 5 ]

−

;

Self-Test 4: A ssuming that the following complexes obey the 18-electron rule, determine n in

each complex: (a) [Fe(CO) n ]; (b) [Fe(CO) n (PPh 3 ) 2 ].

Crystal Field Theory

You have studied crystal field theory last year. We see that the splitting of d orbitals leads to

an overall lowering of energy and consequently the complex is more stable than before the

splitting, accounting for the stability of most complexes.

Splitting of d orbitals in an octahedral ligand field

The 5 degenerate d orbitals are split into two sets; 3 t2g orbitals of lower energy and 2 eg

orbitals of higher energy. The energy separation is labelled Δo or Δoct. The t2g orbitals are

lower in energy by 2/5Δo (or 0.4Δo). The eg orbitals are higher in energy by 3/5 Δo (or 0.6Δo).

These orbitals are shown schematically as

There are now two ways of filling these new energy level with electrons, depending upon the

relative magnitude of Doct. For example filling d

4 in both the high-spin and low spin

arrangement;

High spin arrangements occur when Δoct is small. Low spin complexes are formed when Δoct

is large and too much energy is required to promote the 4

th electron into the eg orbital. We can

calculate the overall stabilisation energy for any configuration. This is the crystal field

stabilisation energy , CFSE.

5 orbitals

t2g

eg

High-spin d

4 Low-spin d

4

Thus, for a particular metal ion, it is the ligand that determines the value of the crystal field

splitting is generally.

X

• donor < O donor < N donor < C donor

Consider the d

6 iron(II) ion.

[Fe(OH 2 ) 6 ]

2+ high spin d

6 CFSE = - 2/5Do

[Fe(CN) 6 ]

4 - low spin d

6 CFSE = - 12/5Do

because Δo CN

• Δo H 2 O

Ligands up to and including H 2 O in the spectrochemical series usually give rise to high spin

complexes.

Self-test 6: Predict which of the following complexes would be most stable:

a) [Cr(OH 2 ) 6 ]

2+ or [Mn(OH 2 ) 6 ]

2 + .

Self-test 7: Explain the following observations:

D o /cm

-^1

[Co(NH 3 ) 6 ]

2+

10 100

[Co(H 2 O) 6 ]

2+

9 300

[Co(NH 3 ) 6 ]

3+ 22 900

Values of Δoct are measured experimentally by UV-vis spectroscopy. For the simplest situation,

a d

1 configurations, for example [Ti(OH 2 ) 6 ]

3 + , there is one possible electron transition:

An absorption of electromagnetic energy causes the electron to shift to the eg orbital. The

electron subsequently returns to the ground state, and the energy is released as thermal

motion rather than as electromagnetic radiation. If the UV-vis spectrum is measured for this

ion the absorption maximum is at about 20 300 cm

• 1 , which represents an energy difference

between the upper and lower d orbital sets of about 243 kJ·mol

• 1 . This energy difference

represents the value of Do, the crystal field splitting.

(wavenumbers)

This transition occurs in the visible region of the electromagnetic spectrum and explains the

violet colour of the complex.

We can covert wavenumbers to the more useful kJ mol

• 1 quite easily using

Δo = E = h νNo = hc No/λ where h = Plank’s constant, c = speed of light

N 0 = Avagadro’s constant

So, for the example above

Δo = {6.63x

• 34 (J s) x 3x

8 (m s

• 1 ) x 6.022 x 10

23 (mol

• 1 )}/49 0 x 10 - 9 m

= 243 x 10

3 J mol

• 1 = 243 kJ mol - 1

eg

t2g

20 ,300 cm

• 1

Self-test 8 : Convert the value of Δoct = 12 ,600 cm

• 1 for [Cu(OH 2 ) 6 ]

2+ into kJ mol

• 1 .

Self-test 9 : a) TiO 2 is the most common white pigment. Why is it white? b) Explain why

[Mn(OH 2 ) 6 ]

2+ is a very pale pink colour. c) Explain why metal chromates (CrO 4 )

2 - have

been used as yellow pigments.

Effect of coordination number

The splitting diagram for a tetrahedral complex in inverted compared to the octahedral.

d x2–y2 & d z

With only four ligands instead of six, and the ligands not quite pointing directly at the three d

orbitals, the crystal field splitting is much less than in the octahedral case, it is about 4/9 of

Doct. As a result of the small orbital splitting, the tetrahedral complexes are almost all high

spin and less stable than analogous octahedral complexes.

Complexes with 8 d electrons tend to form square planar complexes. The configuration

confers additional stability as Δsp is larger than Δoct

DT = 4/9 Do

High energy and never

filled with electrons

5 orbitals

Self-test 10: Show arrangement of electrons in an a) octahedral, b) tetrahedral and c)

square planar d

8 metal ion

d xy, d xz & d yz

d orbital

Jahn-Teller Distortion

Octahedral complexes of d

9 , low spin d

7 and high spin d

4 are often distorted due to

unsymmetrically filled e g orbitals. This is common for Cu

2+ complexes. The distortion

increases the crystal field splitting and enhances stability.

This distortion can lead to an elongated or compressed octahedron and is due to the

unsymmetrically filled eg orbitals.

For d

4 if the single electron in the eg orbital is in the z

2 orbital there will be greater repulsion

in the z direction than the x or y directions and the complex will be elongated. If the single

electron occupies the dx2-y2 orbital then the extra repulsion will be in the x and y directions

and the octahedron will be compressed. Similar arguments hold for the d

9

case. Which type

of distortion happens is a matter of energetics but because axial elongation weakens two

bonds and equatorial elongation weakens four bonds, axial is more common.

dx2-y2, dz

dxy, dyz, dxz

Self-test 12 : Predict which of the following would exhibit Jahn Teller distortion.

[Cr(Η 2 Ο) 6 ]

2+

[Fe(Η 2 Ο) 6 ]

2+

[Cu(Η 2 Ο) 6 ]

2+

Distortion of 2 bonds

® more common

Distortion of 4 bonds

® less common

The chelate and macrocyclic effects

When K f1 for the formation of a complex with a bidentate chelate ligand, such as ethyl-

enediamine (en), is compared with the value of β 2 for the corresponding bis(ammine)

complex, it is found that the former is generally larger:

[Cd(OH 2 ) 6 ]

2 + (aq) + en(aq) ⇌ [Cd(en)(OH 2 ) 4 ]

2 + (aq) + 2 H 2 O(l)

log K f1 = 5.84 Δ H

Ɵ = 2 29.4 kJ mol

• 1 Δ S

Ɵ = 1 13.0 J K

• 1 mol - 1

[Cd(ΟΗ 2 ) 6 ]

2 + (aq) + 2 ΝΗ 3 (aq) (^) ⇌ [Cd(ΝΗ 3 ) 2 (ΟΗ 2 ) 4 ]

2 + (aq) + 2 Η 2 Ο(l)

log β 2 = 4.95 Δ H

Ɵ = 229.8 kJ mol

• 1 Δ S

Ɵ = 25.2 J K

• 1 mol - 1

Two similar Cd–N bonds are formed in each case, yet the formation of the chelate-containing

complex is distinctly more favourable. This greater stability of chelated complexes compared

with their nonchelated analogues is called the chelate effect.

The chelate effect can be traced primarily to differences in reaction entropy between

chelated and nonchelated complexes in dilute solutions. The chelation reaction results in an

increase in the number of independent molecules in solution. By contrast, the nonchelating

reaction produces no net change (compare the two chemical equations above). The former

therefore has the more positive reaction entropy and hence is the more favourable process.

In addition to the thermodynamic rationalization for the chelate effect we have described,

there is an additional role in the chelate effect as once one ligating group of a polydentate

ligand has bound to a metal ion, it becomes statistically more likely that its other ligating

groups will bind, as they are now constrained to be in close proximity to the metal ion, thus

chelate complexes are highly favoured.

The chelate effect extends beyond bidentate ligands, and applies, in principle, to any

polydentate ligand. In fact, the greater the number of donor sites the multidentate ligand

has, the greater is the entropic advantage of displacing monodentate ligands and the more

stable the complex. Macrocyclic ligands, where multiple donor atoms are held in a cyclic

array, such as crown ether or phthalocyanin, give complexes of even greater stability than

might otherwise be expected.

This so-called macrocyclic effect is thought to be a combination of the entropic effect

seen in the chelate effect, together with an additional energetic contribution that comes

from the preorganized nature of the ligating groups, meaning no additional strains are

introduced to the ligand on coordination.

Self-test 13 : TACN is a tridentate ligand. Predict whether it can form fac and/or mer

isomers with an octahedral complex.

Self-test 14 : How many isomers will cyclam (1,4,8,11-tetraazacyclotetradecane)

form with an octahedral complex?

Ligand Field Theory – including covalency

Crystal field theory considers the metal ion and ligands as ‘point charges’ thus only considers

the complex as ‘electrostatic’. In order to understand the spectrochemical series we need to

include the covalency of the metal and ligands. Ligands are Lewis bases, so initially form a

σ-bond between the metal and ligand. In some cases this is supplemented by π-bonding, if the

ligands have either filled or unfilled orbitals of the correct symmetry. The molecular orbital

model of bonding enables us to consider s and π covalent interactions between the metal ion

and the ligands. This model is referred to as Ligand Field Theory.

So let us start with a brief recap of Molecular Orbital Theory. Molecular Orbital Theory tells

us why molecules are stable; i.e. they combine atomic orbitals to form molecular orbitals

which extend over the whole molecule and only then populates them with electrons.

Important points to be noted:

1. N molecular orbitals may be constructed from N atomic orbitals.
2. The same rules that are used for filling atomic orbitals with electrons apply to filling

molecular orbitals with electrons i.e. the build-up principle, Hund’s rule, Pauli exclusion

principle.

Self-test 15 : How many faces does the tren (tris(2-aminoethyl)amine) ligand occupy in

an octahedral complex and a trigonal bipyramidal complex?

σ-donor ligands

If no π-bonding is present the energy difference between the t 2g

and e g

orbitals corresponds to

the Δ oct

from crystal field theory. σ donors donate electrons from lone pairs to the metal

centre from either the s or p orbitals e.g. amines, water, nitrite

For example, [Co(NH 3 ) 6 ]

3+

Orbitals involved

Atomic orbital Mulliken Label Degeneracy

s a1g 1

px, py, pz t 1u 3

dxy, dyz, dxz t2g 3

dx2-y2, dz2 eg 2

For a first row transition metal the valence shell atomic orbitals are 3d, 4s and 4p.

Combinations of the metals and ligand orbitals generate six bonding and six anti-bonding

molecular orbitals. Non-bonding for t2g set

The MO theory of bonding in octahedral complexes gives a similar result to crystal field

theory - this changes if there is also π-bonding present.

σ-bonding only