Crystal Field Theory

•The relationship between colors and complex metal ions

400 500 600 800

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 axisLinear combination ofdz

2-dx2 and dz

2-dy2

d2z2-x

2-y2

Octahedral Field

7

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)

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

eg orbitals

crystal field energy splitting

8

Crystal field splitting of the 5 d orbitals by the “crystal field” of 6 ligands

t2g orbitals

eg orbitals

Crystal field splitting

Orbitals “on axis”: “energy increases”

Orbitals “off axis”: “energy decreases”

Crystal Field Splitting Energy (CFSE)• In Octahedral field, configuration is: t2g

x egy

• Net energy of the configuration relative to the average energy of the orbitals is:

= (-0.4x + 0.6y)O

O = 10 DqBEYOND d3

• In weak field: O P, => t2g3eg

1

• 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

d4

Strong field =Low spin

(2 unpaired)

Weak field =High spin

(4 unpaired)

P < o P > o

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.

Coulombic repulsion energy and exchange energy

[Mn(CN)6]3- Strong field Complextotal spin is 2 ½ = 1Low Spin Complex

Ground-state Electronic Configuration, Magnetic Properties and Colour

[Mn(H2O)6]3+ Weak Field Complexthe total spin is 4 ½ = 2 High Spin Complex

What is the CFSE of [Fe(CN)6]3-?

If the CFSE of [Co(H2O)6]2+ is -0.8 oct, what spin state is it in?

NCFe

NC CN

CN

CN

CN

C.N. = 6 Oh

3-

+ 0.6 oct

- 0.4 oct

CFSE = 5 x - 0.4 oct + 2P =

l.s.h.s.

H2OCo

H2O OH2

OH2

OH2

OH2

C.N. = 6 Oh l.s.h.s.

2++ 0.6 oct

- 0.4 oct

CFSE = (5 x - 0.4 oct) + (2 x 0.6 oct) +2P = - 0.8 oct+2P

eg

t2g

eg

t2g

eg

t2g

eg

t2g

CFSE = (6 x - 0.4 oct) + (0.6 oct) + 3P= - 1.8 oct + P

Fe(III) d5

Co(II) d7

CN- = s.f.l.

- 2.0 oct + 2P

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:

I- Br- S2- SCN- Cl- NO3

- F- C2O42- H2O NCS-

CH3CN NH3 en bipy phen NO2

- PPh3 CN- CO

Weak Field

Strong Field

N N

2,2'-bipyridine (bipy)

NH2 NH2

Ethylenediamine (en)

NN

1.10 - penanthroline (phen)

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.

[CrF6]3- [Cr(H2O)6]3+ [Cr(NH3)6]3+ [Cr(CN)6]3-

Limitations of CFT

Considers Ligand as Point charge/dipole onlyDoes 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