chapter 5: crystal field theory

CHAPTER 5: CRYSTAL FIELD THEORY

CHEM210/Chapter 5/2014/01

The elements in the periodic table are often divided into four categories: (1) main group elements, (2) transition metals, (3) lanthanides, and (4) actinides.

RECALL


TRANSITION METALS vs. MAIN-GROUP ELEMENTS

There is some controversy about the classification of the elements on the boundary between the main group and transition-metal elements on the right side of the table.The elements in question are zinc (Zn), cadmium (Cd), and mercury (Hg).


THE ELECTRON CONFIGURATION OF TRANSITION-METAL IONS

The relationship between the electron configurations of transition-metal elements and their ions is complex.

EXAMPLE

Consider the chemistry of cobalt which forms complexes that contain either Co2+ or Co3+ ions.

Co: [Ar] 4s2 3d7

Co2+: [Ar] 3d7

Co3+: [Ar] 3d6

In general, electrons are removed from the valence shell s orbitals before they are removed from valence d orbitals when transition metals are ionized.


THE ORIGIN OF COLOUR - ABSORPTION


The colour can change depending on a number of factors e.g.• Metal charge• Ligand


Are there any simple theories to explain the colours in transition metal complexes?

There is a simple electrostatic model used by chemists to rationalize the observed results

THIS THEORY IS CALLED CRYSTAL FIELD THEORY

It is NOT A RIGOROUS BONDING THEORY but merely a simplistic approach to understanding the possible origins of photo- and electrochemical properties of the transition metal complexes.

Method of explaining some physical properties that occur in transition metal complexes.

Involves a simple electrostatic argument which can yield reasonable results and predictions about the d orbital interactions in metal complexes.


THE OCTAHEDRAL CRYSTAL FIELD

Consider metal ion, Mm+, lying at the centre of an octahedral set of point charges.


Suppose the metal atom has a single d electron outside of the closed shells (Ti3+ or V4+)

In the free ion, the electron can be in any one of the 5 orbitals, since all are equivalent (degenerate).

Recall the shapes of the d orbitals


2 groups of orbitals

dxy , dyz , dzx

dz2 , dx

2- y

2

t2g

eg


Δo is the difference in energy between eg and t2g.

LFSE = (0.4x – 0.6y)Δo

The net energy of a t2gx eg

y configuration relative to the barycentre is called the ligand field stabilization energy (LFSE).

HIGH- SPIN VS LOW- SPIN IN Oh COMPLEXES

d 1, d 2, d 3 - simple d 4

high- spin low- spin


High-spin d 4

t2g3 eg

1

Low-spin d 4

t2g4 eg

0

x = 3 , y = 1 x = 4 , y = 0

E = (0.4x – 0.6y)Δo = 0.6 Δo

E = (0.4x – 0.6y)Δo = 1.6 Δo + P


What is the LFSE for octahedral ions of the following configurations:

(a) d 3 (b) high-spin d 5

(a) electronic configuration : t2g3eg

0, x = 3, y = 0

Therefore, LFSE = (0.4x – 0.6y)Δo = [(0.4)(3) – (0.6)(0)]Δo = 1.2 Δo

(b) electronic configuration : t2g3eg

2, x = 3, y = 2

Therefore, LFSE = (0.4x – 0.6y)Δo = [(0.4)(3) – (0.6)(2)]Δo = 0

EXAMPLE

SOLUTION

What is LFSE for both high- and low-spin d 6 configuration?EXERCISE FOR THE IDLE MIND


THE SPECTROCHEMICAL SERIES

The splitting of d orbitals in the CF model not only depends on the geometry of the complex, it also depends on the nature of the metal ion, the charge on this ion and the ligands that surround this ion.When the geometry and the ligands are held constant, this splitting decreases in the following order:

Pt4+ > Ir3+ > Rh3+ > Co3+ > Cr3+ > Fe3+ > Fe2+ > Co2+ > Ni2+ > Mn2+

When the geometry and the metal are held constant, the splitting of the d- orbitals increases in the following order:

I- < Br- < [NCS]- < Cl-< F- < OH- < H2O < NH3 < en < CN- < COThe ligand- field splitting parameter, Δo varies with the identity of the ligand.In the series of complexes [CoX(NH3)5]n+ with X = I-, Br-, Cl- H20 and NH3, the colours range from purple (for X = I-) through pink (X = Cl-) to yellow (with NH3).Ligand that give rise to high energy transition (such as CO) is referred to as a strong-field ligand; low energy transitions (such as Br-) referred to as weak-field ligand.


MAGNETIC MEASUREMENTSUsed to determine the number of unpaired spins in a complex, hence identify its ground-state configuration.

Compounds are classified as diamagnetic if they are repelled by a magnetic field and paramagnetic if they are accepted by a magnetic field.

The spin-only magnetic moment, μ, of a complex with total spin quantum number is given by:

μB = Bohr magneton


CALCULATED SPIN-ONLY MAGNETIC MOMENTS

ION N S μ/μB CALC. EXPT.

Ti3+ 1 ½ 1.73 1.7-1.8

V3+ 2 1 2.83 2.7-2.9

Cr3+ 3 1½ 3.87 3.8

Mn3+ 4 2 4.90 4.8-4.9

Fe3+ 5 2½ 5.92 5.9


The magnetic moment of a certain Co(II) complex is 4.0 μB . What is its d- electron configuration?

A Co(II) complex is d 7.

Two possible configurations: t2g5eg

2 (high-spin, S = 1½) with 3 unpaired electrons or t2g

6eg1 (Low-spin, S = ½) with 1 unpaired electron.

The spin-only magnetic moments are 3.87 μB and 1.73 μB.

Therefore, the only consistent assignment is the high-spin configuration t2g

5eg2.

The magnetic moment of the complex [Mn(NCS)6]4- is 6.06 μB. What is its electron configuration?

EXAMPLE

SOLUTION

EXERCISE FOR THE IDLE MIND

chapter 5: crystal field theory

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