Download Crystal Field Theory part A

5.0 The Crystal-Field Theory
By Prof Yeap Guan Yeow
5.1 Introduction
This theory emphasizes on the electrostatic
bonding of the chemical bond in a complex
between the positive nucleus on the metallic
ion with the negative charge on the electrons
coming from the ligands.
The diagram shows that electrons
from the ligands causes electrostatic
field around the metallic ion
Complex M
There are three interactions between the ligand
field with the metallic atom
(i) Ligand field with s orbital
(ii) Ligand field with p orbital
(iii) Ligand field and d orbital
(i) Ligand field with s orbital
For 4s orbital, because of its spheric
shape, all the ligands that enter the
octahedral field or in whatever
arrangement will experience the same
electrons repulsion in every direction in
Cartes system .
(ii) Ligand field with p orbital
p orbitals directed to x, y and z axis causing the
charge density to face along the Cartes axises.
p orbitals in the three directions on the Cartes axis that
interact with the ligands will experience the same
electron repulsion. As a result, the levels of p orbitals
will be elevated and are in the degeneration state.
(iii) Ligand field and d orbital
For d orbital, the scattering of electron density for
the five orbitals can be shown in the diagrams
below:
_ dz2 and dx2-y2 orbitals
have the charge density
which is directed to
(i) z axis ,
(ii) x and y axis,
respectively.
_ The lobes for the three
dxy, dxz, and dyz orbitals
orbitals are placed 45°
in between the axes.
5.2
Types of Complex
5.2.1 Octahedral complex, ML6
(a) As the set of dz2, dx2-y2 and the set of dxy, dxz and dyz
orbitals are oriented in different manner in the space,
therefore, these two sets of orbitals will experience
different electronic repulsion.
(b) Greater electron repulsion in the dz2 and dx2-y2
orbitals set compared to dxy, dxz and dyz orbitals.
(c) As a result, the levels of dz2 and dx2-y2 orbitals
are elevated (destabilized).
(d) the level of dxy, dyz, dxz orbital are decreased
(stabilized).
d orbitals will not degenerate within the ML6
complex but will remain at the different energy
levels as follows :
eg orbital set
t2g orbital set
dz2, dx2-y2
dxy, dxz, and dyz
The splitting of crystal field of ML6 complex can be
represented by the following diagram.
• The
directory of d orbitals
5.2.2 Tetrahedral complex contradicts with those found in
the octahedral complex.
z
• dz2 and dx2-y2 are not
directed parallel with the
charge of ligands and this
causes the energy level to
decrease.
y
x
However, the difference in
energy between the two d
orbital sets in the tetrahedral
complex is found to be lower
as compared to the energy
difference found in an
octahedral complex .
This phenomenon can be illustrated as
follows:
Note:
The subscript g and u are not written for the tetrahedral
complex as this complex does not have a symmetrical centre.
5.2.3 Other complexes
Based on the tetrahedral and octahedral complexes, the
explanations for other complexes (square planar, trigonal
bipyramidal, and square pyramidal) can be obtained.
The conclusion for every complex can be shown in the following
diagram.
5.3
High spin-Low-spin Complexes
The Crystal Field or Ligand Field Theory can be used
to elaborate on the existence of high spin and low spin
complexes.
For octahedral complex: d1 – d10, the occupancy of the
d orbitals by electrons is categorized according to its
ability to do so.
(a)
For d1 , d2 , d3 , d8 , d9 and d10, electrons are filled in between
t2g and eg orbital by one possible method only.
d1
d2
d3
u= 1.7
2 .8
3.9
d8
d9
2.8
1.7
d10
0
(b)
For d4, d5, d6 and d7, electrons are filled in between t2g and eg
orbitals by two possible methods.
In this case, it is clear that two complexes exist; the high spin and low spin
complexes.
A main factor determining the formation of high spin or low spin complex is
the splitting of ligand field parameter Δ.
The value of Δ can be characterized based on the comparison with the
energy value for pairing up the electrons (P). There are two situations in
which either a high spin or low spin complex will be obtained.
There are two situations in which either a high spin or low spin
complex will be obtained.
If Δ > P ; high field (strong) → low spin complex
If
Δ < P ; low field (weak ) → high spin complex
where P = pairing energy
For example,
For low spin complexes:
[Co(NH3)6]3+ (t2g6)
There are three pairs of electrons residing in t2g.
5.4 Spectrochemical series
 Spectrochemical series is a series for
different types of ligands which give different
effect on the field of ligand and central
metallic ion. The differences are caused by
the different ∆ magnitudes (10Dq) and it
depends on the type of ligands.
 The value of Δ can be determined
experimentally through the electron spectrum
analysis obtained for the transition metal
complexes.
The investigation on the effect of different series of
ligands on different metallic ions has been
summarized in the following table.
Δ (cm2) for octahedral complex
Based on the above table, we can see an obvious trend as
follows:
(i) For a certain ligand, Δ
among transition metal ions
will not change much in the
same oxidation state. For
example, Δ for hydrated M2+
is found in the range of
7500-12000 cm-1.
(iii) For a certain ligand and
stereochemical, the metallic
ions can be arranged
following the increasing ∆.
This order is independent
on the natural characteristics
of the ligands.
(ii) For a certain ligand, Δ
increase if the oxidation
state of the metal increases.
For example, Δ for hydrated
M3+ is found in the range of
14000-25000 cm-1.
(iv)For a certain metallic ion, the
ligands can be arranged
according to the natural
characteristics of the metal.
Both characteristics spelt in (iii) and (iv) are known as
spectrochemical series.
 In general, spectrochemical series for metallic ions
can be shown as follows:
Mn2+ < Ni2+ < Co2+ < Fe2+ < V2+ < Fe3+ < Cr3+ < V3+ < Co3+
 As for ligands, the series is as follows:
I- < Br- < CI- < S2- < F- < OH- < CH3COO- < C2O42- = O2< H2O < py = NH3 < en < bipy < phen< PR3 < CO = CN
 Question:
Why do ligands F- and CN- that have negative
charges are found in the position of the weak and
strong series?
This can be explained using the π-bond effect and can be
elaborated through the following diagrams.
 (a)
For complex that contains M-F bond
e g*
e g*
( t2g )
t 2g
(i) Ligands donate electrons to the central metal M through π orbital on
ligand F.
(ii)Electrons from the set orbital t2g that are originated from the metallic
ions are filled in the anti-bonding π* molecular orbital which is at a
higher energy level as compared to t2g
(iii)The effect is the reduction of ∆.
(b)
For a complex which contains M-CN bond
e g*
e g*
t2g
t2g
(i) The ligands have high-energy π* orbital which is empty (CO, CNand H2C=CH2 are ligands that have the empty π* orbitals )
(ii) As a result, the density of electrons from central metal M can be
donated to the ligands through the back-bonding.
(iii) Electrons that are filled in π(t2g) orbital are from metal.
(iv) The effect is the stabilization of t2g orbitals.
•
For octahedral complex, for example d1 complex: electrons
place themselves at t2g orbital which is at the energy level Δo
less than the energy level of d orbital which does not undergo
splitting.
•
The additional stabilization caused by the splitting of d orbital is
known as the crystal field stabilization energy (CFSE).
•
Every electron in the t2g orbital set contribute -Δo for (CFSE).
However, electrons in the eg orbital set resides at the higher
energy level from d orbital which does not undergo splitting and
every electron contributes Δo to CFSE.