Molecular Orbital Theory (MOT)

Molecular Orbital Theory
Dr. Shivaji H Burungale
Head
Department of Chemistry

Molecular Orbital Theory MOT.
Introduction: MOT was first developed by HUND,Mulliken
and Huckel in 1930.
In MO diagram of a molecule, electrons are fill in molecular
orbital according to
1. Aufbau principle.
2. LCAO method are as follows:
a) n atomic orbitals must produce n molecular orbitals (e.g.
6 AO’s must produce 6 MO’s).
b) The atomic orbitals with the appropriate symmetry
combine. c)The atomic orbitals with similar energy
combine. d) Each MO must be normal and must be
orthogonal to every other MO. e)The more interaction
between the atomic orbitals results in formation of more
stable MO

Principles of Ligand Field Theory In coordination
chemistry, the ligand acts as a Lewis base because it is
capable of donating a pair of electrons and metal is a
Lewis acid that accept a pair of electrons resulting
covalent bond between metal and the ligand. This is
also called as a coordinate covalent bond or a dative
covalent bond in order to show that both the bonds are
formed from electron coming from the ligand. A more
specified description of bonding in the coordination
complexes is given by Ligand Field Theory.
Essentially LFT is able to give an understanding of the
true origins of Δo and the spectrochemical series by
taking into account the roles of σ- and π- bonding in
transition metal chemistry.

https://youtu.be/B1vONC7s_rM
https://youtu.be/B1vONC7s_rM

The A1g group orbitals
have the same
symmetry as an s
orbital on the central
metal.

The T1u group orbitals have
the same symmetry as the p
orbitals on the central
metal.
(T representations are
triply degenerate

Ligand Field Theory
The Eg group
orbitals have the
same symmetry as
the dz2 and dx2-y2
orbitals on the
central metal.
(E representations
are doubly
degenerate.)

Ligand Field Theory
Since the ligands
don’t have a
combination with t2g
symmetry, the dxy, dyz
and dxy orbitals on the
metal will be non-
bonding when
considering σ bonding.

Ligand Consideration
In the formation of transition metal complexes,
there is required central metal atom/ion and the
surrounding ligands. The geometry and nature
of the complex depends upon the type of the
metal as well as ligands. The ligands in this
context can be of various types:
(a) σ donor (b) π donors (c) σ+π donors (c) π
acceptors

Nature of Ligands .
There are three types of ligands
1.Pure sigma bonding electron donor
orbitals eg. NH3, H2O
2. σ and π bonding electron donor
orbitals eg. Halogen lignds
3.Weak σ donor and strong π acceptor
ligands eg. CO,CN

In order to decide which atomic orbitals to combine, we use
the following guidelines:
atomic orbitals that combine must be of similar energy;
only atomic orbitals of the same symmetry can combine;
there must be significant overlap of combining orbitals;
n atomic orbitals combine to make n molecular orbitals.

Representation of Symmetry Point Groups.
a = singly degenerate
T= triply degenerate
E= doubly degenerate
g = symmetric
u= unsymmetric
A1g
One (A and B, Two for E and three for triply degenerate symbols
Symmetric with 1 and antisymmetric with 2
Centre of symmetry of molecule g and u for nonsymmetric molecule

Metal orbitals symmetry of orbitals
S a1g
px,py pz t1u
Dz2,dx2-y2 eg
dxy
Dxz T2g
dyz
Matching Metal orbitals of 4s ,4p 3d

Ligand orbitals symmetry of orbitals
Px, Py, Pz a1g, eg t1u
two ligand along the z axis
Two ligands along the x axis
Two ligands along the y axis
Each ligand donate a pair of electrons
Total 12 electrons are donated by six
ligands

Metal Orbital Symmetry Label Degeneracy
s A1g 1
px, T1u 3
py,
pz
dxy, T2g 3
dyx,
dxz
dx2-y2 Eg 2
, dz2
Symmetry Representation

Ligand Group orbitals.
In the octahedral environment
Metal orbital + Ligand group orbital BMO s + AMOS
a1g a1g A1g A1g*
t1u t1u T1u T1u*
eg eg Eg Eg *
σ bonding MO
t2g t2g (n)
T2g non bonding mos
A1g T1u EgT2g Eg * A1g* T1u* antibonding MOS

a metal ion surrounded by six ligands, each
contributing one filled orbital. Thus, we have
five metal d orbitals and six ligand orbitals
from which to construct molecular orbitals for
the complex. We arrange the six ligands to lie
on the x-, y- and z-axes. Let us now see how
the six ligand orbitals overlap with the metal
d orbitals.

Bonding in Octahedral complexes
Bonding in octahedral complexes is divided
into two types
a) Sigma bonding MOs
b) Pi bonding MOS

CONSTRUCTION OF MO DIAGRAM FOR SIGMA BONDING OCTAHEDRAL
COMPLEXES
1. Name of the central metal in complexes
2. Atomic number of central metal atom
3. electronic configuration of metal atom
4. Oxidation state of metal
5. Number of valence electrons in 3d and 4s orbitals.
6. Number of ligands donated 12 elctrons
7. Total number of electrons of metal ion and 12 electrons of six ligands.
8. Distribution of electrons in the order of Molecular orbitals. Like
A1g < T1u < Eg < T2g< Eg * < A1g*< T1u*
12 electrons occupied in bonding MO orbitals and remaining electrons
occupied in non bonding T2g and antibonding Eg * orbitals.
2 6 4

MO diagram in metal complexes
1. [Ti(H2O)6]3+
In this complex, Central metal is Titanium
Atomic number of Titanium is 22
Outer most Electronic configuration of Titanium is 3d2 4s2
Oxidation state of central titanium is +3
therefore 3d1 4s0
Number of electrons in valence orbitals is 1
Total number of electrons in Ti3+ is 1 and 12
electrons from 6 ligands.
total electrons 13

[CoF6]3–
Co -27
3d7 4s2
Co3+
3d6 4s0
6 electrons of
cobalt and 12
electrons of
fluoro ligands
[Co(NH3)6]3
Co 3+
3d6 4s0
6 electrons of
cobalt and 12
electrons of
ammonia ligands

Sigma bonding in transition metal complexes
The atomic orbitals on the central metal ion may be ns ,np, and
(n-1)d orbitals which together are called valence orbitals
There are four important points such
1. Classification of metal valence orbitals in sigma symmetry
in octal hedral complex.
a1g s
T1u px py pz
Eg dz2 dx2-y2d2sp3
Thus hybrid combination required is d2SP3

6 s ligands x 2e each
12 s bonding e
“ligand character”
“d0-d10 electrons”
non bonding
anti bonding
“metal character”
ML6 s-only
bonding
The bonding
orbitals,
essentially
the
ligand lone
pairs,
will not be
worked
with further.

Bonding MOs
Antibonding
MOs
AOs Ti3+ ions
LGOs of 6H2O
a1g 4s
t1u
4 px py pz
t2g eg
3dxy dxz dyz
dx2-y2 dz2
A1g
T1u
T2gn
Eg
Eg*
A1g*
T1u*
∆o

Bonding MOs
Antibonding
MOs
AOs Ti3+ ions
LGOs of 6H2O
a1g 4s
t1u
4 px py pz
t2g eg
3dxy dxz dyz
dx2-y2 dz2
A1g
T1u
T2gn
Eg
Eg*
A1g*
T1u*
∆o
E

Color and spectra of [Ti(H2O)6]3+
1. Ligand is weak field -H2O
2. The reddish violet Purple
3. Maximum absorption at 20300cm-1
4. d-d transition forbidden transition
weak band
5. Charge transfer transition –27000 to
30000cm-1
6. Paramagnetic nature due to one
unpaired electron in nonbonding t2g
orbitals.
E

Bonding MOs
Antibonding
MOs
AOs Co3+ ions
LGOs of 6F-
a1g 4s
t1u
4 px py pz
t2g eg
3dxy dxz dyz
dx2-y2 dz2
A1g
T1u
T2gn
Eg
Eg*
A1g*
T1u*
∆o

MOs Diagram for [Co(F)6]3-
1. Ligand is weak field –F-
2. Color of Complex is Blue
3. Maximum absorption at 15000 cm-1
4. d-d transition forbidden transition
weak band
5. Charge transfer transition –27000 to
30000cm-1
6. Paramagnetic nature due to four
unpaired electron in nonbonding t2g
orbitals.And antibonding Eg orbitals

Antibonding
MOs
AOs Co3+ ions
a1g 4s
t1u
4 px py pz
t2g eg
3dxy dxz dyz
dx2-y2 dz2
A1g
T1u
T2gn
Eg
Eg*
A1g*
T1u*
LGOs of 6 NH3
∆o
Bonding MOs

MO diagram for [Co(NH3)6]3+
1. NH3 is strong field
2. Color of Complex is yellow green
3. Diamagnetic in nature
4. ∆0 is large

Merits and Demerits of MOT
Merits
1.This is a completely theory
2. It has considered interaction between metal orbital's and Ligands orbital's.
3.Pi bonding is explained
4. Strong field and weak field ligands are explained .
5. Charge transfer spectra and d-d transition also explained.
6. Magnetic and stability of complexes are also studied.
7. Spectrochemical series and Nephelauexetic effect are explained on the basis of MOT
Demerits
This is most complicated
Molecular orbital calculation , Computer is required
Multi atom complex cannot be explained.

Molecular Orbital Theory (MOT)

Molecular Orbital Theory (MOT)

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