The document discusses molecular orbital theory (MOT), an approach to bonding in which orbitals encompass the entire molecule rather than being localized between atoms. MOT was put forward by Hund and Mulliken and later modified by Jones and Coulson. It addresses some of the drawbacks of valence bond theory, including explaining the paramagnetic nature of O2. MOT uses the linear combination of atomic orbitals (LCAO) approach and Hund's rule to determine molecular orbital configurations and energies.

1. “AN APPROACH TO BONDING IN WHICH
ORBITALS
ENCOMPASS THE ENTIRE MOLECULE, RATHER
THAN BEING LOCALIZED BETWEEN ATOMS.”
Satyabrata Sendh
MSc Part II(2018-19)
PG Dept of Chemistry
Berhampur University
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2.  INTRODUCTION
 ASSUMPTION AND POSTULATES
 LCAO PRINCIPLE
 MO OF DIATOMIC MOLECULES
 SIGNIFICANCE AND APPLICATIONS OF MOT
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3.  Probably the second and most applicable theory for bonding and structure of
molecules.
 Put forward by HUND and MULLIKEN.
 Later modified by JONES and COULSON.
HUND MULLIKEN
Though there was VBT to explain bonding and
structure of molecules still it was unable to explain
some features. Hence because of the drawbacks
of VBT another theory was given known as
MOLECULAR ORBITAL THEORY.
Drawbacks of VBT -
 Fails to explain paramagnetic nature of O2
 Resonance plays a major role in VBT but no role in MOT.
 VBT did not give any weightage to ionic structure BUT MOT did.
 It didn’t say about Anti bonding orbital thus failed to say about spectral lines.
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4. If two nuclei are positioned at equilibrium distance, the electron are added and
they will go in to molecular orbitals.
 Each molecular orbital is given by a wave function Ψ known as molecular orbital
wave function.
 Ψ2 represents to probability density or total electron charge density.
 Each wave function (Ψ) is associated with a set of quantum no which
determines the energy and the shape of the orbitals.
 Each wave function (Ψ) is associated with certain amount of energy and total
amount of energy is sum of energies of occupied molecular orbitals.
 The number of molecular orbitals (MOs) formed is always equal to the number of
atomic orbitals combined.
 Filling of orbitals takes place accordingly to HUND’s rule, PAULI’s principle and
as that of Aos.
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5. For approximation of correct MO, though there are several methods let’s do
accordingly with Liner Combination of Atomic Orbitals (LCAO)
Liner Combination of Atomic Orbitals (LCAO)
Conditions for LCAO-
 Atomic orbital's must be roughly of the same energy. Atomic orbitals with
differing energies or the wrong spatial orientation (orthogonal) do not combine,
and are called non-bonding orbitals.
 The orbital must overlap one another as much as possible- i.e. atoms must be
close enough for effective overlapping.
 In order to produce bonding and anti bonding MOs, either the symmetry of two
atomic orbital must be same or when rotated about the internuclear line both
atomic orbital's must change symmetry in identical manner.
ΨAB = N(ΨA + ΨB)
Ψ2AB = ( ΨA2 + ΨB 2 + 2 ΨA ΨB )
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6. An analogy of atomic wave functions.
 Increased electron
density between the
two nuclei
 Lower energy than the
two separate atomic
orbitals
 Node between the two
Nuclei ,decreased electron density
 Greater energy than
the two separate
atomic orbitals
Out phase
Destructive
No resultant
wave
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7. COMBINATION OF S ORBITALS
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COMBINATION OF P ORBITALS

8. The general sequence of energy levels is (determined experimentally from
spectroscopic data)
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σ 1s < σ*1s < σ2s < σ*2s < σ2pz < (π2px = π2py) < (π*2px = π*2py) <
σ*2pz

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ORBITAL MIXING
σ 1s < σ*1s < σ2s < σ*2s < (π2px = π2py) < σ2pz < (π*2px = π*2py) <
σ*2pz

10. Lets start with the simplest molecule H2
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11. MOLECULAR OXYGEN(O2)
σ 1s < σ*1s < σ2s < σ*2s < σ2pz < (π2px = π2py) < (π*2px = π*2py) < σ*2pz
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12. MOLECULAR FLUORINE(F2)
σ 1s < σ*1s < σ2s < σ*2s < σ2pz < (π2px = π2py) < (π*2px = π*2py) < σ*2pz
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13. MOLECULAR NITROGEN(N2)
σ 1s < σ*1s < σ2s < σ*2s < (π2px = π2py) < σ2pz < (π*2px = π*2py) <
σ*2pz
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14. MO OF NO
N=1s2 2s2 2p3
O=1s2 2s2 2p4
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Bond Order=2.5
Bond Length=1.15A0

15. MO OF CO C=1s2 2s2 2p2
O=1s2 2s2 2p4
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Bond Order=3
Bond Length=1.112 A0

16. MO OF CO+ (coulson diagram)
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17. CO as a Ligand
 Both σ donor and a π acceptor ligand
 This phenomenon is called back bonding.
 The increased electron density in the antibonding orbitals of CO
causes an increase in the C-O bond length and a decrease in its
stretching frequency
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18. SIGNIFICANCE OF MOT
The molecular behavior can be described on the basis of electronic
configuration.
The distribution of electrons among various molecular orbitals is called the
electronic
configuration of the molecule. From the electronic configuration of the molecule, it
is
possible to get important information about the molecule as discussed below.
Stability of Molecules: If Nb is the number of electrons occupying bonding
orbitals and
Na the number occupying the antibonding
orbitals, then
(i) the molecule is stable if Nb>>Na, and
(ii) the molecule is unstable if Nb <<Na.
In (i) more bonding orbitals are occupied and so the bonding influence is stronger
and a
stable molecule results.
In (ii) the antibonding influence is stronger and therefore the molecule
is unstable.
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19. Bond order
Bond order (b.o.) is defined as one half the difference between the number of
electrons
present in the bonding and the antibonding
orbitals i.e.,
Bond order (b.o.) = ½ (Nb–Na)
The rules discussed above regarding the stability of the molecule can be restated in
terms of bond order as follows: A positive bond order (i.e., Nb > Na) means a stable
molecule while a negative (i.e., Nb<Na) or zero (i.e.,
Nb = Na) bond order means an unstable molecule.
Nature of the bond
Integral bond order values of 1, 2 or 3 correspond to single, double or triple bonds
respectively as studied in the classical concept.
Bond-length
The bond order between two atoms in a molecule may be taken as an approximate
measure of the bond length. The bond length decreases as bond order increases.
Magnetic nature
If all the molecular orbitals in a molecule are doubly occupied, the substance is
diamagnetic (repelled by magnetic field). However if one or more molecular orbitals
are
singly occupied it is paramagnetic (attracted by magnetic field), e.g., O2 molecule
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20. MO diagram for He2
+ and He2.
He2
+ bond order = ½ He2 bond order = 0
(σ1s)2(σ )1*
1s (σ1s)2(σ )2*
1s
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22. Experimental Evidence
 Photoelectron spectroscopy (PES)
is a technique in which a beam of
ultraviolet / X ray light with is used
to irradiate molecules.
 The technique allows for the
measurement of specific ionization
energies
(I). Each ionization energy
represents the removal of an
electron from a specific molecular
orbital.
 Electrons in lower energy levels
require more energy to be
removed, and are ejected with less
kinetic energy.
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hνo = IE + EKinetic
*IE = Ionisation Energy

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