MOT-MOT for diatomic molecules

1. MOLECULAR ORBITAL THEORY
 Molecular orbital theory individual atoms combine to form molecular
orbitals, as the electrons of an atom are present in various atomic
orbitals and are associated with several nuclei.
 electrons may be considered either of particle or of wave nature.
 An electron in an atom may be described as occupying an atomic orbital,
or by a wave function ψ, which are solution to the schrodinger wave
equation.
 The wave function of a molecular orbital may be obtained by :
1. linear combination of atomic orbitals (LCAO) method

2. linear combination of atomic orbitals (LCAO)
 This method the formation of orbitals is because of linear combination (addition or
subtraction) of atomic orbitals which combine to form molecule.
 consider two atoms a and b which have atomic orbitals described by the wave functions
ψa and ψb .
 If electron cloud of these two atoms overlap, then the wave function for the molecule can
be obtained by a linear combination of the atomic orbitals ψa and ψb i.e. by subtraction
or addition of wave functions of atomic orbitals
ψmo= ψa + ψb
 The above equation forms two molecular orbitals

3. BONDING MOLECULAR ORBITALS
 when addition of wave function takes place, the type of molecular orbitals formed are called
bonding molecular orbitals and is represented by ψmo = ψa + ψb.
 they have lower energy than atomic orbitals involved.
 molecular orbital formed by addition of overlapping of two s orbitals shown in figure no. 2.
 it is represented by s
ANTI-BONDING MOLECULAR ORBITALS
 when molecular orbital is formed by subtraction of wave function, the type of molecular orbitals
formed are called antibonding molecular orbitals and is represented byψmo = ψa - ψb.
 They have higher energy than atomic orbitals.
 molecular orbital formed by subtraction of overlapping of two s orbitals are
shown in figure no. 2.
 it is represented by s* (*) is used to represent antibonding molecular orbital called sigma
antibonding.

4. fig. no. 2 FORMATION OF BONDING AND ANTI-BONDING ORBITAL
 combination of two atomic orbitals results in formation of two molecular orbitals,
bonding molecular orbital (BMO) whereas other is anti-bonding molecular orbital
(ABMO).
 BMO has lower energy and hence greater stability than ABMO. first BMO are filled then
ABMO starts filling because BMO has lower energy than that of ABMO .
.

5. BOND ORDER:
 it may be defined as the half of difference between the number of electrons present in
the bonding orbitals and the antibonding orbitals that is,
bond order (b.o.) = (no. of electrons in BMO - no. of electrons in abmo)/ 2
 those with positive bonding order are considered stable molecule while those with
negative bond order or zero bond order are unstable molecule
MAGNETIC BEHAVIOR:
 if all the molecular orbitals in species are spin paired, the substance is diamagnetic.
 if one or more molecular orbitals are singly occupied it is paramagnetic

6. MOT FOR HYDROGEN (H2) MOLECULE
electronic configuration of H is 1s1.
 The 1s orbital's of the two hydrogen atoms overlap forming two molecular orbitals σ1s and σ*1s
 The two electrons are occupied in σ1s orbital
 The electronic configuration of H2 is σ1s2
 H2 is diamagnetic because it has no unpaired electrons

7. MOT FOR He2 MOLECULE:
electronic configuration of He is 1s2.
 The two 1s orbital's overlap to form two molecular orbitals σ1s and σ*1s
 the four electrons from two helium atoms will occupy the σ1s and σ*1s
orbitals
 The electronic configuration of He2 is (σ1s)2, (σ*1s )2
 the zero bond order indicates that the molecule does not exist
 while the two electrons in BMO stabilize the molecule, the other two
electrons in ABMO destabilize the molecule.
 it is diamagnetic in nature

8. NITROGEN:
 electronic configuration of nitrogen molecule is (1σg
21σu
22σg
22σu
21πu
43σg
2)
 the electronic structure of nitrogen atom is leaving out 4 electrons in the 1s orbital of two nitrogen
atoms constituting the molecule (represented as kk), the molecular orbital energy diagram for remaining
10 electrons in nitrogen (N2) is as shown as below:
(i) electronic configuration:
N2 : [kk (σ2s)2 (σ2s)2 (σ2px)1(σ2pz)2]
(i) bond order : N2 = 8 and na = 2
bond order=nb-na/2=8-2/2
=6/2=3
 so the nitrogen molecule bond order is 3.
 the two nitrogen atoms in nitrogen molecule are linked
by three covalent bonds (i.e. a triple bond).
(ii) magnetic character:
 since all the electrons are paired, nitrogen is diamagnetic.

9. OXYGEN MOLECULE:
 electronic configuration of oxygen molecule =
 bond order in oxygen molecule (O2)=
[(number of bonding electrons) – (number of anti-bonding electrons)]
= ½ [10 – 6] = 2
so the oxygen molecule bond order is 2.
 the two oxygen atoms in oxygen molecule are linked by two covalent bonds (i.e. a double
bond).
 (ii) magnetic character: it presence of one unpaired,
so oxygen molecule is paramagnetic in nature.

10. CARBON –OXYGEN MOLECULE (CO)
the bonding molecular orbitals would have more characteristics of atomic orbitals of oxygen and antibonding
molecular orbitals would have more characteristics of carbon.
The electronic configuration of co molecule is σ2s² σ*2s² π2px² π2py² σ2pz²
bond order in oxygen molecule (O2)= [(number of bonding electrons) – (number of anti-bonding electrons)]
= ½ [8 – 2] = 3
so the carbon oxygen molecule bond order is 3.
the carbon and oxygen atoms in carbon oxygen molecule are linked by three covalent bonds (i.e. a triple
bond).
(ii) magnetic character: it , so carbon oxygen molecule is diamagnetic in nature

11. COMPARISON OF VBT AND MOT
Points of differences
Valence Bond Theory(VBT) Molecular Orbital Theory(MOT)
Orbitals of bonded atoms cannot lose their identity Orbitals of bonded atoms lose their individual identity.
Atomic orbitals are monocentric. Molecular orbitals are polycentric
This theory does not take into account of the ionic
structures
This theory takes into account of the ionic structures
In this theory, the concepts of resonance and hybridization
play an important role
In this theory, the concepts of resonance and
hybridization do not play any role
This theory fails to explain the paramagnetic character of
oxygen
This theory explains the paramagnetic character of
oxygen

12. Points of similarity:
 both the theories agree that a covalent bond is formed by the overlapping
of two atomic orbitals
 in both the theories the important requirement is that the overlapping
orbitals should have same symmetry and similar energy
 in both theories the electron density is assumed to reside in the region
between the atomic nuclei
 both the theories follow the rules in distributing electrons in various
orbitals
 both the theories postulates that a covalent bond has directional
property