FSc Notes Chemistry Part 1 Chapter 6 Chemical Bonding Lecture 7

Molecular Orbital Theory ( M.O.T ) :

VSEPR theory and VBT failed in explaining some particular properties of atoms and molecules, like paramagnetism, atomic spectra etc. so MOT was presented by Hund and Millikan to overcome these problems.

Assumptions:

The main postulates or assumptions of M.O.T are described below.

The atomic orbitals ( A.O.S ) of the bonding atoms overlap or mix and produce an equivalent number of new orbitals which are known as molecular orbitals ( M.O.S ) ie we can say that the no. of M.OS is equal to the no.of mixing A.O.S.
Half of the M.Os are known as bonding molecular orbitals ( B.M.Os ) in which bond formation takes place, while half of the M.Os are known as Anti bonding molecular orbitals ( ABMOS ), which are unstable and hence no bond formation takes place in Anti bonding molecular orbitals.
The energy of B.M.O.s isles or lower than the energy of A.Os hence. B.M.Os are stable while the energy of A.B.M.Os is higher than the energy of the A.Os, hence Anti bonding molecular orbitals are unstable. Thus it is clear that sum of the energies of B.M.Os and A.B.M.Os is always equal to the total energy of the A.Os.
The B.M.Os are denoted by the notation s like A.Os while A.B .M.Os are denoted by the notations .
The M.Os are formed by linear or axial overlapping of atomic orbitals similarly the M.Os are formed by parallel or side wise overlapping of atomic orbitals.
The formation of M.Os is shown as follow. M.O.T obeys Aufbau, principle, Hund’s Rule as well as Pauli exclusion principle. The increasing order of energy of the M.Os is Bond order shows the no. of covalent bonds formed between the bonding in a molecule if B.O is Zero then no bond will formed among the atoms. If B.O is 1,then single covalent bond will be formed, if B.O is 2 then double covalent bond will be formed and if B.O is 3, then a triple covalent Bond will be formed among the bonding atoms.

Applications:

The formation of some homo-nuclear di- atomic molecule ( molecules which are made of atoms of some elements ), can be explained with the help of M.O.T as follow.

1. Hydrogen Molecule( H2 )

H2 molecule is made of two hydrogen atoms. Each H has a is 1 atomic orbitals. According to M.O.T the two 1s1 A.Os of the two bonding H atoms overlap and form two M.Cs. one M.O is a B.M.O ( ie SCH ) and the others is an A.B.M.O ( ie S C Is ), So Pauli Exclusion principle is also obeyed A, B.O of H2 molecule is 1, so there is a single covalent bond among H atoms in H2 ,molecule

i.e. H—H

2. Helium Molecule:( He2 )

Helium molecule has two He atoms. The electron configuration of each He atom is,

2He = 1S2 A.O.

Each He atom has a 1S2 atomic orbital when these two is A.Os mix, the form two M.Os. one of the two M.Os is B.M.O which S ( 1S ) and the other is an A.B.M.O which is Sx ( 1S ). As a electron are available, so according to Aufbau principle, two electrons will go to S ( 1S ) and 2 to Sx ( 1S ).

The electrons in the M.Os are with opposite spin, so Pauli Exclusion principle is followed ie As the B.O of He2 molecule is Zero hence He2 molecule is not possible because no bond is formed among the He atoms.

3. Nitrogen Molecule ( N2 ):

A.N2 molecule is made of two N atoms. The electronic configuration of each N atom is:

It is clear that each N atom has five atomic orbitals and hence according to M.O.T ten M.Os will be formed during bond formation among N atoms of N2 molecules is of all the IS2atomic orbital of each N atom will mix to form two M.Os ie S( IS ) ( B.M.O ) and Sx ( IS ) ( A.B.M.O ). But due to presence of 4es, their B.O will be zero, so they don’t participate in bonding. then the 3p ( 2px1, 2py1, 2pz1 ) degenerate A.Os of one N atom will mix with the three P (ie 2px1, 2py1, 2pz1 ) degenerate A orbitals of their N atom, two form six M.Os. three of the M.Os are B.M.Os which are S (2px ) , (2py ) and (2B) ( note : (2py) (2p2) m.os are degenerate ie have same energy and shape.

While the remaining three M.Os are A.B.M.Os which are S (2px), (2py) and (2pz). In case of N atom the valence orbital ie 2p is half filled ( ie has 3 electrons ) hence, it is a bit more stable and due to this extra stabilizing, the energy of (2py) and (2pz), B.M.Os is smaller than the energy of S( 2px ) B.M.O ( it is an exceptional case ) The above explanation can be shown as, from the above diagrams, it is clear that there are a total of 10 electrons in B.M.Os and 4 electrons in the A.B.M.Os so the bond order of N2 molecule will be

So there is a triple covalent bond among N among N atoms of N2 molecule ie N=N

Note: as there is no unpaired electron in N2 molecule ie all its electrons are paired, therefore N2 molecule is diamagnetic.

4. Oxygen Molecule ( O2 ) :

O2 molecule is made of two oxygen atoms . the electronic configuration of each oxygen atom is

O8 = 1S2, 2S2, 2P4 ( ie, 2P2x, 2py1, 2Pz1 )

As each "O" atom has 5 atomic orbitals, so according to M.O.T, ten M.Os will be formed during bonding of the two O atoms to form O2 molecule.

S of the IO M.Os are B.M.Os which are S(1S), S(2S), S(2Px) (2py) and (2pz). While the remaining 5 are A.B.M.Os which are Sx(1S), Sx(2S), Sx(2Px), (2py) and (2pz). First of all, the IS2A.Cs of both " O " atoms mix and form two M.Cs one is B.M.O which S(IS) and the other is A.B.M.O which is Sx (1S). As both B.M.C and A.B.M.O have equal no. of electrons ( ie 2es in each ) so they the is A.OS don’t participate in bonding. Then the 2S2 A.Os of both "O" atoms mix and form two more M.Os one is B.M.O ( ie S (25) ) and the other is A.B.M.O ( which is Sx ( 2S). Due to having equal no. of es in S(2S) and Sx (2S), they also don’t participate in bond formation.

Then the three P degeneration orbitals ( ie, 2P2x, 2py1, 2Pz1 ) of one "O" atom mix with the three P degenerate orbitals ( ie, 2P2x, 2py1, 2Pz1 ) of other "O" atom to form six M.Os. three of them are B.M.Os ( ie S ( 2Px ), (2PY) (2Pz) while the remaining three are A.B.M.Os ( ie S ( 2Px ), (2PY) (2Pz).

As there are 8 electrons in all the 2P orbitals of both the oxygen atoms. So according to Aufbau principle two electrons will go to S(2Px), then 4L-S will go to the (2Py) and (2pz) degenerate orbitals. The remaining two electrons will go into the A.B.M.Os (2Py) and (2pz). As (2Py) and (2pz) orbitals are degenerate to according to Hund's Rule, the two es will occupy them singly with same spin.

The above explanation is shown as, So there is a double covalent bond b/w "O" atoms of O2 molecule ie O==O

Due to the presence of two unpaired es in the (2py) and (2pz) M.Os O2 molecule shows its paramagnetic character.

Before M.O.Ti all other theories failed to explain the paramagnetic character of O2 although whenever liquid O2 had been placed in a magnetic field, it got attracted by the magnet. Thus it was clear that O2 molecule has one or more unpaired electrons but where are the located was a real problem

M.O.T is the only theory which solved the above mentioned problem and showed the unpaired electrons in O2 molecule.

Thus M.O.T is superior to all other theories.

FSc Notes

FSc Notes Chemistry Part 1 Chapter 6 Chemical Bonding Lecture 7