This ppt describe you Molecular orbital energy level diagram, bond order, stabilization energy and magnetic properties of H2, He2, Li2 and Be2 molecules

1. Series of lecture on
Bonding in Molecules
Lecture-6
Molecular Orbital
Theory: Part- II
MO energy level diagram, Bond Order,
Stabilization energy, magnetism,
Formation of H2, He2, Li2 and
Be2 molecules
D. R. Shinde
Associate Professor in
ChemistryDepartment of Chemistry
P.D.E.A’s.
Prof. Ramkrishna More
Arts, Commerce and Science College
Akurdi, Pune-411044
1

2. In this Lecture
we will learn
i. Molecular orbital energy level diagram
ii. Formation of H2, H2
+, He2 He2
+ Be2 molecules/ions
and their MO energy level diagram
iv. Bond order, magnetic properties and stabilization
energy of molecules
iii. Rules for assigning the MO’s and filling of electrons
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
2

3. Energies of bonding and anti-bonding MO’s
When orbital combines to form MO, energies of AO’s get distributed among the MO’s.
 When electrons are filled into Bonding Orbitals then it results into force of attraction among the atoms.
Therefore, the energy of BMO’s is lower than AO’s.
 When electrons are filled into Anti-bonding Orbitals then it results into force of repulsion among the
atoms. Therefore, the energy of ABMO is higher than AO as well as bonding MO’s.
+ +- -
1S AO 1S AO
Energy
Bonding MO
Anti Bonding MO
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
3

4. Energy
↑ ↑
1s orbital
of HA
1s orbital
of HB
MO’s of H2
σ*1s-Anti-Bonding MO
σ1s - Bonding MO
+∆
- ∆
 MO Energy level diagram: This is graphical representation where AO’s in atom and MO’s
in Molecule are organized systematically according to their relative energies or increasing
energies.
 Example -H2 Molecule: In H2 molecule one bonding and one antibonding MO is formed by
interaction between 1s orbitals of two hydrogen atoms.
 They are sigma type MO’s. hence they are labelled as σ1s and σ*1s MOs. In following MO energy level
diagram energies of these orbitals are shown systematically.
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
4

5. How electrons are filled into MOs?
Electrons from AO are filled into MO according to Pauli’s
exclusion principle, Aufbau principle and Hund’s rules
 Bond order
 Pauli’s exclusion principle – maximum two electrons with opposite spin can be filled in one MO
 Aufbau principle: Electrons are filled into MO’s according to their increasing energy
 Hund’s rules: If two or more MO’s have same energies then each orbitals is first half filled with
same spin and then pairing starts with opposite spin.
Stabilization
Energy
Magnetic
Properties of
molecule
=
𝐍𝐨 𝐨𝐟 𝐞𝐥𝐞𝐜𝐭𝐫𝐨𝐧𝐬𝐢𝐧 𝐁𝐌𝐎−𝐍𝐨 𝐨𝐟 𝐞𝐥𝐞𝐜𝐭𝐫𝐨𝐧𝐬𝐢𝐧 𝐀𝐁𝐌𝐎
𝟐
The energy of the bonding MO is lower than that of the AO by an amount ∆ (-∆). This is
known as the stabilization energy.
 The energy of the antibonding MO is higher than that of the AO by an amount ∆ (+∆).
This is known as the destabilization energy.
Total stabilization energy = [(-∆ × e- in BMO) – (+∆ × e- in ABMO)]
 If Total stabilization energy is -ve - molecule is formed,
 Total stabilization energy zero - molecule cannot be formed.
If molecule consist of all electrons in MO in paired state then
molecule is diamagnetic. If molecule consists of unpaired
electrons in MO’s then molecule is paramagnetic in nature
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
5

6. Energy
↑ ↑
↑↓
1s orbital
of HA
1s orbital
of HB
MO’s of H2
MO energy level diagram for H2
σ*1s
σ1s
+∆
- ∆
For H2 molecule, (E.C. = H (1) – 1s1)
 2 electrons are filled in BMO.
 Bond order =
𝟐−𝟎
𝟐
= 1
 Total stabilization energy =
=[(-∆ × e- in BMO) – (+∆ × e- in ABMO)]
= [(-∆ × 2e- in BMO) – (+∆ × 0 e- in ABMO)]
= - 2∆
 Thus, For H2 molecule stabilization energy is -2∆.
Therefore, H2 molecule is stable and formed.
 The bond dissociation energy of H2 molecule is 434 kJ
per mole i.e. 2∆ = 434 kJ .
 Thus, BMO is located at -217kJ per mole in H2 and ABMO
at +217 kJ per mole w.r.t. to AO’s.
 Two electrons are in paired state in BMO hence H2
molecule, is diamagnetic in nature.
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
6

7. For H2
+ molecular ion,
Electronic Configuration (E.C.): H(1) – 1s1, H+– 1s0
 1 electrons are filled in BMO.
 Bond order =
𝟏−𝟎
𝟐
= ½
 Total stabilization energy =
=[(-∆ × e- in BMO) – (+∆ × e- in ABMO)]
= [(-∆ × 1e- in BMO) – (+∆ × 0 e- in ABMO)]
= - 1∆
 Thus, For H2
+ molecular ion, stabilization energy is
-∆. Therefore, H2
+ molecular ion can be formed
but is less stable than H2 Molecule.
 One electrons is in unpaired state in BMO hence H2
molecular ion is paramagnetic in nature.
Energy
↑
↑
1s orbital
of HA
1s orbital
of HB
+
MO’s of H2
+ ion
MO energy level diagram for H2
+ ion
σ*1s
σ1s
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
7

8. For He2
+ molecular ion,
E.C= He (2) – 1s2, and He+ – 1s1
 2 electrons are filled in BMO and one in ABMO.
 Bond order =
𝟐−𝟏
𝟐
= ½
 Total stabilization energy =
=[(-∆ × e- in BMO) – (+∆ × e- in ABMO)]
= [(-∆ × 2e- in BMO) – (+∆ × 1 e- in ABMO)]
= - 1∆
 Thus, For He2
+ molecule stabilization energy is -∆.
Therefore, He2
+ molecular ion can be formed but is
less stable.
 One electrons is in unpaired state in ABMO hence He2
+
molecular ion is paramagnetic.
Energy
↑↓
↑↓
↑
1s orbital
of HeA
1s orbital
of HeB
+
MO’s of He2
+ ion
MO energy level diagram for He2
+ ion
σ*1s
σ1s
↑
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
8

9. For He2 molecule
E.C= He (2) – 1s2,
 2 electrons are filled in bonding orbitals and two in
antibonding MO.
 Bond order =
𝟐−𝟐
𝟐
= 0
 Total stabilization energy =
=[(-∆ × e- in BMO) – (+∆ × e- in ABMO)]
= [(-∆ × 2e- in BMO) – (+∆ × 2 e- in ABMO)]
= 0∆
 Thus, For He2 molecule stabilization energy is 0.
Bond order is zero. Therefore, He2 molecule cannot
be formed i.e. do not exists.
Energy
↑↓
↑↓
↑↓
1s orbital
of HeA
1s orbital
of HeB
MO’s of He2 Molecule
MO energy level diagram for He2 Molecule
σ*1s
σ1s
↑↓
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
9

10. For Li2 molecule
E.C= Li (2) – 1s2, 2s1
 In Li atom 1s orbital is lower in energy hence it will not
take part in bonding. It remains non-bonding.
 In Li2 molecule 2 electrons are filled in bonding
orbitals
 Bond order =
𝟐−𝟎
𝟐
= 1
 Total stabilization energy =
=[(-∆ × e- in BMO) – (+∆ × e- in ABMO)]
= [(-∆ × 2e- in BMO) – (+∆ × 0 e- in ABMO)]
= -2∆
 Thus, For Li2 molecule stabilization energy is -2∆.
Bond order is one. Therefore, Li2 molecule is formed.
Li2 molecule exists only in gaseous state.
Energy
↑
↑↓
2s orbital
of LiA
2s orbital
of LiB
MO’s of Li2 molecule
MO energy level diagram for Li2 molecule
σ*2s
σ2s
↑
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
10

11. For Be2 molecule
E.C= Be (4) – 1s2, 2S2
 In Be atom 1s orbital is lower in energy hence it will not
take part in bonding. It remains non-bonding.
 In Be2 molecule 2 electrons are filled in BMO and 2 in
ABMO.
 Bond order =
𝟐−𝟐
𝟐
= 0
 Total stabilization energy =
=[(-∆ × e- in BMO) – (+∆ × e- in ABMO)]
= [(-∆ × 2e- in BMO) – (+∆ × 2 e- in ABMO)]
= 0∆
 Thus, For Be2 molecule stabilization energy is 0∆.
Bond order is Zero. Therefore, Be2 molecule cannot
be formed hence molecule do not exists.
Energy
↑↓
↑↓
↑↓
2s orbital
of BeA
2s orbital
of BeB
MO’s of Be2 molecule
MO energy level diagram for Be2 molecule
σ*2s
σ2s
↑↓
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
11

12. In Summary
1) MO energy level diagram
2) How MO energy level diagram can be used
i. Calculation of Bond order,
ii. Stabilization energy,
iii. Magnetism of molecule
iv. Existence or non-existance of molecule
05/08/2020
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
12