- The document discusses molecular orbital theory, which describes chemical bonding through the combination of atomic orbitals into molecular orbitals. - Key features include molecular orbitals being formed from linear combinations of atomic orbitals, with bonding, antibonding, and nonbonding molecular orbitals resulting. Electrons fill these orbitals based on orbital energy. - The formation of molecular orbitals from atomic orbitals of hydrogen is used as an example, with bonding and antibonding molecular orbitals illustrated.

1. Molecular Orbital Theory
B.Sc. SEM-V
Paper-II (Physical Chemistry)
Dr. N. G. Telkapalliwar
Associate Professor
Department of Chemistry
Dr. Ambedkar College, Nagpur

2. Molecular Orbital Theory
The Molecular Orbital Theory (often abbreviated to MOT) is a theory on chemical
bonding developed at the beginning of the twentieth century by F. Hund and R. S.
Mulliken to describe the structure and properties of different molecules.
The key features of the molecular orbital theory are listed below.
The total number of molecular orbitals formed will always be equal to the total
number of atomic orbitals offered by the bonding species.
There exist different types of molecular orbitals viz; bonding molecular orbitals,
anti-bonding molecular orbitals, and non-bonding molecular orbitals. Of these, anti-
bonding molecular orbitals will always have higher energy than the parent orbitals
whereas bonding molecular orbitals will always have lower energy than the parent
orbitals.
The electrons are filled into molecular orbitals in the increasing order of orbital
energy (from the orbital with the lowest energy to the orbital with the highest
energy).

3. The most effective combinations of atomic orbitals (for the formation of
molecular orbitals) occur when the combining atomic orbitals have similar
energies.
In simple terms, the molecular orbital theory states that each atom tends to
combine together and form molecular orbitals.
Each molecular orbital is associated with a wave function denoted by  and
probability of finding electron is given by 2. Wave function of molecular orbital
can be obtained by linear combination of atomic orbitals.
 Shape and size of molecular orbital is determined by shapes and sizes of atomic
orbitals from which they are formed.
 Electrons are filled in various molecular orbitals according to Aufbau principle,
Hund’s rule and Pauli’s exclusive principle.
Continue …………

4. Conditions for formation of molecular orbitals
The conditions that are required for the linear combination of atomic orbitals are as
follows:
1) Same Energy of Combining Orbitals
The atomic orbitals combining to form molecular orbitals should have comparable
energy. This means that 2p orbital of an atom can combine with another 2p orbital of
another atom but 1s and 2p cannot combine together as they have appreciable energy
difference.
2) Same Symmetry about Molecular Axis
The combining atoms should have the same symmetry around the molecular axis for
proper combination, otherwise, the electron density will be sparse. For e.g. all the sub-
orbitals of 2p have the same energy but still, 2pz orbital of an atom can only combine
with a 2pz orbital of another atom but cannot combine with 2px and 2py orbital as they
have a different axis of symmetry. In general, the z-axis is considered as the molecular
axis of symmetry.
3) Proper Overlap between Atomic Orbitals
The two atomic orbitals will combine to form molecular orbital if the overlap is proper.
Greater the extent of overlap of orbitals, greater will be the nuclear density between the
nuclei of the two atoms.
The condition can be understood by two simple requirements. For the formation of
proper molecular orbital, proper energy and orientation are required. For proper energy,
the two atomic orbitals should have the same energy and for the proper orientation, the
atomic orbitals should have proper overlap and the same molecular axis of symmetry.

5. Formation of Hydrogen molecule on the basis of molecular orbital theory

6. Figure: Probability distribution curves of bonding and antibonding molecular orbitals
Energy probability in molecular orbitals

7. Difference between bonding molecular orbital sand antibonding molecular orbitals

8. Formation of bonding molecular orbital and antibonding molecular orbitals

9. Difference between sigma (σ) and pi (π)molecular orbitals

13. •The valence bond theory was proposed by Heitler and London to
explain the formation of covalent bond quantitatively using quantum
mechanics.
•Later on, Linus Pauling improved this theory by introducing the
concept of hybridization.
•Valence bond (VB) theory assumes that all bonds are localized bonds
formed between two atoms by the donation of an electron from each
atom.
•Valence Bond theory describes covalent bond formation as well as the
electronic structure of molecules.
•The theory assumes that electrons occupy atomic orbital's of individual
atoms within a molecule, and that the electrons of one atom are attracted
to the nucleus of another atom.
Formation of hydrogen molecule on the basis of
Valence bond theory

14. •A covalent bond is formed by the overlapping of two half filled valence
atomic orbital's of two different atoms.
•The electrons in the overlapping orbital's get paired and confined between
the nuclei of two atoms.
•The electron density between two bonded atoms increases due to
overlapping. This confers stability to the molecule.
•Greater the extent of overlapping, stronger is the bond formed.
•The direction of the covalent bond is along the region of overlapping of the
atomic orbital's i.e., covalent bond is directional.
•Example: Hydrogen molecule (H2)
Continue………….

15. VB theory looks at covalent bonding as an overlap of atomic orbitals rather
than just a sharing of electrons as in previous theories. A covalent bond in VB
theory is a bond formed when the atomic orbitals of two atoms overlap and
each share one electron each having opposite spins in the overlap region
between the atoms. This overlap region is a region of high electron
density which serves to hold the atoms together.
The reason this overlap creates a bond between the atoms is there's a
reduction in the overall potential energy of the molecule compared to the
combined potential energies of the atoms separately.

20. Example of the diatomic hydrogen molecule (H2)
A relative plot of potential energy versus distance apart between two hydrogen
atoms. To the far right, the hydrogen atoms are separated from each other, seen as a
gap between the two spheres. The nominal potential energy of the separate atoms is
at the level of the x-axis. As the atoms begin to overlap (center image), there's a
reduction in potential energy (PE) relative to the separated atoms. This reduction in
PE continues as the atoms overlap more until it reaches a minimum (left image).
This is where we consider the bond being formed and the distance between the atoms
as being the associated bond length of that covalent bond. If we were to increase the
overlap of the atomic orbitals more, the PE goes up sharply suggesting that other
interactions come into play increasing the overall PE. The optimum distance between
the two atoms, the bond length, for H-H bond is 75 pm (picometers). So, atoms can
only get so close before problems begin to arise but must be close enough in order to
minimize the potential energy of the molecule.

21. Comparison of VBT and MOT