Molecular Orbital Theory

 

Molecular Orbital Theory

Molecular orbital theory is also called Band Theory.

This theory was purposed by Arnold Sommerfeld and Felix Bloch.

According to this theory,

“Atomic orbitals (AO) overlap to form Molecular orbitals (MO).”

Number of molecular orbitals is equal to the number of atomic orbitals.

No of (MO) = no of (AO)

MO having less energy than the energy of AO is called Bonding MO (BMO).

MO having energy greater than the energy of AO,  is called Antibonding MO (ABMO).

Therefore in metals “n” number of AO overlap to produce “n” number of MO.

As the number of atoms increases, number of AO increases, number of MO increases.

Inner atomic orbital don’t participate in bonding.

Metals have high density therefore larger number of atoms is present in very small space.

Therefore in metals MO are closely spaced. The group of closely spaced MO is called band.

Therefore for metals MOT is called band theory. 

The electrons in outermost shell are called valence electrons. They have highest orbital energy but least binding energy. The valence electron are most effected when atom come close to each other. The band (group of closely spaced MO) occupied by valance electron called valance bond. The valance band may be completely or partially filled but never empty. The electrons which have left valance bond are called conduction electrons. They are loosely held with nucleus. The MO occupied by conduction electrons are called conduction band. The conduction band may be empty or partially filled but never be completely filled. The electron in conduction band moves freely and conducts electric current.

In metals there is no energy gaps between valance band and conduction band due to overlapping of two types of bands and electron require very small amount of energy to jump from valance to conduction band. There is no forbidden energy zone in metals. Therefore metals are very good conductor of electricity.

 In non-metals there is a wide energy gap between valance band and conduction band and electron require a large amount of energy to jump from valance to conduction band. This gap is called forbidden zone. Therefore non-metals are poor conductor of electricity. They have completely filled valance band, empty conduction band and large gap between valance band and conduction band.

In semimetals or metalloids there is low energy gap between valance band and conduction band and electron require sufficient amount of energy to jump from valance to conduction band. Therefore metalloids are semiconductor of electricity. Semiconductors have partially filled valance band, partially filled conduction band and very narrow energy gap between valance band and conduction band (1eV order).

They are nonconductor at absolute zero (0K) because at its temperature valance bond is completely filled and no electrons is in conduction band. They become conductor at high temperature because at high temperature electrons can jump from valence to conduction band.

Effect of temperature on conductivity of Semiconductors

Electrical conductivity of semiconductors increases with temperature.

In lithium, band originating from 2s orbital makes valance bond. It is half filled. The bond formed by 2p orbital are called conduction band. In metals energy gap between valance band and conduction band is negligible and electron can easily jump from valence band and conduction band while in nonmetals energy gap between valence band and conduction band is large and electrons can’t easily jump from valance band to conduction band.

Li= 1s²2s¹   2p_x⁰ 2p_y⁰2p_z⁰

For sodium:

Na= 1s²2s²2p⁶ 3s¹ 3p_x⁰ 3p_y⁰3p_z⁰

In sodium, band originating from 1s, 2s, and 2p orbitals don’t take part in bonding. 3s orbital is half filled and it makes valance band.

While the band formed by empty 3p (3p_x  3p_y  3p_z ) orbitals is called  conduction band.