The new orbitals that are formed due to intermixing of atomic orbitals are also known as hybrid orbitals, which have mixed characteristics of atomic orbitals. The shapes of hybrid orbitals are identical. Usually they have one big lobe associated with a small lobe on the other side. The hybrid orbitals are degenerate i.e., they are associated with same energy. The hybrid orbitals participate in the `sigma` bond formation with other atoms.

The number of hybrid orbitals formed is equal to the number of pure atomic orbitals undergoing hybridization. E.g. If three atomic orbitals intermix with each other, the number of hybrid orbitals formed will be equal to `3`. The hybrid orbitals are filled with those electrons which were present in the pure atomic orbitals forming them.The filling up of electrons in them follows Pauli's exclusion principle and Hund's rule.

Why atomic orbitals in a given atom undergo hybridization?

The hybrid orbitals are oriented in space so as to minimize repulsions between them. This explains why the atomic orbitals undergo hybridization before bond formation. The reason for hybridization is to minimize the repulsions between the bonds that are going to be formed by the atoms by using hybrid orbitals. Remember that the hybridization is the process that occurs before bond formation. The bond angles in the molecule are equal to or almost equal to the angles between the hybrid orbitals forming the `sigma` bonds. The shape of the molecule is determined by the type of hybridization, number of bonds formed by them and the number of lone pairs.

There are many different types of hybridisation depending upon the type of orbitals involved in mixing such as `sp^3`, `sp^ 2`, `sp`, `sp^3d`, `sp^3d^2`, etc.

Let us now discuss various types of hybridisation along with some examples with reference to the compounds of carbon, boron and beryllium.

The type of hybridisation involves the mixing of one orbital of `s`-sub-level and three orbitals of `p`-sub-level of the valence shell to form four `sp^3` hybrid orbitals of equivalent energies and shape. Each `sp^3` hybrid orbital has `25%` `s`-character and `75%` `p`-character. These hybridised orbitals tend to lie as far apart in space as possible so that the repulsive interactions between them are minimum. The four `sp^3` hybrid orbitals are directed towards the four corners of a tetrahedron. The angle between the `sp^3` hybrid orbitals is `109.5^(o)` (Fig.1).

`sp^3` hybridisation is also known as tetrahedral hybridisation. The molecules in which central atom is `sp^3` hybridised and is linked to four other atoms directly, have tetrahedral shape. Let us study some examples of molecules where the atoms assume `sp^3` hybrid state.

`text(Formation of methane)` `(CH_4)`. In methane carbon atom acquires `sp^3` hybrid states as described below. Here, one orbital of `2s`-sub-shell and three orbitals of `2p`-subshell of excited carbon atom undergo hybridisation to form four `sp^3` hybrid orbitals. The process involving promotion of `2s`-electron followed by hybridisation is shown in fig.2.

As pointed out earlier the `sp^3` hybrid orbitals of carbon atom are directed towards the corners of regular tetrahedron. Each of the `sp^3` hybrid orbitals overlaps axially with half-filled `1 s`-orbital of hydrogen atom constituting a sigma bond fig.3.

Because of `sp^3` hybridisation of carbon atom, `CH_4` molecule has tetrahedral shape..

Formation of ethane (`CH_3-CH_3`). In ethane both the carbon atoms assume `sp^3` hybrid state as shown in figure below. One of the hybrid orbitals of carbon atom overlaps axially with similar orbitals of the other carbon atom to form `sp^ 3 - sp^ 3` sigma bond. The other three hybrid orbitals of each carbon atom are used in forming `sp^3- s` sigma bonds with hydrogen atoms as described in fig.4.

This type of hybridisation involves the mixing of one orbital of `s`-sub-level and two orbitals of `p`-sub-level of the valence shell to form three `sp^2` hybrid orbitals. These `sp^2` hybrid orbitals lie in a plane and are directed towards the corners of equilateral triangle (Fig.1). Each `sp^2` hybrid orbital has one-third `s` -character and two-third `p` -character. `sp^2` hybridisation is also called trigonal hybridisation. The molecules in which central is `sp^2` hybridised and is linked to three other atoms directly have triangular planar shape.



Formation of boron trifluoride `(BF_3)` :

Formation of boron trifluoride (`BF_3`) : Boron (`B`) atom has ground state configuration as `1 s^2 2s^2 2 p^1`. But in the excited state its configuration is `1 s ^2 , 2 s^ 1 , 2 p_x ^1 , 2 p_y ^1`. One `2 s` - orbit of boron intermixes with two `2p-` orbits of excited boron atom to form three `sp^2` hybrid orbital as shown in fig.2.

The `sp^2` hybrid orbitals of boron are directed toward the corners of equilateral triangle and lie in a plane. Each of the `sp^2` hybrid orbitals of boron overlaps axially with half-filled orbital `B-F` sigma bonds a shown in fig.3.

Because of `sp_2` hybridisation of boron, `BF_3` molecule has triangular planar shape.


Formation of ethylene `(C_2H_4)` :

Both the carbon atoms in ethylene assume `sp^2` hybrid state. In acquiring `sp^2` hybrid state, one `2 s` -orbital and two `2 p`-orbitals of excited carbon atom get hybridised to form three `sp^2` hybridised orbitals. However, one orbital of `2 p`-sub-shell of the excited carbon atom does not take part in hybridisation. The promotion of electron and hybridisation in carbon atom is shown in fig.4.

As already indicated, the three `sp^2` hybrid orbitals lie in one plane and are oriented in space at an angle of `120^o` to one another.
The unhybridised `2p` -orbital is perpendicular to the plane of `sp^2` hybrid orbitals as shown in fig.5.

In the formation of ethylene, one of the `sp^2` hybrid orbital of carbon atom overlaps axially with similar orbital of the other carbon atom to form `C-C` sigma bond. The other two `sp^2` hybrid orbitals of each carbon atom are utilised for forming `sp^2`- s sigma bond with two hydrogen atoms.

The unhybridised `p` -orbitals of the two carbon atoms overlap side wise each other to form two `p` clouds distributed above and below the plane of carbon and hydrogen atoms fig.6.

Thus, in ethylene, the six atoms (bonded by sigma bonds) lie in one plane while the p bond is projected perpendicular to the plane of six atoms (two C atoms and four H atoms). In ethylene molecule, the `C = C` bond consists of one `sp^2- sp^2` sigma bond and one p bond. Its bond length is 134 pm. `C - H` bond is `sp^2` - s sigma bond with bond length `108` pm. The `H - C - H ` angle is `117.5^o` while `H- C-C` angle is `121^o` .

This type of hybridisation involves the mixing of one orbital of `s` -sublevel and one orbital of `p `-sublevel of the valence shell of the atom to form two sp -hybridised orbita ls of equivalent shapes and energies. These `sp` - hybridised orbitals are oriented in space at an angle of `180^o` figure below. This hybridisation is also called diagonal hybridisation. See fig.1.

Each sp hybrid orbital has equal s and p character, i.e. `50%` `s`-character and `50%` `p`-character. The molecules in which the central atom is `sp`-hybridised and is linked to two other atoms directly have linear shape.

Let us study some examples of molecules involving `sp` hybridisation.

Formation of beryllium fluoride `(BeF_2)`: Beryllium (4Be) atom has a ground state configuration as `1 s ^2, 2 s^ 2` . In the excited state one of the `2 s` -electron is promoted to `2 p` -orbitals. One `2 s` -orbital and one `2 p `-orbitals of excited beryllium atom undergo hybridisation to form two `sp ` - hybridised orbitals as described in fig.2.

In this type of hybridization, one 's', three 'p' and one 'd' orbitals of the same shell mix to give five `sp^3d ` hybrid orbitals. These five `sp^3d` hybrid orbitals orient themselves towards the corners of a trigonal bipyramidal.

In this type of hybridization, one 's', three 'p' and two 'd' orbitals of the same/different shell mix to give six `sp^3d^2` hybrid orbitals.
These six `sp^3d^2` hybrid orbitals orient themselves towards the corners of an octahedron. This type of hybridization is exhibited by `SF_6`, SCI6 etc.

The hybrid state of the central atom in simple covalent molecule or polyatomic ion can be predicted by using the generalized formula as
described in fig.1.

In the formulae given in fig.1, `V` = Number of monovalent atoms or groups attached to the central atom

`G =` Number of outer shell electrons in ground state of the central atom

`a = ` Magnitude of charge on anion

`c = ` Magnitude of charge on cation

Calculate the value of `X` and decide the hybrid state of central atom as follows : See fig.2.

For Example : See fig.3.