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HYBRIDIZATION
A linear ombination of the orbitals of same atom is called “hybridization”. The combination of n- atomic orbitals of an atom generates ‘n’ hybrid orbitals.
The hybrid orbitals have better directional properties and can form stronger bonds.
The important consideration is that.
I. The hybrid orbitals must be equivalent, which means that a symmetry operation of the molecule can transform one hybrid orbital into another II. It must be normalized III. It must be orthogonal
s-p hybridization
the combination of one 2s and one 2p orbital, giving two hybrid orbitals and may be expressed as. (1) (2) The values of the linear combination coefficient may be determined by the following considerations. I. are normalized II. are orthogonal, and III. are equivalent From Ist condition (normalization)
From (ii) condition (orthogonality)
Sine the s-orbital is sperically symmetrical and the two hybrid orbitals are equivalent, the share of ‘s’ function is equal in both i.e.
(6)
Then from equation (3) we have
We have
Or
(7)
So that,
Further from equation (5)
we have
Therefore
Where are given by equations (8) and (10) represent two sp-hybrid orbitals.
Directional characteristics of s-p hybrid orbitals can be determined as follows.
Using the normalized for 2s and 2p- orbitals and choosing , for example , as 2p orbital, we get the two sp-hybrid orbitals as:
and
Taking out the factor , we get the functions which determine the directions of the two hybrid
orbitals
and
Wave function of sp^2 hybrid orbitals
For the three hybrid orbitals, we may write
i. Since the charge density of s orbital is equally divded among the three hybrid orbitals, we get i.e ii. If we assume to point towards x-axis, then the contribution of orbital in this will be zero, i.e
iii. Normalization condition of gives
Since we get
iv. Orthogonal conditions of and gives
Hence
v. Normalization condition of gives Hence
vi. Normalization condition of gives
(For to be different, we take the mius root of ) Hence three functions are (1) (2) (3)
Angle between the hybrid orbitals
Utilizing the expressions
(Where is tha angle which radius vector makes with z-axis and is tha angle which the projection of radius vector in xy plane makes with x-axis)
we get,
Since the orbital does not appear in the equation (1)-(3), we may conclude that all three orbitals lie in the xy-plane for which angle is equal to 90o. thus, the above relation become
(4)
Let have its maximum on x-axis. In order to find the direction of maximum of we equate
. Thus, we have
Wave function of sp^3 hybrid orbitals
For the four hybrid orbitals, we may write
i. Since the charge density of s orbital is to be distributed equally over all the four orbitals, we get i.e ii. Let us develop on the x-axis. It is obvious that the combination of in the function will be zero and hence we may write and
iii. Normalization condition of gives or
Hence
iv. Orthogonal conditions of and and and gives
Hence
v. We assume that lies on xz-plane. Hence the contribution of in will be zero i.e
vi. Normalization condition of gives Hence
vii. Orthogonal conditions of and and gives
Hence
viii. Normalization condition of gives
i.e
ix. For the normalization condition of , we take
Hence the four functions are
Angle between the hybrid orbitals
Utilizing the expression
Shape of the hybrid orbitals
Is given in the following diagram.
