82.CHEMICAL BONDING (29)- Covalent Bonding(28) – Molecular Orbital Theory(3)- LCAO approximation(1).

 

LINEAR COMBINATION OF ATOMIC ORBITALS (LCAO approximation)

 

 

MOT is incorporated in quantum mechanics.  As we have already discussed that classical physics (physics related to macroscopic things e.g.  gravity , acceleration etc applied to everyday objects )and quantum mechanics( physics related to microscopic things e.g.sub atomic particles) are two very different approaches. So, we need different quantum techniques and parameters to describe phenomenon and species in the quantum realm.LCAO approximation is one such technique which allows us to combine atomic orbitals together.

 

We already know that , in MOT,

The LCAO  technique is used in quantum mechanics and it  helps in quantum superimposing two atomic orbitals.

Superimposition means to lay one over the other.After two waves superimpose , their wave functions can either add or subtract i.e they can either superimpose constructively or destructively.

Thus, LCAO  technique is used to construct molecular orbitals by adding or subtracting atomic wave functions.Wave functions are synonymous to orbitals. Thus ,this is a technique to add or subtract atomic orbitals to form new molecular orbitals.

Thus, in MOT molecular orbitals are expressed as linear combination of atomic orbitals using LCAO method.

 

According to LCAO approximation ,

N atomic orbitals give N molecular orbitals.

Let us apply this method to two s- orbitals.Consider two atoms a and b. The following figure shows how the atomic orbitals superimposing to form a bonding molecular orbital .

But we know that when two atomic orbitals superimpose, they also form anti bonding orbitals. So, the above two orbitals will form ABMOs too as follows –

 

Have a closer look at both the BMO and ABMO in the above figures. What difference do you see??

Bonding MO	Anti Bonding MO
In the BMO , electron density  between the two nuclei is enhanced. So, electrons in this orbital will be more stable as they get attracted by both nuclei and also because the nuclear-nuclear repulsion decreases.	Here, there is no or very little electron density between two atoms and thus the nuclear repulsions are more.This increases the energy of these orbitals.

 

How can we explain the same phenomenon by considering wave functions? We shall learn that in our next post. Till then,

Be a perpetual student of life and keep learning..

Good day !