Question

List the rule of linear combination of atomic orbitals (LCAO) method.

Answer 1

Hint: In quantum mechanics, electron configurations of atoms are described as wave-functions. When these wave functions interfere, then, new orbitals are said to form. This concept was introduced by Sir John Lennard-Jones in 1929 with the explanation of the bonding in the diatomic molecules.

Complete step by step answer:
Let us first understand what Linear combination of atomic orbitals is, and then we will go through its rules and conditions. The Linear combination of atomic orbitals is a method of representing molecular orbitals. It is a kind of superimposition method where destructive interference of two atomic wave functions produces non-bonding molecular orbital whereas constructive interference produces a bonding molecular orbital.

The rules of LCAO method are-
(1) Combining orbitals having the same energy: The atomic orbitals which are about to combine should have the same or nearly the same energy. Like, $2\text{p}$ orbital of an atom can combine with the other $2\text{p}$ orbital of another atom but $1\text{s}$ cannot combine with $2\text{p}$ as they have noticeable energy difference.
(2) Proper Overlapping of the atomic orbitals: The two atomic orbitals combine to form molecular orbital if and only if the overlapping is proper. More the extent of overlapping of orbitals, more will be the nuclear density of the nuclei of the two atoms.
(3) Same symmetry about the molecular axis: The combining atomic orbitals should have the same symmetry around the molecular axis, otherwise, the electron density will be sparse. Like, all the orbitals of $2\text{p}$ have same energy but the $2{{\text{p}}_{\text{z}}}$ orbital of an atom can combine with $2{{\text{p}}_{\text{z}}}$ orbital only of another atom. Do not think that $2{{\text{p}}_{\text{x}}}$ and $2{{\text{p}}_{\text{y}}}$ orbitals can combine because they have a different axis of symmetry. Generally, the z-axis is considered as the molecular axis of symmetry.

Note: For the formation of a proper molecular orbital, proper energy and proper orientation of atomic orbitals are required. For the proper orientation, the atomic orbitals should have proper overlapping and the same molecular axis of symmetry and for proper energy, the two atomic orbitals should have the same energy of orbitals.