**Linear Combination of Atomic Orbitals**

According to quantum physics, exact position and momentum of an electron cannot be determined accurately (Heisenberg’s Uncertainty principle). So to understand the structure of atom or chemical combination, wave mechanics is used. According to wave mechanics, atomic orbitals can be expressed by wave functions.The amplitude of these wave functions represents the atomic orbitals. This concept of atomic orbital came from the solution of Schrödinger’s wave equation. However, the equation cannot be solved for the systems with more than one electron, so for them, an approximate method is used which is named as Linear combination of atomic orbitals.

- The method works on superimposition of wave functions to make molecular orbital.
- The superimposition of wave functions will be constructive if both the wave functions have no phase difference while the superimposition of a wave will be destructive if both the wave functions have a phase difference of 180
^{o}. - This constructive and destructive superimposition of wave leads to the formation of bonding molecular orbital and anti-bonding molecular orbital respectively.
- In the bonding atomic orbitals, the electron density is located between the nuclei of two atoms and so the repulsion is very less. It is because the electron density is attracted by both the nuclei of atoms and so it stabilizes the atom and molecule as a whole.
- In the anti-bonding atomic orbitals, the electron density is located away from the space between the nuclei of two atoms and so the repulsion is high. It is because the two positively charged nuclei repel each other and this repulsion force is more than the attractive force between nuclei and electron cloud. Thus, it causes instability.
- Due to different configurations of electron density in bonding and anti-bonding orbitals as discussed above, they two have different energies. Bonding atomic orbital has lower energy than nonbonding orbital due to its stability.

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