Linear combination of atomic orbitals (LCAO):
1. The wave functions for the molecular orbitals can be obtained by solving Schrodinger wave equation for the molecule. Since solving Schrodinger wave equation is too complex, a most common method linear combination of atomic orbitals (LCAO) is used to obtain wave function for molecular orbitals.
2. Atomic orbitals are represented by wave functions ψ. Consider two atomic orbitals represented by the wave functions \(\psi_A\) and \(\psi_B\) with comparable energy that combines to form two molecular orbitals.
3. One is bonding molecular orbitai (ψ bonding) and the other is anti-bonding molecular orbital (ψ anti-bonding).
4. The wave function for molecular orbitals, \(\psi_A\) and \(\psi_B\) can be obtained by the LCAO as shown below:
\(\psi_{bonding}\) = \(\psi_A\) + \(\psi_B\)
\(\psi_{Anti-bonding}\) = \(\psi_A\) - \(\psi_B\)
5. The formation of bonding molecular orbital can be considered as the result of constructive interference of the atomic orbitals and the formation of anti-bonding molecular orbital can be the result of the destructive interference of the atomic orbitals.
6. The formation of two molecular orbitals from two is orbitals is show below.
Constructive interaction:
The two is orbitals are in phase and have the same signs.
Destructive interaction:
The two is orbitals are out of phase and have opposite signs
