be solved for any system containing more than one electron, molecular orbitals which are one electron wave functions for molecules are difficult to obtain directly from the solution of Schrödinger wave equation. To overcome this problem, an approximate method known as linear combination of atomic orbitals (LCAO) has been adopted. Let us apply this method to the homonuclear diatomic hydrogen molecule. Consider the hydrogen molecule consisting of two atoms A and B.
Each hydrogen atom in the ground state has one electron in s orbital. The atomic orbitals of these atoms may be represented by the wave functions ψ A and ψ B . Mathematically, the formation of molecular orbitals may be described by the linear combination of atomic orbitals that can take place by addition and by subtraction of wave functions of individual atomic orbitals as shown below : ψ MO = ψ A + ψ B Therefore, the two molecular orbitals σ and σ * are formed as : σ = ψ A + ψ B σ * = ψ A – ψ B The molecular orbital σ formed by the addition of atomic orbitals is called the bonding molecular orbital while the molecular orbital σ * formed by the subtraction of atomic orbital is called antibonding molecular orbital as depicted in Fig. .
. Fig. . Formation of bonding ( σ ) and antibonding ( σ *) molecular orbitals by the linear combination of atomic orbitals ψ A and ψ B centered on two atoms A and B respectively.
Qualitatively, the formation of molecular orbitals can be understood in terms of the constructive or destructive interference of the electron waves of the combining atoms. In the formation of bonding molecular orbital, the two electron waves of the bonding atoms reinforce each other due to constructive interference while in the formation of σ * = ψ A – ψ B ψ A ψ B σ = ψ A + ψ B antibonding molecular orbital, the electron waves cancel each other due to destructive interference. As a result, the electron density in a bonding molecular orbital is located between