Quantum Theory of Covalent Bond

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Although the Lewis structures give an idea of the valence electrons around the atom, in reality it does not precisely locate the position of the electrons in the chemical bond. The behaviour of electrons in molecules and compounds is made by the valence bond theory in terms of the quantum mechanical model.

The postulates of the orbital concept of covalent bonding (valence bond theory) are:

• Due to the overlap of the outermost half-filled orbitals a covalent bond is formed between the combining atoms. The extent of overlap determines the strength of this bond.

• The two half filled orbitals involved in the bond formation should contain electrons of opposite spins.

• Completely filled orbitals do not take part in the bond formation.

• The non spherical orbitals such as 'p' and 'd' orbitals tend to form bonds in the direction of maximum overlap.

• When two orbitals are of same energy, the orbitals which is non-spherical ('p' or 'd' orbitals) forms stronger bonds than the spherically symmetrical orbital ('s' orbital).

In the above orbital concept (valence bond model) of bond formation, the stability of the molecule can be explained on the basis of:

• Electron - nuclei attractive interactions (electrons of one atom are attracted by the nucleus of the other).

• Electron - electron repulsive interactions (electrons of one atom are repelled by the electrons of the other).

• Nucleus - nucleus repulsive interactions (nucleus of one atom is repelled by the nucleus of the other).

These attractive and repulsive forces act opposite to each other. When the attractive forces are stronger than the repulsive forces, energy is released. Lowering of energy makes the molecule stable.

For example,

The formation of hydrogen molecule can be described in terms of the valence bond theory with the following steps:

• When two hydrogen atoms H_A and H_B are at large distance from each other, there is no interaction between them. The total energy of the system is equal to the sum of the energies of the two H atoms.

• When the two atoms approach each other, electrons of one atom attract the nucleus of the other atom. Electrons of both the atoms are attracted by both the nuclei. These attractive interactions lead to a decrease in the energy.

• When the two hydrogen atoms come still closer, the electron-electron and nucleus-nucleus repulsive interactions start operating. Repulsive interaction tends to increase the energy of the system. The energy of the system decreases as long as the attractive interactions are stronger than the repulsive interactions. At a certain distance there is a balance between the attractive and repulsive interaction and the system attains a minimum value. At this stage the two H atoms are at fixed distance and for m a stable H₂ molecule. The inter-nuclear separation when the energy of the system is minimum is called bond length.

Fig: 6.1 - Attractive and repulsive forces acting between two H atoms

• Now if the H atoms are forced to come closer than the equilibrium inter-nuclear distance, the repulsive forces start predominating and the energy of the system increases sharply.

Fig: 6.2 - Potential energy of the system during bond formation