Metallic Bond (Band Theory)

Metals constitute about three fourths of all the known elements. They have characteristic properties such as bright luster, high electrical and thermal conductivity, malleability, ductility and high tensile strength. The attractive force, which binds various metal atoms, is called metallic bond. The metallic bond is neither a covalent nor an ionic bond. Molecular orbitals form between two atoms when atomic orbitals of the two atoms overlap. In some cases (such as benzene), the atomic orbitals of three or more atoms overlap to form molecular orbitals that are associated with all the atoms. Such molecular orbitals are said to be delocalized. The number of molecular orbitals formed is equal to the number of atomic orbitals participating in overlapping.

Bonding in metals can be explained by thinking about what happens when a large number of atoms are brought together to form a metallic crystal. In a metal, the outer orbitals of a very large number of atoms overlap to form a very large number of molecular orbitals that are delocalized over the metal. As a result, a large number of energy levels are crowded together into 'bands'. Because of these energy bands, the molecular orbital theory of metals is also known as band theory.

As an illustration the bonding in sodium metal can be studied. Imagine that a crystal of sodium is being built by bringing sodium atoms together one at a time. Each sodium atom has one valence electron in 3s orbital. When two sodium atoms are brought together their 3s orbitals overlap to form two molecular orbitals s3s and s*3s. Now imagine that a third sodium atom is added to this diatomic molecule to form Na₃ molecule. The three 3s orbitals of the three sodium atoms overlap to form three molecular orbitals. Each molecular orbital is delocalized over all the three atoms. Similarly, Na₄ would have four molecular orbitals, Na₁₀ would have ten molecular orbitals and Na_n would have n molecular orbitals. Then molecular orbitals would be delocalized over all the n atoms is the crystal.

fig 1.21 - Formation of energy band in sodium metal

The figure1.21 shows how the molecular orbital energy level diagram changes as the number of atoms in the crystal increases. With increase in number of atoms, the number of energy levels increases and the energy spacing between them decreases. For a huge number of atoms, the molecular orbitals are spaced so closely that they behave as if they were merged together to form a continuous band of energy. A group of very closely spaced energy levels is called a band.

The difference between bonding and antibonding molecular orbitals is called an energy gap. When atomic orbitals of a very large number of atoms combine, the energy gap disappears. Energy bands are separated by spaces called forbidden bands. In the forbidden bands there are no allowed energy states. Each energy band is formed by combining a certain number of orbitals. Each orbital can accommodate only two electrons. Therefore, in an energy band only a certain number of electrons can be accommodated. For e.g., a 3s band formed from n atoms will have n orbitals and can hold a maximum of 2n electrons. Since each sodium atom has only one valence electrons, n atoms will supply n electrons and hence 3s band would be half-filled.