When solids made of an infinite number of atoms are formed, it is a common misconception to consider each atom individually. Rather, we must consider the structure of the solid as a whole. This provides the basis for the description of metals and other types of solids to account for their unique chemical and physical properties.
To fully understand the properties,it is essential to start with molecular orbital theory. In the basic theory, it was assumed that if atoms were brought together, they would form bonding, non-bonding and antibonding orbitals of different energies. These molecular orbitals are described by wave functions. The most important point to come out of the theory is that for N atomic orbitals in a molecule, N molecular orbitals must be the outcome.
For example, consider a molecule with two atomic orbitals. The result must be that two molecular orbitals will be formed from these atomic orbitals: one bonding and one antibonding, separated by a certain energy.
If this is expanded to a molecule with three atoms, assuming 1 atomic orbital for each, then the result must be that 3 molecular orbitals will be formed: one bonding, one non-bonding and one anti-bonding.
Now , let's take it to 10 atoms. This will produce 10 molecular orbitals: 5 bonding and 5 anti-bonding. Now lets take a close look at the separation between each set of orbitals. As the number of molecular orbitals inceases, the energy difference between the lowest bonding and the higherst antibondig increases, while the space between each individual orbital decreases. As the number of molecular orbitals increses with the number of atoms in a molecule, it will the observed that the spaciung between the lowest bonding and highest antibonding orbital will reach a maximum.
Now consider a metal with an infinite number of atoms. This will form an infinite number of molecular orbitals so close together they blur into one another forming a band. This whole process is shown below.
In the above image, the origin fo the band becomes quite clear because as the number of molecular orbitals incerases, they bonding and antibonding orbitals get closer together filling in the middle. This results in the band seen on the right hand side. It becomes quite clear that the molecular orbitals become blurred and hence mix with each other, which creates the delocalised cloud of electrons that metals are said to posses.
By describing the molecular orbitals of certain materials as bands, it becomes much easier to understand the properties of metals and semi-metals. Other materials like insulators and semi-conductors will be discussed and concepts such as the valence band, conduction band and the Fermi Level will be defined using the band theory