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Band theory deals with the concept of molecular orbitals from a mass of atoms combining in order to form a confirming band with groups of molecular orbitals that are extremely close in energy.
When a group of atoms with similar energy combine, their molecular orbitals begin to form a band. A band contains molecular orbitals with only small energy differences between them allowing the system to behave as a whole rather than individuals. A simplified model and a more detailed model exists to help identify the properties these bands can represent. These theories can help categorize the differences between insulators and metallic substances.
A band can be simplified by looking at only the occupied molecular orbitals of the system. The interaction of atoms with the same atomic orbital energies will create a system composed of molecular orbitals that can share electrons within the band.
A more direct model for band theory says that bands are also formed by higher energy orbitals in the system. These unoccupied orbitals can vary in energy differences or in some cases can be overlapping. These models help us understand the relationship between lower bands and higher bands. An insulator contains a fully occupied lower band seperated by a large energy band gap. A metallic material can have a partially occupied band or a fully occupied band overlapped by a vacant band.
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