Final answer:
The density of states (DOS) of bonding and antibonding molecular orbitals can be considered complementary, with high DOS in bonding states corresponding to low DOS in antibonding states at certain energy levels because the total number of states is constant.
Step-by-step explanation:
When two identical atomic orbitals on different atoms combine, they form a bonding molecular orbital and an antibonding molecular orbital. The bonding orbital is lower in energy than the original atomic orbitals due to in-phase combinations, leading to energy stabilization, while the antibonding orbital is higher in energy due to out-of-phase combinations, resulting in energy destabilization.
In a solid with a massive number of atoms, a significant number of atomic orbitals combine to form molecular orbitals, resulting in valence bands for bonding orbitals and conduction bands for antibonding orbitals. The density of states (DOS) for these orbitals can vary. If the DOS of the bonding states is high at certain energy levels, the DOS of the antibonding states at the corresponding energy levels is typically low since the total number of available states is a constant.
The interaction between atomic orbitals is greatest when they have the same energy, influencing the resulting molecular orbital energy levels. Therefore, qualitatively, there is a complementary relationship between the DOS of bonding and antibonding molecular orbitals.