Are the density of states of bonding and the corresponding antibonding states complementary?

As for the bonding and the corresponding antibonding molecular orbitals formed between two types of atomic orbitals, are their density of states (DOS) complementary? This means if the DOS of the bonding states is high, then the DOS of the antibonding states is low, and vice versa.


Intuitively, I think it is a correct statement since the total DOS of the two types of atomic orbitals is a constant, but I can't find a reference which discusses this point.


