if there is an uneven number of atomic orbitals, the orbitals don't meet the criteria for bonding, or if the bonding interactions are weak, there will be molecular orbitals on the molecule that have non-bonding character
when molecular orbitals have energies similar to their original atomic orbitals, they will have some non-bonding character
the closer the energies of atomic and molecular orbitals, the more non-bonding the molecular orbitals
in the case that there is an uneven number of atomic orbitals with compatible symmetry, orbitals with non-bonding character will form
in the case where three atomic orbitals combine, the most common result is formation of a low-energy bonding orbital, a high energy antibonding orbital, and a non-bonding orbital of intermediate energy
combination of orbitals with different energies may lead to orbitals with non-bonding character
atomic orbitals that have similar energies will have the strongest interactions, resulting in bonding molecular orbitals with much lower energies than the atomic orbitals
atomic orbitals with very unequal energies have a weaker interaction because the molecular orbitals are closer in energy to the atomic orbital energies, resulting in less energy benefit to putting electrons in the bonding molecular orbitals
when bonding or antibonding orbitals are close to the energies of the contributing atomic orbitals, those molecular orbitals may have some non-bonding character