Recently I came across nonbonding orbitals. I know something about bonding and antibonding orbitals and their formation, but I have no idea about nonbonding orbitals. Could someone explain their formation and the difference when compared with the other two?
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1$\begingroup$ Could you edit your question to include where you came across nonbonding orbitals? Could you also describe your understanding of bonding and antibonding orbitals to give an indication what level of theory would be helpful as an answer? $\endgroup$– Karsten ♦Commented Jul 19, 2019 at 19:58
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In basic MO theory, when two atomic orbitals mix, they form an in-phase (bonding) and out-of-phase (antibonding) molecular orbital. The primary criteria for this mixing are having the same symmetry and being near in energy. If you mix your atomic orbitals together, but find that some of the atomic orbitals have no symmetry match with a similar enough energy, then these unmatched atomic orbitals do not mix and become non-bonding MOs.
Consider hydrogen fluoride. The 1s orbital on hydrogen has the same symmetry as the $p_z$ orbital on fluorine. These mix into a bonding and antibonding orbital. Hydrogen however does not offer any other occupied atomic orbitals with matching symmetry for the $p_x$ and $p_y$ atomic orbitals on fluorine. Therefore, these orbitals remain as non-bonding. Furthermore, the 2s fluorine atomic orbitals are much lower in energy than hydrogen's 1s orbital, so this does not mix appreciably either, and can therefore also be treated as non-bonding.
For elementary concepts, I think you just need to know about how these contribute to bond order. The occupancy of non-bonding orbitals does not have any effect on the bond order and are typically considered lone-pairs.
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2$\begingroup$ In MO theory there are no non-bonding orbitals, this is a simplification which arises from mixing localised orbitals (possibly from valence bond theory) into the theory. It is within the framework of the theory, that all MO are delocalised. Except for diatomic molecules the division into bonding and anti-bonding can become a lot more complicated. It is often the case that the same MO is bonding with respect to one pair of nuclei, and anti-bonding with respect to another. However, within the valence bond picture, the concept of non-bonding orbitals may offer some more insight. $\endgroup$– Martin - マーチン ♦Commented Jul 19, 2019 at 8:24
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$\begingroup$ @martin thanks for the correction. Ill edit it when i am not on mobile. I did aim to limit the answer to the diatomic case, in order to avoid the complexities you mentioned, which i assumed was more appropriate for the level of question. $\endgroup$– BlaiseCommented Jul 19, 2019 at 12:30