# Formation of Bonding and Anti-bonding Molecular Orbitals

If two orbitals combine in-phase, a bonding molecular orbital is formed. When they combine out-of-phase, an anti-bonding molecular orbital is formed. For a single molecule, how are both orbitals present at the same time? They are formed differently.

First, remember that orbitals are a more or less theoretical construct, based on mathematical models. With that in mind, remember that an orbital in the strictest quantum-mechanical sense is a wave function of one and exactly one electron. (I am separating α and β spins here.) Since an orbital somehow nicely corresponds to one possible particle state, it may seem logical to postulate a ‘rule of conservation of orbitals’ — and exactly that happens in quantum chemistry.

So if we take one 1s orbital of one hydrogen atom and another 1s orbital of another hydrogen atom, we need to create two new orbitals by linear combination if we choose to do so. The two orbitals we create correspond to σ and σ*, respectively. (In a spintastic sense, we would have taken two orbitals of each hydrogen, one corresponding to α the other to β. We would receive four orbitals: $\unicode[Times]{x3c3}_\unicode[Times]{x3b1}, \unicode[Times]{x3c3}_\unicode[Times]{x3b2}, \unicode[Times]{x3c3}^*_\unicode[Times]{x3b1}$ and $\unicode[Times]{x3c3}^*_\unicode[Times]{x3b2}$. The electrons now occupy the lowest energy orbitals which are $\unicode[Times]{x3c3}_\unicode[Times]{x3b1}$ and $\unicode[Times]{x3c3}_\unicode[Times]{x3b2}$.)

• Finally, based on my question on SN2 mechanism, the antibonding orbital was already present. The electrons from the nucleophile filled the antibonding orbital of C-X. That weakened the C-X bond. But since the electrons from Nu fill ABMO of Carbon how does it form a bond? shouldn't it fill the BMO to make a bond? – Aditya Dev Oct 28 '15 at 9:50
• @AdityaDev And once again, I unfortunately fail to understand the exact question you’re asking … sorry ^^' – Jan Oct 28 '15 at 9:55
• 1)C-X has both bonding and antibonding orbital – Aditya Dev Oct 28 '15 at 10:41
• 2)Nucleophile's lone pair electrons fills ABMO of C-X bond. – Aditya Dev Oct 28 '15 at 10:41
• @AdityaDev Just because an orbital is antibonding concerning one bond does not mean it is always antibonding everywhere. – Jan Oct 28 '15 at 10:43

If you have read about Linear Combination of Atomic Orbitals, it should help you.

If two orbitals combine in-phase, a bonding molecular orbital is formed. When they combine out-of-phase, an antibonding molecular orbital is formed. For a single molecule, how are both orbitals present at the same time? They are formed differently.

What you have said is absolutely right. As per my knowledge, the MO theory was established to explain the paramagnetism of O2 and the violation of octet rule. It is again like the hybridization concept, a hypothetical one, in which they have emphasized more on the wave like nature of the electron. And you may read in the LCAO the rules for combination of Atomic orbitals to give molecular orbitals. One of them states that the number of Molecular orbitals formed should be equal to the number of Atomic orbitals participating.

So I may suggest, first read that up. And again we can't question much in chemistry as the laws are based on the observations, whether hypothetical or not.

• That was not my question. Are BMO and ABMO present together? – Aditya Dev Oct 28 '15 at 4:32
• Yes they are... – Adit Daftary Oct 28 '15 at 4:35
• In the other empty orbital maybe. – Adit Daftary Oct 28 '15 at 4:54
• "Bad models" - Newton's gravity law is actually wrong, but it works just fine for most of terrestrial experiences. It worked well enough to get men to the moon and back, but it doesn't work good enough for GPS satellites. But the "true" equation is just painful to use in most circumstances, the precision isn't justified, so why bother? – MaxW Oct 28 '15 at 4:55
• @AdityaDev You seem to implicitly assume that an AO which takes part in the formation of one MO is "spent" and can't take part in more MOs. This is not so. Whether an empty ABMO actually "exists" is a philosophical question; let's turn to something simple and unambiguous. Think of $sp^3$ carbon; all four of its $sp^3$ orbitals exist at once, and all are different combinations of s and p orbitals. How can it be? Well, just like that. – Ivan Neretin Oct 28 '15 at 6:04