# 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

• @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