Question

In `ddotCX_2`,both the electron get paired up in `sp^2` hybrid orbital.Thus,`ddotCX_2` exists in the form of singlet state.Why?{here `X` refers to halogen}

Answer 1

Because an even number of electrons are placed into a set of only singly-degenerate molecular orbitals. Thus, spin-pairing is going to happen for all the filled molecular orbitals, leading to a singlet state, i.e. diamagnetic molecule.

In the MO diagram below, the `sp^2` hybrid orbital you speak of that holds the lone pair is labeled `1a_2 ("nb")`, as it is a nonbonding molecular orbital that forms since the `2xx"F"` `2p_y` group orbitals aren't compatible with anything else.

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With orbital potential energies from here (Appendix B.9), an MO diagram can be constructed for `:"CF"_2` (difluorocarbene) as an example.

We place the molecule on the `xz` plane, `z` vertical. For carbon we look at `2s+2p` electrons, but for the fluorine atoms, we only look at their `2p` orbitals (ignore the `2s`, which are over `"20 eV"` below).

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As you can see, there are only singly-degenerate molecular orbitals, which means there are no two molecular orbitals of identical energies. That arises when...

• Two different atomic orbitals interact, forming one bonding and one antibonding `sigma` orbital, when no other atomic orbitals are the same energy within each atom.

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• Three different atomic orbitals interact, forming one bonding, one nonbonding, and one antibonding `sigma` orbital, when no other atomic orbitals are the same energy within each atom.

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When the molecular orbitals are only singly-degenerate, no unpaired electrons can result when there are an even number of electrons coming from the atoms (`"C"`: `4` valence `2s+2p` electrons, `"F"`: `5` valence `2p` electrons per `"F"`).

Since there are `14` valence electrons shown in the diagram, there is no way they can get unpaired when they fill one orbital per energy level.