Question

What is the molecular orbital diagram for $C_2^{-}$ ?

Answer 1

Hint :We know that $C_2$ is a component of vapours of carbon. According to a research paper, carbon vapours contain around $28$ but this depends on the temperature and pressure. The electrons are distributed among the atomic orbitals according to Aufbau’s principle. This produces unique quantum states, with corresponding energy levels.

Complete Step By Step Answer:
The quantum state which has the lowest energy level is known as the ground state. The ground state is a singlet state. There are several excited singlet and triplet states that are relatively similar energy to the ground state. Molecular orbital theory shows that it has two sets of paired electrons in a degenerate bonding set of orbitals. This gives a bond order of two, which means that there should exist a double bond between the two carbons in a $C_2$ .
 As you know, a neutral carbon atom has a total of six electrons. This, of course, implies that a $C_2$ molecule has a total of $2\times 6e^{-}=12e^{-}$
Thus follows that the $C_2^{-}$ species will have; $12e^{-}+1e^{-}=13e^{-}$
It will be added to lowest energy unoccupied molecular orbital/lowest unoccupied molecular orbital, LUMO, that follows that the highest energy occupied molecular orbital/highest occupied molecular orbital, HOMO. The diagram below shows the two $2p\pi$ orbitals, let's say $2p\pi x$ and $2p\pi y$ , are the highest energy occupied molecular orbitals. The lowest energy unoccupied molecular orbital is $2p\sigma$ , so that is where extra electrons will be added.

Also, an unpaired electron will make the $C_2^{-}$ ion paramagnetic, i.e. it is attracted by an externally applied magnetic field. On the other hand, the neutral $C_2$ molecule has no unpaired electrons, so it is diamagnetic, i.e. it is not attracted by an externally applied magnetic field.

Note :
The various quantum states of dicarbon form significant proportions of dicarbon under ambient conditions. The problem provides you with a MO diagram for the $C_2$ molecule, so all we really have to do here is add an electron to that diagram. We need to add an electron and not remove one because of overall negative charge that exists on molecule