Question

The ground-state electron configuration of the H₂⁺ molecular ion is ${\mathbf{\left(}{\mathbf{\sigma }}_{g1s}\mathbf{\right)}}^1$.

(a) A molecule of H₂⁺ absorbs a photon, promoting the electron to the${\mathbf{\left(}{{\mathbf{\sigma }}^{\mathbf{*}}}_{\mathbf{u}\mathbf{1}\mathbf{s}}\mathbf{\right)}}^1$molecular orbital. Predict what happens to the molecule.

(b) Another molecule of H₂⁺ absorbs even more energy promoting the electron to the${\mathbf{\sigma }}_{g2s}$ molecular orbital. Predict what happens to this molecule.

Short answer

In first condition, the molecule will fly apart while in second case${{\text{H}}_{\text{2}}}^{\text{+}}$dissociatesto$H$ and${\text{H}}^{\text{+}}$

Step-by-step solution

Bonding and anti-bonding orbital

According to molecular orbital theory, electrons first gets filled in bonding orbitals and then in anti-bonding orbitals. Anti-bonding orbitals have energy higher than bonding orbitals. In ground state, electron resides in bonding orbital only.

(a) Promotion of electron to 𝛔*u1s 

Excitation of the electron in ${{\text{H}}_{\text{2}}}^{\text{+}}$ to an anti-bonding orbital $\sigma *$will lead to the dissociation of the molecule. The effect of an anti-bonding electron is to oppose the continued association of the nuclei Thus as the ground state has one bonding electron and the excited state has one anti-bonding electron (and no bonding electrons) the molecule will fly apart.

(b) Promotion of electron to 𝛔g2s

When ${{\text{H}}_{\text{2}}}^{\text{+}}$molecule absorbs more energy in an interaction with a photon, the electron can be move into a higher-level bonding molecular orbital The molecule should persist for a while in this bound state, but it will also eventually dissociate to ${\text{H}}^{}$and ${\text{H}}^{\text{+}}$.