Question

Explain with the help of Molecular Orbital Theory why the $H{{e}_{2}}$ molecule does not exist.

Answer 1

Hint: In MO theory, molecular orbitals form by the overlap of atomic orbitals.
Atomic orbital energy correlates with electronegativity, as electronegative atoms hold electrons more tightly, lowering their energies.
MO modelling is only valid when the atomic orbitals have comparable energy; when the energies differ greatly, the bonding mode becomes ionic.
A second condition for overlapping atomic orbitals is that they have identical symmetry.
According to MOT, for an element to not exist, the bond order and energy that we calculate of the molecule must equate to 0.

Complete step-by-step answer:
$H{{e}_{2}}$ molecule contains 4 electrons. Each atom gives 2 electrons in 1s orbitals. This way 2 (1s) orbitals combine to give 2 molecular orbitals that is $\sigma {{(1s)}^{2}}$and $\sigma *{{(1s)}^{2}}$i.e, bonding (BMO )and anti-bonding molecular orbitals (ABMO).
2 electrons are first filled in $\sigma {{(1s)}^{2}}$M.O.
After bonding M.O. is filled the electrons are filled in anti-bonding M.O ie $\sigma *{{(1s)}^{2}}$.
As a result, the 2 electrons in the antibonding M.O. cancel the bonding effect of the 2 electrons in bonding M.O.
$\begin{align}
 & Stabilisation\text{ Energy = }\!\![\!\!\text{ -}\beta \text{(No}\text{. of BMO}\text{ electrons)+}\beta \text{(No}\text{. of ABMO}\text{ electrons) }\!\!]\!\!\text{ } \\
 & \Rightarrow Stabilisation\text{ Energy =}-2\beta +2\beta \\
& \Rightarrow Stabilisation\text{ Energy =}0 \\
\end{align}$
As the stabilization energy is zero, the molecule is NOT stable.
\[\begin{align}
  & Bond\text{ }order=\dfrac{1}{2}\left[ \left\{ (no.\text{ }Of\text{ }electrons\text{ }in\text{ }BMO \right\}-\{\left( no.\text{ }Of\text{ }electrons\text{ }in\text{ }ABMO \right)\} \right] \\
 & \begin{array}{*{35}{l}}
   =\dfrac{1}{2}\left( 22 \right) \\
   =0 \\
\end{array} \\
\end{align}\]
The bond order comes out to be zero.
This indicates that there is no bond formation between 2 He atoms and hence the $H{{e}_{2}}$ molecule does not exist.

NOTE: It is very important to be thorough with the concepts and calculations required to prove why the $H{{e}_{2}}$ molecule does not exist according to the MOT as while it is fairly intuitive that its existence is impossible, to answer this question properly simply intuition will not suffice and the logic behind the solution must be accompanied with mathematical expressions showing the same.