Provide the $MO$ diagram and explain why the $Ne_{2}$ molecule does not exist.

(N/A) $Ne_{2}$ $(Z=10)$: $1s^{2} 2s^{2} 2p^{6}$.
Electron configuration in $MO$ for $Ne_{2}$:
$KK(\sigma 2s)^{2} (\sigma^{*} 2s)^{2} (\sigma 2p_{z})^{2} (\pi 2p_{x})^{2} (\pi 2p_{y})^{2} (\pi^{*} 2p_{x})^{2} (\pi^{*} 2p_{y})^{2} (\sigma^{*} 2p_{z})^{2}$
Bond order $= \frac{1}{2} (N_{b} - N_{a}) = \frac{1}{2} (10 - 10) = 0$
Since the bond order is $0$,the molecule is unstable and does not exist. The energy level diagram for $Ne_{2}$ is shown below: