There should be 8 electrons in ${Be}_2$ molecule. The MO electronic configuration must be
$\sigma 1 s^2 \sigma^* 1 s^2 \sigma 2 s^2 \sigma^* 2 s^2$
$N_b=4 \text { and } N_a=4$
Bond order of ${Be}_2$ is $\frac{1}{2}(4-4)=0$
${Be}_2$ molecule is therefore unstable and does not exist.