$\mathrm{Be}_{2}$ has an electronic configuration of:

$\sigma 1 s^{2} \sigma^{*} 1 s^{2} \sigma 2 s^{2} \sigma^{*} 2 s^{2}$

$\text { Bond order }=\frac{4-4}{2}=0$

Thus, Be $_{2}$ does not exist.