The electronic configuration of Beryllium is $1 s^{2}\, 2 s^{2}$

The molecular orbital electronic configuration for $Be _{2}$ molecule can be written as:

$\sigma _{1s}^2\,\,\sigma _{1s}^{ + 2}\,\,\sigma _{2s}^2\,\,\sigma _{2s}^{ + 2}$

Hence, the bond order for $Be _{2}$ is $\frac{1}{2}\left(N_{b}-N_{a}\right)$

Where

$N_{b}=$ Number of electrons in bonding orbitals

$N_{a}=$ Number of electrons in anti-bonding orbitals

$\therefore $ Bond order of $Be_{2}$ $=\frac{1}{2}(4-4)=0$

A negative or zero bond order means that the molecule is unstable. Hence, $Be _{2}$ molecule does not exist.