Compact molecule of beryllium

The interaction potential for beryllium atoms is calculated using the Ritz variational method with molecular wave functions as trial functions. The results of calculations for $\mathrm{Be}_2$ molecules in the $^1\Sigma^+_g$ state, which from the well–known data is considered ground, coincide with the results of previous studies. Similar calculations for the $^3\Sigma^+_u$ state show that the minimum energy for this state is reached at horter internuclear distance and is lower than that for the $^1\Sigma^+_g$ state.