Concept: Molecular Orbital Theory (MOT) is used to predict the existence and stability of diatomic molecules. The stability of a molecule is directly related to its bond order. A bond order of zero indicates that the molecule does not exist.

Why (C) is correct:

To determine the existence of a species, we calculate its bond order using Molecular Orbital Theory. Bond order (B.O.) is given by the formula: $\text{B.O.}=\frac{1}{2}(N_b-N_a)$, where $N_b$ is the number of electrons in bonding molecular orbitals and $N_a$ is the number of electrons in antibonding molecular orbitals.

• A) ${\mathrm{Li}}_2$: Lithium (Li) has 3 electrons. So, ${\mathrm{Li}}_2$ has 6 electrons. The electronic configuration is $(\sigma 1s{)}^2({\sigma }^{\ast }1s{)}^2(\sigma 2s{)}^2$.
  $N_b=4$ (from $\sigma 1s$ and $\sigma 2s$)
  $N_a=2$ (from ${\sigma }^{\ast }1s$)
  $\text{B.O.}=\frac{1}{2}(4-2)=1$. Since the bond order is 1, ${\mathrm{Li}}_2$ exists.
• B) ${\mathrm{Be}}_2^{+}$: Beryllium (Be) has 4 electrons. So, ${\mathrm{Be}}_2$ has 8 electrons. ${\mathrm{Be}}_2^{+}$ has 7 electrons. The electronic configuration is $(\sigma 1s{)}^2({\sigma }^{\ast }1s{)}^2(\sigma 2s{)}^2({\sigma }^{\ast }2s{)}^1$.
  $N_b=4$
  $N_a=3$
  $\text{B.O.}=\frac{1}{2}(4-3)=0.5$. Since the bond order is 0.5, ${\mathrm{Be}}_2^{+}$ exists (though it is less stable).
• C) ${\mathrm{Be}}_2$: Beryllium (Be) has 4 electrons. So, ${\mathrm{Be}}_2$ has 8 electrons. The electronic configuration is $(\sigma 1s{)}^2({\sigma }^{\ast }1s{)}^2(\sigma 2s{)}^2({\sigma }^{\ast }2s{)}^2$.
  $N_b=4$
  $N_a=4$
  $\text{B.O.}=\frac{1}{2}(4-4)=0$. Since the bond order is 0, ${\mathrm{Be}}_2$ does not exist under normal conditions.
• D) ${\mathrm{B}}_2$: Boron (B) has 5 electrons. So, ${\mathrm{B}}_2$ has 10 electrons. The electronic configuration is $(\sigma 1s{)}^2({\sigma }^{\ast }1s{)}^2(\sigma 2s{)}^2({\sigma }^{\ast }2s{)}^2(\pi 2p_x{)}^1(\pi 2p_y{)}^1$.
  $N_b=6$
  $N_a=4$
  $\text{B.O.}=\frac{1}{2}(6-4)=1$. Since the bond order is 1, ${\mathrm{B}}_2$ exists.

Therefore, ${\mathrm{Be}}_2$ does not exist under normal conditions because its bond order is zero.

Correct Answer: (C)