The question asks us to identify which species does not exist according to molecular orbital theory. Let's analyze each option using the molecular orbital theory to understand their existence.
\(He _{2}^{+}\): \(He_2^+\) has a total of 3 electrons based on its electronic configuration. Molecular orbital electron configuration: \(\sigma(1s)^2 \, \sigma^*(1s)^1\). Bond Order = \(\frac{1}{2}(N_b - N_a) = \frac{1}{2}(2 - 1) = \frac{1}{2}\). Since the bond order is non-zero, \(He _{2}^{+}\) can exist.
\(He _{2}^{-}\): \(He_2^−\) has a total of 3 electrons. Molecular orbital electron configuration: \(\sigma(1s)^2 \, \sigma^*(1s)^1\). Bond Order = \(\frac{1}{2}(2 - 1) = \frac{1}{2}\). Since the bond order is non-zero, \(He _{2}^{-}\) can exist.
\(Be _{2}\): \(Be_2\) has a total of 8 electrons based on its electronic configuration: Molecular orbital electron configuration: \(\sigma(1s)^2 \, \sigma^*(1s)^2 \, \sigma(2s)^2 \, \sigma^*(2s)^2\). Bond Order = \(\frac{1}{2}(4 - 4) = 0\). Since the bond order is zero, \(Be _{2}\) does not exist.
\(O _{2}^{2-}\): \(O _{2}^{2-}\) has a total of 18 electrons. Molecular orbital electron configuration: . Bond Order = \(\frac{1}{2}(10 - 8) = 1\). Since the bond order is non-zero, \(O _{2}^{2-}\) can exist.
Hence, the species that does not exist is \(Be _{2}\).
Molecular Orbital theory is a chemical bonding theory that states that individual atoms combine together to form molecular orbitals. Due to this arrangement in MOT Theory, electrons associated with different nucleican be found in different atomic orbitals. In molecular orbital theory, the electrons present in a molecule are not assigned to individual chemical bonds between the atoms. Rather, they are treated as moving under the influence of the atomic nuclei in the entire molecule.
