The bonding in He₂, Li₂ and Be₂

Molecular orbital theory can be applied to any homonuclear diatomic molecule, but as more valence atomic orbitals become available, the MO diagram becomes more complex.

Treatments of the bonding in He₂, Li₂ and Be₂ are similar to that for H₂. In practice, He does not form He₂, and the construction of an MO diagram for He₂ is a useful exercise because it rationalizes this observation. Figure 1.2a shows that when the two 1s atomic orbitals of two He atoms interact, σ and σ^* MOs are formed as in H₂. However, each He atom contributes two electrons, meaning that in He₂, both the bonding and antibonding MOs are fully occupied. The bond order (equation 1.1) is zero and so the MO picture of He₂ is consistent with its non-existence.

Using the same notation as for H₂, the ground state electronic configuration of He₂ is σ_g (1s)² σ_u σ^*_g (1s)² σ^*_u.

The ground state electronic configuration of Li (Z = 3) is 1s² 2s¹ and when two Li atoms combine, orbital overlap occurs efficiently between the 1s atomic orbitals and between the 2s atomic orbitals. To a first approximation we can ignore 1s–2s overlap since the 1s and 2s orbital energies are

poorly matched. An approximate orbital interaction diagram for the formation of Li₂ is given in Figure 1.2b.

Each Li atom provides three electrons, and the six electrons in Li₂ occupy the lowest energy MOs to give a ground state electronic configuration of σ_g (1s)² σ^*_u (1s)² σ_g (2s)².    Effectively, we could ignore the interaction between the core 1s atomic orbitals since the net bonding is determined by the interaction between the valence atomic orbitals, and a simpler, but informative, electronic ground state is σ_g (2s)².

Figure 1.2b also shows that Li₂ is predicted to be diamagnetic in keeping with experimental data. By applying equation 1.1 , we see that MO theory gives a bond order in Li₂ of one. Note that the terminology ‘core and valence orbitals’ is equivalent to that for ‘core and valence electrons’.

  (1.1)

Like Li, Be has available 1s and 2s atomic orbitals for bonding; these atomic orbitals constitute the basis set of orbitals. An orbital interaction diagram similar to that for Li₂ (Figure 1.2b) is appropriate. The difference between Li₂ and Be2 is that Be2 has two more electrons than Li₂ and these occupy the σ^*(2s) MO. The predicted bond order in Be₂ is thus zero. In practice, this prediction is essentially fulfilled, although there is evidence for an extremely unstable Be₂ species with bond length 245pm and bond energy 10 kJ mol^-1.

Fig. 1.1 Schematic representations of (a) the bonding and (b) the antibonding molecular orbitals in the H2 molecule. The H nuclei are represented by black dots. The red orbital lobes could equally well be marked with a ‏ sign, and the blue lobes with a + sign to indicate the sign of the wavefunction.

Fig. 1.2 Orbital interaction diagrams for the formation of (a) He₂ from two He atoms and (b) Li₂ from two Li atoms.

A basis set of orbitals is composed of those which are available for orbital interactions. In each of Li₂ and Be₂, it is unnecessary to include the core (1s) atomic orbitals in order to obtain a useful bonding picture. This is true more generally, and throughout this book, MO treatments of bonding focus only on the interactions between the valence orbitals of the atoms concerned.