3.1. Ethylene

We could start from the AOs of two carbons and four hydrogens to derive the MOs of ethylene (which is exactly what MO-programs do), but it is far more effective and easy to understand if we start from the group orbitals of two methylenes. These are exactly the orbitals derived in Sect 2.4.1, but we will limit ourselves to the two CH-bonding, the n- and the p-orbitals. The two remaining antibonding orbitals can be treated exactly analogously. The orbital-combination-procedure is very simple. We simply have to form bonding and antibonding combinations of each of the different types of group orbital (see Figure 3.4), starting from the lowest, the s_CH.

Figure 3.4 Formation of the lowest lying s_CH-orbitals of ethylene.

Because the electron density of these two orbitals is not directed along what will be the C=C bond, their overlap is relatively small and the energy splitting between the bonding and antibonding combinations is also small (Note that we use "bonding" and "antibonding" in this context to denote the relative phases of the two group orbitals, not that a new bonding interaction is formed).

We can use exactly the same technique to combine the second CH-bonding group orbitals, the p_CH2 (see Figure 3.5).

Figure 3.5 Combination of methylene p_CH2-orbitals to form two ethylene CH-bonding MOs.

The above two combinations demonstrate one of the guiding principles of understanding molecular orbitals: MOs can usually be considered to be either bonding or antibonding combinations of group orbitals. In the above two cases, no new bond is formed (we take four CH-bonding AOs and form four CH-bonding MOs), and thus the bonding and antibonding combinations are not split as strongly as they would be if a new bond were formed, which is the case for the n- and p-group orbitals, as demonstrated in Figures 3.6 and 3.7.

Figure 3.6 Combination of methylene n-orbitals to form the CC-bonding and antibonding s-orbitals of ethylene.

Figure 3.7 Formation of the p- and p*-MOs of ethylene.

Note that the splitting between the s- and s*- MOs is considerably larger than found for the CH-bonding group orbitals and that a new s-bonding MO is formed. This large splitting will play a significant role in determining the energetic ordering of the ethylene MOs.

The final group orbitals that we will consider here are the p-orbitals prependicular to the CH₂-plane. These MOs are formed as combinations of the pure carbon p-orbitals that form the Lowest Unoccupied Molecular Orbital (LUMO) of singlet methylene and the highest Singly Occupied Molecular Orbital (SOMO) of the triplet.

The valence electrons (4 each for the two carbons and 1 each for the hydrogens = 12) can now be assigned to the MOs according to their energetic ranking. The orbital energies are not given by the qualitative group-orbital-combination-technique outlined above, but generally the correct energetic ordering can be deduced using the following simple rules:

1. Bonding orbitals are more stable than nonbonding, which in turn are more stable than antibonding.

If the characters (bonding, nonbonding, antibonding) of two orbitals are the same:

2. s-MOs are more stable than p, p* are more stable than s*.

3. Orbitals with high coefficients on electronegative atoms are more stable than those that are concentrated on more electropositive ones.

If the central elements of the MOs are the same:

4. MOs with high s-coefficients are more stable than those that are mainly p.

This gives the following orbital scheme for ethylene:

Figure 3.8 Schematic diagram of the occupied valence MOs and LUMO of ethylene.

Note that in this scheme only the p* unoccupied or virtual orbital has been included.There are, of course, unoccupied antibonding equivalents for all 6 occupied valence MOs (the p*, and, not shown, the s*_CC and the four CH-antibonding MOs derived from the CH-antibonding group orbitals).

Ethylene
Next:
Cyclopropane
p-Systems
Hyperconjugation