3.2. Cyclopropane

The molecular orbitals of cyclopropane can be built from the CH₂ group-orbitals in exactly the same way as shown above for ethylene. We will, however, limit the discussion of cyclopropane to the CC-bonding and antibonding MOs, although the complete set of CH-bonding and antibonding MOs can be derived in the same way from the corresponding methylene group-orbitals. For the CC-bonding and antibonding MOs we need only the methylene n- and p-orbitals given below:

Figure 3.9 The n- and p-group orbitals of methylene.

If we first consider the n-orbitals, we can form three combinations from the three methylene groups (see Figure 3.10).

Figure 3.10 Combination of three methylene n-group orbitals in cyclopropane.

The most stable of these is that in which all three orbitals enjoy bonding overlap to form a completely bonding, symmetrical combination. This MO will clearly be very stable because it is strongly bonding and because it consists of a very high proportion of contributions from s-AOs. The remaining two MOs are energetically degenerate, and can only be constructed with a sum of one antibonding interaction. Degenerate orbitals will be treated in Sect. 5.4, so it suffices to note here that the degenerate set formed by combination of three methylene n-orbitals is drawn as if the symmetry of the molecule had been reduced to make them slightly different in energy and either symmetric or antisymmetric relative to a mirror plane perpendicular to the ring plane and including the uppermost methylene group. Quite generally, combination of three equivalent AOs or group orbitals in a symmetric geometry leads to a single MO and a degenerate pair. This can also be seen, for instance, for the cyclopropenium cation or for the p_CH2-group orbitals for CH₃. The important feature of the degenerate s_CC-orbitals in cyclopropane is that they are net antibonding, and therefore lie high in energy (Figure 3.11). Thus, only one bonding combination can be formed from the energetically relatively low lying n-group orbital of methylene. This clearly represents a significant energetic disadvantage for cyclopropane relative to an acyclic alkane, which would be expected to be able to use the methylene n-group orbitals better. This factor alone should result in strain energy in cyclopropane. In molecular orbital terms, strain results when the molecule cannot form MOs that are as stable as those found in the strain-free reference molecule(s). These orbitals are, however, not the main cause of strain in cyclopropane. Not only must the remaining two s_CC-orbitals be built up from the energetically unfavourable p-group orbitals of methylene (remember this orbital is the LUMO in the singlet carbene), but they are also unfavourable because there are no completely bonding combinations. In this case, there are two degenerate bonding and a single antibonding MOs.

Figure 3.11 Combination of three methylene p-group orbitals in cyclopropane.

The two degenerate orbitals are net bonding and are the HOMOs in cyclopropane. The nature of these two orbitals was first pointed out by Walsh, and they are therefore often called Walsh orbitals. The Walsh orbitals are particularly unstable relative to other s_CC-MOs both because they are made up exclusively of p-contributions and because the bonding overlap is less efficient than in unstrained CC-bonds. In order to understand this, we should consider the overlap between two p-orbitals in different orientations to each other (Figure 3.12, see also Sect. 2.3):

Figure 3.12 s-, "banana", and p-MOs formed from two p-orbitals.

The overlap between two p-orbitals is greatest when the axes of the two orbitals are collinear, as is the case for the s-bond shown above. The minimum overlap (at a fixed interatomic distance) is found when the two orbital axes are parallel to each other, as found in p-bonds. The situation for the Walsh orbitals in cyclopropane is intermediate between these two extremes. Thus, Walsh orbitals represent a situation in which much of the bonding electron density is situated outside the line joining the two atoms. Such bonds are often called "bent" or "banana" bonds. They lie higher in energy than normal s-bonds and therefore are a manifestation of strain in the molecule. They are, however, also responsible for the unusual reactivity of cyclopropanes, which undergo some reactions, such as hydrogenation or bromination, that are more typical for olefins than for alkanes. These reactions lead to ring-opening in cyclopropanes and addition to the double bond in alkenes.

Ethylene
Cyclopropane
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p-Systems
Hyperconjugation