3.4: Frontier Molecular Orbital Theory

Molecular orbital theory can make powerful predictions about reactions and complex molecular geometries, but it is often too complex to conveniently apply to most organic molecules and reactions. To address this issue, a new theory, Frontier Molecular Orbital (FMO) theory, uses a combination of the basic tenants of both Valence Bond theory and Molecular Orbital theory to qualitatively assess the reactivity of the FMO (i.e. the HOMO and LUMO or filled/unfilled orbital interactions). This hybrid approach is very powerful and versions of it are commonly utilized in both organic and inorganic chemistry.

Lets start with a FMO analysis of ethane. For this analysis, we are going to focus on the central carbon-carbon bond. This can be depicted in a MO-type diagram where we are examining the combination of each carbon’s sp³ orbital. Mixing of these two atomic orbitals leads to new bonding and antibonding molecular orbitals. The bonding orbital (σ-orbital) has the most density between the two atoms while the antibonding orbital has a node between the two central carbons (i.e. the wavefunctions do not have the same sign) and the largest lobes are outside the two carbons. This analysis is not quantitatively true, but is an extremely good approximation both of the shape and rough energy of both the bonding and antibonding orbitals.

Now, lets do a similar analysis of the bonding in fluoromethane, focusing on the carbon-fluorine bond. Compared to our previous carbon-carbon bond example, the carbon and fluorine sp³ orbitals are no longer at the same energy level. In this case, fluorine is lower because it has a higher effective nuclear charge (more electronegative) than carbon. This energy difference in the atomic orbitals leads to less stabilization of the bonding orbital and a correspondingly lower-lying σ*-orbital. You will see ramifications of this energy difference in reactions we will cover at the end of the term.

As we have seen in the past two examples, a σ-orbital has most of the electron density between the two atoms and the σ*-orbital has most of the electron density pointing away from each atom. In contrast, π-orbitals have most of the density above and below the internuclear axis, while the π*-orbitals are also above and below the internuclear axis, but at 107° from the plane of the two atoms.