Frontier molecular orbitals

While we are looking at HF, it is worth digressing to discuss (briefly) the concept of frontier molecular orbitals (to which you will be exposed more in organic chemistry). The term ``frontier'' refers to the orbitals that are at the outer edges of a molecule. These tend to be the orbitals that are the most spatially delocalized and hence, the orbitals with the highest energies (either occupied or unoccupied). In particular, two orbitals are of particular importance. These are the highest occupied molecular orbital or (HOMO) and the lowest unoccupied molecular orbital (LUMO). ``Highest'' and ``lowest'' refer to the energies. In HF, the HOMO orbital(s) are the double degenerate $\pi_{2p_x}$ and $\pi_{2p_y}$ orbitals, while the LUMO is the $\sigma^*_{2p_z}$ orbital.

The HOMO and LUMO can help us predict what will happen in a chemical reaction. Consider the reaction of HF with H$_2$O:

$${\rm HF} + {\rm H}_2{\rm O} \longrightarrow {\rm F}^- + {\rm H}_3{\rm O}^+$$

In terms of Lewis structures, the reaction can be depicted as show below:

Figure: Reaction of HF with H$_2$O in Lewis structures.

Here we see the H of HF trading the shared pair in the HF bond for one in the H$_3$O$^+$ (as depicted by the arrow in the diagram). The arrow attempts to convey that the water molecule donates one of its lone pairs to the HF molecule, causing the HF bond to rupture, thereby allowing liberated proton to attach to the water molecule.

In terms of frontier molecular orbitals, we can view the reaction as follows: The electron pair donated by the water molecule must go into the LUMO of HF. Since the LUMO is a $\sigma^*_{2p_z}$ orbital, the occupancy of this orbital by two electrons changes the bond order of HF from 1 to 0, and this causes the bond to be destabilized and rupture, thereby freeing up the proton (H$^+$) to react with the H$_2$O.