In Section 12, we found that B and C were each able to form covalent bonds with H using their singly occupied 2p orbitals. But B and C both share a trait with Be: they each have at least one occupied 2p orbital. In Be, we found that one of its three seemingly unused 2p orbitals is used by Be to allow it to bond to H via recoupled pair bonding. Given that B and C each also have at least one unoccupied 2p orbital, it's prudent for us to return to these elements to determine if we missed something.

B + H revisited. The figures shows something very interesting about the interaction of B and H. There are two bound forms of BH, as indicated by the red and green potential energy curves in the graph. The red curve corresponds to the covalently bonded form of BH that we've considered previously. The diagram labeled "covalent" goes with that curve and shows that the covalent bond forms when the single singly occupied 2p orbital of B is pointed at the H orbital. There are two unoccupied 2p orbitals that both point away from the internuclear bond axis.

15.1

However, it's also possible to orient B so that one of its unoccupied 2p orbitals points at H. The diagram labeled "new" shows this orientation, and it is responsible for the second, green curve in the graph that is also labeled "new." This second potential is due to H recoupling the 2s² pair of B. Just as we saw with Be interacting with H, this form of BH is possible because there's an unoccupied 2p orbital on B. Like Be, the B 2s² pair mixes in some 2p² character to form lobe orbitals.

The next figure shows the bonding in the two forms of BH using a representation for B where the doubly occupied 2s² orbital and one of the empty 2p orbital have been replaced with lobe orbitals, just as we did for Be in the previous section.

15.2

In the top row, we see the coupled pair as two gray lobes connected by the red ring. The pair points toward the H atom on the left side, and it points away from the H on the right side. On the left side, H is able to recouple the lobe pair on B, forming the new bond pair. That leaves the other lobe orbital uncoupled to anything. This form of BH has a recoupled pair bond. The covalent bond forms when the 2p orbital on B is coupled to the H 1s orbital, as shown on the right side of the figure. The coupled lobe pair is not affected by forming the covalent bond.

If the discussion in this section makes sense to you, you should be able to answer the following questions:

The form of BH with the covalent bond has no unpaired electrons, answer (a). The singly occupied orbitals of B and H are coupled to form a bond pair. The lobe pair on B remains coupled together.

The form of BH with the recoupled pair bond has two unpaired electrons, answer (c). The lobe orbital counts as one, as does the 2p orbital that is oriented vertically in the figure. Don't count both parts of the yellow 2p orbital. It is a singly occupied orbital, as indicated by its coloring.

C + H revisited. Carbon behaves almost exactly the same as boron when H approaches it: there are also two forms of CH. First, the potential energy curves are quite similar to the ones depicted in Figure 15.1:

15.3

As for the B interaction with H, there are two bound potential energy curves for the interaction of C with H. If H approaches one of the two singly occupied 2p orbitals of C, a covalent bond forms (as long as the spins of the two electrons are antiparallel, of course). If the H approaches the unoccupied 2p orbital, a new state forms, which involves recoupling the lobe pair of C. One difference between B and C is that the new state of CH is bound by nearly as much as the covalently bonded state. This will turn out to be extremely important in Chapter 3 when we build polyatomic molecules around a carbon atom.

Here are the updated bonding diagrams for C forming bonds with H the two ways. As in B, in one case (left side), the coupled lone pair points at the H. In the other case (right side), it points away from the H. The formation of the recoupled pair and covalent bonds in CH are shown in the second row.

15.4

Here's a follow-up question about CH:

The form of CH with the recoupled pair bond has three unpaired electrons, answer (d). Two of the unpaired electrons are in the singly occupied 2p orbitals that point away from the CH bond axis. The final unpaired electron is in the outer lobe orbital that points away from CH bond pair between the inner lobe orbital and the H 1s orbital.

Here are the orbital animations for forming the recoupled pair bonds (RPB) in the second forms of both BH and CH:

15.5

Seen side by side, the animations are very similar. They are also very similar to the animations for BeH depicted in figure 14.3. At long separations, the lobe pairs on B and C are evident in σ₁ and σ₃. The outer lobe orbital switches places with the H 1s orbital so that the H orbital is coupled to the B or C inner lobe orbital to form a bond pair at the minimum separation.

The final subject we will cover in this chapter is multiple bonding. We will explore what happens when we bring together two N atoms and then a N atom and an O atom.