Back in Section 6 we found that the Be atom has two valence electrons that are paired together as 2s². We created the following representations for it with the 2D and 3D models:

14.1

On several previous occasions we investigated what happens if H interacts with a pair of electrons. Every case proved to be repulsive. When H interacts with He 2s² or Ne 2p_x²2p_y²2p_z², we found a repulsive potential energy curve. We also tested the interaction of H with one of the 2p² pairs of F, and it was again repulsive. Of the possibilities, Be most resembles He.

The figure below shows the potential energy curves for both the H-Be and H-He interactions:

14.2

As the figure shows, BeH forms if H interacts with Be. It is not a repulsive interaction by any means. The figure shows that BeH is bound by about 50 kcal/mol, and its minimum separation is about 1.3 Å. It's quite clear that our prior experience with interactions like H-He and He-Ne does not help us to understand the Be-H interaction.

Let's look at animations of the orbitals for the interaction of Be and H and see if they help us to make sense of what happens:

14.3

The Be atom is on the left, and H is on the right in these orbital animations. These are very, very different from every other bond formation we've examined so far.

However, if you watch the animations for a while, you will see some familiar things. The σ₁ orbital looks wrong at long separations: it's all on one side of the Be nucleus. But the orbital is drawn across toward H as the atoms come together, which is something we've seen in covalent bond formation. Also, when Be and H are far apart, σ₂ looks the H 1s¹ orbital. But then it inexplicably disappears and becomes something on the far side of Be when the atoms come together. While that's happening, the reverse process is occuring in σ₃: the odd outer orbital on Be vanishes and reappears as something that looks like the H 1s¹ orbital.

The first mystery we'll look at is why the Be atom has inner and outer parts on either side of the nucleus instead of a spherical 2s orbital (like what we saw in the Li-H interaction, in Figure 13.2). The clue is visible in Figure 14.1: Be has three unoccupied 2p orbitals. By mixing in just a small amount of 2p² character, the 2s² pair of electrons can reduce their mutual overlap and avoid each other a little better.

The figure below helps to explain this:

14.4

If the 2s² pair has no 2p² character mixed in, the overlap between the two orbitals is 1.00. But if just a small amount is added—at most only a few percent—the overlap between the two orbitals is reduced significantly. As the figure shows, adding just 1.34% 2p² character reduces the overlap to 0.77. Increasing to 3.34% 2p² character reduces the overlap to 0.69. You can see what happens to orbitals. The two spherical, pure 2s² orbitals become lobe orbitals on the left and right side of the Be nucleus. These are the odd Be orbitals we see in the animations of Figure 14.3 above.

That's a big part of the story about what happens when BeH forms. It means that the orbital on the right side of Be can interact advantageously with H. We'll call this the inner lobe orbital. This is why σ₁ is seen moving toward H in the animation.

But there's one more thing that needs to happen to form the bond. In Be, the two lobe orbitals are coupled together to form the pair allowed by the Pauli principle. But in BeH, the inner lobe orbital is coupled with the H 1s¹ orbital. That means that the pair coupling needs to change, and that's why the σ₂ and σ₃ orbitals swap character as the nuclei move together.

The figure below shows the orbitals from the animations at long separation (R_e + 2 Å) and at the minimum separation for BeH:

14.5

At all separations, σ₁ and σ₃ are coupled together, as indicated in the figure. The overlap between them is always about 0.7 to 0.85, as depicted in the graph. At large R, the pair is the two Be orbitals, but at R_e, the pair is the bond pair consisting of the Be inner orbital and the H orbital.

At large R, the unpaired orbital is the H orbital. At R_e, the unpaired orbital is the outer Be orbital

The type of bonding that occurs in BeH is different than any of the other types we've encountered so far. It is still about how electrons are paired off, but three electrons are involved instead of two. This type of bonding is called recoupled pair bonding, because it involves recoupling an atomic pair of electrons into a bond pair, with one electron left over.

The discovery that Be can participate in bonding in spite of having only a pair of valence electrons available means that our original representations for Be atom are not accurate. Better forms are shown here:

14.6

In both representations, we've replaced the doubly occupied 2s orbital and one of the unoccupied 2p orbitals with two lobe orbitals. The lobe orbitals resemble the ones in Figure 14.5. We've also included a coupler (the pink bar in the 2D version and red ring in the 3D version). The coupled pair is color gray in the 3D version because it remains a pair of electrons in atomic Be. The other unoccupied 2p orbitals are still present.

The next figure shows the sequence for thinking about how the bond in BeH forms.

14.7

In the first step, H approaches Be. The pair of valence electrons on Be is coupled as above. In the second step, H is able to force the pair to recouple. The ring has been removed, and the lobes are colored yellow and blue to indicate that one of the electrons is spin up while the other is spin down. In the final step, the new coupling is formed between H and the inner lobe orbital of Be to indicate the BeH bonding. The bond pair is colored gray, and the remaining, uncoupled outer Be lobe is yellow.

The discovery that electron pairs can be broken up in some cases tells us that we should not take pairs for granted and treat them as unreactive. However, recoupling does not always happen. We saw three casese where H did not induce recoupling before we found one case where recoupling occurs. Recoupled pair bonding is therefore a conditional form of bonding.

We need to expand our list of bond types again. Here's the updated version:

If you look at our collection of symbols for the p-block atoms B through Ne back in Figure 6.15 in Section 6, you'll recall that Be isn't the only element in the second row with unoccupied 2p orbitals: B has two of them and C has one. We'll now return to both of these atoms look at their interactions with H again to see if we missed something in Section 12.