ENTRY 1 :: BUILDING CHn Molecules

This discussion is written for someone who has at least a high school level background in chemistry. You should know:

  • about the nature of electrons and nuclei
  • that two electrons or two nuclei repel each other while an electron and a nucleus are attracted to each other
  • atomic and molecular structure is dictated by quantum mechanics
  • electrons are found in orbitals with ordered energy levels and characteristic shapes
  • s orbitals are spherical and centered on the nucleus
  • the three p orbitals each line up with one of the cartesian xyz axes and are therefore 90° away from each other, and each p orbital has a lobe on either side of the nucleus
  • the sequence in which the lowest energy orbitals are filled in atoms is 1s, 2s, and 2p
  • electrons have two kinds of spin, sometimes labeled "up" and "down"
  • the Pauli principle tells us that an orbital can hold no more than two electrons and only if they have opposite spins

You will notice that I have included no illustrations on this page. On the first pass, I'm going to tell the story only using words. I hope the words will paint a sufficiently accurate initial picture in your mind about what's going on with the bonding in CHn compounds. At the bottom of this page I will include a link to a page the retells the story almost entirely with images (many of them animated).


Adding a series of hydrogen atoms (H) to a single carbon atom (C) to form CH, CH2, CH3, and finally CH4 (methane) is an interesting exercise with some surprises.

First, let's look at hydrogen and how it often bonds to other atoms. The most common form of hydrogen atom consists of one electron and one proton, its nucleus. One way H can form a bond is to share a pair of electrons with another atom, which is called a covalent bond. In its lowest, most stable state (its ground state), the single electron of hydrogen is in a 1s orbital. One H can form a covalent bond with another H atom if the electrons in their two orbitals have opposite spins. Or H could form a covalent bond with an atom like fluorine (F). F has a singly occupied 2p orbital and some doubly occupied orbitals: the 1s2, 2s2, and two 2p2 orbitals. As in H + H → H2, H + F → HF can only happen if electrons in the H 1s and F 2p singly occupied orbitals have opposite spins. In both H + H and H + F, the interaction between the two atoms will be repulsive if the electrons in the singly occupied orbitals have the same spin.

Now let's review the nature of a carbon atom. Carbon has a total of six electrons and a nucleus with a charge of +6 due to its six protons. The most stable form of the C nucleus also includes 6 neutrons for a total mass of 12 amu. In the ground state of C, the 6 electrons are distributed with two electrons in the 1s2 orbital, two more electrons in the 2s2 orbital, and one electron in each of two of the 2p orbitals. That leaves one 2p orbital without an electron. It will turn out that this is an oversimplification, but it's a good starting point. What matters at this point is that we note that C has two singly occupied 2p orbitals and one unoccupied 2p orbital.

Before moving on to how C can interact with H, it's a good idea to note something very important about pairs of electrons, and it may seem seem contradictory. Electrons repel each other and therefore don't want to be close to each other, but a pair of electrons with opposite spins can tolerate being in the same space if there's a good reason for it. The ability of electrons to tolerate each other if and only if they have opposite spins is due to the Pauli principle. The only reason two electrons will tolerate each other has to do with their attraction to nuclei. In H2, the electrons will tend to be found most often between the two nuclei. Each electron is attracted to each of the two nuclei. The electrons repel each other, but their opposite spins allow them to make a compromise of sorts while they interact with the two protons.


Now we can consider how carbon and hydrogen atoms interact. Since C has two singly occupied 2p orbitals, we would expect that it could form a covalent bond with H, as long as the electrons from H and C have opposite spins. This is the case and yields CH. It is a radical form of CH because chemists use the term radical to indicate that a compound has at least one unpaired electron. Since C has two singly occupied 2p orbitals and we formed a covalent bond with one of them, there is still one singly occupied 2p orbital in the CH radical we form.

That suggests that we can form a second CH bond if another H atom forms a second covalent bond with the electron in the other singly occupied 2p orbital. That would give us CH2. It has no unpaired electrons left, which means that it is not a radical. A compound with no unpaired electrons is sometimes called closed-shell because every electron is paired off.

Before we continue (because the story is far from over), let's think about the structures of the CH and CH2 molecules we've formed so far. CH is easy. It's linear, with the C and H nuclei located on its bond axis. For CH2, we get a big clue to its structure by remembering that the two bonds are formed with 2p orbitals on C that are 90° away from each other. So we might expect CH2 to have a bond angle of 90°. In fact, it's about 102°, but that's pretty close to 90°. That means there's something about how the atoms come together that makes the bond angle open a little from 90°.


It might seem that we've exhausted the possible ways to put together C and H atoms. But that's the first surprise in this story. It turns out that there's another way to put together C and H to form a second kind of CH. Then when we add the second H, we also get a different kind of CH2 as well.

Let's try to visualize this. Suppose the H atom approaches C so that the two singly occupied 2p orbitals are both perpendicular to the line connecting C and H. If the two singly occupied 2p orbitals are lined up with the x and y axes, that would put the approach along the z axis. When H approaches from this direction, it doesn't encounter either of the singly occupied 2p orbitals. Instead, it encounters the empty 2p orbital and the 2s2 pair of electrons. Something unexpected happens. One of the electrons in the 2s2 pair breaks away from the pair and pairs off with 1s electron from H. A bond forms, but it's not a covalent bond. We can call this a recoupled pair bond, because an existing pair of electrons is broken up to form a new pair. It leaves a leftover, unpaired electron on C. Before the bond forms, there is an atomic pair on C and a unpaired electron on H. After the bond forms, there is a bond pair between H and C and an unpaired electron on C.

Remember that electrons repel each other and only tolerate being in the same region if they have opposite spins. They can and will form new pairing combinations if it's favorable to do so, and it is when H approaches C in the way described above. The CH bond pair provides more stability to the system than the atomic C 2s2 does.

One more thing. The second type of CH has a total of three unpaired electrons, because the two singly occupied 2p orbitals are not affected when the recoupled pair bond forms. Recall that the first type of CH has one unpaired electron. We will call the first type "doublet CH" and the second type "quartet CH" because doublet means one paired electron and quartet means three unpaired electrons.

So we have doublet CH and quartet CH. Which of these is more stable? To assess this, we need to know the bond energies of the two types of CH. The bond energy tells us how hard it is to pull apart a bond. The larger the bond energy, the stronger the bond.

Doublet CH has a bond energy of 82.4 kcal/mol, while quartet CH has a bond energy of 66.0 kcal/mol. We note that doublet CH is more stable than quartet CH, but quartet CH is still quite stable.

We found we could add a second H to doublet CH because it had an unpaired electron and forms closed-shell CH2. Since quartet CH has three unpaired electrons, it would seem quite likely that we should be able to add a second H atom to form a second bond. This is indeed what happens. But this type of CH2 is a different from the first one we formed: it still has two unpaired electrons. A molecule with no unpaired electrons is a called singlet, while one with two unpaired electrons is a triplet, so we now have singlet CH2 and triplet CH2.

We found that the bond energy in doublet CH was a little stronger than the bond energy of triplet CH. Let's look at the bond energies for the second CH bond in the two types of CH2. For singlet CH2, the second bond energy is 99.5 kcal/mol, while for triplet CH2 the second bond energy is much larger, 121.3 kcal/mol.

The total bond energy for a molecule is the sum of all of its bond energies. For singlet CH2 we add 82.4 and 66.0 kcal/mol and get 181.9 kcal/mol. For triplet CH2, we add 66.0 and 121.3 kcal/mol and get 187.2 kcal/mol. This is the second surprise: triplet CH2 is slightly more stable than singlet CH2 because it has more total bond energy.

Back when we formed quartet CH with a recoupled pair bond, it cost something to break apart the 2s2 pair of electrons on C. That's why quartet CH has a weaker bond energy than doublet CH. But when we formed a second bond, we gained so much more energy that the type of CH2 with a recoupled pair bond is more stable that the type of CH2 with two covalent bonds.


Let me try to give you some sense of how significant this is. If C didn't form a recoupled pair bond with H so that triplet CH2 is more stable than singlet CH2, the biggest common molecule with C would be singlet CH2. (Water behaves like this. As important as it is, it is a very simple compound.) Triplet CH2 can form more bonds: with H, with O, with N, and with other other elements. That means that amino acids and proteins and DNA and RNA can form. Life as we know it exists because triplet CH2 is more stable than singlet CH2, so the recoupled pair bond that makes triplet CH2 possible is arguably the most important bit of chemistry in biology.


When H forms the second bond with an unpaired electron on quartet CH, it can interact with the orbital that lies on the CH bond axis on the far side from H or with one of the singly occupied 2p orbitals that are perpendicular to the CH bond axis. If it interacted only with the orbital on the CH axis, it would be linear (H-C-H) and thus have a bond angle of 180°. If it intereacted only with one of the singly occupied 2p orbitals, we might expect the bond angle to be similar to singlet CH2, or about 100°. But we again encounter a surprise. The H doesn't interact with one or the other of these options, it finds a compromise between the two. The bond angle of triplet CH2 is 134° about half way between 100° and 180°

The consequence of this compromise is that one of the unpaired electrons of triplet CH2 is in an orbital that lies in the same plane as the C and H atoms, along the line that bisects the flattened v-shape of triplet CH2 but on the far side, away from the H atoms. The other unpaired electron is found in a an orbital that is perpendicular to the CH2 plane and still looks a lot like the original 2p orbital.


Now we're almost done with our story. Triplet CH2 has two singly occupied orbitals and cam form two more covalent bonds. One might expect that maybe we'll see an another compromise, but a third H atoms forms a bond with in-plane orbital, and doesn't interact with the out-of-plane orbital at all. So CH3 is planar and has three bond angles of 120°. The remaining singly occupied orbital is the same 2p-like orbital we've been tracking all the way back to quartet CH. The energy of the third CH bond is 110.j kcal/mol. CH3 is a doublet because it has one unpaired electron.

When a fourth H atom forms a bond with the remaining singly occupied orbital of CH3, the planar CH3 part adjusts to accomodate the new bond. Each of the three CH bonds bends back away from the new, fourth bond. When formed, CH4 has a tetrahedral structure with four equal CH bond lengths and bond angles of 109.47° The energy of the fourth CH bond is 116.6 kcal/mol. CH4 is a singlet because it has no unpaired electrons. CH4 is also known as methane. Unlike CH, CH2, and CH3, methane is stable enough to store in a tank (it is a gas).


In this installment of Fun with Molecules, we found that the C atom exhibits very curious behavior. A simple count of its unpaired electrons suggests that it might only form two bonds. We did make a closed-shell singlet version of CH2 that follows this expectation, but then we found that C can form a second type of CH with a recoupled pair bond. That made a second, triplet type of CH2 possible, which turned out to be more stable than singlet CH2. The greater stability of triplet CH2 meant than we could subsequently form planar doublet CH3 and tetrahedral singlet CH4.


In the next entry of Fun with Molecules (coming soon), I'll show images of the orbitals I described above and how the two types of CH and the two types of CH2 differ from each other and how the stability of triplet CH2 makes CH3 and CH4 possible. I'll also show what happens with the covalent and recoupled pair bonds form in these compounds.

Written by DE Woon
Copyright reserved.
Updated 1 February 2019