Bonding in Methane

You will be familiar with drawing methane, CH₄, using dots and crosses diagrams, but it is worth looking at its structure a bit more closely.

There is a serious mis-match between this structure and the modern electronic structure of carbon, 1s²2s²2p_x¹2p_y¹. The modern structure shows that there are only 2 unpaired electrons to share with hydrogens, instead of the 4 which the simple view requires.

You can see this more readily using the electrons-in-boxes notation. Only the 2-level electrons are shown. The 1s² electrons are too deep inside the atom to be involved in bonding. The only electrons directly available for sharing are the 2p electrons. Why then isn't methane CH₂?

Promotion of an electron

When bonds are formed, energy is released and the system becomes more stable. If carbon forms 4 bonds rather than 2, twice as much energy is released and so the resulting molecule becomes even more stable.

There is only a small energy gap between the 2s and 2p orbitals, and so it pays the carbon to provide a small amount of energy to promote an electron from the 2s to the empty 2p to give 4 unpaired electrons. The extra energy released when the bonds form more than compensates for the initial input.

The carbon atom is now said to be in an excited state.

Now that we've got 4 unpaired electrons ready for bonding, another problem arises. In methane all the carbon-hydrogen bonds are identical, but our electrons are in two different kinds of orbitals. You aren't going to get four identical bonds unless you start from four identical orbitals.

Hybridization

The electrons rearrange themselves again in a process called hybridization. This reorganizes the electrons into four identical hybrid orbitals called sp³ hybrids (because they are made from one s orbital and three p orbitals). You should read "sp³" as "s p three" - not as "s p cubed".

sp³ hybrid orbitals look a bit like half a p orbital, and they arrange themselves in space so that they are as far apart as possible. You can picture the nucleus as being at the centre of a tetrahedron (a triangularly based pyramid) with the orbitals pointing to the corners. For clarity, the nucleus is drawn far larger than it really is.

What happens when the bonds are formed?

Remember that hydrogen's electron is in a 1s orbital - a spherically symmetric region of space surrounding the nucleus where there is some fixed chance (say 95%) of finding the electron. When a covalent bond is formed, the atomic orbitals (the orbitals in the individual atoms) merge to produce a new molecular orbital which contains the electron pair which creates the bond.

Four molecular orbitals are formed, looking rather like the original sp³ hybrids, but with a hydrogen nucleus embedded in each lobe. Each orbital holds the 2 electrons that we've previously drawn as a dot and a cross.

The principles involved - promotion of electrons if necessary, then hybridisation, followed by the formation of molecular orbitals - can be applied to any covalently-bound molecule.

The shape of methane

When sp³ orbitals are formed, they arrange themselves so that they are as far apart as possible. That is a tetrahedral arrangement, with an angle of 109.5°. Nothing changes in terms of the shape when the hydrogen atoms combine with the carbon, and so the methane molecule is also tetrahedral with 109.5° bond angles.

Ethane, \(C_2H_6\)

Ethane isn't particularly important in its own right, but is included because it is a simple example of how a carbon-carbon single bond is formed. Each carbon atom in the ethane promotes an electron and then forms sp³hybrids exactly as we've described in methane. So just before bonding, the atoms look like this:

The hydrogens bond with the two carbons to produce molecular orbitals just as they did with methane. The two carbon atoms bond by merging their remaining sp³ hybrid orbitals end-to-end to make a new molecular orbital. The bond formed by this end-to-end overlap is called a sigma bond. The bonds between the carbons and hydrogens are also sigma bonds.

In any sigma bond, the most likely place to find the pair of electrons is on a line between the two nuclei.

The shape of ethane around each carbon atom

The shape is again determined by the way the sp³ orbitals are arranged around each carbon atom. That is a tetrahedral arrangement, with an angle of 109.5°. When the ethane molecule is put together, the arrangement around each carbon atom is again tetrahedral with approximately 109.5° bond angles. Why only "approximately"? This time, each carbon atoms doesn't have four identical things attached. There will be a small amount of distortion because of the attachment of 3 hydrogens and 1 carbon, rather than 4 hydrogens.

Free rotation about the carbon-carbon single bond

The two ends of this molecule can spin quite freely about the sigma bond so that there are, in a sense, an infinite number of possibilities for the shape of an ethane molecule. Some possible shapes are:

In each case, the left hand CH₃ group has been kept in a constant position so that you can see the effect of spinning the right hand one.

Other alkanes

All other alkanes will be bonded in the same way:

• The carbon atoms will each promote an electron and then hybridize to give sp³ hybrid orbitals.
• The carbon atoms will join to each other by forming sigma bonds by the end-to-end overlap of their sp³ hybrid orbitals.
• Hydrogen atoms will join on wherever they are needed by overlapping their 1s¹ orbitals with sp³ hybrid orbitals on the carbon atoms.

Contributors

• Jim Clark (Chemguide.co.uk)