Covalent Bonding

"Atoms share electrons" is the standard one-line definition and it explains nothing, because sharing is a metaphor borrowed from property law and atoms do not own things.

Here is what actually happens. Bring two hydrogen atoms together and each electron finds itself attracted by both nuclei rather than one. That doubling of attraction lowers the system's energy — until the nuclei get close enough to repel each other strongly, at which point the energy climbs again. In between there is a minimum, and the separation at that minimum is the bond length: 74 pm for H₂, with 436 kJ/mol required to pull the atoms apart again.

A covalent bond is that energy minimum. Everything else on this page is a way of predicting where the minima will be and how many of them a given set of atoms can form.

Building a Lewis structure: carbon dioxide, then carbonate

A Lewis structure is a map of where every valence electron sits. The procedure is fixed, and following it in order matters more than being clever.

1. Total the valence electrons for the whole species, adjusting for charge.
2. Pick the central atom — usually the least electronegative one, and never hydrogen, which can only ever form one bond.
3. Join the central atom to each outer atom with a single bond, two electrons each.
4. Distribute remaining electrons as lone pairs to complete the outer atoms' octets.
5. Any electrons still left go on the central atom.
6. If the central atom is short of eight, convert a lone pair from a neighbour into a second bond.

Carbon dioxide. Carbon contributes 4 valence electrons and each oxygen 6, for a total of 16. Carbon takes the centre. Two single bonds consume 4, leaving 12, which exactly completes both oxygens with three lone pairs apiece. Nothing remains — and carbon has only 4 electrons around it. Step 6 applies twice: shift a lone pair from each oxygen into a second bond, giving O=C=O. Now carbon has eight, each oxygen has four bonding electrons plus two lone pairs for eight, and the total is still 16.

The carbonate ion, CO₃²⁻. The count is 4 + (3 × 6) + 2 for the charge = 24. Three single bonds use 6; the remaining 18 complete all three oxygens; carbon is left with 6 and needs one double bond.

Which oxygen gets it? Nothing distinguishes them, and that is the point. Three equivalent structures can be drawn, and the real ion is none of them — it is a single structure in which the extra bonding is spread evenly over all three positions. This is resonance, and the double-headed arrows between drawn structures do not mean the ion flickers between them.

The evidence is measurable. A carbon–oxygen single bond is about 143 pm and a double bond about 123 pm. All three bonds in carbonate measure the same, about 129 pm — intermediate, identical, and impossible for any one of the three drawings.

One bond, two bonds, three — and why three is not triple

Bond order, length and strength move together in a way that is worth memorising as a pattern rather than as three separate facts. For carbon–carbon bonds:

More shared pairs pull the nuclei closer and hold them more firmly. But notice what the numbers do not say: 839 is not three times 346, and 614 is not twice it.

The reason is that the bonds in a multiple bond are not equivalent. The first is a head-on overlap along the axis between the nuclei — a strong one. The second and third are sideways overlaps above and below, which are weaker because the orbitals meet less directly. This is why the second bond in an alkene is the one that reacts: it is the cheapest thing in the molecule to break, and alkene chemistry is essentially the chemistry of that fact.

A molecule can have polar bonds and no polarity

When the two atoms sharing a pair differ in electronegativity, the pair sits closer to one of them. Hydrogen chloride's bond is shared between an atom at 2.20 and one at 3.16, so chlorine takes the larger share and the bond carries partial charges, written δ+ on hydrogen and δ− on chlorine.

Whether the molecule is polar depends on shape as well, and this is where the topic catches people out.

Carbon dioxide has two strongly polar bonds. It is linear, so the two pulls point in exactly opposite directions and cancel completely — CO₂ has no dipole moment at all. Water has two similar bonds and is bent at 104.5°, so they do not cancel; water's dipole moment is 1.85 D and almost everything unusual about water follows from it.

Carbon tetrachloride is the same trap in three dimensions: four polar bonds arranged tetrahedrally, summing to nothing. Replace one chlorine with a hydrogen and the symmetry breaks, so chloroform is polar.

Shape comes from VSEPR — electron pairs around an atom arrange themselves as far apart as possible, and lone pairs, being held by one nucleus rather than two, spread out more and squeeze the bonding pairs. The effect is visible as a progression: methane, with four bonding pairs, sits at 109.5°; ammonia, with one lone pair, closes to 107°; water, with two, closes further to 104.5°.

Three classes of octet failure

The octet rule holds for most second-period elements and fails in three recognisable ways.

Electron-deficient centres. Boron trifluoride leaves boron with six electrons and stops there. Completing the octet would require a double bond to fluorine, which would place a positive formal charge on boron and a negative one on the most electronegative element there is — energetically worse than the deficiency. Beryllium chloride manages only four. These molecules are strongly electron-accepting as a direct result.

Odd electron counts. Nitrogen monoxide has 11 valence electrons. No arrangement of an odd number can give every atom an even octet, so one electron is left unpaired. Such radicals are usually highly reactive, though NO is stable enough to serve as a signalling molecule in mammals — including in the mechanism by which blood vessels dilate.

Expanded shells. Phosphorus pentachloride puts 10 electrons around phosphorus and sulfur hexafluoride puts 12 around sulfur. This never happens for second-period elements. There is no PF₅ analogue with nitrogen at the centre, and no NF₅ exists.

The d-orbital explanation is probably wrong

Textbooks explain expanded octets by saying that period-3 elements have empty 3d orbitals available, and that the extra electron pairs go into them. It is a tidy story and it is very likely false.

Computational studies from the 1980s onward consistently find that d-orbital participation in molecules like SF₆ is negligible — a few per cent at most, far too little to hold twelve electrons. The explanations that survive scrutiny are more mundane: a third-period atom is simply larger and can fit six fluorines around it where a nitrogen atom cannot, and the bonds are polar enough that much of the electron density that would formally sit on sulfur is actually on the fluorines.

Nitrogen's inability to form NF₅ is then a matter of size and crowding rather than of missing orbitals. If your course requires the d-orbital answer, give it — but knowing that it is a historical convenience rather than a result is the difference between learning chemistry and memorising it.

Boiling water does not break a single covalent bond

The most consequential confusion in this topic is between the bonds inside molecules and the attractions between them.

An O–H bond in water takes 463 kJ/mol to break. Boiling a mole of water takes 40.7 kJ — about a twelfth as much. Water vapour is made of intact H₂O molecules that have merely been separated from one another. The same is true of every molecular substance: melting and boiling points measure intermolecular forces, and say almost nothing about covalent bond strength.

Those intermolecular forces come in a small family — London dispersion forces between all molecules, dipole–dipole attractions between polar ones, and hydrogen bonding where hydrogen is attached to nitrogen, oxygen or fluorine. All are weak compared with covalent bonds, which is why molecular substances tend to be gases, liquids or soft, low-melting solids, and why solid carbon dioxide turns straight to vapour at −78.5 °C.

The contrast with giant covalent structures makes the point unmistakable. In quartz and in diamond there are no separate molecules — the covalent bonding continues unbroken through the whole crystal, so melting it means breaking covalent bonds directly. Quartz melts at 1,713 °C and diamond has no ordinary melting point at all. Graphite is the same element as diamond arranged in sheets, with one electron per carbon delocalised across each sheet, which is why one form of pure carbon conducts electricity and cleaves under a pencil while the other is the hardest natural substance known.