Exceptions to the Octet Rule and Resonance

The previous chapter built Lewis structures on a single working assumption: every atom (except hydrogen) ends up surrounded by exactly eight electrons. That assumption is an excellent default, but it is not a law of nature — it is a consequence of how stable a filled $s$ and $p$ outer shell happens to be for the elements most commonly encountered. This chapter catalogues the three genuine ways real, stable molecules depart from it, and then develops resonance, a refinement needed whenever more than one valid Lewis structure can be drawn for the same molecule.

You should bring forward from the previous chapter the full four-step Lewis-structure procedure and fluency in electron counting. Nothing here revisits VSEPR shape or hybridization — those are developed in the next three chapters, using the structures (including the exceptions below) built here as their starting point.

1. Why the Octet Rule Is a Guideline, Not a Law

The octet rule works as well as it does because, for carbon, nitrogen, oxygen, fluorine and their close neighbours, a filled $2s^22p^6$ configuration is a genuinely low-energy, stable arrangement, and bonding electron pairs naturally accumulate to reach it. Three circumstances break this pattern:

• Too few electrons are available to give the central atom four bonding/lone pairs at all — an incomplete octet.
• The central atom can accommodate more than four electron pairs, typically because it belongs to Period 3 or beyond — an expanded octet.
• The total valence electron count is odd, so no arrangement of complete pairs is possible for every atom — an odd-electron species (free radical).

Key distinction. These are not "wrong" Lewis structures requiring correction. Each is the genuinely correct, most stable structure for its molecule; the octet rule simply does not apply to it, in the same principled way it does not apply to hydrogen's duplet.

2. Incomplete Octets

An incomplete octet occurs when the central atom is left with fewer than eight electrons even after every available valence electron has been used — most often for central atoms from Groups 2 and 13, which simply do not have enough valence electrons to reach four bonding pairs with typical terminal atoms.

Worked example. Construct the Lewis structure of boron trifluoride, $\text{BF}_3$.

Boron (Group 13) contributes $3$ valence electrons; three fluorines (Group 17) contribute $7$ each, giving $3+3(7)=24$ electrons total. Three single B–F bonds use $6$ electrons, leaving $18$, placed as three lone pairs on each fluorine (completing each fluorine's octet). All $24$ electrons are now used, but boron has only $3$ bonding pairs $=6$ electrons — two short of an octet, with no further electrons available to fix it:

This is not an error: $\text{BF}_3$ is a genuinely stable, isolable molecule with boron carrying only six electrons. It is precisely this incomplete octet that gives boron an empty orbital, making $\text{BF}_3$ an excellent acceptor in coordinate bonding — exactly the role it played forming an adduct with ammonia in the previous chapter.

3. Expanded Octets

An expanded octet occurs when a central atom is surrounded by more than eight electrons — more than four electron pairs. This is only possible for central atoms from Period 3 or below, whose larger size and available low-lying $d$ orbitals can accommodate the extra electron density; it never occurs for Period 2 elements (C, N, O, F), whose $n=2$ shell has no $d$ subshell to draw on.

Worked example. Construct the Lewis structure of sulfur hexafluoride, $\text{SF}_6$.

Sulfur (Group 16) contributes $6$ valence electrons; six fluorines contribute $7$ each, giving $6+6(7)=48$ electrons total. Six single S–F bonds use $12$ electrons, leaving $36$, placed as three lone pairs on each fluorine ($6\times6=36$ electrons) — exactly using up the total, with no electrons left for sulfur itself. Sulfur ends up with six bonding pairs, $12$ electrons, a clear expansion beyond the octet, made possible because sulfur is a Period 3 element.

Phosphorus pentachloride, $\text{PCl}_5$ (phosphorus, Period 3, with $5$ bonding pairs $=10$ electrons), and chlorine trifluoride, $\text{ClF}_3$ (chlorine, Period 3, with $3$ bonding pairs and $2$ lone pairs $=10$ electrons on the central atom), are further standard examples.

Warning. Never force an expanded octet onto a Period 2 central atom (C, N, O, F) — it is never genuinely required, since these atoms always have a valid Lewis structure within the ordinary octet, achieved if necessary through multiple bonding (Section 3 of the previous chapter) rather than more than four electron pairs.

4. Odd-Electron Species (Free Radicals)

When the total valence electron count of a molecule is odd, it is structurally impossible to arrange every electron into complete pairs — at least one atom must be left with a single, unpaired electron. Such a species is called a free radical.

Worked example. Construct the Lewis structure of nitrogen monoxide, $\text{NO}$.

Nitrogen contributes $5$; oxygen contributes $6$; the total, $11$, is odd. A N=O double bond ($4$ electrons) uses part of the total, leaving $7$ electrons to distribute as lone pairs — necessarily an odd number, so one atom (conventionally nitrogen, the less electronegative atom) ends up with a single unpaired electron rather than a full lone pair:

Check: nitrogen has $1+2+4=7$ electrons, oxygen $4+4=8$, total $11$; both formal charges are zero.

Free radicals are generally far more reactive than ordinary molecules, since the unpaired electron readily pairs up with an electron from another species — a property returned to when organic reaction mechanisms are developed later in the course.

Key distinction. An odd-electron species is identified immediately at the electron-counting step (Step 1): if the total is odd, a complete-octet structure is impossible for every atom from the outset, regardless of how the bonds are subsequently arranged.

5. Formal Charge

When more than one Lewis structure can be drawn for the same molecule by placing a multiple bond in different positions, formal charge is the bookkeeping tool used to judge which structure is the more realistic depiction of the true electron distribution. The formal charge of an atom is:

The most favourable Lewis structure is generally the one in which formal charges are as close to zero as possible, and any negative formal charge is placed on the more electronegative atom.

Worked example. Compute the formal charges in the cyanate ion, $\text{OCN}^-$ (carbon central, $6+4+5+1=16$ electrons), for the candidate structure $\text{O}\!=\!\text{C}\!=\!\text{N}^-$ (two lone pairs on each terminal atom), and compare it with the alternative ${}^{-}\text{O}\!-\!\text{C}\!\equiv\!\text{N}$.

For oxygen (one double bond, two lone pairs): $\text{FC} = 6 - 4 - \tfrac{1}{2}(4) = 0$. For carbon (two double bonds, no lone pairs): $\text{FC} = 4 - 0 - \tfrac{1}{2}(8) = 0$. For nitrogen (one double bond, two lone pairs): $\text{FC} = 5 - 4 - \tfrac{1}{2}(4) = -1$. The formal charges, $0, 0, -1$, sum to the ion's overall charge of $-1$, as they must for any valid structure, and the negative charge sits on nitrogen — plausible, since nitrogen is reasonably electronegative, making this a chemically sensible candidate structure. For the alternative ${}^{-}\text{O}\!-\!\text{C}\!\equiv\!\text{N}$: oxygen (one single bond, three lone pairs) $6-6-\tfrac{1}{2}(2)=-1$, carbon $0$, nitrogen (one triple bond, one lone pair) $5-2-\tfrac{1}{2}(6)=0$. Both structures have the same formal-charge magnitudes, but the second places the negative charge on the more electronegative oxygen ($\chi=3.44$ against $3.04$ for nitrogen), so it is the preferred single depiction; the real ion is a resonance hybrid of the two (Section 6).

Warning. The sum of all formal charges in a structure must always equal the overall charge of the species (zero for a neutral molecule). This is a fast, mandatory check — a structure whose formal charges fail to sum correctly contains an arithmetic error.

6. Resonance Structures

Some molecules cannot be described accurately by any single Lewis structure at all. Resonance occurs when two or more valid Lewis structures differ only in the position of multiple bonds and lone pairs (never in the position of atoms), each an equally legitimate but incomplete description of the true, single molecule.

Worked example. Construct the Lewis structure(s) of ozone, $\text{O}_3$.

Three oxygen atoms contribute $6$ each, giving $18$ valence electrons. With oxygen as the central atom, one O–O single bond and one O=O double bond, together with appropriate lone pairs, complete every atom's octet — but nothing distinguishes which terminal oxygen receives the double bond. Two equally valid structures exist:

In each structure the central oxygen (one lone pair, three bonds) has formal charge $6-2-\tfrac{1}{2}(6)=+1$, the single-bonded terminal oxygen (three lone pairs) $6-6-\tfrac{1}{2}(2)=-1$, and the double-bonded oxygen $0$; the sum is $0$, as required for a neutral molecule.

Experimentally, both terminal oxygen-oxygen bonds in real ozone are found to have identical, intermediate length and strength — neither a pure single bond nor a pure double bond, but something in between. Neither individual structure above is "the" structure of ozone; the true molecule is a resonance hybrid, an average (specifically, a quantum-mechanical superposition) of all contributing structures, connected in diagrams by a double-headed resonance arrow, $\leftrightarrow$, never an equilibrium arrow.

The same pattern governs the carbonate ion, $\text{CO}_3^{2-}$, and the nitrate ion, $\text{NO}_3^-$: each has three equivalent resonance structures (the double bond rotating among the three terminal oxygens), and experimentally all carbon-oxygen (or nitrogen-oxygen) bonds in the real ion are found to be identical, with a bond order of $\tfrac{4}{3}$ for carbonate (one C=O-type double bond shared, in effect, across three equivalent positions) — directly consistent with the bond order/bond length relationship from the previous chapter, since this intermediate bond order predicts (and matches) an intermediate bond length between a single and a double C–O bond.

Key distinction. Resonance structures are not different molecules interconverting back and forth in time (that would be an equilibrium, with a double arrow $\rightleftharpoons$). They are different depictions of one single, unchanging molecule whose true electron distribution lies between them, at every instant — the resonance arrow $\leftrightarrow$ signals this explicitly.

7. Common Exam Pitfalls

• Forcing an octet onto $\text{BF}_3$ or similar electron-deficient molecules. Adding an extra bond or lone pair that electron-counting does not support creates an impossible structure; an incomplete octet, once confirmed by the arithmetic, is the correct final answer.
• Using an expanded octet for a Period 2 central atom. Carbon, nitrogen, oxygen and fluorine can never exceed an octet; if electron-counting seems to demand it, re-check for a missed multiple bond instead.
• Missing that a total valence electron count is odd. Always add up the total in Step 1 before attempting to pair every electron — an odd total guarantees a free radical from the outset.
• Forgetting that the sum of formal charges must equal the overall molecular/ionic charge. This fast check catches most formal-charge arithmetic slips immediately.
• Treating resonance structures as rapidly interconverting isomers. They are not separate molecules in equilibrium; they are incomplete individual depictions of one single, unchanging resonance hybrid.
• Averaging resonance structures incorrectly when predicting bond order. The bond order is the total bond order shared evenly across the equivalent resonance positions (e.g. $\tfrac{4}{3}$ for each C–O bond in carbonate, not simply "between 1 and 2" without the correct fraction).

Summary

• The octet rule has three principled exceptions: incomplete octets (too few electrons, e.g. $\text{BF}_3$), expanded octets (more than eight electrons, restricted to Period 3 and below, e.g. $\text{SF}_6$, $\text{PCl}_5$), and odd-electron species/free radicals (odd total valence electron count, e.g. $\text{NO}$).
• Formal charge, $\text{FC} = (\text{valence e}^-) - (\text{lone pair e}^-) - \tfrac{1}{2}(\text{bonding e}^-)$, helps select the most realistic Lewis structure among several valid candidates, favouring formal charges near zero and negative charge on the more electronegative atom; formal charges must always sum to the overall charge of the species.
• Resonance occurs when two or more valid Lewis structures differ only in the position of multiple bonds/lone pairs; the true molecule is a single resonance hybrid, with identical, intermediate bond lengths and bond orders (e.g. $\tfrac{4}{3}$ for carbonate) — not a mixture of interconverting molecules.
• Resonance structures are connected by a double-headed arrow, $\leftrightarrow$, never an equilibrium arrow, $\rightleftharpoons$.
• These exceptions and refinements complete the Lewis-structure toolkit; the next chapter uses completed Lewis structures (ordinary or exceptional) as the direct input for predicting three-dimensional molecular shape via VSEPR theory.