Lewis structures and the octet rule

Result

Lewis structures and the octet rule

T-008Home CU-102Threads bonding · quantum

Statement

A molecule's total valence electrons can be distributed as bonding pairs (shared between two atoms) and lone pairs (localised on one atom) so that, wherever possible, every main-group atom is surrounded by eight electrons (two, for hydrogen). Where more than one such distribution is possible, the formal charge \(FC=V-L-\tfrac{B}{2}\) (valence electrons \(V\), lone-pair electrons \(L\), bonding electrons \(B\)) on each atom selects the best structure: minimise the magnitude of formal charges, and place any necessary negative formal charge on the more electronegative atom.

Why it matters

The octet rule is the single most-used bookkeeping tool in introductory chemistry precisely because it is a direct, visualisable consequence of the quantum-mechanical result this unit builds on: a filled \(n{=}2\) shell (the aufbau-hund-pauli result, applied to the eight electrons of \(2s^22p^6\)) is a particularly stable, closed-subshell electron configuration, the same stability that makes noble gases chemically inert. Lewis structures let that stability principle be applied by simple electron-counting, without redoing quantum mechanics for every new molecule.

Formal charge is what turns Lewis-structure drawing from guesswork into a genuinely predictive tool: it is what correctly identifies, before any experiment, which of several electron-counting-valid structures is the best single representation of a real molecule's bonding — and, in the resonance case, which structures contribute most to the true, blended electronic structure. This is the direct input to the next two results in this unit, VSEPR geometry and orbital hybridisation, both of which start from a correct Lewis structure.

Hypotheses

Only valence electrons (those in the outermost occupied shell) participate in bonding; core electrons are chemically inert.Core electrons are held far more tightly (much larger ionisation energy, per the periodic-trends result's effective-nuclear-charge argument) and do not meaningfully overlap with neighbouring atoms' orbitals at typical bonding distances, so they are omitted from the electron count entirely. Formal charge, not the true partial charge from a real quantum-mechanical charge distribution, is used to compare candidate structures.Formal charge assigns each bonding pair's two electrons equally between the bonded atoms (splitting \(B\) exactly in half), regardless of the atoms' actual electronegativity difference. This is a bookkeeping convention, not a claim about where the electron density really sits — the true charge distribution (captured better by electronegativity-driven bond polarity, this unit's next-but-one result) is generally less extreme than formal charges suggest. Formal charge remains useful precisely because, despite this crudeness, it reliably ranks candidate Lewis structures in the same order as more sophisticated calculations do.

Proof

V_{\text{total}} = \sum_i V_i \ \mp\ (\text{ion charge})

Sum the valence electrons contributed by every atom (equal to the main group number for representative elements); for a polyatomic ion, add one electron per unit of negative charge or subtract one per unit of positive charge. A

\text{Place one bonding pair (2 electrons) between each pair of directly bonded atoms in the skeleton.}

The skeleton (which atoms are connected to which) is typically given or inferred from the least-electronegative non-hydrogen atom occupying the central position, since a central atom must bond to the most neighbours. A

\text{Distribute remaining electrons as lone pairs, outer atoms first, until every outer atom has 8 electrons (2 for H).}

Outer (terminal) atoms are completed to a full octet before any leftover electrons are placed on the central atom, since outer atoms in a typical Lewis structure only ever have one bonding partner and so need lone pairs to reach 8. A

\text{If the central atom has fewer than 8 electrons, convert an outer atom's lone pair into an additional bonding pair (a multiple bond).}

Moving a lone pair from an already-complete outer atom into a second (or third) bond with the central atom increases the central atom's electron count by 2 without changing the total electron count, since the pair simply moves from "lone on outer atom" to "shared between outer and central atom." Repeat until the central atom also has 8 electrons (or, for period 3+ central atoms, as many as the molecule's total electron count permits — see Fails without). A

FC = V - L - \frac{B}{2}

For each atom, formal charge is its own valence-electron count minus its lone-pair electrons minus half its bonding electrons (the "its share" of each shared pair, splitting every bond exactly evenly regardless of the real electronegativity difference, per Hypotheses). Where Step 4 leaves a choice of which outer atom to convert, compute \(FC\) for every atom under each candidate structure. A

\text{Select the structure minimising } \textstyle\sum|FC|, \text{ breaking ties by placing negative } FC \text{ on the more electronegative atom.}

Large formal charges (magnitude \(\ge2\) on any single atom, in an otherwise ordinary molecule) indicate an electronically strained, high-energy arrangement and are strongly disfavoured; where equally small formal charges remain, the more electronegative atom is the one that genuinely "wants" the extra electron density, so a structure agreeing with that is preferred. A

Result

V_{\text{total}}=\textstyle\sum V_i\mp q, \qquad FC=V-L-\tfrac{B}{2}, \qquad \text{best structure: minimise } \textstyle\sum|FC|

Reading. A short, purely arithmetic procedure (count electrons, fill octets outward-in, form multiple bonds only as needed to complete the central atom, then rank any remaining candidates by formal charge) reproduces the correct bonding pattern for the great majority of small main-group molecules and ions.

Scope. Applies directly to molecules and ions built from period 2 (and, with the extension in Fails without, period 3+) main-group elements; genuinely open-shell species (odd-electron radicals) and metals in typical ionic or metallic bonding are outside its scope.

Corollaries & converses

When two or more structures with equally low, equally well-placed formal charges exist and differ only in which equivalent bond carries a double bond (e.g. ozone, or the nitrate ion), the true electronic structure is a resonance hybrid — a genuine quantum-mechanical blend, not a molecule flickering between the drawn structures over time. Bond lengths and bond orders in such molecules are experimentally observed to be intermediate between the single- and double-bond values of the individual contributing structures.
A structure satisfying every atom's octet with all formal charges equal to zero (when such a structure exists, as for \(\text{CO}_2\) or \(\text{PCl}_5\)) is always the best or tied-for-best structure, since \(\sum|FC|=0\) is the global minimum possible.
Converse: a large, unavoidable formal charge on some atom in every possible structure for a given skeleton (rather than one avoidable by choosing a different bonding pattern) signals either that a different atom should be central, or that the molecule genuinely departs from simple octet behaviour (an electron-deficient or expanded-octet species, per Fails without).

Fails without

Genuinely electron-deficient central atoms (boron, beryllium): \(\text{BF}_3\) (24 valence electrons) reaches an all-zero-formal-charge structure with only 6 electrons around boron (three single B–F bonds, no lone pair) — the octet is never completed, and forcing a B=F double bond to complete it would place formal charges of \(+1\) on F (a highly electronegative atom, exactly backwards from Step 6's rule) and \(-1\) on B, a strictly worse structure by both formal-charge criteria. The genuinely electron-deficient, 6-electron structure is correct and is why \(\text{BF}_3\) is such a strong Lewis acid.
Expanded octets for period 3 and beyond (P, S, Cl, and lower): \(\text{PCl}_5\) (40 valence electrons) has no valid Lewis structure with only 8 electrons around phosphorus and every valence electron placed — the only way to use all 40 electrons with five P–Cl single bonds requires 10 electrons around P. Period 3+ atoms can accommodate this (empty, energetically accessible \(d\)-type or diffuse-orbital character allows more than 4 electron pairs), whereas period 2 atoms (with a strict 2s/2p, 4-orbital valence shell) genuinely cannot exceed 8. Applying the strict period-2 octet cutoff to \(\text{PCl}_5\) or \(\text{SF}_6\) gives no valid structure at all.

Common errors

Forgetting to adjust the total valence-electron count for the charge on a polyatomic ion (adding for a cation instead of subtracting, or vice versa, or simply omitting the adjustment).
Filling lone pairs on the central atom before terminal atoms have full octets, leading to terminal atoms with fewer than 8 electrons and an artificially electron-rich (and usually formal-charge-poor) central atom.
Treating formal charge as if it were the atom's true, physically measured partial charge (from a real charge-density calculation) rather than an even-split bookkeeping convention — the two are related in trend but not equal in value; see electronegativity-polarity for the physically-grounded alternative.
Stopping at the first octet-satisfying structure found without checking formal charges, missing that a different (often lower-energy, better) structure exists with smaller or better-placed formal charges.

Discussion

Gilbert N. Lewis introduced the shared-electron-pair bond and the dot-structure notation in 1916, years before Schrödinger's equation (1926) gave a rigorous quantum-mechanical account of why electron pairing is favourable at all — the octet rule and Lewis structures were originally an empirical pattern-matching success, later given a firm theoretical foundation once quantum mechanics explained closed-shell stability directly. This is a recurring pattern in the history of chemistry: extremely useful predictive rules (the octet rule, VSEPR, Hund's rule) were discovered empirically well before the underlying quantum mechanics was available to justify them rigorously.

The apparent conflict between \(\text{BF}_3\)'s electron deficiency and \(\text{PCl}_5\)'s electron excess is fully consistent, not contradictory: both are the formal-charge-minimising, octet-rule-respecting-where-possible structure for their respective total electron counts and skeletons. The "rule" was never that every atom always reaches exactly 8; it is that 8 is the target when it can be reached without worse formal-charge consequences, and departures from it are themselves systematic and explicable (small period-2 atoms with too few electrons to share versus period 3+ atoms with genuine room for more).

Common misconception: that resonance structures represent a molecule rapidly interconverting between two (or more) distinct bonding arrangements over time. They do not — a resonance hybrid is a single, static, time-independent electronic structure that is more delocalised than any one drawn Lewis structure can show; the individual resonance structures are a notational limitation of the dot-and-line diagram, not a physical oscillation.

Worked examples

\text{CO}_2:\ V=4+6+6=16,\quad \text{O=C=O},\quad FC(\text{C})=4-0-\tfrac{8}{2}=0,\ \ FC(\text{O})=6-4-\tfrac{4}{2}=0

Carbon, needing 4 more electrons to reach 8, forms two double bonds to the two oxygens; every atom reaches an octet (C: 2 double bonds \(=8\) electrons; each O: 2 lone pairs \(+\) 1 double bond \(=8\) electrons) with all formal charges exactly zero — the unambiguous best structure. A

\text{NO}_3^-:\ V=5+18+1=24,\quad FC(\text{N})=5-0-\tfrac{8}{2}=+1,\ \ FC(\text{O}_{=})=6-4-\tfrac{4}{2}=0,\ \ FC(\text{O}_{-})=6-6-\tfrac{2}{2}=-1

One resonance structure: N double-bonded to one O, single-bonded to the other two. Formal charges sum to \(+1+0+(-1)+(-1)=-1\), correctly matching the ion's overall charge — a required consistency check for every valid structure. Three equivalent resonance structures exist (the double bond can be to any one of the three oxygens), so the true structure is a symmetric blend with all three N–O bonds equal in length, intermediate between single and double. A

\text{CO}_2:\ \textstyle\sum FC=0 \text{ (unique best structure)}; \qquad \text{NO}_3^-:\ \textstyle\sum FC=-1 \text{ (matches ion charge; 3-fold resonance)}

Reading. The same electron-counting-then-formal-charge procedure both confirms a single unambiguous structure (\(\text{CO}_2\)) and correctly identifies a resonance situation (\(\text{NO}_3^-\)), in each case with the formal-charge sum providing an automatic check against the known total charge.

Scope. The formal-charge sum check (\(\sum FC = \) ion charge, or \(0\) for a neutral molecule) applies to every valid Lewis structure and is a fast way to catch electron-counting errors before proceeding to geometry (VSEPR) or hybridisation.

Problems

Ozone, \(\text{O}_3\) (18 valence electrons), has a bent, resonance-stabilised structure with a central oxygen double-bonded to one terminal O and single-bonded to the other. Compute the formal charge on each of the three oxygens and verify they sum to zero.
Solution
Central O (1 lone pair, bonds to both terminal O's \(=\) 1 double \(+\) 1 single \(=6\) bonding electrons): \(FC=6-2-\tfrac{6}{2}=6-2-3=+1\). Terminal double-bonded O (2 lone pairs, 4 bonding electrons): \(FC=6-4-\tfrac{4}{2}=0\). Terminal single-bonded O (3 lone pairs, 2 bonding electrons): \(FC=6-6-\tfrac{2}{2}=-1\). Sum: \(1+0+(-1)=0\), correctly matching neutral ozone's overall charge. This is the same formal-charge pattern (\(+1\), \(0\), \(-1\)) as \(\text{NO}_3^-\)'s central/double/single-bonded atoms in Worked example 2, since both are isoelectronic in their bonding-electron arrangement.
Phosphorus pentachloride, \(\text{PCl}_5\) (40 valence electrons), has five P–Cl single bonds with no lone pair on P. Compute the formal charge on P and on each Cl, and explain why this expanded-octet structure, despite P having 10 electrons around it, is still the correct (all-zero formal charge) structure.
Solution
P (0 lone pairs, 5 bonds \(=10\) bonding electrons): \(FC=5-0-\tfrac{10}{2}=5-5=0\). Each Cl (3 lone pairs, 1 bond \(=2\) bonding electrons): \(FC=7-6-\tfrac{2}{2}=7-6-1=0\). All formal charges are zero, the global minimum possible, so despite exceeding the period-2 octet limit, this is still the best structure — consistent with phosphorus (period 3) being able to accommodate more than 8 electrons, per Fails without.
Two candidate Lewis structures are proposed for the thiocyanate ion \(\text{SCN}^-\) (16 valence electrons, skeleton S–C–N): (A) \(\text{S=C=N}^-\) with two lone pairs on S and two on N, or (B) \(\text{S–C}{\equiv}\text{N}^-\) with three lone pairs on S and one on N. Compute the formal charge on every atom in both structures and determine which structure the formal-charge rule (Step 6) prefers.
Solution
Structure A (S=C=N, 2 lone pairs each on S and N): \(FC(\text{S})=6-4-\tfrac{4}{2}=0\); \(FC(\text{C})=4-0-\tfrac{8}{2}=0\); \(FC(\text{N})=5-4-\tfrac{4}{2}=-1\). Sum: \(0+0-1=-1\), correct. Structure B (S–C≡N, 3 lone pairs on S, 1 on N): \(FC(\text{S})=6-6-\tfrac{2}{2}=-1\); \(FC(\text{C})=4-0-\tfrac{8}{2}=0\); \(FC(\text{N})=5-2-\tfrac{6}{2}=0\). Sum: \(-1+0+0=-1\), also correct. Both structures have identical \(\sum|FC|=1\), so Step 6's tiebreaker applies: place the negative formal charge on the more electronegative atom. Nitrogen (electronegativity \(\approx3.04\)) is more electronegative than sulfur (\(\approx2.58\)), so Structure A (negative charge on N) is the preferred structure.
Boron trifluoride, \(\text{BF}_3\) (24 valence electrons), is often drawn with only three B–F single bonds and no lone pair on boron, leaving boron with just 6 electrons rather than a full octet. Explain, using formal charge, why forcing a fourth bond (a B=F double bond, converting one F lone pair into a second bonding pair to that fluorine) does not improve the structure.
Solution
In the all-single-bond structure, every atom already has formal charge zero (\(FC(\text{B})=3-0-\tfrac{6}{2}=0\); \(FC(\text{F})=7-6-\tfrac{2}{2}=0\) each), which is the global minimum \(\sum|FC|=0\) — it cannot be improved. Forming a B=F double bond instead would give that fluorine \(FC=7-4-\tfrac{4}{2}=+1\) and boron \(FC=3-0-\tfrac{8}{2}=-1\): now \(\sum|FC|=2\), strictly worse, and the positive formal charge sits on fluorine, the most electronegative element on the periodic table — directly violating Step 6's placement rule as well. Both criteria agree: the electron-deficient, all-single-bond structure is correct, and \(\text{BF}_3\) genuinely does not complete boron's octet.