Lewis Structure

A Lewis structure (also termed a Lewis dot diagram or electron-dot structure) is a two-dimensional topological representation of the valence electron distribution within a molecule or polyatomic ion. Introduced by the American physical chemist Gilbert N. Lewis in his seminal 1916 article "The Atom and the Molecule", the formalism represents atomic nuclei and core inner-shell electrons by their standard element symbols, localized covalent bonds (shared pairs of electrons) by single, double, or triple lines (—, =, ≡), and non-bonding valence electrons (lone pairs or unpaired radical electrons) by paired or single dots (:) positioned around the atomic symbols.

Although written prior to the 1926 formulation of quantum mechanics by Erwin Schrödinger, Walter Heitler, and Fritz London, Lewis structures successfully capture the localized two-center two-electron (2c-2e) pairing of valence electrons and the energetic stability of closed-shell noble-gas configurations—formalized by Irving Langmuir in 1919 as the octet rule. Combined with formal charge minimization and resonance theory, a Lewis structure provides the essential starting point for predicting three-dimensional molecular geometry via Valence Shell Electron Pair Repulsion (VSEPR) theory, orbital hybridization, dipole moments, and reactive nucleophilic or electrophilic sites in organic and biological chemistry.

Turn 2D Dots into 3D Molecules: Build Lewis structures and observe how bonding pairs and lone pairs determine 3D geometry in our interactive VSEPR Lab!

Valence Electron Counting and Connectivity

Constructing an accurate Lewis structure follows a rigorous five-step electron-bookkeeping algorithm:

1. Sum the Total Valence Electrons (N_val): Count the valence s and p electrons contributed by every atom in the chemical formula according to its main-group column number (Group 1 = 1, Group 2 = 2, Group 13 = 3, Group 14 = 4, Group 15 = 5, Group 16 = 6, Group 17 = 7, Group 18 = 8). For polyatomic anions, add one electron per unit of negative charge; for polyatomic cations, subtract one electron per unit of positive charge. For example, the nitrate ion (NO₃⁻) contains 5 (from N) + 3 × 6 (from O) + 1 (from −1 charge) = 24 valence electrons.
2. Identify the Central Atom and Draw the Skeletal σ-Framework: The least electronegative atom (excluding hydrogen, which can only form one bond and is always terminal) typically occupies the central position (e.g., C, N, P, S, or Xe). Connect each peripheral atom to the central atom with a single covalent bond (2 electrons per bond), subtracting 2n_bonds from N_val.
3. Complete Terminal Octets (and Hydrogen Duets): Distribute the remaining electrons as lone pairs around the more electronegative terminal atoms first so that each second-row terminal atom achieves a closed-shell octet of 8 valence electrons (2s²2p⁶, isoelectronic with neon) and each hydrogen atom achieves a duet of 2 valence electrons (1s², isoelectronic with helium).
4. Assign Leftover Electrons to the Central Atom: If valence electrons remain after all terminal octets are satisfied, place them as non-bonding lone pairs on the central atom (common in hypervalent species or lone-pair-bearing p-block centers such as NH₃, H₂O, SF₄, and XeF₄).
5. Form Multiple Bonds if the Central Atom Lacks an Octet: If the central atom has fewer than 8 electrons after all valence electrons have been placed, convert one or more lone pairs from adjacent terminal atoms into shared π-bonding pairs to form double bonds (4 shared electrons, bond order 2) or triple bonds (6 shared electrons, bond order 3). In NO₃⁻, placing 6 electrons in three N–O single bonds and 18 electrons as lone pairs on the three oxygen atoms leaves nitrogen with only 6 electrons; converting one oxygen lone pair into an N=O double bond satisfies the octet rule on both nitrogen and all three oxygen atoms.

Formal Charge Calculation and Structural Selection

When multiple topological arrangements or multiple-bond placements satisfy the octet rule, the thermodynamically favored Lewis structure is identified by calculating the formal charge (FC) on every atom. Formal charge represents the hypothetical electric charge an atom would carry if all bonding electron pairs were shared equally between the bonded atoms (ignoring electronegativity differences):

FC = V − N_nonbonding − ½ N_bonding = V − L − B

where V is the number of valence electrons in the neutral isolated atom, N_nonbonding (L) is the number of non-bonding lone-pair electrons assigned to the atom, and ½N_bonding (B) is the number of covalent bonds (lines) attached to the atom. The sum of formal charges across all atoms in a structure always equals the net ionic charge of the molecule or ion.

To evaluate competing Lewis structures (or resonance contributors), chemists apply three hierarchical rules:

1. Minimize Formal Charge Magnitude: Structures in which all atoms have formal charges of zero (FC = 0) are favored over structures with charge separation (+1 / −1), which in turn are strongly favored over structures carrying larger charges (+2 / −2).
2. Match Negative Formal Charges to Electronegative Atoms: When non-zero formal charges are unavoidable, the structure that places negative formal charges on the most electronegative atoms (e.g., O, N, F) and positive formal charges on the less electronegative atoms is lower in energy.
3. Avoid Like Charges on Adjacent Atoms: Structures that place adjacent positive or adjacent negative formal charges incur strong Coulombic repulsion and contribute negligibly to the ground state.

For example, the cyanate ion (NCO⁻, 16 valence electrons) can be drawn with three octet-compliant resonance structures: (A) [:N≡C–O:]⁻ (FC: N = 0, C = 0, O = −1), (B) [:N=C=O:]⁻ (FC: N = −1, C = 0, O = 0), and (C) [::N–C≡O:]⁻ (FC: N = −2, C = 0, O = +1). Structure C is eliminated by its large −2/+1 charge separation, and Structure A contributes more heavily than Structure B because the −1 formal charge resides on the more electronegative oxygen atom (χ_O = 3.44) rather than nitrogen (χ_N = 3.04).

Breakdown of Single Localized Structures

Because a single Lewis structure restricts every bonding electron pair to lie strictly between two atoms, it cannot accurately represent molecules with delocalized π-electron systems. For instance, a single Lewis structure for the carbonate ion (CO₃²⁻) or ozone (O₃) predicts one short double bond (C=O ≈ 1.21 Å; O=O ≈ 1.21 Å) and one or two longer single bonds (C–O ≈ 1.43 Å; O–O ≈ 1.48 Å). Experimentally, X-ray crystallography and microwave spectroscopy demonstrate that all three C–O bonds in CO₃²⁻ have an identical intermediate bond length of 1.28 Å (bond order = 4/3 = 1.33), and both O–O bonds in O₃ have an identical length of 1.278 Å (bond order = 3/2 = 1.50).

Introduced by Linus Pauling in the 1930s within Valence Bond theory, resonance resolves this limitation by representing the true electronic ground state as a quantum-mechanical linear combination—a resonance hybrid—of multiple canonical Lewis structures connected by double-headed arrows (↔):

[O=C(–O⁻)₂] ↔ [⁻O–C(=O)–O⁻] ↔ [(⁻O)₂C=O]

Crucially, resonance structures are not distinct isomers oscillating back and forth in a dynamic equilibrium; the atomic nuclei remain fixed in a single average geometry, and the electron density is permanently delocalized across the entire conjugated framework (corresponding in Molecular Orbital theory to a multi-center bonding π orbital spanning all participating atoms).

Biochemical Consequence: Planarity of the Peptide Bond

Resonance in Lewis structures directly explains the three-dimensional folding architecture of proteins. In a polypeptide backbone, the amide peptide bond (–C(=O)–NH–) linking consecutive amino acids is a resonance hybrid of two major Lewis contributors:

1. The neutral carbonyl structure: –C(=O)–N̈H– (approx. 60% weight, FC = 0 on O and N).
2. The charge-separated zwitterionic iminium structure: –C(–O⁻)=N⁺H– (approx. 40% weight, FC = −1 on O and +1 on N), formed by delocalizing the nitrogen 2p lone pair into the carbonyl C=O π* system.

Because of this ~40% double-bond character (C–N bond order ≈ 1.4), the peptide C–N bond is 1.33 Å long—significantly shorter than a standard aliphatic C–N single bond (1.47 Å) and close to a C=N double bond (1.27 Å). Rotating around the C–N peptide bond (the ω torsion angle) requires breaking this p-orbital π overlap, imposing a rotational energy barrier of ~84 kJ mol⁻¹ (~20 kcal mol⁻¹). Consequently, the six atoms of the peptide group are locked into a rigid plane (ω ≈ 180° trans or 0° cis), reducing the conformational degrees of freedom of the protein backbone exclusively to the φ and ψ angles plotted on a Ramachandran plot.

While second-period elements carbon, nitrogen, oxygen, and fluorine adhere to the octet limit because their n = 2 valence shell contains only four orbitals (one 2s and three 2p, holding at most 8 electrons), three important classes of molecules deviate from the octet rule:

1. Electron-Deficient (Hypovalent) Molecules: Covalent compounds of Group 2 and Group 13 elements—such as gaseous BeCl₂ (4 valence electrons around Be) and BF₃, BCl₃, or AlCl₃ (6 valence electrons around B or Al)—have fewer than 8 electrons around the central atom in their zero-formal-charge Lewis structures. Because these central atoms possess a vacant valence p orbital, they react readily as Lewis acids or dimerize via three-center two-electron (3c-2e) banana bonds (as in diborane, B₂H₆) or bridging halide lone pairs (as in Al₂Cl₆).
2. Odd-Electron Molecules (Free Radicals): Any species with an odd total number of valence electrons cannot pair all electrons into two-electron bonds and lone pairs, leaving at least one atom with a 7-electron valence shell and an unpaired spin (S = ½, paramagnetic). Biologically and environmentally significant free radicals include nitric oxide (•NO, 11 valence e⁻, a vascular signaling messenger), nitrogen dioxide (•NO₂, 17 valence e⁻), and the superoxide radical anion (O₂^•−, 13 valence e⁻).
3. Hypervalent (Expanded-Octet) Molecules: Elements in Period 3 and below (such as P, S, Cl, As, Se, Br, I, and Xe) form stable compounds in which the central atom coordinates more than four substituents, seemingly surrounded by 10, 12, or 14 valence electrons in conventional Lewis drawings—such as PF₅ and SF₄ (10 e⁻), SF₆ and SO₄²⁻ (12 e⁻), and XeF₄ (12 e⁻) or IF₇ (14 e⁻). Although early textbooks attributed hypervalency to sp³d or sp³d² hybridization using high-energy 3d orbitals, modern ab initio quantum-chemical calculations demonstrate that 3d orbitals lie too high in energy to participate significantly in main-group bonding. Instead, hypervalent molecules obey the octet rule through charge-separated ionic resonance contributors and three-center four-electron (3c-4e) hypervalent bonds (formulated by George C. Pimentel and R. E. Rundle in 1951), which require highly electronegative terminal ligands (such as F, O, or Cl) to withdraw electron density from the larger central atom.

Why can nitrogen never form NF₅ whereas phosphorus readily forms PF₅?

Nitrogen (Period 2, valence shell 2s²2p³) has a small covalent radius (0.71 Å) and lacks any low-lying orbitals beyond its four 2s and 2p orbitals, which hold an absolute maximum of 8 electrons. Even under the modern 3-center 4-electron (3c-4e) ionic bonding model—which represents PF₅ as resonance forms of [PF₄⁺]F⁻ without invoking 3d orbitals—surrounding a tiny nitrogen core with five fluorine atoms causes severe steric crowding and strong ligand–ligand Pauli repulsion between the five fluorine electron clouds. Phosphorus (Period 3, covalent radius 1.07 Å) is both larger (accommodating five fluorine atoms in a trigonal bipyramid without steric clash) and substantially less electronegative (χ_P = 2.19 vs χ_N = 3.04), enabling strong P^δ+–F^δ− bond polarity that stabilizes 3c-4e axial bonding.

Why does a simple Lewis structure fail to predict the paramagnetism of molecular oxygen (O₂)?

For dioxygen (O₂, 12 valence electrons), the standard Lewis algorithm yields the double-bonded structure :Ö=Ö:, in which all 12 valence electrons are paired (4 in the O=O double bond and 8 in four lone pairs) and every oxygen atom satisfies the octet rule with zero formal charge. This Lewis diagram predicts that O₂ should be diamagnetic (repelled by a magnetic field). In reality, liquid O₂ is strongly paramagnetic and stays suspended between the poles of a magnet. Molecular Orbital (MO) theory resolves this discrepancy: when the two oxygen 2p orbitals combine, the two highest-energy electrons occupy a pair of degenerate π*_2px and π*_2py antibonding orbitals. By Hund's rule of maximum multiplicity, these two electrons occupy separate π* orbitals with parallel spins (a triplet ground state, ³Σ_g⁻), giving O₂ two unpaired electrons while preserving a net bond order of (8 − 4)/2 = 2.

Should sulfate (SO₄²⁻) and phosphate (PO₄³⁻) be drawn with double bonds or single bonds?

In introductory chemistry, sulfate (SO₄²⁻) is often drawn with two S=O double bonds and two S–O⁻ single bonds (12 electrons around sulfur) because this minimizes formal charges (FC_S = 0), whereas the octet-compliant structure with four S–O⁻ single bonds gives sulfur a formal charge of +2 and each oxygen −1. Quantum-mechanical natural bond orbital (NBO) and electron-density topological analyses show that the true electronic distribution is closer to the octet-compliant single-bonded structure [S²⁺(–O⁻)₄]: the S–O bonds are short and strong (1.49 Å) not because of 3d-orbital π-bonding, but because of strong electrostatic attraction between the positively charged central sulfur (+2) and the four negatively charged oxygens (−1), supplemented by negative hyperconjugation (donation of oxygen 2p lone pairs into opposing S–O σ* antibonding orbitals).

1. Lewis, G. N. (1916). The atom and the molecule. Journal of the American Chemical Society, 38(4), 762–785. https://doi.org/10.1021/ja02261a002
2. Langmuir, I. (1919). The arrangement of electrons in atoms and molecules. Journal of the American Chemical Society, 41(6), 868–934. https://doi.org/10.1021/ja02227a002
3. Gillespie, R. J., & Robinson, E. A. (2007). Gilbert N. Lewis and the chemical bond: The electron pair and the octet rule from 1916 to the present day. Journal of Computational Chemistry, 28(1), 87–97. https://doi.org/10.1002/jcc.20545
4. Weinhold, F., & Landis, C. R. (2012). Discovering Chemistry with Natural Bond Orbitals. Wiley. https://doi.org/10.1002/9781118229101