Lewis Langmuir Concept

Covalent bonding arises when two atoms share one or more pairs of electrons rather than transferring them completely. The Lewis–Langmuir model, developed independently by Gilbert N. Lewis (1916) and Irving Langmuir (1919), provides a simple yet powerful framework for understanding how and why atoms form covalent bonds. At its heart lies the octet rule: most main-group elements achieve stability by surrounding themselves with eight valence electrons, mimicking the electron configuration of the nearest noble gas. Lewis dot structures (electron-dot diagrams) are symbolic representations of molecules that show every valence electron as a dot around the element symbol. Shared electron pairs appear between two atom symbols as bonding pairs, while unshared pairs remain on a single atom as lone pairs. These diagrams allow chemists to predict molecular connectivity, count bonds, and identify lone pairs—all from nothing more than the periodic table and a count of valence electrons. Formal charge is an accounting tool embedded within the Lewis model that helps identify which Lewis structure among several plausible alternatives is the most stable. By comparing the number of electrons formally 'owned' by an atom in a structure against its neutral valence electron count, chemists can rank competing structures and predict observed bond lengths, bond orders, and reactivity. Together, the octet rule, Lewis structures, and formal charge form the foundation of covalent bonding theory taught in high school and undergraduate chemistry.

Key takeaways
  • Count Total Valence Electrons
  • Identify the Central Atom
  • Draw a Skeletal Structure with Single Bonds
  • Complete Octets on Terminal Atoms First
  • Complete the Central Atom's Octet
  • Calculate Formal Charges
  • Select the Best Structure

Count Total Valence Electrons

Add the valence electrons contributed by every atom in the molecule or ion. For anions, add one electron per unit of negative charge; for cations, subtract one electron per unit of positive charge. Example: SO₄²⁻ has S (6) + 4×O (4×6) + 2 (charge) = 32 valence electrons.

Identify the Central Atom

The central atom is usually the one with the lowest electronegativity (excluding hydrogen, which is always terminal). It is often the unique atom in the formula (e.g., S in SO₄²⁻, C in CO₂). Hydrogen can never be a central atom because it can form only one bond.

Draw a Skeletal Structure with Single Bonds

Connect all atoms to the central atom with single bonds. Each single bond uses 2 electrons. Subtract these electrons from the total count. For SO₄²⁻: 4 single bonds use 8 electrons, leaving 32 − 8 = 24 electrons to distribute.

Complete Octets on Terminal Atoms First

Distribute remaining electrons as lone pairs on terminal atoms (not hydrogen) until each has 8 electrons. Oxygen already has 2 electrons from the bond, so each terminal O needs 6 more (3 lone pairs). Four oxygens use 4×6 = 24 electrons. Remaining electrons for SO₄²⁻: 24 − 24 = 0.

Complete the Central Atom's Octet

If the central atom has fewer than 8 electrons after step 4, convert lone pairs from adjacent atoms into additional bonds (double or triple bonds). Each conversion uses no electrons—it simply repositions them. Check: if the central atom now has 8 electrons, the octet rule is satisfied.

Calculate Formal Charges

For each atom: Formal Charge (FC) = (Valence electrons of neutral atom) − (Lone-pair electrons on atom) − ½×(Bonding electrons on atom). The preferred Lewis structure minimises the magnitude of formal charges, gives negative formal charges to more electronegative atoms, and has a sum of formal charges equal to the overall charge of the species.

Select the Best Structure

Among all valid Lewis structures: (a) prefer the one where all formal charges are zero or as small as possible; (b) if nonzero charges are unavoidable, place negative formal charge on the more electronegative atom; (c) avoid placing like charges on adjacent atoms. Multiple valid structures with the same energy indicate resonance (see related concept C04.2.4).

The Key Equation

FC=V−L−B2FC = V - L - \frac{B}{2}
  • FC — Formal Charge (dimensionless (integer)): The hypothetical charge assigned to an atom in a Lewis structure, assuming electrons in each bond are shared equally between the two bonded atoms.
  • V — Valence Electrons (electrons): The number of valence electrons of the atom in its neutral, isolated state; determined directly from the atom's group number on the periodic table.
  • L — Lone-pair Electrons (electrons): The total number of non-bonding electrons (lone pairs) assigned exclusively to the atom in the Lewis structure.
  • B — Bonding Electrons (electrons): The total number of electrons the atom shares in all covalent bonds (single, double, or triple). Each bond contributes 2 electrons to B; these are divided equally (½ each) between the two bonded atoms.

Worked Example

Problem. Draw the best Lewis structure for the nitrate ion, NO₃⁻, and calculate the formal charge on each atom.

FCN=+1,FCO (double)=0,FCO (single)=−1,∑FC=−1FC_{\text{N}} = +1,\quad FC_{\text{O (double)}} = 0,\quad FC_{\text{O (single)}} = -1,\quad \sum FC = -1

Answer. The Lewis structure of NO₃⁻ has one N=O double bond and two N–O single bonds (one of three equivalent resonance forms). Formal charges: N = +1, double-bonded O = 0, each single-bonded O = −1. Total = −1 ✓

Figure
Diagram
Lewis Dot Structure of NO₃⁻N+1O0O−1O−1[NO₃]⁻ ΣFC = −1double bond
Origins · 1 minGilbert Newton Lewis and how this was discovered
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Gilbert Newton Lewis
1875–1946 · American

Lewis introduced the concept of the covalent bond as a shared electron pair in his landmark 1916 paper 'The Atom and the Molecule.' He proposed electron-dot diagrams (Lewis structures) and the octet rule, arguing that atoms achieve stability by attaining a filled shell of eight electrons. He also introduced the concept of Lewis acids and bases (electron-pair acceptors and donors), extending acid-base theory far beyond proton transfer. Despite his revolutionary contributions to chemical bonding and thermodynamics—and being nominated for the Nobel Prize in Chemistry 41 times—Lewis never won the award, making him one of the most notable scientists to be repeatedly overlooked by the Nobel Committee. He spent most of his career at UC Berkeley, where he transformed the chemistry department into one of the world's finest.

  • Exceptions to the Octet Rule — While Lewis structures are built around the octet rule, many real molecules violate it. Electron-deficient species (e.g., BF₃, with only 6 electrons on B), odd-electron radicals (e.g., NO), and expanded-octet species (e.g., PCl₅, SF₆) cannot be described by standard Lewis structures. Understanding these exceptions is the natural next step after mastering the Lewis–Langmuir model.
  • Resonance — When two or more equivalent Lewis structures can be drawn for the same molecule (e.g., the three forms of NO₃⁻ worked above), the concept of resonance explains that the true structure is a hybrid of all contributors. Formal charge analysis is essential for weighting resonance contributors, making resonance a direct extension of the Lewis–Langmuir model.
  • Bond Parameters — Lewis structures predict bond order (single, double, triple), which directly determines bond length and bond energy. Understanding how to draw and interpret Lewis dot structures is a prerequisite for quantitative discussion of bond length, bond enthalpies, and bond polarity.
  • Dipole Moment — Lewis structures reveal the distribution of bonding and lone-pair electrons, which determines bond polarity and molecular polarity. The formal charges and electronegativity differences identified through Lewis structures directly feed into the calculation and interpretation of molecular dipole moments.
  • VSEPR Postulates — VSEPR theory uses the electron pairs identified in Lewis dot structures (both bonding pairs and lone pairs) as its starting point for predicting molecular geometry. Without an accurate Lewis structure, VSEPR predictions are impossible, making the Lewis–Langmuir concept a direct prerequisite.
  • Conditions for Formation of Ionic Bonds — Comparing the conditions under which ionic bonds form (large electronegativity difference, metal + non-metal) versus covalent bonds (similar electronegativities, non-metal + non-metal) provides essential context for why Lewis structures apply to covalent but not ionic species, and how electron sharing differs from electron transfer.
  • Covalent Nomenclature — Naming covalent compounds systematically requires knowing the number of bonds (and hence atoms) in a molecule, which Lewis structures provide. Recognising that CO₂ has two double bonds while CO has a triple bond, for example, is essential background for correct IUPAC naming.