# Chemical bond A **chemical bond** is a lasting attraction between [[Atom|atoms]], ions or [[Molecule|molecules]] that holds a [[Chemical_compound|compound]] together. Every bond is at bottom electrostatic: positively charged nuclei attract negatively charged [[Electron|electrons]], and when two atoms come close enough for their electrons to be attracted by both nuclei at once, the arrangement can have a lower [[Energy|energy]] than the separated atoms, and the atoms stay together. What differs from one bond to another is how the electrons are shared. In a [[Covalent_bond|covalent bond]] a pair of electrons sits between two nuclei and belongs to both; in an [[Ionic_bonding|ionic bond]] one atom has taken electrons from the other and the resulting ions attract; in [[Metallic_bonding|metallic bonding]] electrons are shared by every atom in the solid at once.[^os-af-ch4] The single number that best predicts which of these a given pair of atoms will form is the difference in their [[Electronegativity|electronegativity]], the power of an atom in a molecule to attract the shared electrons to itself.[^pauling1932] On the Chemistry flagship the article serves the section *Bonding* (Part IV — Bonding), and the same microsim is the shared bonding embed of the Materials science and Physics flagships. In the microsim below the reader picks two elements from the electronegativity table and watches the shared electron cloud between the two nuclei skew toward the more electronegative atom as the difference `ΔEN` grows. The bond then lands as a point in the van Arkel–Ketelaar triangle, plotted at `(ΔEN, mean EN)`: nonpolar covalent for `ΔEN` below about 0.4, polar covalent up to roughly 1.7–2.0, ionic beyond, and metallic in the low-electronegativity corner where neither atom holds electrons tightly.[^blackstock-en] Two readouts answer the quantitative questions. Pauling's estimate of ionic character, `% ionic = 100·(1 − exp(−ΔEN²/4))`, gives the fraction of the bond that behaves as an ion pair, and the [[Electric_dipole_moment|dipole moment]] `μ = q·d` gives the separated charge times the bond length.[^pauling1960] ## Overview of main types of chemical bonds The bonds that hold compounds together are called strong or primary bonds, and there are three idealised kinds. A covalent bond is a shared electron pair between two atoms, localised between them and directional, so that a molecule has a definite shape. An ionic bond is the attraction between a cation and an anion after one or more electrons have moved from one atom to the other; it is not directional, and the ions pack into a lattice in which each is surrounded by as many of the opposite charge as will fit. A metallic bond is the attraction between a lattice of cations and a sea of delocalised electrons that no single atom owns.[^os-af-ch4] Weaker attractions between whole molecules, the [[Intermolecular_force|intermolecular forces]], are treated separately below. The three kinds are corners of a continuum rather than boxes, and the microsim's triangle is the map of that continuum. Its horizontal axis is `ΔEN`, the electronegativity difference, which measures how unequally the two atoms share electrons; its vertical axis is the mean electronegativity, which measures how tightly either atom holds electrons at all.[^jensen1995] The Portal Book's own examples place the corners. H–H has `ΔEN = 0` and sits at the covalent corner. H–Cl, with `ΔEN = 0.9`, is a polar covalent bond, and H–F at 1.9 is still described as polar covalent because both atoms are nonmetals. Na–Cl at 2.1 is ionic. Mn–I, at only 1.0, is nevertheless classed as ionic, because it joins a metal to a nonmetal and its mean electronegativity is low.[^blackstock-en] The last two cases are the reason the triangle needs two axes: `ΔEN` alone would put Mn–I among the polar covalent bonds and H–F near the ionic ones. Pauling's formula turns the first axis into a number: for H–Cl it gives `100·(1 − exp(−0.81/4)) = 18 %` ionic character, for Mn–I 22 %, for H–F 59 % and for Na–Cl 67 % (derived from the book's `ΔEN` values with Pauling's expression).[^pauling1960] The sim prints these on the readout as the reader moves between elements, and the thresholds it draws are ILLUSTRATIVE: the boundaries at 0.4 and 1.7–2.0 are conventions of the Portal Book, not measured lines. ## History The idea that atoms are held together by a definite force has three ages: a chemistry of affinities before atoms were accepted, an atomic chemistry that counted bonds without explaining them, and an electronic chemistry that explained them.[^os-af-ch4] Each age kept what the previous one had measured. The affinity tables survive as the [[Reactivity_series|reactivity series]], Dalton's ratios as the formulas, and the valence lines of the 1850s as the electron pairs of the 1910s, so that the microsim's electronegativity scale, a product of the third age, is calibrated on bond energies that the second age learned to count. ### Pre-atomic chemical theory Before the atom, chemists spoke of affinity, the tendency of one substance to combine with or displace another. Étienne-François Geoffroy's *Table des différents rapports* of 1718 arranged substances in columns by how readily each displaced the others from combination, the first systematic table of affinities.[^geoffroy1718] Isaac Newton had already asked, in the Queries to his *Opticks*, whether the smallest particles of bodies might "cohere by the strongest attractions" and whether chemical change was the work of such attractions, and the affinity tables of the eighteenth century were the chemists' answer, a ranking of attractions that predicted reactions without saying what the attracting things were.[^newton-opticks] [[Antoine_Lavoisier|Lavoisier]]'s reform of nomenclature and his insistence on the balance gave the affinities fixed compositions to work on. ### Atomic theory [[John_Dalton|John Dalton]]'s *New System of Chemical Philosophy* of 1808 gave the affinities something to act between: atoms of fixed weight combining in small whole-number ratios, drawn as touching circles.[^dalton1808] Berzelius then supplied the first physical theory of the bond, the electrochemical dualism of 1819, in which every compound was the union of an electropositive and an electronegative part held by the attraction of opposite charges; the theory explained salts well and organic compounds badly.[^berzelius1819] The counting of bonds came in the 1850s. Edward Frankland, studying organometallic compounds in 1852, observed that each element combines with a fixed number of others, the idea later called valence,[^frankland1852] and August Kekulé in 1858 gave carbon a valence of four and let carbon atoms bond to one another in chains, which made organic structural formulas possible.[^kekule1858] By the end of the century a bond was a line on paper with a well-tested meaning and no known cause. ### Modern chemical theory The cause arrived with the electron. In 1916 Gilbert N. Lewis proposed that a covalent bond is a pair of electrons shared between two atoms and that atoms combine so as to complete an outer shell of eight, and Walther Kossel in the same year explained ionic bonding as electron transfer toward the same closed shell.[^lewis1916][^kossel1916] Irving Langmuir extended and named the scheme, including the [[Octet_rule|octet rule]], in 1919.[^langmuir1919] The quantum explanation of why a shared pair binds came in 1927, when Walter Heitler and Fritz London solved the hydrogen molecule approximately and showed that the bond energy arises from the exchange of the two electrons between the nuclei.[^heitler1927] [[Linus_Pauling|Linus Pauling]] built that result into the valence bond theory of chemistry from 1931 and, in 1932, defined the electronegativity scale by comparing the energy of a bond A–B with the mean of A–A and B–B, taking the excess as the work of the ionic contribution.[^pauling1931][^pauling1932] The van Arkel–Ketelaar triangle of the 1950s put the three bond types on one diagram, and Jensen's quantitative version of 1995 fixed its axes as the electronegativity difference and mean that the microsim uses.[^vanarkel1956][^ketelaar1958][^jensen1995] ## Bonds in chemical formulas In a structural formula a covalent bond is drawn as a line between two element symbols, one line per shared electron pair, so that H–H, O=O and N≡N are single, double and triple bonds and the number of lines is the [[Bond_order|bond order]]. A Lewis structure adds the unshared electrons as dots, which shows the [[Lone_pair|lone pairs]] that shape a molecule and take part in [[Hydrogen_bond|hydrogen bonding]]. The line says nothing about the strength of the bond, which must be measured: breaking the single bond of hydrogen, `H₂ → 2H`, costs 436 kJ per mole, and the lines in a formula are best read as an inventory of electron pairs rather than as a statement about energies.[^blackstock-h2] Ionic bonds are not drawn as lines. An ionic compound's [[Chemical_formula|formula]], NaCl or MgCl₂, is an empirical ratio of ions in a lattice, and the charges are written on the ions, Na⁺ and Cl⁻, when the structure is shown. Polar covalent bonds are marked with partial charges, δ+ and δ−, at the two ends, or with an arrow pointing toward the more electronegative atom; the microsim's skewed cloud is that arrow drawn as electron density. The [[Chemical_polarity|polarity]] of a whole molecule is the vector sum of its bond dipoles, which is why carbon dioxide, with two polar C=O bonds pointing in opposite directions, has no net dipole moment while water, whose two O–H bonds are bent, does.[^os-af-ch4] ## Strong chemical bonds Strong bonds are the ones whose breaking changes the chemical identity of a substance. Their energies run from roughly 100 to 1000 kJ per mole, and the Portal Book's 436 kJ/mol for H–H is a representative single bond.[^blackstock-h2] All three types are the same physics, the electrostatic attraction of nuclei for electrons, differently distributed; the sim's cloud is the visual record of the distribution, and the triangle is the record of where a given pair of elements falls. ### Ionic bond An ionic bond forms when the electronegativity difference is large enough that one atom takes an electron from the other outright, which in practice means a metal of low [[Ionization_energy|ionization energy]] meeting a nonmetal of high electron affinity. In [[Sodium_chloride|sodium chloride]] the transfer itself costs energy, 496 kJ/mol to ionise sodium against 349 kJ/mol recovered when chlorine accepts the electron, and it is the lattice that pays: bringing the ions together into the crystal releases 787 kJ/mol, so that the compound forms with an overall enthalpy of −411 kJ/mol from its elements.[^blackstock-bh] That accounting, the [[Born–Haber_cycle|Born–Haber cycle]], is why the strength of an ionic bond is quoted as a [[Lattice_energy|lattice energy]] rather than a bond energy: an ion in a crystal is not bonded to one neighbour but to all six, or eight, around it. The sibling article on ionic bonding walks the reader through the pair potential and the lattice; here the sim's triangle simply places Na–Cl, at `ΔEN = 2.1`, on the ionic side.[^blackstock-en] ### Covalent bond A covalent bond is a shared pair of electrons whose density is concentrated between the two nuclei, where both attract it, so that the electron pair pulls the nuclei together while the nuclei's own repulsion holds them apart at the bond length. Between identical atoms, as in H₂, the sharing is exactly equal and the bond is nonpolar; the microsim's cloud is symmetric and its `ΔEN` readout is zero.[^blackstock-en] Between different atoms the pair sits closer to the more electronegative one, the bond has a dipole moment, and the sim's cloud leans. For H–Cl the Portal Book's `ΔEN` of 0.9 puts the bond well into the polar range, and Pauling's expression gives it 18 % ionic character (derived); for H–F at 1.9 the estimate is 59 %, yet the compound is a gas of discrete molecules, which is why the book keeps it on the covalent side of the line.[^blackstock-en][^pauling1960] Covalent bonds are directional, because the shared pair lies along the line between the nuclei, and that is what gives molecules definite shapes and bond angles; they can also be multiple, with two or three pairs shared, and the extra pairs shorten and strengthen the bond.[^os-af-ch4] ### Metallic bonding Metallic bonding is what happens at the bottom corner of the triangle, where both atoms hold their outer electrons loosely. Neither can take an electron from the other and neither can hold a shared pair in place, so the outer electrons leave their atoms altogether and move through the solid as a delocalised sea in which the cations sit.[^sanny-ch9] The sim's Na–Na and Cu–Cu presets show this as a cloud that spreads across the whole cell rather than concentrating between two nuclei. Because the electrons are free to move, metals conduct electricity and heat; because the bonding is not directional, the cations can slide past one another without the bonds breaking, which is why metals are ductile and malleable rather than brittle like ionic crystals. Alloys are possible for the same reason: a foreign atom of similar size can take a place in the lattice without disturbing a bond that was never localised. The [[Free_electron_model|free-electron model]] and its refinement into [[Electronic_band_structure|band structure]] are the quantitative theories, and they belong to the Physics and Materials flagships this sim is shared with.[^sanny-ch9] ## Intermolecular bonding Between molecules there are weaker attractions that do not change chemical identity but decide whether a substance is a gas, a liquid or a solid at a given temperature. The strongest is the hydrogen bond, in which a hydrogen atom already covalently bonded to nitrogen, oxygen or fluorine is attracted to a lone pair on a second such atom; water's high boiling point and the structure of ice are its work. Dipole–dipole attractions act between any polar molecules, and the [[London_dispersion_force|London dispersion force]], which arises from momentary fluctuations of the electron cloud, acts between all molecules and grows with the number of electrons.[^blackstock-imf] Together these are the [[Van_der_Waals_force|van der Waals forces]]; their energies are typically a few to a few tens of kJ per mole, an order of magnitude below the strong bonds, which is why molecular solids melt at low temperatures while ionic and metallic ones do not. The microsim's cloud is the seed of all of them: the skew that gives a bond its dipole is what one molecule presents to the next. ## Theories of chemical bonding The Lewis picture of shared and transferred pairs is still the working language of chemistry, and the quantitative theories are ways of computing what it describes. [[Valence_bond_theory|Valence bond theory]], from Heitler and London through Pauling, builds a molecule from atoms whose orbitals overlap; a bond is a pair of electrons in two overlapping [[Atomic_orbital|atomic orbitals]], and hybridisation and resonance are its tools for bond angles and delocalisation.[^heitler1927][^pauling1931] [[Molecular_orbital_theory|Molecular orbital theory]] instead spreads every electron over the whole molecule in [[Molecular_orbital|molecular orbitals]] formed from all the atomic orbitals at once; it handles delocalised and multiple bonding naturally, gives bond orders as half the difference between bonding and antibonding electrons, and explains why oxygen is paramagnetic, which the Lewis structure cannot.[^os-af-ch4] Both are approximations to the [[Schrödinger_equation|Schrödinger equation]], and the electronegativity that drives the microsim is itself an empirical summary of what those calculations find: electrons shift toward the atom whose orbitals lie lower in energy. For molecules and solids of any size the practical tool is [[Density_functional_theory|density functional theory]], which replaces the many-electron wavefunction by the electron density and rests on the theorems of Hohenberg and Kohn (1964) and the working equations of Kohn and Sham (1965).[^hohenberg1964][^kohnsham1965] Its output is exactly what the sim draws by hand: an electron-density map whose skew between two nuclei is the bond's polarity and whose integral over a region is the charge on an atom. The microsim's cloud is therefore ILLUSTRATIVE, a two-centre density shaped by `ΔEN` alone, while a computed density would also show the lone pairs, the multiple bonds and the crystal environment that the triangle leaves out. ## See also - [[Electronegativity]] - [[Covalent_bond]] - [[Metallic_bonding]] - [[Octet_rule]] - [[Chemical_polarity]] - [[Van_Arkel–Ketelaar_triangle]] - [[Ionic_bonding]] - [[Intermolecular_force]] - [[Bond_order]] - [[Linus_Pauling]] ## References [^os-af-ch4]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 4, "Chemical Bonding and Molecular Geometry", pp. 185–244 (§4.1 ionic bonding, §4.2 covalent bonding and electronegativity, molecular polarity; page to pin). Portal Book 051. https://openstax.org/details/books/chemistry-atoms-first-2e [^pauling1932]: Pauling, Linus (1932). "The Nature of the Chemical Bond. IV. The Energy of Single Bonds and the Relative Electronegativity of Atoms." *Journal of the American Chemical Society* 54 (9): 3570–3582. https://doi.org/10.1021/ja01348a011 [^blackstock-en]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter "Chemical Bonding I — Basic Concepts", pp. 232–236 (electronegativity bands; ΔEN examples on p. 234: H–H 0, H–Cl 0.9, Na–Cl 2.1; H–F 1.9 polar covalent; N–H 0.9; Mn–I 1.0 ionic). Portal Book 054. https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry [^pauling1960]: Pauling, Linus (1960). *The Nature of the Chemical Bond*, 3rd ed. Ithaca: Cornell University Press. Chapter 3, "The partial ionic character of covalent bonds and the relative electronegativity of atoms" (the relation `fraction ionic = 1 − exp(−ΔEN²/4)`; page to pin). [^jensen1995]: Jensen, William B. (1995). "A Quantitative van Arkel Diagram." *Journal of Chemical Education* 72 (5): 395–398. https://doi.org/10.1021/ed072p395 [^geoffroy1718]: Geoffroy, Étienne-François (1718). "Table des différents rapports observés en chimie entre différentes substances." *Mémoires de l'Académie Royale des Sciences* (1718): 202–212. [^newton-opticks]: Newton, Isaac (1718). *Opticks*, 2nd English edition. Book III, Query 31. [^dalton1808]: Dalton, John (1808). *A New System of Chemical Philosophy*, Part I. Manchester: R. Bickerstaff. [^berzelius1819]: Berzelius, Jöns Jacob (1819). *Essai sur la théorie des proportions chimiques et sur l'influence chimique de l'électricité*. Paris: Méquignon-Marvis. [^frankland1852]: Frankland, Edward (1852). "On a New Series of Organic Bodies Containing Metals." *Philosophical Transactions of the Royal Society of London* 142: 417–444. [^kekule1858]: Kekulé, August (1858). "Ueber die Constitution und die Metamorphosen der chemischen Verbindungen und über die chemische Natur des Kohlenstoffs." *Annalen der Chemie und Pharmacie* 106 (2): 129–159. [^lewis1916]: Lewis, Gilbert N. (1916). "The Atom and the Molecule." *Journal of the American Chemical Society* 38 (4): 762–785. https://doi.org/10.1021/ja02261a002 [^kossel1916]: Kossel, Walther (1916). "Über Molekülbildung als Frage des Atombaus." *Annalen der Physik* 354 (3): 229–362. [^langmuir1919]: Langmuir, Irving (1919). "The Arrangement of Electrons in Atoms and Molecules." *Journal of the American Chemical Society* 41 (6): 868–934. [^heitler1927]: Heitler, Walter; London, Fritz (1927). "Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik." *Zeitschrift für Physik* 44 (6–7): 455–472. https://doi.org/10.1007/BF01397394 [^pauling1931]: Pauling, Linus (1931). "The Nature of the Chemical Bond. Application of Results Obtained from the Quantum Mechanics and from a Theory of Paramagnetic Susceptibility to the Structure of Molecules." *Journal of the American Chemical Society* 53 (4): 1367–1400. https://doi.org/10.1021/ja01355a027 [^vanarkel1956]: van Arkel, Anton Eduard (1956). *Molecules and Crystals in Inorganic Chemistry*. London: Butterworths. [^ketelaar1958]: Ketelaar, Jan Arnold Albert (1958). *Chemical Constitution: An Introduction to the Theory of the Chemical Bond*, 2nd ed. Amsterdam: Elsevier. [^blackstock-h2]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter "Chemical Bonding I — Basic Concepts", p. 231 (bond dissociation of H₂ → 2H, +436 kJ/mol). Portal Book 054. [^blackstock-bh]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter "Chemical Bonding I — Basic Concepts", pp. 222–225 (Born–Haber cycle for NaCl: 107 + 496 + 122 − 349 + LE = −411 kJ/mol, so LE = −787 kJ/mol). Portal Book 054. [^sanny-ch9]: Sanny, Jeff; Ling, Samuel (2016). *University Physics Volume 3*. OpenStax. Chapter 9, "Condensed Matter Physics", pp. 393–440 (§9.1–9.2 ionic, covalent and metallic bonding; the free-electron model of metals; page to pin). Portal Book 079. https://openstax.org/details/books/university-physics-volume-3 [^blackstock-imf]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter "Intermolecular Forces and Liquids and Solids", pp. 363–381 (hydrogen bonding, dipole–dipole and dispersion forces; page to pin). Portal Book 054. [^hohenberg1964]: Hohenberg, Pierre; Kohn, Walter (1964). "Inhomogeneous Electron Gas." *Physical Review* 136 (3B): B864–B871. https://doi.org/10.1103/PhysRev.136.B864 [^kohnsham1965]: Kohn, Walter; Sham, Lu Jeu (1965). "Self-Consistent Equations Including Exchange and Correlation Effects." *Physical Review* 140 (4A): A1133–A1138. https://doi.org/10.1103/PhysRev.140.A1133 ## External links - [Chemistry: Atoms First 2e](https://openstax.org/details/books/chemistry-atoms-first-2e), OpenStax — Chapter 4, the open text behind Portal Book 051 - [University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3), OpenStax — Chapter 9, the open text behind Portal Book 079 - [Chemical Bonding and Organic Chemistry](https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry), Open Textbook Library record for Portal Book 054 - For the pair's other external links, see the Wikipedia article's *External links* section. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Chemical_bond.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Chemical bond* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Chemical_bond.html" data-title="Chemical bond"></div> *Built from `MICROSIM_GUIDE/specs/sims/Chemical_bond.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Chemical_bond) : [Wikitube](https://en.wikitube.io/wiki/Chemical_bond) · pinned revision [1368837112](https://en.wikipedia.org/w/index.php?oldid=1368837112) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. 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