# Coordination complex A **coordination complex** is a chemical species in which a central [[Atom|atom]] or [[Ion|ion]], usually a [[Transition_metal|transition metal]], is bound to a surrounding set of molecules or ions called [[Ligand|ligands]]. Each ligand donates an electron pair to the metal, so the metal is the acid and the ligand the base in the sense of [[Lewis_acids_and_bases|Lewis acid–base theory]]. The number of donor atoms attached to the metal is its [[Coordination_number|coordination number]]; six is the most common value, with the ligands at the corners of an octahedron.[^openstax-ch19] Complexes give transition-metal chemistry its colors and magnetism and carry [[Oxygen|oxygen]] in blood as [[Hemoglobin|hemoglobin]]. In the microsim below the reader selects one of the five real d orbitals (dxy, dxz, dyz, dz², dx²−y²) and watches its lobe surface `r = |d(θ, φ)|` sit either on or between six point-charge ligands, which glow in proportion to the orbital amplitude along their axis; the energy tag `E = E0 + 3/5·Δo` (eg) or `E = E0 − 2/5·Δo` (t2g) answers which orbitals pay for pointing at the ligands and by how much.[^boyd-oh] On Wikitube's [[PORTAL_Chemistry|Chemistry]] flagship this is the main article for the Part XIII — Practice section *Inorganic chemistry: coordination complexes* (row K59); its sibling sim, the octahedral spin-state diagram, is the transition-metal family root and uses the same splitting bookkeeping. ## Nomenclature and terminology The metal and its directly bound ligands form the *coordination sphere*, written inside square brackets; counter-ions that balance the charge sit outside them, so in [Co(NH₃)₆]Cl₃ the cation [Co(NH₃)₆]³⁺ is the complex and the three chloride ions are counter-ions.[^openstax-ch19] The atom of the ligand that supplies the electron pair is the *donor atom*. A ligand with one donor atom is monodentate; one with two or more that bind the same metal is bidentate or polydentate, and the ring it closes with the metal is a *chelate* ring. Ethylenediamine (en) is the standard bidentate example and the EDTA⁴⁻ anion, with six donor atoms, the standard hexadentate one.[^openstax-ch19] Two numbers label every complex: the [[Oxidation_state|oxidation state]] of the metal and its d-electron count. Boyd's counting rule is `dⁿ = group number − oxidation state`, so the [[Iron|iron]] in [Fe(H₂O)₆]²⁺ (group 8, +2) is d⁶, FeCl₄⁻ (group 8, +3) is d⁵, and CoF₆³⁻ ([[Cobalt|cobalt]], group 9, +3) is d⁶.[^boyd-dn] ## History The modern picture is Alfred Werner's. In an 1893 paper in the *Zeitschrift für anorganische Chemie* he proposed that a metal has a "primary valence" (its oxidation state, satisfied by anions) and a "secondary valence" (its coordination number, satisfied by neutral or anionic ligands), and that the six ligands of a cobalt(III) ammine sit at the corners of an octahedron.[^werner1893] The rival chain theories predicted a different number of isomers for compounds such as [CoCl₂(NH₃)₄]⁺, and the counts came out Werner's way. He received the 1913 Nobel Prize in Chemistry for this work on the linkage of atoms in molecules, which opened new fields in [[Inorganic_chemistry|inorganic chemistry]].[^nobel1913] The electronic explanation of why the octahedron splits the d orbitals, crystal-field theory, came decades later and is the subject of *Electronic properties* below.[^boyd-assumptions] ## Structures Ligands range from single atoms and small ions (Cl⁻, CN⁻, O²⁻) through small molecules ([[Water|water]], [[Ammonia|ammonia]], carbon monoxide) to large organic and biological molecules, and a ligand may bridge two metals.[^openstax-ch19] The metal–ligand bond is a coordinate [[Covalent_bond|covalent bond]] in which both electrons come from the ligand; its strength runs from aqua ligands that exchange in microseconds to cyanide ligands that make a complex kinetically inert. Coordination numbers from two to nine are known, but four and six dominate the first-row transition metals, and the octahedron is the reference case for the whole subject.[^openstax-ch19] Polynuclear complexes hold several metals together through bridging ligands; the largest grade into clusters and, in biology, into the metal cofactors of [[Enzyme|enzymes]]. ## Geometry Geometry follows coordination number, with two possibilities at four and at five.[^openstax-ch19] | Coordination number | Geometry | Example | |---|---|---| | 2 | linear | [Ag(NH₃)₂]⁺ | | 4 | tetrahedral | [CoCl₄]²⁻ | | 4 | square planar | [PtCl₄]²⁻ | | 5 | trigonal bipyramidal or square pyramidal | [Fe(CO)₅] | | 6 | octahedral | [Fe(H₂O)₆]²⁺ | The octahedron is what the microsim draws. In the crystal-field model the six ligands are point charges at (±R, 0, 0), (0, ±R, 0) and (0, 0, ±R), one on each Cartesian axis, and the five d orbitals are compared against that frame.[^boyd-oh] The lobe surfaces in the sim are the standard real angular functions: dz² ∝ 3cos²θ − 1, dx²−y² ∝ sin²θ cos 2φ, dxy ∝ sin²θ sin 2φ, dxz ∝ sin θ cos θ cos φ and dyz ∝ sin θ cos θ sin φ.[^boyd-ylm] Along the +x axis (θ = 90°, φ = 0) the values are −1, +1, 0, 0 and 0 in those units, and along +z (θ = 0) they are +2, 0, 0, 0 and 0. The two orbitals with non-zero amplitude on the ligand axes, dz² and dx²−y², are the eg pair; the three with zero amplitude on every axis, dxy, dxz and dyz, are the t2g set, whose lobes thread between the ligands.[^boyd-oh] A tetrahedral complex puts its four ligands on alternating corners of a cube, which inverts the ordering, and a square-planar complex is an octahedron with the two axial ligands removed.[^boyd-td] ## Stereochemistry A fixed geometry still leaves choices about which ligand sits where, and complexes show every kind of [[Stereochemistry|stereoisomerism]] that organic molecules do, plus some of their own.[^openstax-ch19] ### Cis–trans isomerism and facial–meridional isomerism In an octahedral complex MA₄B₂ the two B ligands are either adjacent (cis, 90° apart) or opposite (trans, 180° apart). The same distinction exists in square-planar MA₂B₂ complexes: cisplatin, the anticancer drug, is the cis isomer of [PtCl₂(NH₃)₂], and the trans isomer is not an active drug.[^openstax-ch19] With three of each ligand, MA₃B₃, the three B ligands occupy one triangular face of the octahedron (facial, fac) or a meridian through it (meridional, mer). ### Optical isomerism An octahedral complex with three bidentate chelate rings, such as [Co(en)₃]³⁺, has no mirror plane and exists as a pair of non-superimposable mirror images, labelled Δ and Λ by the handedness of the propeller the rings form. This is [[Chirality_(chemistry)|chirality]] without a carbon stereocenter, and the resolution of such pairs was among the strongest confirmations of Werner's octahedral model.[^openstax-ch19] ### Other kinds of isomerism Linkage isomers bind an ambidentate ligand through different donor atoms: nitrite attaches through nitrogen (nitro, –NO₂) or oxygen (nitrito, –ONO). Ionization isomers swap a ligand with a counter-ion, as in [Co(NH₃)₅Br]SO₄ against [Co(NH₃)₅SO₄]Br; hydrate isomers do the same with water, and coordination isomers redistribute ligands between the cation and anion of a salt built from two complexes.[^openstax-ch19] ## Electronic properties The microsim's home is here. Crystal-field theory treats the ligands as six negative point charges on the axes and asks what they do to the five d orbitals, which are degenerate in the free ion. Boyd's text gives the result: the two eg orbitals, whose lobes meet the ligands head-on, rise to `E(eg) = E0 + (3/5)·Δo`, and the three t2g orbitals, whose lobes miss them, fall to `E(t2g) = E0 − (2/5)·Δo`, where Δo is the octahedral splitting and E0 is the energy the orbitals would have in a spherical field of the same total charge.[^boyd-oh] The average is unchanged: two orbitals up by 3/5 and three down by 2/5 give 6/5 − 6/5 = 0, the barycenter rule that the energy tag in the sim obeys.[^boyd-oh] The sim has one control, the orbital index, a categorical choice rather than a slider because no real-valued symbol stands behind it. Choosing dz² or dx²−y² lights the ligands on the axes the lobes hit and tags the orbital +3/5·Δo; choosing dxy, dxz or dyz leaves the six ligand spheres dark and tags it −2/5·Δo. A numerical check that the eg pair really is degenerate, and that the t2g set really escapes, comes from summing the squared normalized angular function over the six ligand directions: with dz² = √(5/16π)(3cos²θ − 1) and dx²−y² = √(15/16π) sin²θ cos 2φ, the sums are 2·(20/16π) + 4·(5/16π) = 60/16π for dz² and 4·(15/16π) = 60/16π for dx²−y², and exactly zero for all three t2g functions (computed here).[^boyd-ylm] The lobe surface is the angular function, not a probability isosurface, and the ligands are point charges, the crystal-field assumption of zero covalency; the sim is ILLUSTRATIVE for the geometry of the splitting, not a computed electron density.[^boyd-assumptions] Ligand-field theory, which replaces the point charges with [[Molecular_orbital|molecular orbitals]], keeps the same eg/t2g labels and the same bookkeeping.[^boyd-assumptions] For the hexaaqua ions of iron, Boyd quotes Δo = 9,350 cm⁻¹ for [Fe(H₂O)₆]²⁺ and 14,000 cm⁻¹ for [Fe(H₂O)₆]³⁺, about 112 and 167 kJ/mol (the conversion from wavenumbers is made here).[^boyd-series] For a given metal the size of Δo is set by the ligand, and the ordering of ligands by the splitting they produce is the [[Spectrochemical_series|spectrochemical series]]: I⁻ < Br⁻ < Cl⁻ < … < H₂O < NH₃ < en < … < CO, CN⁻.[^boyd-series] In a tetrahedral field the splitting is inverted and smaller, `ΔT = (4/9)·Δo` for the same metal and ligands, a relation Boyd warns "should not be taken too literally".[^boyd-td] ### Color of transition metal complexes Most d–d absorptions fall in or near the visible range, so the color of a complex is the complement of what it absorbs, and the position of the absorption follows Δo. The two iron values above set the scale: 9,350 cm⁻¹ corresponds to a wavelength of about 1,070 nm, in the near infrared, while 14,000 cm⁻¹ corresponds to about 714 nm, at the red edge of the visible spectrum (wavelengths computed here as 1/Δo).[^boyd-series] Replacing water with a stronger-field ligand pushes the absorption to higher wavenumber and shorter wavelength, and the color changes with it.[^boyd-series] Band intensity is measured as [[Absorbance|absorbance]] through the [[Beer–Lambert_law|Beer–Lambert law]]; d–d bands are weak because the parity selection rule forbids them in a centrosymmetric octahedron, while charge-transfer bands between ligand and metal are far stronger. ### Colors of lanthanide complexes The [[Lanthanide|lanthanide]] ions owe their colors to f–f transitions rather than d–d ones. The 4f orbitals are shielded inside the ion by the filled 5s and 5p shells, so the ligands barely perturb them; the absorption lines are sharp, weak and almost independent of which ligands are present, in contrast to the broad, ligand-sensitive bands of the transition metals. ### Magnetism The number of unpaired electrons in a complex is set by the competition between Δo and the pairing energy Π, and is read out through the magnetic moment. Boyd's rule for d⁴–d⁷ octahedral complexes is high spin if Π > Δo and low spin if Π < Δo.[^boyd-dn] The spin-only moment for n unpaired electrons is `μ_eff = μB·√(n(n + 2))`, with the Bohr magneton μB = 9.274 × 10⁻²⁴ J/T, giving 1.73, 2.83, 3.87, 4.90 and 5.92 μB for one to five unpaired electrons.[^boyd-mag] A d⁶ ion such as [Fe(H₂O)₆]²⁺ therefore carries four unpaired electrons and 4.90 μB in its high-spin ⁵T2g ground state but no moment at all in the low-spin ¹A1g state.[^boyd-mag] The bulk property is the susceptibility, which for isolated moments follows the Curie law `χ = N·μ0·μ²/(3·kB·T)`.[^boyd-mag] The spin-only formula assumes a free-electron g of 2 (measured: 2.0023), holds only for A and E ground terms, and is unreliable for second- and third-row metals.[^boyd-mag] Tetrahedral complexes, with their smaller ΔT, are almost always high spin.[^boyd-assumptions] ### Reactivity Complexes react by exchanging ligands, by transferring electrons, and by activating the ligands they hold. Ligand substitution runs from labile complexes, whose aqua ligands exchange in less than a second, to inert ones such as chromium(III) and low-spin cobalt(III), where the filled or half-filled t2g set makes losing a ligand costly. [[Redox|Redox]] reactions between complexes go by an outer-sphere path, in which only an electron crosses between intact coordination spheres, or an inner-sphere path, in which a bridging ligand carries it. ## Classification Complexes are sorted by the kind of ligand and the kind of bond. Classical or Werner-type complexes carry ligands that bind through lone pairs on N, O or halogen donors — ammines, aqua ions, halides and chelates — and are the subject of most of this article. Organometallic complexes carry at least one metal–carbon bond, from carbonyls and alkyls to the π-bound alkenes of homogeneous catalysts. Bioinorganic complexes are the metal sites of proteins and cofactors, and cluster compounds hold several metals in direct contact. ## Nomenclature of coordination compounds The systematic names follow the rules the OpenStax text lays out: the cation is named before the anion; within a complex the ligands are listed alphabetically before the metal; the number of each ligand is shown by di-, tri-, tetra-, penta- and hexa-; anionic ligands end in -o (chloro, cyano, hydroxo, oxalato) while neutral ligands keep their names, with ammine for NH₃, aqua for H₂O and carbonyl for CO; the metal's oxidation state follows in Roman numerals; and an anionic complex gives its metal the ending -ate.[^openstax-ch19] So [Co(NH₃)₆]Cl₃ is hexaamminecobalt(III) chloride, K₄[Fe(CN)₆] is potassium hexacyanoferrate(II), and [Pt(NH₃)₂Cl₂] is diamminedichloroplatinum(II).[^openstax-ch19] The 2005 IUPAC recommendations spell anionic ligand names with -ido (chlorido, cyanido), so the same compounds appear in newer literature as hexacyanidoferrate(II) and diamminedichloridoplatinum(II).[^iupac2005] ## Stability constant The formation of a complex from the hydrated metal ion and its ligands is an equilibrium, and the [[Equilibrium_constant|equilibrium constant]] for forming it is the formation or stability constant Kf. For Ag⁺ + 2NH₃ ⇌ [Ag(NH₃)₂]⁺, Kf = 1.7 × 10⁷, and the OpenStax text tabulates constants for dozens of complexes in its Appendix K.[^openstax-appK] Ligands add one at a time, so an overall constant βn is the product of stepwise constants K₁K₂…Kn. Chelating ligands form far more stable complexes than the same number of comparable monodentate ligands, an effect that is largely entropic, because one polydentate ligand replacing several separate ligands releases molecules into solution. In the chelate example worked in Boyd's Chapter 8, the entropy term −TΔS° = −43.0 kJ/mol supplies most of the −55.3 kJ/mol of ΔG°, which corresponds to K ≈ 4.7 × 10⁹.[^boyd-chelate] The constant connects to the [[Gibbs_free_energy|Gibbs free energy]] through `ΔG° = −RT·ln K`, and a ligand that binds a metal strongly can pull an otherwise insoluble salt into solution.[^openstax-appK] ## Application of coordination compounds Complexes matter in three places: in living systems, in industry and in the analytical laboratory. ### Bioinorganic chemistry The oxygen carrier [[Hemoglobin|hemoglobin]] holds each of its four iron atoms in a porphyrin ring, with a histidine nitrogen below the plane and the O₂ molecule binding above it; chlorophyll holds magnesium in a related ring; and vitamin B₁₂ is a cobalt complex with a metal–carbon bond, one of the few organometallic species in biology.[^openstax-ch19] Metal ions are also the working parts of many enzymes, from the zinc of carbonic anhydrase to the manganese–calcium cluster of the [[Oxygen-evolving_complex|oxygen-evolving complex]] in photosynthesis. ### Industry Homogeneous catalysts are coordination complexes designed to bind a substrate, transform it and release the product; hydroformylation with cobalt and rhodium carbonyls and the polymerisation of alkenes with titanium-based Ziegler–Natta catalysts are the classic examples in the [[Chemical_industry|chemical industry]]. Complexes also serve as pigments such as Prussian blue, as the soluble metal species in electroplating baths, and as the chelating agents that soften water and treat heavy-metal poisoning by wrapping the offending ion in EDTA.[^openstax-ch19] ### Analysis [[Analytical_chemistry|Analytical chemistry]] uses complex formation in two ways. Complexometric [[Titration|titration]] with EDTA measures calcium and magnesium in water, because the hexadentate ligand binds each ion 1 : 1 up to a sharp end point signalled by a metal-ion indicator. [[Spectrophotometry|Spectrophotometry]] uses a ligand that turns the metal into an intensely colored complex, such as the red iron(II)–phenanthroline complex, and reads the concentration from the absorbance through the Beer–Lambert law. ## See also - [[Crystal_field_theory]] - [[Ligand_field_theory]] - [[Spectrochemical_series]] - [[Octahedral_molecular_geometry]] - [[Ligand]] - [[Coordination_number]] - [[Transition_metal]] - [[Atomic_orbital]] - [[Lewis_acids_and_bases]] - [[Hemoglobin]] ## References [^boyd-oh]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 8, Ligand Field Theory, pp. 195–197 (octahedral point charges on the axes; eg and t2g energies +3/5 and −2/5 Δo). https://open.umn.edu/opentextbooks/textbooks/exploring-inorganic-and-organometallic-chemistry [^boyd-td]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 8, pp. 198–201 (tetrahedral ligands on alternating cube corners; ΔT = (4/9)Δo and its caveat). [^boyd-dn]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 8, pp. 201–203 and p. 209 (dⁿ = group − oxidation state; high spin if Π > Δo; FeCl₄⁻ as d⁵ and CoF₆³⁻ as d⁶). [^boyd-series]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 8, pp. 210–211 (Δo of the iron hexaaqua ions; the spectrochemical series). [^boyd-mag]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 9, §9.9–9.10, pp. 268–273 (Curie law; spin-only moment; Table 9.2 unpaired electrons and moments; g factor; limits of the formula). [^boyd-assumptions]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 8, pp. 193–194 and p. 219 (zero-covalency assumption of crystal-field theory; ligand-field theory; tetrahedral complexes almost always high spin). [^boyd-chelate]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 8, p. 197 (chelate formation example: ΔG° = −55.3 kJ/mol, −TΔS° = −43.0 kJ/mol, K ≈ 4.7 × 10⁹). [^boyd-ylm]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 1, Table 1.2, p. 29 (angular functions; the real d combinations are the standard chemists' convention supplied here in normalized form). [^openstax-ch19]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 19, Transition Metals and Coordination Chemistry, pp. 929–970 (page to pin). https://openstax.org/details/books/chemistry-atoms-first-2e [^openstax-appK]: Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Appendix K, Formation Constants for Complex Ions, pp. 1123–1124; Chapter 15, Equilibria of Other Reaction Classes, pp. 719–752 (page to pin). https://openstax.org/details/books/chemistry-atoms-first-2e [^werner1893]: Werner, Alfred (1893). "Beitrag zur Konstitution anorganischer Verbindungen." *Zeitschrift für anorganische Chemie* 3: 267–330. [^nobel1913]: Nobel Prize Outreach. "The Nobel Prize in Chemistry 1913." NobelPrize.org. https://www.nobelprize.org/prizes/chemistry/1913/summary/ [^iupac2005]: Connelly, N. G.; Damhus, T.; Hartshorn, R. M.; Hutton, A. T., eds. (2005). *Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005*. RSC Publishing (the "Red Book"). ## Further reading - Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry* — Chapter 8 (Ligand Field Theory) and Chapter 9 (Magnetism); on the Portal Books shelf as book 052. - Flowers, Paul; Neth, Edward; Robinson, William, et al. (2019). *Chemistry: Atoms First 2e*, OpenStax — Chapter 19 (Transition Metals and Coordination Chemistry) and Appendix K; book 051. ## External links - [Chemistry: Atoms First 2e](https://openstax.org/details/books/chemistry-atoms-first-2e), OpenStax — free online text with Chapter 19 on coordination chemistry - [Exploring Inorganic and Organometallic Chemistry](https://open.umn.edu/opentextbooks/textbooks/exploring-inorganic-and-organometallic-chemistry), Open Textbook Library record - The Wikipedia pair's *External links* section lists further reference sites <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Coordination_complex.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Coordination complex* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Coordination_complex.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Coordination_complex.html" data-title="Coordination complex"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Coordination_complex) : [Wikitube](https://en.wikitube.io/wiki/Coordination_complex) · pinned revision [1374365003](https://en.wikipedia.org/w/index.php?oldid=1374365003) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. 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