Coordination Compounds

Addition compounds form when two or more stable compounds combine in a fixed ratio. Some, called double salts, lose their individual identity in water and dissociate completely into simple ions. Mohr's salt, FeSO₄.(NH₄)₂SO₄.6H₂O, is a double salt: in solution it gives Fe²⁺, NH₄⁺ and SO₄^2- ions that can each be detected by ordinary tests. Other addition compounds, called coordination compounds (complexes), keep their identity in solution. K₄[Fe(CN)₆] does not give a simple test for Fe²⁺ or free CN^-, because the [Fe(CN)₆]^4- ion stays intact as a single unit.

Alfred Werner explained this with two kinds of valence a metal shows. The primary valence is ionisable and is satisfied by negative ions; it corresponds to what we now call the oxidation state of the metal. The secondary valence is non-ionisable, is fixed for a given metal, and is satisfied by neutral or negatively charged groups called ligands bonded directly to the metal in a definite geometry; it corresponds to the coordination number. Werner proposed that these secondary valences are directed in fixed positions in space, which is why complexes adopt characteristic shapes such as octahedral, tetrahedral or square planar.

Worked example. Take CoCl₃.6NH₃, written today as [Co(NH₃)₆]Cl₃. Adding excess AgNO₃ precipitates all three chlorides as AgCl, showing all three Cl^- ions are free (ionisable). So the primary valence is 3, satisfied by the 3 Cl^- counter ions, and it matches the oxidation state of cobalt, +3. The six NH₃ molecules are bonded directly to Co and are not precipitated by AgNO₃; they satisfy the secondary valence, which is 6 - the coordination number of cobalt here. This 3 (ionisable) + 6 (non-ionisable, fixed geometry) split is exactly Werner's primary/secondary valence model.

The species written inside square brackets, [Co(NH₃)₆]³⁺, is the coordination entity (or complex ion); the metal inside it is a Lewis acid (electron-pair acceptor) and the surrounding groups are Lewis bases (electron-pair donors).

A ligand is an ion or molecule bonded directly to the central metal atom/ion, donating an electron pair through a donor atom. Ligands are classified by how many donor atoms they use to bind a single metal centre. A unidentate (monodentate) ligand binds through one donor atom, e.g. NH₃, H₂O, Cl^-, CN^-. A didentate (bidentate) ligand binds through two donor atoms simultaneously, e.g. ethane-1,2-diamine (en), H₂N-CH₂-CH₂-NH₂, and the oxalate ion, C₂O₄^2-. A polydentate ligand uses several donor atoms at once; EDTA^4- is hexadentate, using two N and four O donor atoms to wrap almost completely around a metal ion. Ligands that attach through two or more donor atoms to the same metal form a ring called a chelate ring, and this chelation gives chelate complexes extra stability (the chelate effect). An ambidentate ligand has two different possible donor atoms but uses only one at a time, e.g. NO₂^- can bind through N (nitro) or through O (nitrito), and SCN^- can bind through S or through N.

The coordination number (CN) of the central atom is the number of ligand donor atoms directly bonded to it - not simply the number of ligand molecules. In [PtCl₆]^2-, CN = 6 (six unidentate Cl^-). In [Co(en)₃]³⁺, only three ligand molecules are present, but each en is bidentate, so CN = 3 x 2 = 6. Common coordination numbers are 4 (tetrahedral or square planar) and 6 (octahedral); 2 (linear, e.g. [Ag(NH3)2]+) also occurs.

The coordination sphere is the metal plus its directly bonded ligands, written inside square brackets; any ions outside the brackets are counter ions that balance charge but are not directly bonded to the metal. The coordination polyhedron is the spatial arrangement of the donor atoms around the metal (octahedron for CN 6, tetrahedron or square for CN 4).

The oxidation number of the central metal is the charge it would carry if all ligands were removed along with the electron pairs shared with the metal. It is found from a simple charge balance: (oxidation number of metal) + (sum of charges of all ligands) = (overall charge of the coordination entity).

Worked example. Find the oxidation number of cobalt in [Co(NH₃)₅Cl]Cl₂. Two Cl^- ions are outside the bracket as counter ions, so the coordination entity [Co(NH₃)₅Cl] must carry a charge of +2. Inside the sphere, five NH₃ are neutral (0 x 5 = 0) and one Cl^- ligand contributes -1. Let x be the oxidation number of Co: x + 0 + (-1) = +2, so x = +3. Cobalt is in the +3 oxidation state, consistent with the compound's name, pentaamminechloridocobalt(III) chloride.

Coordination compounds are named using a systematic set of IUPAC rules so that a name uniquely describes the structure. The main rules used at this level are as follows.

• The cation is named before the anion, exactly as for simple ionic salts, regardless of whether the complex ion is the cation or the anion.
• Ligand names are listed in alphabetical order before the name of the metal (multiplying prefixes are ignored while alphabetising).
• Anionic ligand names take an -o ending: chlorido (Cl^-), cyanido (CN^-), oxalato (C₂O₄^2-), nitrito (ONO^-/NO₂^-), thiocyanato (SCN^-). Neutral ligands normally keep their molecular name, with a few common exceptions: aqua (H₂O), ammine (NH₃), carbonyl (CO), nitrosyl (NO).
• Multiplying prefixes: di-, tri-, tetra- are used for simple ligand names; bis-, tris-, tetrakis- (with the ligand name in parentheses) are used for bidentate/polydentate ligands or ligand names that already contain di/tri, e.g. bis(ethane-1,2-diamine).
• The oxidation state of the central metal is written as a Roman numeral in parentheses immediately after its name, with no space.
• If the complex ion is an anion, the metal name is given the suffix -ate (ferrate for Fe, cuprate for Cu, cobaltate for Co, plumbate for Pb, argentate for Ag).
• A neutral coordination compound (complex + no counter ion needed) is named as a single word.

Worked examples.

• [Co(NH₃)₆]Cl₃: six ammine ligands (all identical, alphabetically only one name needed) on Co in +3 state (worked out as in the previous section) with chloride counter ions -> hexaamminecobalt(III) chloride.
• K₄[Fe(CN)₆]: complex anion charge is -4 (from 4 K⁺); 6 CN^- = -6; x - 6 = -4, so x = +2. Anionic complex, so Fe -> ferrate -> potassium hexacyanidoferrate(II).
• [Pt(NH₃)₂Cl₂]: neutral complex, Pt is +2 (2 NH3 = 0, 2 Cl- = -2, overall charge 0, so x - 2 = 0, x = +2); ammine before chlorido alphabetically -> diamminedichloridoplatinum(II).
• [Co(en)₃]Cl₃: three bidentate en ligands need the tris- prefix; Co is +3 (each en is neutral, 3 Cl- outside balance +3) -> tris(ethane-1,2-diamine)cobalt(III) chloride.

Coordination compounds show two broad kinds of isomerism. Structural isomers have the same formula but different bonds/connectivity; stereoisomers have identical bonds but different spatial arrangement.

Structural isomerism occurs in several forms. Linkage isomerism arises with ambidentate ligands: [Co(NH₃)₅(NO₂)]Cl₂ (N-bonded, nitro) and [Co(NH₃)₅(ONO)]Cl₂ (O-bonded, nitrito) are linkage isomers. Ionisation isomerism occurs when a ligand and a counter ion exchange places, giving different ions on dissolving: [Co(NH₃)₅Br]SO₄ gives SO₄^2- in solution (tests positive for sulphate), while [Co(NH₃)₅SO₄]Br gives Br^- in solution (tests positive for bromide) instead. Coordination isomerism occurs in salts containing both a complex cation and a complex anion, where ligands can be distributed differently between the two metals, e.g. [Co(NH₃)₆][Cr(CN)₆] versus [Cr(NH₃)₆][Co(CN)₆]. Solvate (hydrate) isomerism occurs when water can sit inside or outside the coordination sphere: [Cr(H₂O)₆]Cl₃ (violet), [Cr(H₂O)₅Cl]Cl₂.H₂O (grey-green) and [Cr(H₂O)₄Cl₂]Cl.2H₂O (dark green) are solvate isomers that differ in colour and in how many Cl^- are precipitated instantly by AgNO₃.

Stereoisomerism has two types. Geometrical (cis-trans) isomerism occurs typically in square planar MA₂B₂ complexes and in octahedral MA₄B₂ or MA₃B₃ complexes. For square planar [Pt(NH₃)₂Cl₂], the cis isomer has the two NH₃ (and two Cl) mutually adjacent (90 degrees apart), while the trans isomer has them opposite each other (180 degrees apart) - exactly two geometrical isomers are possible. For an octahedral MA₃B₃ complex such as [Co(NH₃)₃Cl₃], the facial (fac) isomer has the three identical ligands occupying one triangular face of the octahedron, while the meridional (mer) isomer has them along a plane passing through the metal. Optical isomerism gives non-superimposable mirror images (enantiomers) and is common in octahedral complexes with chelating bidentate ligands: cis-[CoCl₂(en)₂]⁺ is chiral and exists as two enantiomers, whereas trans-[CoCl₂(en)₂]⁺ has an internal plane of symmetry and is optically inactive.

Worked example (why geometry matters medically). Of the two geometrical isomers of [Pt(NH₃)₂Cl₂], only the cis isomer (cisplatin) is used as an anticancer drug: its two Cl^- ligands, being adjacent, can both be displaced by adjacent bases on the same strand of DNA, cross-linking and disrupting replication in rapidly dividing cancer cells. The trans isomer, with the two Cl^- on opposite sides, cannot form this same cross-link geometry and is therapeutically ineffective - a direct consequence of geometrical isomerism.

Valence Bond Theory (VBT) treats metal-ligand bonds as coordinate covalent bonds formed by ligand lone pairs donating into empty hybrid orbitals of the metal. The hybridisation used fixes the geometry: sp³ gives a tetrahedral complex (e.g. [NiCl₄]^2-), dsp² gives a square planar complex (e.g. [Ni(CN)₄]^2-), and for coordination number 6 there are two options: d²sp³ hybridisation uses inner (n-1)d orbitals and gives an inner orbital (low-spin) octahedral complex, while sp³d² hybridisation uses outer nd orbitals and gives an outer orbital (high-spin) octahedral complex. Whether the inner d orbitals are available depends on whether the ligand is strong enough to force pairing of the metal's own d electrons first.

Worked example (VBT). Co³⁺ has a 3d⁶ configuration. In [CoF₆]^3-, F^- is a weak field ligand and does not force pairing, so the complex uses outer sp³d² hybridisation with 4 unpaired electrons remaining (high spin) - it is paramagnetic. In [Co(NH₃)₆]³⁺, NH₃ is a strong field ligand that pairs up all 6 d electrons into the three inner 3d orbitals, freeing two 3d orbitals for d²sp³ hybridisation (low spin, inner orbital complex) - all electrons are paired, so it is diamagnetic. VBT explains geometry and magnetism this way but does not explain colour, which is where Crystal Field Theory (CFT) is needed.

Crystal Field Theory treats ligands as point negative charges (or dipoles) that electrostatically repel the metal's d electrons. In a free metal ion all five d orbitals are degenerate (equal energy), but in an octahedral field the ligands approach along the axes, so orbitals pointing along the axes (d_z2, d_x2-y2) are repelled more than those pointing between the axes (d_xy, d_yz, d_xz). The five orbitals split into a lower-energy triply degenerate set called t_2g and a higher-energy doubly degenerate set called e_g, separated by the crystal field splitting energy, delta-o (also written 10Dq).

Whether electrons fill in a high-spin or low-spin pattern depends on delta-o compared with the pairing energy P (the energy cost of putting two electrons in the same orbital). If delta-o < P (weak field ligand), electrons singly occupy all five orbitals first (Hund's rule), giving a high-spin complex. If delta-o > P (strong field ligand), electrons fill t_2g completely (pairing up) before entering e_g, giving a low-spin complex. This only creates a choice for d⁴ to d⁷ configurations; d¹-d³ and d⁸-d¹⁰ configurations are unambiguous. Ligands are ranked by splitting strength in the spectrochemical series (weak to strong): I^- < Br^- < SCN^- < Cl^- < S^2- < F^- < OH^- < C₂O₄^2- < H₂O < NCS^- < edta^4- < NH₃ < en < CN^- ~ CO.

In a tetrahedral field the splitting pattern is inverted (e set lower, t₂ set higher) and much smaller, so tetrahedral complexes are almost always high spin. The Crystal Field Stabilisation Energy (CFSE) measures the net energy lowering from splitting and can be calculated for a given electron configuration.

Worked example (CFSE). For [Cr(H₂O)₆]³⁺, Cr³⁺ is d³ (Cr, Z = 24, loses 3 electrons from [Ar]3d⁵4s¹). With only 3 electrons, Hund's rule puts one in each t_2g orbital regardless of field strength: configuration t_2g³e_g⁰. CFSE = (-0.4 x 3 + 0.6 x 0) x delta-o = -1.2 delta-o. This substantial stabilisation is part of why d³ octahedral complexes such as [Cr(H₂O)₆]³⁺ are particularly stable and kinetically inert.

Colour in transition metal complexes arises from d-d transitions: an electron absorbs a photon of energy equal to delta-o and jumps from t_2g to e_g; the complementary colour of the absorbed wavelength is what we see. Complexes with d⁰ or d¹⁰ configurations have no d-d transition available and are colourless, e.g. [Sc(H₂O)₆]³⁺ (Sc³⁺ is d⁰) and [Zn(NH₃)₆]²⁺ (Zn²⁺ is d¹⁰), while [Ti(H₂O)₆]³⁺ (Ti³⁺, d¹) is purple.

Magnetic behaviour follows directly from the number of unpaired electrons, using the spin-only magnetic moment formula. Worked example. [Fe(H₂O)₆]²⁺: Fe²⁺ is d⁶ (Fe, Z = 26, loses 2 electrons from 4s); H₂O is a weak field ligand, giving a high-spin configuration t_2g⁴e_g² with n = 4 unpaired electrons. mu = square root of (n(n+2)) = square root of (4 x 6) = square root of 24 = 4.90 BM, so the ion is paramagnetic.

The thermodynamic stability of a complex in solution is measured by its stability constant (formation constant), K, for the equilibrium M + nL <=> ML_n. A larger K means the equilibrium lies further towards the complex, i.e. a more stable complex. Complex formation usually proceeds stepwise, each step having its own stepwise stability constant K₁, K₂, ... K_n; multiplying all the stepwise constants gives the overall (cumulative) stability constant, beta-n.

Worked example. Suppose a metal ion M forms ML and then ML₂ with stepwise stability constants K₁ = 1 x 10³ and K₂ = 1 x 10². The overall stability constant is beta₂ = K₁ x K₂ = (1 x 10³) x (1 x 10²) = 1 x 10⁵. This single number, beta₂ = [ML₂] / ([M][L]²), summarises the overall tendency of M and L to form the fully coordinated complex.

Several factors influence stability. A higher positive charge and smaller size of the central metal ion generally increase electrostatic attraction to ligands and raise stability. For divalent first-row transition metal ions the empirical Irving-Williams order of increasing stability is Mn²⁺ < Fe²⁺ < Co²⁺ < Ni²⁺ < Cu²⁺ > Zn²⁺. The nature of the ligand also matters strongly: chelating (bidentate/polydentate) ligands generally form far more stable complexes than a corresponding number of unidentate ligands, an effect called the chelate effect, and complexes with 5- or 6-membered chelate rings tend to be the most stable.

Coordination compounds are not just a theoretical topic - they underpin real applications. In metallurgy, silver and gold are extracted from their ores by leaching with cyanide ion, forming soluble complexes [Ag(CN)₂]^- and [Au(CN)₂]^-, from which the free metal is later recovered; nickel is purified via the volatile complex [Ni(CO)₄] (Mond process). In biological systems, many essential molecules are metal complexes: haemoglobin is an iron(II) complex (the heme porphyrin ring) that reversibly binds and transports O₂ in blood, chlorophyll is a magnesium complex central to photosynthesis, and vitamin B₁₂ (cyanocobalamin) is a cobalt complex. In medicine, cis-[Pt(NH₃)₂Cl₂] (cisplatin) is used as an anticancer drug, and EDTA is used in chelation therapy to treat poisoning by toxic metals such as lead, by forming a stable, excretable metal-EDTA complex. In analytical chemistry, characteristic colours of complexes are used for qualitative identification (e.g. Ni²⁺ gives a bright red precipitate with dimethylglyoxime) and EDTA-based complexometric titrations are used to quantitatively estimate the hardness of water (Ca²⁺ and Mg²⁺ content). Complex formation is also used in photography, where unreacted AgBr is dissolved off the film as the soluble thiosulfato complex [Ag(S₂O₃)₂]^3- during fixing, and in industrial catalysis (e.g. Wilkinson's catalyst for hydrogenation).