Coordination Compounds

The chapter has five connected parts. First is history and Werner's theory — why primary and secondary valence had to be invented, and how the cobalt-ammine colour series proved it. Second is vocabulary: coordination entity, ligand, denticity, coordination number, coordination sphere, coordination polyhedron, oxidation number, homoleptic and heteroleptic. Third is IUPAC nomenclature, the rule-based skill examiners test most literally, both formula-to-name and name-to-formula. Fourth is isomerism, split into stereoisomerism (geometrical and optical) and structural isomerism (linkage, coordination, ionisation and solvate) — a rich source of "how many isomers" and "is this chiral" questions. Fifth, the conceptual heart for JEE and NEET, is bonding: Valence Bond Theory's hybridisation-and-magnetism story and Crystal Field Theory's d-orbital splitting, spectrochemical series and colour explanation, closing with the synergic bonding of metal carbonyls and the practical reach of coordination chemistry in analysis, metallurgy, biology and medicine.

Werner's theory of coordination compounds

Alfred Werner measured how many moles of AgCl precipitated per mole of a cobalt(III) chloride-ammonia compound with excess silver nitrate, alongside solution conductivity. The results only made sense if a fixed number of groups — six, here — stayed bonded to cobalt regardless of which groups they were, and only the rest were free to precipitate.

Werner's 1898 theory rests on four postulates: metals show two kinds of linkage — primary valence, ionisable and satisfied by negative ions, and secondary valence, non-ionisable, satisfied by neutral molecules or negative ions, and numerically equal to the coordination number, fixed for a given metal. Groups held by secondary linkages occupy characteristic spatial arrangements, coordination polyhedra — octahedral, tetrahedral and square planar are commonest; [Co(NH3)6]3+ is octahedral, [Ni(CO)4] tetrahedral, [PtCl4]2- square planar. The green and violet compounds share the identical empirical formula CoCl3.4NH3 yet are distinct substances — an early example of isomerism, and one of the clues that forced chemists to accept a genuine three-dimensional geometry around the metal. In modern language, primary valence is the metal's oxidation state and secondary valence its coordination number. A related distinction worth fixing early is double salt versus complex. Both form from stoichiometric combination of stable compounds, but a double salt such as carnallite (KCl.MgCl2.6H2O) or Mohr's salt (FeSO4.(NH4)2SO4.6H2O) dissociates completely into simple ions in water, giving the normal tests for Fe2+, NH4+ and SO4^2-. A complex ion such as [Fe(CN)6]4- does not dissociate into Fe2+ and CN- in solution — which is why K4[Fe(CN)6] gives no test for free Fe2+ or free CN-.

Key terms: ligands, denticity and coordination number

A coordination entity is the central metal atom or ion with the fixed set of ions or molecules bonded to it, written inside square brackets — [CoCl3(NH3)3], [Ni(CO)4], [Fe(CN)6]4-. The metal is the central atom or ion, often called a Lewis acid since it accepts electron pairs. The ligands are the ions or molecules donating those pairs: simple ions such as Cl-, small molecules such as H2O or NH3, or larger polydentate species such as ethane-1,2-diamine or hexadentate EDTA4-. Ligands are classified by denticity, the number of donor atoms one ligand uses to bind a single metal simultaneously. A ligand binding through one atom (Cl-, H2O, NH3) is unidentate; through two donor atoms at once (ethane-1,2-diamine, en; oxalate, C2O4^2-) is didentate; through several is polydentate. When a di- or polydentate ligand grips one metal through two or more donor atoms simultaneously it forms a ring and is a chelate ligand — chelate complexes are more stable than similar complexes built from unidentate ligands alone, the chelate effect. EDTA4- is the classic hexadentate chelating ligand, binding through two nitrogen and four oxygen atoms. An ambidentate ligand has two different possible donor atoms: NO2- can bind through nitrogen (nitrito-N) or oxygen (nitrito-O), and SCN- through sulphur or nitrogen. The coordination number (CN) is the number of ligand donor atoms directly bonded to the metal — not the number of ligand molecules. In [PtCl6]2- and [Ni(NH3)4]2+, CN is 6 and 4, one bond per unidentate ligand. But in [Fe(C2O4)3]3- and [Co(en)3]3+, only three ligand molecules are present, yet CN is 6 for both, because oxalate and en are each didentate. Only sigma bonds count toward coordination number; any pi bonding is not counted.

Coordination sphere, oxidation number and heteroleptic complexes

The central atom and its directly bonded ligands, in square brackets, form the coordination sphere; ionisable groups outside are counter ions. In K4[Fe(CN)6], the coordination sphere is [Fe(CN)6]4- and the counter ion is K+. The spatial arrangement of directly bonded ligand atoms defines the coordination polyhedron — octahedral, tetrahedral or square planar are commonest. The oxidation number of the central atom is the charge it would carry if every ligand were removed with the electron pairs it shares with the metal; written as a Roman numeral after the entity's name, e.g. Cu(I) in [Cu(CN)4]3-. Complexes are homoleptic if bonded to only one kind of donor group ([Co(NH3)6]3+) and heteroleptic if bonded to more than one kind ([Co(NH3)4Cl2]+).

IUPAC nomenclature of coordination compounds

For formulas: the central atom is listed first; ligands follow in alphabetical order regardless of charge; polyatomic ligand formulas and abbreviations sit in parentheses; the whole coordination entity, charged or not, sits inside square brackets with no internal spaces; a charged entity's charge is a right superscript outside the bracket, number before sign, as in [Co(CN)6]3-. For names, the cation is named first, whichever side of the compound it falls on. Ligands are named alphabetically before the metal — reversed from formula order. Anionic ligand names end in -o (chlorido, cyanido, oxalato); neutral ligands mostly keep special names (aqua for H2O, ammine for NH3, carbonyl for CO, nitrosyl for NO). Prefixes mono, di, tri, tetra count simple ligand names; bis, tris, tetrakis (ligand name in parentheses) are used instead when the ligand's own name already contains a number or is a complex polydentate name — [NiCl2(PPh3)2] is dichloridobis(triphenylphosphine)nickel(II). The metal's oxidation state follows as a Roman numeral. A cationic or neutral entity keeps the ordinary element name; an anionic entity takes the suffix -ate, sometimes on a Latin root (ferrate, argentate, plumbate). Two examples fix the pattern. [Cr(NH3)3(H2O)3]Cl3 is triamminetriaquachromium(III) chloride: three chlorides balance a +3 cation, and since ammine and aqua are neutral, chromium carries the +3. [Ag(NH3)2][Ag(CN)2] is diamminesilver(I) dicyanidoargentate(I), the same metal named differently as cation and anion.

Isomerism in coordination compounds — stereoisomerism

Isomers share a chemical formula but differ in atomic arrangement. Stereoisomers have identical bonds but different spatial arrangement, splitting into geometrical and optical isomerism.

Geometrical isomerism arises in heteroleptic complexes from different possible ligand arrangements, significant chiefly at coordination numbers 4 and 6. In a square planar [MX2L2], the two X ligands sit adjacent (cis) or opposite (trans) — [Pt(NH3)2Cl2] is the classic case. A square planar MABXL shows three isomers, two cis and one trans. Tetrahedral geometry shows none, since every ligand position is equivalent to every other. In octahedral [MX2L4], such as [Co(NH3)4Cl2]+, X can again be cis or trans, and the same distinction reappears for octahedral [MX2(L-L)2] with two didentate ligands, such as [CoCl2(en)2]+. A further octahedral pattern arises in [Ma3b3], such as [Co(NH3)3(NO2)3]: three donor atoms of one ligand on adjacent corners of an octahedral face give the facial (fac) isomer; around the meridian instead gives the meridional (mer) isomer.

Optical isomerism occurs when two forms of an entity are non-superimposable mirror images, enantiomers; such species are chiral. The two forms are dextro (d) and laevo (l) by which way they rotate plane-polarised light. Optical isomerism is common in octahedral complexes with didentate ligands, such as [Co(en)3]3+. In [PtCl2(en)2]2+, only the cis isomer is optically active — trans has a mirror plane and is superimposable on its reflection.

Isomerism in coordination compounds — structural isomerism

Structural isomers differ in which bonds are present, not just spatial arrangement, and coordination compounds show four kinds. Linkage isomerism arises with ambidentate ligands: thiocyanate can bind as M-NCS or M-SCN, and Jorgensen found [Co(NH3)5(NO2)]Cl2 exists as a red form bonded through oxygen (-ONO) and a yellow form bonded through nitrogen (-NO2). Coordination isomerism occurs when ligands interchange between the cationic and anionic entities of different metals in one compound — [Co(NH3)6][Cr(CN)6] versus its isomer [Cr(NH3)6][Co(CN)6]. Ionisation isomerism happens when the counter ion is itself a potential ligand that can trade places with one already coordinated — [Co(NH3)5(SO4)]Br and [Co(NH3)5Br]SO4 are distinguishable because only the second gives a precipitate with AgNO3 (free Br-) while only the first gives one with BaCl2 (free SO4^2-). Solvate isomerism (hydrate isomerism, for water) differs by whether a solvent molecule is bonded to the metal or merely trapped in the lattice — [Cr(H2O)6]Cl3 (violet) versus [Cr(H2O)5Cl]Cl2.H2O (grey-green).

Valence Bond Theory: hybridisation and magnetic behaviour

Valence Bond Theory (VBT) proposes the metal, under the ligands' influence, hybridises a set of its (n-1)d, ns, np or ns, np, nd orbitals into equivalent orbitals of definite geometry, which overlap with filled ligand orbitals donating electron pairs.

For an octahedral complex, the choice between d2sp3 and sp3d2 depends on whether the ligand field is strong enough to force the metal's (n-1)d orbitals to empty and pair first. If it does, those orbitals join the hybrid set — an inner orbital, or low spin, complex, as in diamagnetic [Co(NH3)6]3+, where Co3+ (3d6) pairs all six electrons into three t2g-type orbitals. If the field is weak, the metal's nd orbitals are used instead, leaving (n-1)d electrons unpaired — an outer orbital, or high spin, complex, as in paramagnetic [CoF6]3- (sp3d2, four unpaired). The same logic gives tetrahedral [NiCl4]2- (sp3, two unpaired, paramagnetic) against diamagnetic [Ni(CO)4] (Ni in the zero oxidation state, no unpaired electrons), and square planar [Ni(CN)4]2- (dsp2, diamagnetic, since CN- is strong enough to pair all of Ni2+'s 3d8 electrons). VBT explains formation, geometry and magnetism reasonably well, but has real limits: it rests on assumptions, gives no quantitative account of magnetic data, cannot explain colour, gives no quantitative thermodynamic or kinetic picture, cannot reliably predict tetrahedral versus square planar, and does not distinguish weak from strong ligands except by fitting observed magnetism after the fact.

Crystal Field Theory: splitting the d orbitals

Crystal Field Theory (CFT) treats the metal-ligand bond as purely electrostatic, ligands as point negative charges or point dipoles. In an isolated ion, the five d orbitals are degenerate; a spherical field keeps them so, but six ligands approaching along the axes of an octahedral complex give a non-spherical field. The two orbitals pointing directly at the ligands, dx2-y2 and dz2, feel more repulsion and rise, forming the higher eg set; the three orbitals pointing between ligand directions, dxy, dyz, dxz, fall, forming the lower t2g set.

where: Delta-o is the crystal field splitting energy for an octahedral field. Its magnitude depends on the ligand and metal charge; ligands giving large Delta-o are strong field, small Delta-o are weak field, ranked experimentally as the spectrochemical series:

For d1-d3, electrons fill the three t2g orbitals singly by Hund's rule, no ambiguity. At d4 a real choice appears: the fourth electron pairs in t2g (cost P) or occupies eg (cost Delta-o). If Delta-o less than P (weak field), it goes to eg, giving t2g3eg1, a high spin complex. If Delta-o greater than P (strong field), it pairs within t2g, giving t2g4eg0, a low spin complex. Calculations show d4-d7 configurations are always more stable strong-field/low-spin than weak-field/high-spin, for the same ligand set. In a tetrahedral field the splitting inverts and shrinks, since no ligand points directly at any orbital.

where: Delta-t is the tetrahedral splitting. Since Delta-t is almost always smaller than the pairing energy, tetrahedral complexes are essentially always high spin. The "g" subscript (gerade) used for octahedral and square planar levels is dropped for tetrahedral complexes, which lack a centre of symmetry.

Colour in coordination compounds

Coordination compounds are famous for colour, and CFT explains it through d-d transitions: light of the right energy excites an electron from t2g to eg, and observed colour is complementary to absorbed colour — absorb blue-green, appear red. In octahedral [Ti(H2O)6]3+ (d1), the single electron sits in t2g in the ground state; absorbing blue-green light (about 500 nm) promotes it to eg, and the compound appears violet. Colour depends entirely on the ligand field: remove the ligands, and there is no splitting and no d-d transition, so the substance turns colourless — heating [Ti(H2O)6]Cl3 to drive off water leaves a colourless solid, and anhydrous CuSO4 is white while CuSO4.5H2O is blue. Colour also tracks ligand identity: adding en progressively to [Ni(H2O)6]2+ (green) gives [Ni(H2O)4(en)]2+ (pale blue), then [Ni(H2O)2(en)2]2+ (blue-purple), then [Ni(en)3]2+ (violet), each substitution changing Delta-o. The same physics colours gemstones: ruby is Al2O3 with trace Cr3+ in octahedral sites, and emerald is the same Cr3+ centre in beryl, where the altered field shifts the absorbed wavelengths from red to green. CFT's real weakness: point charges predict anionic ligands should split the most, yet I-, Br- and Cl- sit at the weak end of the spectrochemical series, while CN- and CO sit at the strong end, and CFT ignores genuine covalent character in the metal-ligand bond. These gaps are addressed by Ligand Field Theory and Molecular Orbital Theory, beyond this chapter's scope.

Bonding in metal carbonyls: the synergic effect

Most transition metals form homoleptic carbonyls with simple, well-defined structures: [Ni(CO)4] is tetrahedral, [Fe(CO)5] trigonal bipyramidal, [Cr(CO)6] octahedral. Polynuclear carbonyls occur too: [Mn2(CO)10] is two square-pyramidal Mn(CO)5 units joined by an Mn-Mn bond, and [Co2(CO)8] has a Co-Co bond bridged by two CO groups. The M-C bond has both sigma and pi character. The M-C sigma bond forms as the lone pair on carbonyl carbon donates into a vacant metal orbital. The M-C pi bond forms oppositely: a filled metal d orbital donates into CO's empty antibonding pi* orbital. This mutual donation is a synergic effect — sigma donation makes the metal more electron-rich, favouring pi back donation, while back donation relieves electron density on the metal, favouring further sigma donation — strengthening the overall M-CO bond beyond either contribution alone.

Applications of coordination compounds

In analytical chemistry, chelating reagents such as EDTA and DMG underlie detection and titration of metal ions — water hardness is measured by titrating Ca2+ and Mg2+ with Na2EDTA, the two distinguished by their differing complex stability constants. In metallurgy, gold and silver are extracted as [Au(CN)2]- before displacement by zinc; impure nickel is purified via volatile [Ni(CO)4], later decomposed to deposit pure metal. In biology, chlorophyll (Mg), haemoglobin (Fe) and vitamin B12 (Co) are coordination compounds, as are enzymes like carboxypeptidase A. In industry, Wilkinson's catalyst [(Ph3P)3RhCl] hydrogenates alkenes, and [Ag(CN)2]- and [Au(CN)2]- give smoother electroplating than simple metal-ion solutions. In photography, unreacted AgBr dissolves out as [Ag(S2O3)2]3-. In medicine, EDTA treats lead poisoning, chelating agents remove excess copper and iron, and platinum complexes including cis-platin inhibit tumour growth.

Board level - Oxidation state, coordination number and IUPAC name of a hexacyanidoferrate complex

For K3[Fe(CN)6], find (a) the oxidation state of iron, (b) the coordination number of iron, and (c) the IUPAC name.

Step 1. Three K+ carry a total of +3, so [Fe(CN)6] must carry -3 to keep the compound neutral.

Step 2. Six CN- contribute 6 times (-1) = -6. If x is iron's oxidation state, x + (-6) = -3, so x = +3.

Step 3. Cyanide is unidentate; six bonded directly to iron give coordination number 6, geometry octahedral.

Step 4. Potassium is named first. Cyanide as ligand is cyanido, six as hexa. Since the entity is an anion, iron takes the Latin-derived suffix, ferrate, plus the oxidation state. Answer: iron is +3, coordination number 6, and the compound is potassium hexacyanidoferrate(III).

Competitive level (JEE / NEET) - From a measured magnetic moment to hybridisation and spin state

An octahedral complex of Mn2+ (3d5) has a measured magnetic moment of 5.9 BM. Find the number of unpaired electrons, state high spin or low spin, and identify the hybridisation.

Step 1. Using $\mu = \sqrt{n(n+2)}\ \text{BM}$: n = 1 gives 1.73 BM; n = 3 gives 3.87 BM; n = 5 gives square root of 35 = 5.92 BM, matching the measured 5.9 BM almost exactly.

Step 2. With n = 5 out of five possible 3d electrons, every d electron in Mn2+ is unpaired — only the high-spin configuration t2g3eg2 achieves this.

Step 3. High spin means a weak field (Delta-o less than P), consistent with H2O or F- rather than a strong ligand like CN-, which would force pairing down to one unpaired electron.

Step 4. With no 3d orbitals freed by pairing, the complex cannot use d2sp3; it must use outer 4d orbitals: sp3d2, an outer orbital complex. Answer: n = 5 unpaired electrons, high spin, outer orbital, sp3d2 hybridisation — consistent with [Mn(H2O)6]2+. Timing note: under two minutes. Testing n = 5 first in the spin-only formula is the fast path, since 5.9 BM is far too large for any low-spin d5 or d6 case, which top out near 1.73-4.90 BM. Once n equals the full electron count for the configuration, the field must be weak and hybridisation must be the outer-orbital one.

Competitive level (JEE / NEET) - Counting geometrical isomers and identifying the optically active one

For [CoCl2(en)2]+, describe all geometrical isomers, and state which (if any) is optically active.

Step 1. Coordination number is 6 (two unidentate Cl-, two didentate en: 2 + 2x2 = 6), an [MX2(L-L)2] type, the pattern giving cis and trans isomers.

Step 2. In trans, the two Cl- occupy opposite corners, the two en ligands sharing the remaining positions symmetrically.

Step 3. In cis, the two Cl- occupy adjacent corners. Testing mirror symmetry: trans has a mirror plane through both axial Cl atoms and the metal, so it is superimposable on its reflection (achiral); cis has no such plane, so its mirror image is a distinct, non-superimposable enantiomer.

Step 4. So [CoCl2(en)2]+ has two geometrical isomers, cis and trans, and only cis is chiral, giving a d/l enantiomer pair — matching [PtCl2(en)2]2+ in the chapter. Answer: two geometrical isomers (cis and trans); only cis is optically active, giving two further enantiomers. Timing note: about ninety seconds once the ligand count is right. Test the trans form for a mirror plane first — if one survives, trans is never chiral, leaving cis as the only candidate and saving a full structural comparison.

The most frequent slip is treating coordination number as "the number of ligands," when it counts donor atoms — [Co(en)3]3+ has three ligand molecules but coordination number 6, since en is didentate. A second error confuses oxidation number with coordination number, unrelated quantities that only sometimes coincide numerically. Third, ligand alphabetical order ignores multiplying prefixes: "diammine" alphabetises under "a," and the choice of di/tri versus bis/tris depends on whether the ligand's own name already contains a number. Fourth, an anionic coordination entity does not take "-ide" like a simple ion — the correct suffix is "-ate," sometimes on a Latin root (ferrate, argentate, plumbate). Fifth, tetrahedral complexes never show cis-trans isomerism, since all four positions are equivalent to one another. Sixth, double salts dissociate completely while complex ions do not — FeSO4.(NH4)2SO4.6H2O gives free Fe2+ tests, but K4[Fe(CN)6] gives no free Fe2+ or CN- test.

• State Werner's postulates and explain, using the cobalt-ammine conductivity data, how primary and secondary valence were distinguished experimentally.
• Define coordination entity, central atom, ligand, coordination number, coordination sphere, coordination polyhedron, oxidation number, homoleptic and heteroleptic, with two examples each.
• Classify a ligand as unidentate, didentate, polydentate or ambidentate, and explain what makes a ligand a chelate.
• Write the formula of a coordination compound from its IUPAC name, and the name from its formula, applying the alphabetical-ligand and -ate-suffix rules correctly.
• Identify which kind of structural isomerism (linkage, coordination, ionisation, solvate) a pair of compounds illustrates, and distinguish it from stereoisomerism.
• Predict the number of geometrical isomers for a coordination formula and determine which, if any, is optically active.
• Given a metal ion and a ligand's field strength, predict hybridisation, inner/outer orbital character, geometry and magnetic behaviour using Valence Bond Theory.
• Use Crystal Field Theory and the spectrochemical series to decide high spin or low spin for a d4-d7 octahedral complex, and calculate the spin-only magnetic moment.
• Explain why coordination compounds are coloured, why removing the ligand removes the colour, and describe synergic bonding in metal carbonyls.

Ask the tutor: Want to work through predicting the hybridisation, magnetic moment and IUPAC name for any coordination formula you throw at me?