Co-Ordination Compounds

Coordination compounds sit at the intersection of inorganic bonding, geometry and magnetism, and NEET almost always draws 1–2 questions from them — typically on hybridisation/magnetic moment, isomer counting, IUPAC names, or crystal field splitting. Once you internalise a small set of rules, this chapter becomes one of the most predictable scoring areas in inorganic chemistry.

Werner's Idea and the Working Vocabulary

When crystals of CoCl₃ and ammonia are combined, several distinct compounds with the same formula ratio but different colours and different chemical behaviour appear. Alfred Werner explained this by proposing that a metal ion exercises two kinds of valence: a primary valence, satisfied by ions that simply balance charge and can wander off into solution, and a secondary valence, satisfied by groups locked directly onto the metal in fixed number and fixed spatial arrangement. His classic evidence was silver nitrate titration: CoCl₃·6NH₃ precipitates three moles of AgCl per mole, CoCl₃·5NH₃ gives two, CoCl₃·4NH₃ gives one. The chloride that refuses to precipitate is the chloride that is bonded inside the sphere of secondary valence.

A coordination compound therefore has a coordination sphere (written in square brackets) that survives dissolution, plus counter ions outside the brackets that ionise freely. This distinguishes it from a double salt such as carnallite or potash alum, which falls apart into all of its constituent ions in water. Terms you must use precisely:

• Central atom/ion: the Lewis-acidic metal accepting electron pairs, e.g. Co³⁺ in [Co(NH₃)₆]³⁺.
• Ligand: a Lewis base donating a lone pair to the metal. Classified by the number of donor atoms actually attached — unidentate (NH₃, Cl⁻, CN⁻), bidentate (ethane-1,2-diamine "en", oxalate), polydentate (EDTA⁴⁻, hexadentate). A ligand that bites the metal at two or more points forming a ring is a chelating ligand. An ambidentate ligand can attach through either of two different donor atoms — NO₂⁻ (via N or O), SCN⁻ (via S or N).
• Coordination number (CN): number of donor atoms (σ-bonds) around the metal, not the number of ligand molecules. In [Cr(en)₃]³⁺ there are 3 ligands but CN = 6.
• Oxidation number of the metal: the charge it would carry if all ligands were removed along with their donated pairs. Neutral ligands contribute 0; count anionic ligand charges.
• Coordination polyhedron: the geometry — octahedral (CN 6), tetrahedral or square planar (CN 4), linear (CN 2).
• Homoleptic complexes have only one kind of ligand; heteroleptic have more than one.

The effective atomic number (EAN) is the total electron count of the metal after coordination: EAN = (atomic number of metal − oxidation number) + 2 × CN. Many stable complexes, especially carbonyls, land on the next noble gas number (36, 54, 86) — for Ni(CO)₄, EAN = 28 − 0 + 8 = 36.

Naming Coordination Compounds

IUPAC nomenclature rewards mechanical practice. Apply these steps in order:

1. Cation before anion, exactly as in ordinary salts, whichever one is the complex.
2. Ligands are named first, in alphabetical order, before the metal, all as one word. Alphabetise by the ligand's name, ignoring the multiplying prefix (so diammine files under "a", trichlorido under "c").
3. Anionic ligands end in -o (modern usage: chlorido, cyanido, hydroxido, oxalato, nitrito-N); neutral ligands keep their names, with the special cases aqua (H₂O), ammine (NH₃), carbonyl (CO), nitrosyl (NO).
4. Prefixes di-, tri-, tetra- for simple ligands; bis-, tris-, tetrakis- with the ligand name in parentheses when the ligand name itself contains a numerical prefix or when confusion would arise — e.g. bis(ethane-1,2-diamine), tris(oxalato).
5. Oxidation state of the metal in Roman numerals in parentheses right after the metal name, with no space.
6. If the complex ion is an anion, the metal name takes the suffix -ate, often on the Latin stem: ferrate, cuprate, argentate, aurate, stannate, plumbate, but cobaltate, nickelate, zincate, chromate, platinate.
7. Neutral complexes are named as a single word with no suffix.

Worked examples:

• [Co(NH₃)₅Cl]Cl₂ → pentaamminechloridocobalt(III) chloride
• K₃[Fe(CN)₆] → potassium hexacyanidoferrate(III)
• [Pt(NH₃)₂Cl₂] → diamminedichloridoplatinum(II)
• [Cr(H₂O)₄Cl₂]Cl·2H₂O → tetraaquadichloridochromium(III) chloride dihydrate
• [Ni(CO)₄] → tetracarbonylnickel(0)
• [Co(en)₂Cl₂]⁺ → dichloridobis(ethane-1,2-diamine)cobalt(III) ion

Bridging ligands in polynuclear complexes get the prefix μ-, as in [(NH₃)₅Cr–OH–Cr(NH₃)₅]⁵⁺, named with μ-hydroxido.

Isomerism

Two broad families: structural (different bonds) and stereo (same bonds, different spatial arrangement).

Structural isomerism

1. Ionisation isomerism — the ion inside and outside the sphere are swapped, giving different ions in solution: [Co(NH₃)₅SO₄]Br and [Co(NH₃)₅Br]SO₄.
2. Hydrate (solvate) isomerism — water inside versus outside the coordination sphere: [Cr(H₂O)₆]Cl₃ (violet) and [Cr(H₂O)₅Cl]Cl₂·H₂O (grey-green).
3. Linkage isomerism — arises with ambidentate ligands: [Co(NH₃)₅(NO₂)]²⁺ bonded through N (nitrito-N) or through O (nitrito-O).
4. Coordination isomerism — when both cation and anion are complexes and the ligands are interchanged: [Co(NH₃)₆][Cr(CN)₆] and [Cr(NH₃)₆][Co(CN)₆].

Stereoisomerism

Geometrical (cis–trans) isomerism needs a rigid geometry with non-equivalent positions. Key patterns to memorise:

• Square planar MA₂B₂ → cis and trans (2 isomers). MABCD → 3 isomers.
• Octahedral MA₄B₂ → cis and trans.
• Octahedral MA₃B₃ → facial (fac) and meridional (mer).
• Octahedral M(AA)₂B₂ with a bidentate AA (e.g. [Co(en)₂Cl₂]⁺) → cis and trans.
• Tetrahedral complexes never show geometrical isomerism, because all four positions are mutually adjacent.

Optical isomerism requires a non-superimposable mirror image. It is common in octahedral chelates: [Co(en)₃]³⁺ exists as d and l forms; cis-[Co(en)₂Cl₂]⁺ is chiral while the trans form has a plane of symmetry and is achiral. [Pt(en)₃]⁴⁺ similarly is optically active. Square planar complexes are essentially never optically active (the molecular plane is a mirror plane).

Valence Bond Theory: Hybridisation and Magnetism

VBT treats complex formation as ligand lone pairs entering empty hybrid orbitals of the metal. The metal first rearranges (sometimes pairing up d electrons under ligand pressure) to create the required number of vacant orbitals.

Complexes using inner (3d) orbitals are low-spin/spin-paired; those using outer (4d) orbitals are high-spin/spin-free. Strong-field ligands such as CN⁻, CO, NO₂⁻ force pairing; weak ligands like H₂O, F⁻, Cl⁻ usually do not.

Magnetic moment is estimated from the spin-only formula:

μ = √[n(n+2)] BM, where n = number of unpaired electrons.

n = 1, 2, 3, 4, 5 → μ ≈ 1.73, 2.83, 3.87, 4.90, 5.92 BM. Learn these five numbers; questions often give μ and ask for the geometry.

Illustrations:

• [Fe(CN)₆]³⁻: Fe³⁺ is d⁵. CN⁻ pairs the electrons → t configuration with one unpaired electron, d²sp³, octahedral, μ ≈ 1.73 BM.
• [FeF₆]³⁻: same d⁵ metal but weak field → 5 unpaired, sp³d², μ ≈ 5.92 BM.
• [Ni(CN)₄]²⁻: Ni²⁺ is d⁸; electrons pair to vacate one 3d orbital → dsp², square planar, diamagnetic.
• [NiCl₄]²⁻: Ni²⁺ d⁸ with weak ligands → sp³, tetrahedral, 2 unpaired, μ ≈ 2.83 BM.
• [Ni(CO)₄]: Ni(0) is 3d⁸4s²; it becomes 3d¹⁰4s⁰ → sp³, tetrahedral, diamagnetic.
• [Co(NH₃)₆]³⁺: Co³⁺ d⁶, strong field → all paired, d²sp³, diamagnetic.

VBT's limitations: it does not explain colour, cannot predict quantitatively why one ligand is strong and another weak, gives no account of the spectrochemical series, and fails to explain the exact magnetic data of some complexes or the relative stability of geometries.

Crystal Field Theory, Colour and Applications

Crystal field theory (CFT) treats ligands as point negative charges (or dipoles) that approach the central metal ion and electrostatically repel its d electrons, without invoking any covalent overlap. In a free ion, all five d orbitals are degenerate; in an octahedral field, ligands approach along the axes, so orbitals pointing directly at ligands (d_x²−y², d_z²) are repelled more and rise in energy, while orbitals pointing between the axes (d_xy, d_yz, d_zx) are repelled less and fall in energy. This splits the d set into a higher e_g pair (2 orbitals) and a lower t₂g set (3 orbitals), separated by the crystal field splitting energy, Δ₀. In a tetrahedral field the splitting pattern inverts (e below t₂) and Δ_t is intrinsically smaller (roughly 4/9 of Δ₀ for the same metal and ligand), which is why tetrahedral complexes are essentially always high-spin.

Whether electrons pair up in the lower set or spread out into the upper set depends on the balance between Δ₀ and the pairing energy (P): if Δ₀ > P, electrons pair preferentially in t₂g first, giving a low-spin complex; if Δ₀ < P, electrons occupy all five orbitals singly before any pairing (Hund's rule wins), giving a high-spin complex. The strength of a ligand's field is captured empirically in the spectrochemical series, an experimentally determined order independent of the metal:

I⁻ < Br⁻ < SCN⁻ < Cl⁻ < F⁻ < OH⁻ < oxalate < H₂O < NCS⁻ < NH₃ < en < NO₂⁻ < CN⁻ ≈ CO

Ligands to the left are weak field (favour high spin); ligands to the right are strong field (favour low spin). This series is CFT's genuine advance over VBT: it lets you predict, from the ligand alone, whether a complex will be high-spin or low-spin — the [Fe(CN)₆]³⁻ versus [FeF₆]³⁻ contrast noted above follows directly from CN⁻ sitting at the strong end and F⁻ at the weak end.

CFT also explains colour. White light falling on a coloured complex has some wavelengths absorbed to promote an electron from a lower to a higher d orbital (a d–d transition), and the complex displays the complementary colour of what is absorbed. This is why colour depends on the ligand (changing ligands changes Δ₀ and hence the absorbed wavelength/colour), on the oxidation state of the metal, and on the geometry — and why a complex with an empty (d⁰) or completely filled (d¹⁰) d subshell, such as Ti⁴⁺ or Zn²⁺ complexes, is typically colourless, since no d–d transition is possible.

CFT's own limitation is that it treats ligands as point charges and ignores any genuine covalent/orbital-overlap character of the metal–ligand bond, so it cannot fully explain why some neutral ligands (like CO) produce such an intense field despite carrying no charge — this requires the more advanced ligand field/molecular orbital treatment, which accounts for π-backbonding.

Coordination compounds are far from a theoretical curiosity. Applications regularly tested include: EDTA complexes used in estimating water hardness and in treating heavy-metal poisoning; cisplatin, [Pt(NH₃)₂Cl₂], an anticancer drug (its cis isomer is active, trans is not); haemoglobin, an iron–porphyrin complex that carries oxygen in blood; chlorophyll, a magnesium–porphyrin complex central to photosynthesis; and extraction of silver and gold via cyanide complexes, [Ag(CN)₂]⁻ and [Au(CN)₂]⁻, followed by displacement with zinc.

Common Mistakes and Exam Traps

1. Confusing coordination number with number of ligands. CN counts donor atoms, not ligand molecules — [Cr(en)₃]³⁺ has only 3 ligands but CN = 6 because ethane-1,2-diamine is bidentate; students frequently just count ligand molecules and get CN = 3.
2. Predicting spin state from a fixed rule per metal, ignoring the spectrochemical series. Whether a complex is high-spin or low-spin depends on the actual ligand's field strength versus pairing energy, not on the metal alone — the same metal ion gives different spin states with different ligands, as in [Fe(CN)₆]³⁻ versus [FeF₆]³⁻.
3. Assuming all d-block complexes are coloured. Complexes with d⁰ or d¹⁰ configurations (Sc³⁺, Ti⁴⁺, Zn²⁺, Cu⁺) have no possible d–d transition and are colourless — colour requires partially filled d orbitals, not simply "being a transition metal complex".
4. Missing tetrahedral complexes as an exception to geometrical isomerism. Tetrahedral MA₂B₂-type complexes never show cis-trans isomerism because all four positions are mutually adjacent (there is no "opposite" position) — this is unlike square planar MA₂B₂, which does show cis/trans forms, and the two are commonly confused.