Ligands and Complex Ions

Spec Mapping — OCR H432 Module 5.3.1 — Transition elements (complex ion formation), covering the definitions of ligand, complex ion, coordination number, and dative covalent (coordinate) bond; the six monodentate ligands H₂O, NH₃, Cl⁻, OH⁻, CN⁻, and CO; the bidentate ligands 1,2-diaminoethane (en) and ethanedioate (C₂O₄²⁻); the hexadentate polydentate ligand EDTA⁴⁻; the shapes of complex ions with coordination numbers 2 (linear), 4 (tetrahedral or square planar), and 6 (octahedral); and the calculation of overall complex charge from metal oxidation state and ligand charges (refer to the official OCR H432 specification document for exact wording).

A complex ion is the central object of transition-metal chemistry: a small, highly charged metal cation surrounded by ligands — molecules or anions that donate lone pairs of electrons into the metal's empty 3d, 4s, and 4p orbitals via dative covalent (coordinate) bonds. Lesson 1 introduced complex-ion formation as the fourth characteristic property of transition elements; lesson 2 supplied the electronic basis (small ions with empty d/s/p orbitals available to accept lone pairs). This lesson assembles the formal vocabulary (ligand, complex ion, coordination number, dative bond) and the catalogue of ligand types (monodentate, bidentate, polydentate) that every subsequent lesson in the topic will draw on. Five of the lessons that follow — naming (4), substitution (5), cisplatin/haemoglobin (6), stereoisomerism (7), qualitative analysis (8) — assume fluent control of the conventions developed here. Get the bracket-and-charge notation right, get the coordination-number rules right, and the rest of the topic falls into place.

Key Definitions:

• Ligand — a molecule or ion with at least one lone pair of electrons that can be donated to a central metal cation to form a dative covalent (coordinate) bond.
• Complex ion — a central metal cation bonded to one or more ligands by dative covalent bonds.
• Dative covalent (coordinate) bond — a covalent bond in which both shared electrons come from the same atom (the donor); represented in a diagram by an arrow from donor to acceptor.
• Coordination number — the number of dative covalent bonds in a complex ion (equivalently, the total number of lone pairs donated by all ligands). For monodentate ligands, equal to the number of ligand molecules; for polydentate ligands, larger than the number of ligand molecules.
• Monodentate / bidentate / polydentate ligand — a ligand donating one / two / more than two lone pairs from one molecule respectively.

Learning Objectives

By the end of this lesson you should be able to:

• Define ligand, complex ion, coordination number and dative covalent (coordinate) bond with reference to lone-pair donation
• Identify common monodentate ligands: H₂O, NH₃, Cl⁻, OH⁻, CN⁻, CO — and the donor atom in each
• Distinguish monodentate, bidentate and polydentate ligands and count coordination number correctly for each
• Describe the shapes of complex ions with coordination numbers 2 (linear, 180°), 4 (tetrahedral 109.5° or square planar 90°), and 6 (octahedral, 90°/180°)
• Calculate the overall charge on a complex ion from the oxidation state of the metal and the charges on the ligands
• Use formulae like [Cu(H₂O)₆]²⁺ correctly (square brackets, ligand multiplicities, charge superscript)

Why the OCR Definition of a Ligand Matters

A ligand is a molecule or ion with a lone pair of electrons that can form a dative covalent bond to a central metal ion. The OCR specification phrasing is precise on three points:

1. The ligand must have a lone pair of electrons (not just any electrons — the lone pair is the donor).
2. The bond formed is dative covalent (coordinate): both electrons of the new bond come from the ligand.
3. The central species is a metal ion, typically a transition-metal cation but also a main-group cation (Al³⁺, Mg²⁺, Be²⁺ all form complexes).

A complex ion (or complex) is a central metal ion surrounded by and bonded to one or more ligands by dative covalent bonds. The complex carries an overall charge equal to the sum of the metal oxidation state and the charges on the ligands.

A dative covalent (coordinate) bond is a covalent bond where both shared electrons come from the same atom (the ligand), not one from each as in a normal covalent bond. In a diagram, dative bonds are sometimes shown with an arrow from donor to acceptor; once formed, the bond is indistinguishable from any other covalent bond — it just has a particular history.

The coordination number is the number of dative covalent bonds in the complex (equivalently, the number of lone pairs donated to the metal). For monodentate ligands, this equals the number of ligand molecules; for bidentate and polydentate ligands, it is more than the number of ligand molecules.

Writing Complex Ion Formulae

Complex ions are always written with:

• Square brackets around the whole complex
• The metal symbol first, then the ligands
• Anionic ligands before neutral ligands (alphabetical within each class in modern IUPAC; OCR is flexible)
• The overall charge as a superscript outside the brackets

Examples of the correct notation:

• [Cu(H2O)6]2+
• [CuCl4]2-
• [Ag(NH3)2]+
• [Fe(CN)6]3-
• [Cr(OH)6]3-

The oxidation state of the metal is not shown in the formula (you calculate it from the charge on the complex and the charges on the ligands).

Calculating Metal Oxidation State in a Complex

The overall charge on the complex equals the sum of the metal oxidation state and the charges on all ligands.

Worked examples:

• [Cu(H2O)6]2+: H2O is neutral, so 0 + x = +2, x = +2. Copper is in the +2 oxidation state.
• [CuCl4]2-: each Cl- is -1, so 4(-1) + x = -2, x = +2. Copper is +2.
• [Fe(CN)6]3-: each CN- is -1, so 6(-1) + x = -3, x = +3. Iron is +3 (ferricyanide, a classic reagent).
• [MnO4]-: each O2- is -2, so 4(-2) + x = -1, x = +7. Manganese is +7 (permanganate).
• [Co(NH3)6]3+: NH3 is neutral, so 0 + x = +3, x = +3. Cobalt is +3.

Common Monodentate Ligands

A monodentate ligand donates exactly one lone pair (has one donor atom that binds once).

Ligand	Formula	Donor atom	Charge
Water	H2O	O	0
Ammonia	NH3	N	0
Chloride	Cl-	Cl	-1
Hydroxide	OH-	O	-1
Cyanide	CN-	C	-1
Carbon monoxide	CO	C	0

These are the six monodentate ligands OCR expects you to know by name and formula. The most important are water (the default in aqueous solution), ammonia (common in substitution), chloride (makes large tetrahedral complexes) and cyanide (strong-field, coloured complexes).

Bidentate Ligands

A bidentate ligand has two donor atoms and forms two dative bonds from the same molecule. OCR expects you to know two examples:

• 1,2-diaminoethane, H2N-CH2-CH2-NH2 (abbreviation en): two nitrogen donor atoms
• Ethanedioate (oxalate), -O-CO-CO-O- or (COO-)2 (abbreviation ox or C2O4^2-): two oxygen donor atoms, charge 2-

A complex like [Ni(en)3]2+ contains three bidentate ligands, each donating two lone pairs - so the coordination number is 6 even though there are only 3 molecules.

Polydentate Ligands

A polydentate (or multidentate) ligand has more than two donor atoms and forms three or more dative bonds.

The most important polydentate ligand is EDTA4- (ethylenediaminetetraacetate). It has six donor atoms (2 N + 4 O-) and wraps around a single metal ion to fill all six coordination sites. An EDTA complex is therefore [M(EDTA)]^(n-4) where n is the charge on the metal.

Haem, the iron-containing porphyrin group in haemoglobin, is a tetradentate ligand - four nitrogen atoms of the porphyrin ring bind one Fe2+ ion. (A fifth coordination site binds the globin protein, and the sixth accepts O2 or CO - more on this in lesson 6.)

Coordination Number

The coordination number tells you how many dative bonds are formed, not how many ligand molecules there are. Count donor atoms, not molecules.

Complex	Ligand type	No. of molecules	Coordination number
[Cu(H2O)6]2+	Monodentate (x6)	6	6
[CuCl4]2-	Monodentate (x4)	4	4
[Ni(en)3]2+	Bidentate (x3)	3	6
[Fe(C2O4)3]3-	Bidentate (x3)	3	6
[Cu(EDTA)]2-	Hexadentate (x1)	1	6
[Ag(NH3)2]+	Monodentate (x2)	2	2

Shapes of Complex Ions

The shape of a complex ion is determined by its coordination number. The rules are simpler than for covalent molecules (no lone pairs on the central atom to worry about, at least at A-Level).

Coordination number	Shape	Bond angle	Example
2	Linear	180 deg	[Ag(NH3)2]+
4	Tetrahedral	109.5 deg	[CuCl4]2-, [CoCl4]2-, [FeCl4]-
4	Square planar	90 deg	[Pt(NH3)2Cl2] cisplatin, [Ni(CN)4]2-
6	Octahedral	90 deg	[Cu(H2O)6]2+, [Fe(H2O)6]3+, [Co(NH3)6]3+, [Cr(OH)6]3-

Coordination number 6 is by far the most common for first-row transition metals because H2O and NH3 are small enough for six to fit around a first-row cation. Coordination number 4 (tetrahedral) becomes important when the ligands are larger, such as Cl-: [CuCl4]2- forms instead of [Cu(Cl)6]4- because six chlorides cannot fit around a Cu2+ ion.

graph TD
  A[Coordination number?] --> B["2: Linear<br/>180 deg<br/>Ag+, Cu+"]
  A --> C["4: Tetrahedral<br/>109.5 deg<br/>large ligands like Cl-"]
  A --> D["4: Square planar<br/>90 deg<br/>d8: Pt II, Ni II"]
  A --> E["6: Octahedral<br/>90 deg<br/>small ligands: H2O, NH3"]

Why Tetrahedral or Square Planar for Four?

Most four-coordinate complexes are tetrahedral. The important exception is complexes of d8 metal ions (Ni2+, Pt2+, Pd2+), which prefer square planar geometry. In square planar the four d-orbitals split into a pattern that stabilises the d8 configuration more than a tetrahedral splitting would.

At OCR A-Level the two cases you must know are:

• [CuCl4]2- - tetrahedral, yellow, from [Cu(H2O)6]2+ + conc. HCl
• cisplatin [Pt(NH3)2Cl2] - square planar (Pt is d8), covered in lesson 6

Drawing Octahedral Complexes

An octahedron has four ligands in a square around the metal (the equatorial plane) and two more above and below (axial positions). Bond angles are 90 degrees between adjacent ligands and 180 degrees between trans ligands. Drawing conventions:

At A-Level you should draw the octahedron with solid and dashed wedge bonds to show depth, and label ligand atoms clearly (use H2O for water, NH3 for ammonia, Cl for chloride etc.).

The Most Important Complex: [Cu(H₂O)₆]²⁺

The hexaaquacopper(II) ion [Cu(H₂O)₆]²⁺ is the form that Cu²⁺(aq) takes when copper(II) salts dissolve in water. Its key features are:

• Pale blue colour (d–d transitions in the partially-filled 3d⁹ sub-shell)
• Octahedral shape (coordination number 6)
• +2 overall charge (Cu is in the +2 oxidation state; six neutral water ligands contribute 0)
• Starting point for almost every exam substitution reaction (lesson 5)