7

An Introduction to Coordination Compounds

Exploring the structural arrangements, isomerism, and thermodynamics of metal complexes with their surrounding ligands

The Language of Coordination Chemistry

In the context of metal coordination chemistry, the term complex means a central metal atom or ion surrounded by a set of ligands. A ligand is an ion or molecule that can have an independent existence.

Key Definitions
  • Complex: A Lewis acid (metal) combined with Lewis bases (ligands)
  • Coordination compound: A neutral complex or ionic compound containing a complex ion
  • Donor atom: The atom in the ligand that forms the bond to the metal
  • Acceptor atom: The metal atom or ion (Lewis acid)
  • Coordination number: The number of ligands in the primary coordination sphere

Inner-Sphere vs Outer-Sphere Complexes

Inner-Sphere Complex

Ligands are attached directly to the central metal atom or ion, forming the primary coordination sphere.

Example: [Co(NH₃)₆]³⁺

Outer-Sphere Complex

Complex cations associate electrostatically with anionic ligands without displacing existing ligands.

Example: {[Mn(OH₂)₆]²⁺SO₄²⁻}

Factors Governing Coordination Number

Factor Effect on Coordination Number
Size of central atom/ion Larger atoms favor higher coordination numbers
Steric interactions Bulky ligands lead to lower coordination numbers
Electronic interactions Few d electrons → higher CN; many d electrons → lower CN
Multiple bonding π-bonding ligands reduce coordination number

7.1 Representative Ligands

Key Points Polydentate ligands can form chelates; a bidentate ligand with a small bite angle can result in distortions from standard structures.

Ligand Classifications

Monodentate
Bidentate
Polydentate
Ambidentate

Monodentate ligands have only one point of attachment to the metal.

Name Formula Donor Atom
AmmineNH₃N
AquaH₂OO
CarbonylCOC
ChloridoCl⁻Cl
CyanidoCN⁻C
HydroxidoOH⁻O
PyridinepyN

Bidentate ligands have two points of attachment to the metal.

Name Abbreviation Donor Atoms
1,2-Diaminoethaneen2N
Acetylacetonatoacac⁻2O
Oxalatoox²⁻2O
2,2'-Bipyridinebpy2N
Phenanthrolinephen2N
Glycinatogly⁻N, O

Polydentate ligands have more than two points of attachment.

Name Abbreviation Donor Atoms Denticity
Diethylenetriaminedien3N3
Triaminotriethylaminetren4N4
Tetraazacyclotetradecanecyclam4N4
Ethylenediaminetetraacetatoedta⁴⁻2N, 4O6
18-Crown-618-crown-66O6

Ambidentate ligands can attach through different donor atoms.

Ligand Binding Mode Name
Thiocyanate (NCS⁻)M—NCSThiocyanato-κN
M—SCNThiocyanato-κS
Nitrite (NO₂⁻)M—NO₂Nitrito-κN
M—ONONitrito-κO

Chelates and Bite Angle

Chelate

A complex in which a polydentate ligand forms a ring that includes the metal atom. The term comes from the Greek word for "claw."

🔗 Chelate Ring Formation
M N N 5-membered ring

1,2-Diaminoethane (en)

M O O 6-membered ring

Acetylacetonato (acac⁻)

The bite angle is the L—M—L angle in the chelate ring

7.2 Nomenclature

Key Points The cation and anion of a complex are named according to a set of rules; cations are named first and ligands are named in alphabetical order.

Naming Rules

  1. Cation before anion (as for simple ionic compounds)
  2. Ligands in alphabetical order (ignoring numerical prefixes)
  3. Metal name followed by oxidation state in parentheses
  4. Add -ate suffix if complex is an anion
  5. Use square brackets for the complex formula

Numerical Prefixes

Number Simple Prefix Complex Prefix
2di-bis-
3tri-tris-
4tetra-tetrakis-
5penta-pentakis-
6hexa-hexakis-

Note: Use bis-, tris-, tetrakis- when the ligand name already includes a prefix (e.g., 1,2-diaminoethane) or has parentheses.

Example 7.1: Naming Complexes
Formula Name
[PtCl₂(NH₃)₄]²⁺ Tetraamminedichloridoplatinum(IV)
[Ni(CO)₃(py)] Tricarbonylpyridinenickel(0)
[Cr(edta)]⁻ Ethylenediaminetetraacetatochromate(III)
[CoCl₂(en)₂]⁺ Dichloridobis(1,2-diaminoethane)cobalt(III)
[Rh(CO)₂I₂]⁻ Dicarbonyldiiodidorhodate(I)

Interactive Naming Practice

🏷️ Complex Naming Quiz

What is the correct name for [Co(NH₃)₆]Cl₃?

Hexaamminecobalt(II) chloride
Hexaamminecobalt(III) chloride
Cobalt hexaammine trichloride
Trichloridohexaamminecobalt(III)
Write the formulas for: (a) diaquadichloridoplatinum(II); (b) tris(1,2-diaminoethane)rhodium(III); (c) chloridotris(triphenylphosphine)rhodium(I).

7.3-7.5 Constitution and Geometry

Key Points The number of ligands in a complex depends on the size of the metal atom, the identity of the ligands, and the electronic interactions.

Coordination Geometries by Number

2
4
5
6
7+

Two-Coordinate Complexes

Linear complexes (D∞h symmetry) are found for Cu⁺, Ag⁺, Au⁺, and Hg²⁺.

Ag Cl Cl

[AgCl₂]⁻

Linear

Four-Coordinate Complexes

Two main geometries: tetrahedral and square planar.

[CoCl₄]²⁻

Tetrahedral (Td)

Small metal, large ligands

[PtCl₄]²⁻

Square Planar (D4h)

d⁸ metals (Pt²⁺, Pd²⁺, Au³⁺)

Five-Coordinate Complexes

Two main geometries with similar energies: trigonal bipyramidal and square pyramidal.

a a e e

Trigonal Bipyramidal

D3h

a = axial, e = equatorial

a b

Square Pyramidal

C4v

a = axial, b = basal

Berry Pseudorotation

Five-coordinate complexes can interconvert between trigonal bipyramidal and square pyramidal geometries through a low-energy pathway.

Six-Coordinate Complexes

The most common coordination number. Almost all are octahedral (Oh).

[Co(NH₃)₆]³⁺

Octahedral (Oh)

Distortions from Octahedral

Distortion Symmetry Description
TetragonalD4hTwo trans ligands at different distance
RhombicD2hTwo pairs of trans ligands at different distances
TrigonalD3dCompression along C₃ axis

Higher Coordination Numbers (7-12)

Found mainly for larger atoms: late 4d/5d metals and f-block elements.

CN Geometries Examples
7 Pentagonal bipyramid, capped octahedron, capped trigonal prism [ZrF₇]³⁻, [UO₂(OH₂)₅]²⁺
8 Square antiprism, dodecahedron, cube [Mo(CN)₈]³⁻, [Zr(ox)₄]⁴⁻
9 Capped square antiprism [Nd(OH₂)₉]³⁺, [ReH₉]²⁻
12 Icosahedral [Ce(NO₃)₆]²⁻

7.7-7.10 Isomerism

Key Point A molecular formula may not be sufficient to identify a coordination compound: linkage, ionization, hydrate, and coordination isomerism are all possible.

Types of Isomerism

Structural
Geometric
Optical

Structural Isomerism

Linkage Isomerism

Same ligand bonds through different atoms.

Example: [Co(NH₃)₅(NO₂)]²⁺

  • Red: nitrito-κO (M—ONO)
  • Yellow: nitrito-κN (M—NO₂)
Ionization Isomerism

Ligand and counter-ion exchange places.

Example:

  • [PtCl₂(NH₃)₄]Br₂
  • [PtBr₂(NH₃)₄]Cl₂
Hydrate Isomerism

Water as ligand vs water of crystallization.

Example: CrCl₃·6H₂O

  • Violet: [Cr(OH₂)₆]Cl₃
  • Pale green: [CrCl(OH₂)₅]Cl₂·H₂O
  • Dark green: [CrCl₂(OH₂)₄]Cl·2H₂O
Coordination Isomerism

Ligands distributed differently between metal centers.

Example:

  • [Co(NH₃)₆][Cr(CN)₆]
  • [Cr(NH₃)₆][Co(CN)₆]

Geometric Isomerism

Square Planar [MA₂B₂]

A B A B
cis isomer

C2v symmetry

A A B B
trans isomer

D2h symmetry

Octahedral [MA₄B₂]

cis

B's adjacent

trans

B's opposite

Octahedral [MA₃B₃]

mer (meridional)

C2v symmetry

fac (facial)

C3v symmetry

Optical Isomerism

Chiral complexes exist as enantiomers - non-superimposable mirror images that rotate plane-polarized light in opposite directions.

Δ and Λ Configurations

View along the C₃ axis of an octahedral tris-chelate complex:

  • Δ (Delta): Clockwise helix rotation
  • Λ (Lambda): Anticlockwise helix rotation
🔄 Enantiomeric Pairs
Co

Δ

Clockwise

Co

Λ

Anticlockwise

[Co(en)₃]³⁺ enantiomers

Example 7.5: Recognizing Chirality

Which complexes are chiral?

Complex Chiral? Reason
[Cr(edta)]⁻ Yes No mirror plane or center of inversion
[Ru(en)₃]²⁺ Yes Tris-chelate with D₃ symmetry
[Pt(dien)Cl]⁺ No Has a mirror plane

7.11 Ligand Chirality

Key Point Coordination to a metal can stop a ligand inverting and hence lock it into a chiral configuration.

In certain cases, achiral ligands can become chiral upon coordination to a metal, leading to a chiral complex. This typically occurs when the free ligand contains a donor atom that rapidly inverts but becomes locked upon coordination.

Example: MeNHCH₂CH₂NHMe Complexes

When MeNHCH₂CH₂NHMe coordinates to a square-planar metal, the two N atoms become chiral centers. This results in:

  • One pair of chiral enantiomers
  • Two achiral meso complexes

7.12-7.13 Thermodynamics of Complex Formation

Key Points
  • A formation constant (Kf) expresses ligand binding strength relative to solvent
  • Stepwise constants typically follow Kfn > Kfn+1
  • Deviations indicate structural changes

Formation Constants

[Fe(OH₂)₆]³⁺(aq) + SCN⁻(aq) ⇌ [Fe(SCN)(OH₂)₅]²⁺(aq) + H₂O(l)

Kf = [Fe(SCN)(OH₂)₅²⁺] / [Fe(OH₂)₆³⁺][SCN⁻]

Stepwise vs Overall Formation Constants

Stepwise Formation Constants
M + L ⇌ ML     Kf1
ML + L ⇌ ML₂     Kf2
MLn-1 + L ⇌ MLn     Kfn
Overall Formation Constant
M + nL ⇌ MLn     βn

βn = Kf1 × Kf2 × ... × Kfn

Formation Constants Table

Ion Ligand Kf log Kf
Mg²⁺NH₃1.70.23
Ni²⁺NH₃5252.72
Cu²⁺NH₃2.0 × 10⁴4.31
Hg²⁺NH₃6.3 × 10⁸8.8
Fe³⁺SCN⁻2342.37
Pd²⁺Cl⁻1.25 × 10⁵6.1

Trends in Successive Formation Constants

The decrease in stepwise constants (Kf1 > Kf2 > ... > Kfn) reflects:

  1. Statistical factor: fewer H₂O molecules available for replacement
  2. Increased likelihood of reverse reaction with more bound ligands
Ni(II) Ammine Formation Constants
n Kf log Kf Kn/Kn-1
15252.72—
21482.170.28
345.71.660.31
413.21.120.29
54.70.630.35
61.10.030.23
Example 7.6: Anomalous Formation Constants

Problem: For Cd²⁺ with Br⁻: Kf1=36.3, Kf2=3.47, Kf3=1.15, Kf4=2.34. Why is Kf4 > Kf3?

Answer: The anomaly suggests a structural change. Aqua complexes are typically 6-coordinate while halogeno complexes of M²⁺ are often tetrahedral. The fourth Br⁻ addition releases three H₂O molecules:

[CdBr₃(OH₂)₃]⁻ + Br⁻ ⇌ [CdBr₄]²⁻ + 3H₂O

The entropy gain from releasing three water molecules increases Kf4.

7.14-7.15 The Chelate and Macrocyclic Effects

Key Points
  • The chelate effect: greater stability of complexes with polydentate ligands vs equivalent monodentate ligands
  • The chelate effect is largely entropic in origin
  • The macrocyclic effect adds an enthalpic contribution

The Chelate Effect

📊 Chelate Effect Comparison
[Cd(OH₂)₆]²⁺ + en ⇌ [Cd(en)(OH₂)₄]²⁺ + 2H₂O
log Kf1 = 5.84    ΔS° = 113 J K⁻¹mol⁻¹
[Cd(OH₂)₆]²⁺ + 2NH₃ ⇌ [Cd(NH₃)₂(OH₂)₄]²⁺ + 2H₂O
log β₂ = 4.95    ΔS° = 25 J K⁻¹mol⁻¹

Two similar Cd—N bonds are formed in each case, yet the chelate complex is more stable due to the more positive reaction entropy.

Origin of the Chelate Effect

The chelation reaction increases the number of independent molecules in solution:

  • Chelate reaction: 2 reactants → 3 products (+1 molecule)
  • Non-chelate reaction: 3 reactants → 3 products (no change)

More products = more positive ΔS = more favorable ΔG

The Macrocyclic Effect

Macrocyclic ligands (e.g., crown ethers, porphyrins, cyclam) form even more stable complexes than their open-chain analogues due to:

  1. Entropic contribution (same as chelate effect)
  2. Enthalpic contribution from pre-organized donor atoms (no additional strain upon coordination)

Porphyrin

N N N N

Tetradentate N₄ macrocycle

Crown Ether

Hexadentate O₆ macrocycle

Steric Effects and Electron Delocalization

Ring Size Stability Notes
5-memberedVery stableBond angles near ideal, minimal strain
6-memberedStableFavored when electron delocalization occurs
3, 4, 7+RareBond angle distortions and steric strain
π-Acceptor Ligands

Diimine ligands like bipyridine (bpy) and phenanthroline (phen) form exceptionally stable complexes with d-metals due to:

  • σ-donation from N lone pairs to metal
  • π-backbonding from filled metal t₂g to empty ligand π* orbitals

Example: [Ru(bpy)₃]²⁺ has exceptional stability and is used in photochemistry and solar cells.

Chapter Summary

Coordination Fundamentals
  • Complex = metal + ligands
  • Coordination number varies 2-12
  • Ligands classified by denticity
  • Inner vs outer sphere coordination
Isomerism Types
  • Structural: linkage, ionization, hydrate, coordination
  • Geometric: cis/trans, mer/fac
  • Optical: Δ/Λ enantiomers
Common Geometries
  • CN 4: tetrahedral, square planar
  • CN 5: trigonal bipyramidal, square pyramidal
  • CN 6: octahedral (most common)
Thermodynamics
  • Kf measures ligand binding strength
  • Chelate effect: entropic origin
  • Macrocyclic effect: entropic + enthalpic

Key Equations

Formation constant: Kf = [ML]/[M][L]

Overall constant: βn = Kf1 × Kf2 × ... × Kfn

Dissociation constant: Kd = 1/Kf

ΔG° = -RT ln Kf