Coordination Number

Definition and Basic Concept

Coordination Number Explained

Coordination number (CN): number of ligand donor atoms directly bonded to central metal ion in a coordination complex. Defines immediate bonding environment. Independent of ligand denticity but counts each donor atom individually.

Historical Development

Origin: Alfred Werner’s coordination theory (1893). Concept refined in 20th century with X-ray crystallography. Fundamental in distinguishing inner coordination sphere from outer sphere.

Distinguishing Coordination Number from Coordination Sphere

Coordination sphere: metal + ligands directly bonded. Coordination number: count of ligand donor atoms in coordination sphere. Essential for predicting geometry and reactivity.

Importance in Coordination Chemistry

Structural Determination

CN guides prediction of spatial arrangement of ligands around metal center. Directly affects molecular geometry, bond angles, and complex stability.

Catalytic Activity

CN influences accessibility of active sites in catalysts. Lower CN often yields more reactive sites; higher CN can stabilize intermediates.

Electronic Properties

CN impacts ligand field splitting, affecting electronic spectra, magnetic properties, and redox potentials.

Determination Methods

X-ray Crystallography

Direct structural determination. Identifies number and position of ligand atoms bonded to metal center. Most reliable method.

Spectroscopic Techniques

Infrared, UV-Vis, NMR spectroscopies provide indirect evidence of CN by analyzing ligand environment and electronic transitions.

Computational Approaches

Density functional theory (DFT) and molecular modeling predict CN and geometries when experimental data unavailable or ambiguous.

Common Coordination Numbers

Coordination Number 2

Linear geometry. Typical for soft metal ions and bulky ligands. Example: Ag(I) complexes.

Coordination Number 4

Tetrahedral or square planar geometries. Common in d8 metals (Ni(II), Pd(II), Pt(II)).

Coordination Number 6

Octahedral geometry. Most prevalent CN in transition metal complexes (Fe(III), Co(III), Cr(III)).

Coordination Geometries

Linear

CN = 2. Ligands aligned 180°. Minimal steric hindrance. Example: [Ag(NH3)2]+.

Tetrahedral

CN = 4. Ligands at 109.5° angles. Favored by smaller, less electronegative metals.

Square Planar

CN = 4. Ligands at 90°. Prominent in d8 metal ions due to ligand field stabilization.

Octahedral

CN = 6. Ligands at 90°. Most common; high symmetry and stability.

Higher Coordination Numbers

CN = 7, 8, 9 or more. Less common; geometries include pentagonal bipyramidal, square antiprismatic, tricapped trigonal prismatic.

Effect of Ligand Types

Monodentate Ligands

Each ligand donates one donor atom; CN equals number of ligands.

Bidentate and Polydentate Ligands

One ligand contributes multiple donor atoms; CN counts total donor atoms, not ligand count.

Bridging Ligands

Ligands connecting multiple metal centers; CN calculated per metal based on donor atoms bonded.

Steric and Electronic Factors

Steric Hindrance

Bulky ligands reduce CN by preventing close approach of multiple ligands.

Electronic Effects

Metal oxidation state and electronic configuration influence CN via ligand field stabilization energy (LFSE).

Solvent and Temperature

Environmental conditions can shift equilibrium between coordination numbers via ligand substitution kinetics.

Representative Examples

Hexaaquairon(III) Ion

CN = 6. Octahedral geometry. Formula: [Fe(H2O)6]3+. Common in aqueous solutions.

Tetraamminecopper(II) Ion

CN = 4. Square planar. Formula: [Cu(NH3)4]2+. Exemplifies ligand field effects.

Silver(I) Complexes

CN = 2. Linear complexes such as [Ag(NH3)2]+ demonstrate soft acid-soft base interaction.

Coordination Numbers in Transition Metals

Early Transition Metals

Typically higher CN (6-8) due to larger ionic radii and preference for high coordination.

Late Transition Metals

Lower CN (4-6) common; influenced by d-electron count and ligand field stabilization.

Variable CN

Many transition metals exhibit multiple CNs, depending on ligand environment and oxidation state.

Coordination in Main Group Metals

Alkali and Alkaline Earth Metals

CN often higher (6-12) due to large ionic radii and electrostatic bonding.

Post-Transition Metals

Variable CN; often lower than transition metals due to inert pair effect and softer bonding.

Examples

Calcium commonly CN = 8; lead complexes often CN = 4 or 6.

Exceptions and Anomalies

Low Coordination Numbers

Some metals exhibit CN = 1 or 2 due to sterics or electronic reasons (e.g., Au(I) complexes).

High Coordination Numbers Beyond 12

Reported in solid state or cluster compounds; less common in molecular species.

Fluxional Behavior

Dynamic ligand exchange can lead to apparent variable CN in solution.

Applications in Synthesis and Catalysis

Coordination Number Control in Catalysts

Manipulating CN tunes catalytic selectivity and activity. Example: 4-coordinate Pd catalysts in cross-coupling.

Design of Metal-Organic Frameworks (MOFs)

CN critical in framework connectivity and porosity.

Bioinorganic Chemistry

Metal centers in enzymes exhibit characteristic CN affecting function and substrate binding.

References

• J. E. Huheey, E. A. Keiter, R. L. Keiter, Inorganic Chemistry: Principles of Structure and Reactivity, 4th ed., HarperCollins, 1993, pp. 345-370.
• F. A. Cotton, G. Wilkinson, C. A. Murillo, M. Bochmann, Advanced Inorganic Chemistry, 6th ed., Wiley, 1999, pp. 705-740.
• R. G. Wilkins, Chemical Principles of Coordination Chemistry, Wiley, 1974, pp. 120-150.
• G. L. Miessler, D. A. Tarr, Inorganic Chemistry, 3rd ed., Pearson, 2004, pp. 260-290.
• C. Janiak, “A Critical Account on π–π Stacking in Metal Complexes with Aromatic Nitrogen-Containing Ligands,” J. Chem. Soc., Dalton Trans., 2000, 3885-3896.

Tables

Common Coordination Numbers and Geometries

Effect of Ligand Denticity on Coordination Number

Formulas and Structured Information

General Coordination Number Calculation

Coordination Number (CN) = Σ (Number of donor atoms per ligand × Number of such ligands)

Example: [Co(en)3]3+ Complex

Ligand: ethylenediamine (en), bidentate, 2 donor atoms per ligandNumber of ligands: 3CN = 3 × 2 = 6Geometry: Octahedral