Coordination Compounds

Werner's Theory of Coordination Compounds

**Werner's theory** (1898) revolutionized our understanding of how metal ions bond with ligands. Alfred Werner proposed that metals exhibit two types of valences:

**Primary valence (ionisable)**: Satisfied by negative ions; determines the overall charge of the complex

**Secondary valence (non-ionisable)**: Satisfied by neutral molecules or negative ions; equal to the coordination number and fixed for each metal

**Key postulates of Werner's theory**:

1. Metals show primary and secondary linkages

2. Primary valences are ionisable and satisfied by negative ions

3. Secondary valences are non-ionisable; satisfied by neutral molecules or negative ions; equal to coordination number

4. Groups bound by secondary linkages have characteristic spatial arrangements (coordination polyhedra)

**Experimental evidence**: Werner studied cobalt(III) chloride-ammonia complexes. Using AgNO₃ precipitation, he determined how many chloride ions were ionisable (precipitated as AgCl) versus coordinated to cobalt:

[Co(NH₃)₆]³⁺3Cl⁻ → 3 mol AgCl per mole (yellow, 1:3 electrolyte)

[CoCl(NH₃)₅]²⁺2Cl⁻ → 2 mol AgCl per mole (purple, 1:2 electrolyte)

[CoCl₂(NH₃)₄]⁺Cl⁻ → 1 mol AgCl per mole (green/violet, 1:1 electrolyte)

This proved that exactly 6 groups (ammonia molecules or chloride ions) remained bonded to Co³⁺. The ionisable chlorides outside the square brackets are **counter ions**.

**Common coordination polyhedra**: Octahedral (6-coordinate), tetrahedral (4-coordinate), and square planar (4-coordinate) are most prevalent.

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Double Salts vs. Coordination Compounds

**Double salts** (e.g., Mohr's salt FeSO₄·(NH₄)₂SO₄·6H₂O, carnallite KCl·MgCl₂·6H₂O) are stoichiometric combinations that **completely dissociate** into simple ions when dissolved in water.

**Coordination compounds** (e.g., K₄[Fe(CN)₆]) do **not dissociate** into simple ions; the complex ion remains intact in solution. The Fe²⁺ and CN⁻ ions do not exist as free species under normal conditions.

**Exam distinction**: Double salts show conductivity patterns of simple salts; complexes show reduced conductivity due to the presence of large, intact complex ions.

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Definitions of Important Terms Pertaining to Coordination Compounds

**Coordination Entity**

A coordination entity consists of a central metal atom or ion bonded to a fixed number of ions or molecules in a specific geometric arrangement. Examples: [CoCl₃(NH₃)₃], [Ni(CO)₄], [Fe(CN)₆]⁴⁻, [Co(NH₃)₆]³⁺.

**Central Atom/Ion**

The atom or ion to which ligands are directly bonded in a definite geometrical arrangement. In [NiCl₂(H₂O)₄], the central ion is Ni²⁺. Central atoms/ions function as **Lewis acids** (electron pair acceptors).

**Ligands**

Ions or molecules bonded to the central atom/ion. Ligands are **Lewis bases** (electron pair donors).

**Types of ligands based on denticity**:

**Unidentate**: Binds through one donor atom (e.g., Cl⁻, NH₃, H₂O, CN⁻, NO₂⁻, SCN⁻)

**Didentate**: Binds through two donor atoms (e.g., ethane-1,2-diamine H₂NCH₂CH₂NH₂ (en), oxalate C₂O₄²⁻, 1,10-phenanthroline)

**Polydentate**: Binds through multiple donor atoms (e.g., EDTA⁴⁻ is hexadentate, binding via 2 nitrogen and 4 oxygen atoms; NTA (nitrilotriacetate) is tetradentate; N(CH₂CH₂NH₂)₃ is tetradentate)

**Chelate ligands**: Di- or polydentate ligands that use multiple donor atoms simultaneously to bind a single metal ion, forming **chelate complexes**. Chelate complexes are significantly more **stable** than analogous complexes with unidentate ligands (chelate effect).

**Ambidentate ligands**: Possess two different donor atoms; either atom can coordinate to the metal. Examples:

NO₂⁻ can coordinate through N (nitro, M-NO₂) or O (nitrito, M-ONO)

SCN⁻ can coordinate through S (thiocyanato-S) or N (thiocyanato-N, isothiocyanato)

CN⁻ can theoretically coordinate through C or N, but always coordinates through C

**Coordination Number (CN)**

The number of **sigma bonds** formed between ligand donor atoms and the central metal atom/ion. Pi bonds are not counted.

In [PtCl₆]²⁻, CN of Pt = 6

In [Ni(NH₃)₄]²⁺, CN of Ni = 4

In [Fe(C₂O₄)₃]³⁻, CN of Fe = 6 (oxalate is didentate; 3 × 2 = 6 sigma bonds)

In [Co(en)₃]³⁺, CN of Co = 6 (en is didentate; 3 × 2 = 6 sigma bonds)

**Common coordination numbers**: 4 (tetrahedral, square planar), 6 (octahedral), 2 (linear, rare).

**Coordination Sphere**

The central atom/ion and all ligands bonded to it, enclosed in **square brackets**. The coordination sphere represents the complex ion.

In K₄[Fe(CN)₆]:

Coordination sphere: [Fe(CN)₆]⁴⁻

Counter ion: K⁺

**Coordination Polyhedron**

The spatial arrangement of ligand atoms directly attached to the central atom. Common polyhedra:

**Octahedral**: 6 ligands at vertices of octahedron (e.g., [Co(NH₃)₆]³⁺, [Cr(H₂O)₆]³⁺)

**Tetrahedral**: 4 ligands at vertices of tetrahedron (e.g., [Ni(CO)₄], [ZnCl₄]²⁻)

**Square planar**: 4 ligands in square plane (e.g., [PtCl₄]²⁻, [Ni(CN)₄]²⁻)

**Oxidation Number of Central Atom**

The charge the central atom would carry if all ligands (with their electron pairs) are removed. Represented by Roman numeral in parentheses.

In [Cu(CN)₄]³⁻: Cu oxidation number = +1 (written Cu(I)); each CN⁻ carries −1 charge

In [Fe(CN)₆]⁴⁻: Fe oxidation number = +2 (Fe(II))

In [Co(NH₃)₆]³⁺: Co oxidation number = +3 (Co(III)); NH₃ is neutral

**Calculation method**: Charge on complex = oxidation number of metal + (number of ligands × charge on ligand)

**Homoleptic and Heteroleptic Complexes**

**Homoleptic**: Metal bonded to only one type of ligand (e.g., [Co(NH₃)₆]³⁺, [Ni(CO)₄])

**Heteroleptic**: Metal bonded to two or more types of ligands (e.g., [Co(NH₃)₄Cl₂]⁺, [CoCl(NH₃)₅]²⁺)

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Nomenclature of Coordination Compounds

**Formulas of Mononuclear Coordination Entities**

**Rules for writing formulas**:

1. Central atom listed first

2. Ligands listed in **alphabetical order** (ignoring numerical prefixes and charges)

3. Entire coordination entity enclosed in **square brackets**

4. Polyatomic ligand formulas and abbreviations enclosed in parentheses within the bracket

5. No space between ligand and metal within bracket

6. Charge indicated outside bracket as right superscript (number before sign): [Co(CN)₆]³⁻, [Cr(H₂O)₆]³⁺

7. Cation charge balanced by anion(s) outside bracket

**Examples**:

[Pt(NH₃)₂Cl(NO₂)] — alphabetically: Cl, NO₂, then NH₃; charge = +1 (Pt(II), 2 neutral NH₃, 1 Cl⁻, 1 NO₂⁻)

[CoCl₂(en)₂]⁺ — chlorido before ethane-1,2-diamine

K₃[Al(C₂O₄)₃] — potassium counter ions outside

**Naming of Mononuclear Coordination Compounds**

**Rules for naming** (alphabetical order of ligands **precedes** metal name, reverse of formula order):

1. **Cation named first** in both cationic and anionic complexes

2. **Ligands listed alphabetically** before central atom name

3. **Anionic ligands** end in **–o** (or –ido): chloro/chlorido, bromo/bromido, iodo/iodido, cyano, oxalato, hydroxo, sulfato, nitrato

4. **Neutral ligands**: Same name as molecule except:

H₂O → **aqua**

NH₃ → **ammine** (double m)

CO → **carbonyl**

NO → **nitrosyl**

5. **Prefixes**: mono, di, tri, tetra, penta, hexa for simple ligands. For ligands with numerical prefixes (like triphenylphosphine), use **bis, tris, tetrakis** with ligand in parentheses: bis(triphenylphosphine), tris(ethane-1,2-diamine)

6. **Oxidation state** of metal as Roman numeral in parenthesis after metal name

7. **Metal naming**:

In **cationic complex**: Use element name (e.g., cobalt, platinum, chromium)

In **anionic complex**: Use metal name + **–ate** suffix (e.g., cobaltate, ferrate, argentate); Latin names sometimes used (ferrate for Fe, cuprate for Cu)

8. **Neutral complexes**: Named like cations

**Worked examples**:

Example 1: [Cr(NH₃)₃(H₂O)₃]Cl₃

Complex cation: [Cr(NH₃)₃(H₂O)₃]³⁺

Ligands alphabetically: ammine before aqua

Name: **triamminetriaquachromium(III) chloride**

Oxidation state: Cr(III) because 3 Cl⁻ counter ions balance +3 charge from complex

Example 2: [Co(H₂NCH₂CH₂NH₂)₃]₂(SO₄)₃

Complex cation: [Co(en)₃]³⁺

Name: **tris(ethane-1,2-diamine)cobalt(III) sulphate**

Note: 2 complex cations × 3 charge = 6 positive; 3 SO₄²⁻ = 6 negative

Example 3: K₃[Cr(C₂O₄)₃]

Complex anion: [Cr(C₂O₄)₃]³⁻

Name: **potassium trioxalatochromate(III)**

Metal named as "chromate" (anionic complex); C₂O₄²⁻ → oxalato

Example 4: [Pt(NH₃)₂Cl(NO₂)]

Ligands alphabetically: chlorido, nitrito-N, then ammine (but ammine comes alphabetically after the others in the complex formula due to reverse order)

Name: **diamminechloridonitrito-N-platinum(II)**

Nitrito-N indicates coordination through nitrogen

Example 5: [CoCl₂(en)₂]Cl

Complex cation: [CoCl₂(en)₂]⁺

Name: **dichloridobis(ethane-1,2-diamine)cobalt(III) chloride**

"bis" used because "ethane-1,2-diamine" already contains a numerical prefix

Example 6: Hg[Co(SCN)₄]

Complex anion: [Co(SCN)₄]⁻

Name: **mercury(I) tetrathiocyanato-S-cobaltate(III)**

Hg(I) is the counter cation; SCN⁻ coordinates through S

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Isomerism in Coordination Compounds

**Isomerism**: Two or more compounds with the same molecular formula but different arrangements of atoms, resulting in different physical/chemical properties.

**Stereoisomerism (Same Bonds, Different Spatial Arrangement)**

#### **Geometrical Isomerism**

Arises in heteroleptic complexes (two or more types of ligands) where different spatial arrangements of ligands are possible.

**Square planar complexes** [MA₂B₂] where A and B are different unidentate ligands:

**cis-isomer**: A ligands adjacent (90° apart)

**trans-isomer**: A ligands opposite (180° apart)

Example: [PtCl₂(NH₃)₂]

**cis-[PtCl₂(NH₃)₂]** (cis-diamminedichloridoplatinum(II)): Cl atoms at 90°

**trans-[PtCl₂(NH₃)₂]** (trans-diamminedichloridoplatinum(II)): Cl atoms at 180°

These are **distinct compounds** with different properties (different colors, different reactivity, different solubility).

**Octahedral complexes** [MA₄B₂] where A is one ligand, B is another:

**cis-isomer**: B ligands at 90° (adjacent)

**trans-isomer**: B ligands at 180° (opposite)

Example: [CoCl₂(NH₃)₄]⁺

cis-[CoCl₂(NH₃)₄]⁺: Both Cl⁻ adjacent

trans-[CoCl₂(NH₃)₄]⁺: Both Cl⁻ opposite

**Octahedral complexes** [MA₃B₃] (also called meridional and facial isomers):

**Meridional (mer)**: B ligands occupy one meridian plane of octahedron

**Facial (fac)**: B ligands occupy one face of octahedron

Example: [CoCl₃(NH₃)₃]

**fac-[CoCl₃(NH₃)₃]**: Three Cl form one triangular face

**mer-[CoCl₃(NH₃)₃]**: Three Cl arranged meridionally

**Octahedral complexes** [MA₂B₂C₂]:

Can show cis-trans isomerism for different pairs of similar ligands

#### **Optical Isomerism**

Arises when a complex exhibits **chirality** (non-superimposable mirror images).

**Octahedral complexes** [MA₃B₃] with didentate ligands like en (ethane-1,2-diamine):

[Co(en)₃]³⁺ exists as two optical isomers: **d-form** and **l-form** (or (+) and (−))

These are **enantiomers** — mirror images that cannot be superimposed

They rotate plane-polarized light in opposite directions

They are chemically and physically identical except in direction of optical rotation

**Square planar [MA₂B₂]** (e.g., some platinum complexes) can show optical activity if the ligands create a chiral environment.

**Exam point**: Optical isomerism requires the complex to be **chiral** — lack of a plane of symmetry or inversion center.

**Structural Isomerism (Different Bonds)**

#### **Linkage Isomerism**

Arises when an **ambidentate ligand** (two possible donor atoms) coordinates to the metal through different donor atoms.

Example: NO₂⁻ (nitrite ion)

**Nitro complex**: [Co(NO₂)(NH₃)₅]²⁺ — NO₂ coordinates through N, forming Co-N bond

**Nitrito complex**: [Co(ONO)(NH₃)₅]²⁺ — NO₂ coordinates through O, forming Co-O bond

These are distinct compounds with different stability, reactivity, and properties.

Other ambidentate ligands:

**SCN⁻**: Thiocyanato-S (M-S-C≡N) vs. thiocyanato-N (isothiocyanato, M-N≡C-S)

**CN⁻**: Almost always coordinates through C (rare linkage through N)

#### **Coordination Isomerism**

Arises when the **distribution of ligands between two metal ions** in a polynuclear complex differs.

Example: [Co(NH₃)₆][CrCl₆] vs. [CrCl(NH₃)₅][CoCl₆]

First: All ammonia on Co, all chloride on Cr

Second: Ammonia and chloride shared between metals

This results in different colors and reactivity despite the same molecular formula.

#### **Ionisation Isomerism**

Arises when **ionisable groups** (counter ions and ligands) are exchanged between the coordination sphere and outside.

Example: [Co(NH₃)₅Cl]SO₄ vs. [Co(NH₃)₅(SO₄)]Cl

First: Chloride in coordination sphere, sulfate as counter ion → gives Cl⁻ in solution

Second: Sulfate in coordination sphere, chloride as counter ion → gives SO₄²⁻ in solution

Both have same molecular formula but different ionic composition and conductivity.

Another example: [Pt(NH₃)₄][PtCl₄] vs. [Pt(NH₃)₃Cl][PtCl₃(NH₃)]

#### **Solvate Isomerism (Hydrate Isomerism)**

Arises when the number of **solvent molecules (usually water)** coordinated vs. present outside the coordination sphere differs.

Example: [Cr(H₂O)₆]Cl₃ vs. [CrCl(H₂O)₅]Cl₂·H₂O

First: 6 water molecules coordinated, 3 Cl⁻ as counter ions

Second: 5 water molecules coordinated, 1 Cl⁻ coordinated, 1 H₂O as solvate molecule, 2 Cl⁻ as counter ions

All show different properties and chemical reactions despite same empirical formula.

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Bonding in Coordination Compounds

**Valence Bond Theory (VBT)**

**Basis**: Ligands donate electron pairs to empty orbitals on the central metal atom/ion. Bond formation is through **sigma bonding** (orbital overlap).

**Steps in complex formation**:

1. Metal ion has empty orbitals available for bonding

2. Ligand (Lewis base) donates electron pair into metal orbital

3. Dative covalent bond (coordinate bond) forms

4. Metal acts as Lewis acid; ligand as Lewis base

**Hybridization for common geometries**:

**Tetrahedral**: sp³ hybridization (e.g., [Ni(CO)₄], [ZnCl₄]²⁻)

**Octahedral**: d²sp³ hybridization (inner d orbitals) or sp³d² (outer d orbitals)

d²sp³: [Cr(NH₃)₆]³⁺, [Fe(CN)₆]⁴⁻ (inner orbital complexes, diamagnetic)

sp³d²: [Fe(H₂O)₆]³⁺ (outer orbital complexes, paramagnetic)

**Square planar**: dsp² hybridization (e.g., [Ni(CN)₄]²⁻, [PtCl₄]²⁻)

**Limitations of VBT**:

Cannot explain color of coordination compounds

Cannot explain magnetic properties accurately

Does not account for π bonding

Cannot predict relative stability of complexes

**Crystal Field Theory (CFT)**

**Basis**: Ligands produce an **electrostatic field** around the central metal ion, causing **d-orbital splitting**. Bonding is not necessarily covalent; ligands treated as point charges or dipoles.

**Key concepts**:

**d-orbital splitting in octahedral field**:

Ligands approach along x, y, z axes toward the metal ion

d_z² and d_x²-y² orbitals (pointing toward ligands) experience stronger repulsion → higher energy (e_g)

d_xy, d_xz, d_yz orbitals (pointing between ligands) experience weaker repulsion → lower energy (t_2g)

**Energy gap Δ (crystal field splitting parameter)**: Δ = E(e_g) − E(t_2g)

**d-orbital splitting in tetrahedral field**:

Ligands approach between the d orbitals (opposite to octahedral)

Splitting is **inverted**: t_2 orbitals higher than e orbitals

Splitting is smaller (~4/9 of octahedral splitting)

**Spectrochemical series** (ligands arranged by increasing field strength):

I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO

**Weak field ligands** (I⁻, H₂O): Small Δ, **high-spin** complexes (electron pairing unfavorable)

**Strong field ligands** (CN⁻, CO): Large Δ, **low-spin** complexes (electron pairing favorable)

**Crystal Field Stabilisation Energy (CFSE)**:

Energy gain from placing electrons in lower-energy d orbitals

For d⁶ in octahedral field with strong-field ligands (low-spin): CFSE = −1.6Δ (more stable)

For d⁶ in octahedral field with weak-field ligands (high-spin): CFSE = −0.4Δ (less stable)

**Color of coordination compounds**:

d-d transitions: Electrons absorb energy (photons) and jump from t_2g to e_g (octahedral)

Absorbed light color depends on Δ (related to ligand field strength)

Transmitted (observed) color is complementary

Example: [Cr(H₂O)₆]³⁺ is green (absorbs red light); [Cr(NH₃)₆]³⁺ is yellow (larger Δ, absorbs different wavelength)

**Magnetic properties**:

**Diamagnetic**: All electrons paired (low-spin d⁶, d⁸, etc.)

**Paramagnetic**: Unpaired electrons present (high-spin complexes)

**Limitations of CFT**:

Ligands treated as point charges; covalent character ignored

Cannot fully explain spectrochemical series

Overestimates electrostatic repulsion

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Stability of Coordination Compounds

**Complex stability** depends on:

**Chelate effect**: Chelate ligands form more stable complexes than unidentate ligands (entropy-driven; complex has more favorable entropy change)

**Ligand field strength**: Stronger field ligands form more stable complexes

**Nature of central metal ion**: Charge and size affect stability; higher charge and smaller size → more stable complex

**Stability constant (formation constant) K_f**:

For complex [M(L)_n] ⇌ M + nL

K_f = [M(L)_n] / ([M][L]^n)

Higher K_f → more stable complex. EDTA forms extremely stable complexes with many metal ions (high K_f values), making it useful in chelation therapy and analytical chemistry.

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Applications of Coordination Compounds

**Biological systems**: Hemoglobin (Fe²⁺ complex with porphyrin), chlorophyll (Mg²⁺ complex), vitamin B₁₂ (Co³⁺ complex), enzymes (metal cofactors)

**Metallurgical processes**: Extraction of metals; refining

**Industrial catalysts**: Hydrogenation catalysts, polymerization catalysts

**Analytical reagents**: EDTA for metal ion determination, complexometry

**Electroplating**: Metal surface deposition

**Textile dyeing**: Metal complexes as dyes

**Medicinal chemistry**: Cisplatin (anticancer drug), [Fe(CN)₆]⁴⁻ (treatment), chelation therapy

**Photography and pigments**: Metal complex dyes and sensitizers

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**Summary**: Coordination compounds are characterized by their coordination entity (metal + ligands), defined geometry, and rich isomerism patterns. VBT explains bonding as electron pair donation; CFT explains color and magnetism through d-orbital splitting. IUPAC nomenclature follows strict rules for unambiguous identification. Understanding these compounds is essential for biochemistry, industrial chemistry, and analytical methods.