21

Coordination Chemistry

Reactions of Complexes

M
L
L
L
L
L
X
Y

Exploring reaction mechanisms, ligand substitution, electron transfer, and photochemistry in coordination compounds

21.1 Rates of Ligand Substitution

Key Points

Rates of substitution reactions span a very wide range and correlate with complex structures. Complexes that react quickly are called labile; those that react slowly are called inert or nonlabile.

The most fundamental reaction a complex can undergo is ligand substitution:

Y + M−X → M−Y + X

Lability Scale of Aqua Complexes

Characteristic lifetimes for H₂O exchange vary from nanoseconds to years:

Labile (10⁻¹⁰ s) Nonlabile (10⁸ s)
Extremely Labile
K⁺, Na⁺, Ba²⁺, Ca²⁺
Moderately Labile
Cu²⁺, Zn²⁺, Mn²⁺, Fe²⁺
Less Labile
Ni²⁺, Co²⁺, Fe³⁺
Nonlabile
Cr³⁺, Co³⁺, Ir³⁺, Rh³⁺

Factors Affecting Lability

Electronic Configuration

Complexes with d³ and low-spin d⁶ configurations (Cr(III), Fe(II), Co(III)) are generally nonlabile due to high LFSE.

Metal Ion Size

Very small ions (Be²⁺, Mg²⁺) are less labile due to stronger M−L bonds and steric hindrance to approaching ligands.

Metal Charge

M(III) ions are generally less labile than M(II) ions due to stronger electrostatic attraction to ligands.

Chelate Effect

Chelate complexes like [Fe(phen)₃]²⁺ are particularly nonlabile due to entropic stabilization.

Timescale Process Example
10⁸ s (~32 years) Ligand exchange (inert) [Cr(OH₂)₆]³⁺ − H₂O
60 s Ligand exchange (nonlabile) [V(OH₂)₆]³⁺ − H₂O
1 ms Ligand exchange (labile) [Pt(OH₂)₄]²⁺ − H₂O
1 μs Intervalence charge transfer Ru(II)−Ru(III) mixed valence
1 ns Ligand exchange (very labile) [Ni(OH₂)₅(py)]²⁺ − H₂O
10 ps Ligand association Cr(CO)₅ + THF
1 fs Molecular vibration Sn−Cl stretch

21.2 Classification of Mechanisms

Key Points

Mechanisms are classified as associative (A), dissociative (D), or interchange (I). The rate-determining step may be associatively activated (a) or dissociatively activated (d).

Dissociative (D)

ML₅X ML₅ + X ML₅Y

ML₅X → ML₅ + X
ML₅ + Y → ML₅Y

Intermediate with reduced coordination number

Associative (A)

ML₅X + Y ML₅XY ML₅Y

ML₅X + Y → ML₅XY
ML₅XY → ML₅Y + X

Intermediate with increased coordination number

Interchange (I)

ML₅X + Y ‡ [X···M···Y] ML₅Y + X

ML₅X + Y → [X···ML₅···Y]‡ → ML₅Y + X

Single step with transition state (no intermediate)

Reaction Profile Diagrams

Reaction Coordinate Potential Energy Dissociative (D) Associative (A) Interchange (I) X−M + Y X + M−Y
Mechanism A I D
Activation a or d a or d a or d
Rate-determining step (a) Y attaching to ML₅X Y attaching to ML₅X Y attaching to ML₅
Rate-determining step (d) Loss of X from YML₅X Loss of X from YML₅X Loss of X from ML₅X
Detect intermediate? ML₅XY (if Ad) No ML₅ (if Dd)

21.3-21.4 Ligand Substitution in Square-Planar Complexes

Key Points

Square-planar complexes (especially Pt(II)) typically undergo associative substitution through a trigonal-bipyramidal transition state. The trans effect and nucleophilicity of the entering group are crucial factors.

Rate Law for Square-Planar Substitution

rate = (k₁ + k₂[Y])[PtL₄]

This two-term rate law indicates:

Nucleophilicity Parameter (nPt)

nPt = log(k₂(Y) / k₂°)

where k₂° is the rate constant for the reference nucleophile (methanol).

Nucleophilicity Values

Nucleophile Donor nPt
CH₃OHO0
Cl⁻Cl3.04
Br⁻Br4.18
I⁻I5.42
SCN⁻S5.75
CN⁻C7.14
(C₆H₅)₃PP8.93

Nucleophilicity correlates with soft Lewis basicity

Nucleophilic Discrimination Factor (S)

log k₂(Y) = S·nPt(Y) + C

S characterizes sensitivity to nucleophilicity:

Complex S
trans-[PtCl₂(PEt₃)₂]1.43
trans-[PtCl₂(py)₂]1.00
[PtCl₂(en)]0.64
trans-[PtCl(dien)]⁺0.65

The Trans Effect

The trans effect is the ability of a ligand T to labilize the ligand trans to itself. It combines:

Trans Effect Series

OH⁻ < NH₃ < Cl⁻ < Br⁻ < I⁻, SCN⁻ < PR₃, H⁻ < CN⁻, CO, C₂H₄

Synthesis of cis-[PtCl₂(NH₃)₂] (Cisplatin)

[PtCl₄]²⁻ + NH₃ → [PtCl₃(NH₃)]⁻ + Cl⁻
[PtCl₃(NH₃)]⁻ + NH₃ → cis-[PtCl₂(NH₃)₂] + Cl⁻

Starting from [PtCl₄]²⁻, Cl⁻ has higher trans effect than NH₃, so the second NH₃ substitutes trans to Cl⁻ → cis product

Synthesis of trans-[PtCl₂(NH₃)₂]

[Pt(NH₃)₄]²⁺ + Cl⁻ → [PtCl(NH₃)₃]⁺ + NH₃
[PtCl(NH₃)₃]⁺ + Cl⁻ → trans-[PtCl₂(NH₃)₂] + NH₃

Starting from [Pt(NH₃)₄]²⁺, the second Cl⁻ enters trans to the first Cl⁻ (higher trans effect) → trans product

Stereochemistry

Substitution of square-planar complexes generally preserves geometry (cis → cis, trans → trans) through a trigonal-bipyramidal transition state.

M

Square Planar

→
M

Trigonal Bipyramidal TS

→
M

Square Planar Product

21.5-21.9 Ligand Substitution in Octahedral Complexes

Key Points

Most octahedral complexes react by the interchange (I) mechanism. The key question is whether the rate-determining step is Ia (associative activation) or Id (dissociative activation).

The Eigen-Wilkins Mechanism

Involves formation of an encounter complex in a pre-equilibrium step:

ML₆ + Y ⇌ {ML₆, Y}    KE (pre-equilibrium)
{ML₆, Y} → ML₅Y + L    k (rate-determining)

Resulting Rate Law

rate = kKE[M]tot[Y] / (1 + KE[Y])

When KE[Y] ≪ 1:

rate = kobs[M]tot[Y]    where kobs = kKE

Fuoss-Eigen Equation

Estimates the encounter equilibrium constant:

KE = (4πa³NA/3) × e−V/kBT

where a is the distance of closest approach and V is the Coulombic potential energy.

Factors Affecting Octahedral Substitution

Leaving Group Effects

Large effect in Id reactions. Linear free-energy relation (LFER):

ln k = ln K + c

Rate increases: F⁻ < H₂PO₄⁻ < Cl⁻ < Br⁻ < I⁻ < NO₃⁻

Spectator Ligand Effects

Stronger σ-donors (like NH₃ vs H₂O) increase rates by:

  • Increasing electron density at metal
  • Facilitating M−X bond breaking
  • Stabilizing reduced coordination number

Steric Effects

Bulky ligands favor Id by:

  • Crowding that inhibits association
  • Strain relief in transition state

Tolman cone angles quantify steric bulk

Ligand Field Activation Energy

LFAE = LFSE‡ − LFSE

Large LFAE → nonlabile complexes

d³, d⁶ (low-spin) have largest LFAE

Volume of Activation (Δ‡V)

Metal Ion Configuration Δ‡H (kJ/mol) Δ‡V (cm³/mol) Mechanism
V²⁺ d³ 68.6 −4.1 Ia
Mn²⁺ d⁵ (hs) 33.9 −5.4 Ia
Fe²⁺ d⁶ (hs) 31.2 +3.8 Id
Co²⁺ d⁷ (hs) 43.5 +6.1 Id
Ni²⁺ d⁸ 58.1 +7.2 Id

Negative Δ‡V indicates associative character (shrinkage); positive indicates dissociative (expansion)

Base Hydrolysis

For complexes with N−H bonds, OH⁻ acts as a Brønsted base, not a nucleophile:

[CoCl(NH₃)₅]²⁺ + OH⁻ ⇌ [CoCl(NH₂)(NH₃)₄]⁺ + H₂O    (fast equilibrium)
[CoCl(NH₂)(NH₃)₄]⁺ → [Co(NH₂)(NH₃)₄]²⁺ + Cl⁻    (slow, rate-determining)
[Co(NH₂)(NH₃)₄]²⁺ + H₂O → [Co(OH)(NH₃)₅]²⁺    (fast)

Evidence: 18O/16O ratio in product matches H₂O, not OH⁻

Why is this fast?

  • NH₂⁻ is a strong σ-donor (lowers charge on complex)
  • NH₂⁻ is a π-donor (stabilizes 5-coordinate transition state)

Isomerization Reactions

Berry Pseudorotation

Exchange of axial and equatorial ligands in trigonal-bipyramidal intermediates through a square-pyramidal transition state.

Can lead to cis ↔ trans isomerization

Bailar Twist

Intramolecular twist in octahedral complexes without bond breaking. Racemization of [Ni(en)₃]²⁺ occurs this way.

Ray-Dutt Twist

Alternative twist mechanism for octahedral isomerization, also without ligand loss.

21.10-21.12 Redox Reactions

Key Points

Electron transfer in complexes occurs by two mechanisms: inner-sphere (with bridging ligand) and outer-sphere (electron tunneling without bridging). The Marcus equation predicts rates for outer-sphere reactions.

Inner-Sphere Mechanism

Coordination spheres share a bridging ligand transiently:

M-Cl M' Cl
[CoIIICl(NH₃)₅]²⁺ + [CrII(OH₂)₆]²⁺ →
[CoII(OH₂)₆]²⁺ + [CrIIICl(OH₂)₅]²⁺

Evidence:

  • Cl transfers from Co to Cr
  • No ³⁶Cl incorporation from solution
  • Products contain nonlabile Cr(III)

Good bridging ligands:

Cl⁻, Br⁻, I⁻, N₃⁻, CN⁻, SCN⁻, pyrazine, 4,4'-bipyridine

Outer-Sphere Mechanism

Electron tunnels between metals without bridging ligand:

Fe³⁺ Fe²⁺ e⁻
[Fe(OH₂)₆]³⁺ + [Fe(OH₂)₆]²⁺ →
[Fe(OH₂)₆]²⁺ + [Fe(OH₂)₆]³⁺

Requirements:

  • Orbital overlap for tunneling
  • Nuclear reorganization (Franck-Condon)
  • Conservation of energy

Marcus Theory

The Marcus Equation

kET = νNκe exp(−Δ‡G/RT)

where:

  • νN = nuclear frequency factor
  • κe = electronic factor (probability of electron transfer)
Δ‡G = ¼λ(1 + ΔrG°/λ)²

where λ is the reorganization energy:

  • Inner-sphere λ: Changes in M−L bond lengths
  • Outer-sphere λ: Solvent reorganization

Key Predictions

Self-Exchange (ΔrG° = 0)

Δ‡G = λ/4

Rate controlled by reorganization energy

Activationless (ΔrG° = −λ)

Δ‡G = 0

Maximum rate achieved

Inverted Region (|ΔrG°| > λ)

Rate decreases as reaction becomes more favorable!

Important in photosynthesis

Marcus Cross-Relation

Predicts rate constants for reactions between different species:

k12 = (k11 k22 K12 f12)1/2

where k11 and k22 are self-exchange rate constants

Reaction Electron Config Δd (pm) k₁₁ (dm³/mol·s)
[Cr(OH₂)₆]³⁺/²⁺ t₂g³/t₂g³eg¹ 20 1 × 10⁻⁵
[V(OH₂)₆]³⁺/²⁺ t₂g²/t₂g³ 13 1 × 10⁻⁵
[Fe(OH₂)₆]³⁺/²⁺ t₂g³eg²/t₂g⁴eg² 13 1.1
[Ru(OH₂)₆]³⁺/²⁺ t₂g⁵/t₂g⁶ 9 20
[Co(NH₃)₆]³⁺/²⁺ t₂g⁶/t₂g⁵eg² 22 6 × 10⁻⁶
[Fe(bpy)₃]³⁺/²⁺ t₂g⁵/t₂g⁶ 0 3 × 10⁸
[Ru(bpy)₃]³⁺/²⁺ t₂g⁵/t₂g⁶ 0 4 × 10⁸

Key observations: t₂g ↔ t₂g transfers (nonbonding) are fast; eg involvement (σ* antibonding) causes large Δd and slow rates; bipyridyl shields from solvent and allows π-delocalization.

21.13-21.15 Photochemical Reactions

Key Points

Photon absorption (170-600 kJ/mol) opens new reaction channels. Reactions are classified as prompt (immediate dissociation) or delayed (long-lived excited state). d−d transitions typically cause photosubstitution; charge-transfer transitions enable photoredox.

Prompt Reactions (< 10 ps)

Immediate dissociation after photon absorption:

[Cr(CO)₆] + hν → [Cr(CO)₅] + CO
[CoIIICl(NH₃)₅]²⁺ + hν → [CoII(NH₃)₅]²⁺ + Cl·

Quantum yield increases with shorter λ (higher energy photons)

Delayed Reactions

Long-lived excited states act as energetic isomers:

Example: *[Ru(bpy)₃]²⁺ has a lifetime of ~600 ns

Can be treated as Ru(III) with radical anion ligand

d−d vs Charge-Transfer Transitions

Photoexcitation of [Ru(bpy)₃]²⁺

[RuII(bpy)₃]²⁺ Ground state [RuIII(bpy)(bpy·⁻)(bpy)]²⁺* Excited state hν (590 nm) +202 kJ/mol Energy

E° = −0.84 V (ground state) → E° = +1.26 V (excited state as oxidant)

Types of Photoreactions

Transition Type Electronic Change Typical Reaction Example
d−d t₂g → eg (angular redistribution) Photosubstitution, Photoisomerization [Cr(NH₃)₆]³⁺ + H₂O → [Cr(NH₃)₅(OH₂)]³⁺
MLCT Metal → Ligand (radial redistribution) Photoredox (metal oxidation) [Ru(bpy)₃]²⁺* + oxidant
LMCT Ligand → Metal (radial redistribution) Photoredox (metal reduction) [CoIIICl(NH₃)₅]²⁺ → CoII + Cl·

Metal-Metal Bonded Systems

δ* ← δ Transitions

Population of metal-metal antibonding orbitals can initiate:

  • Photodissociation of M−M bond
  • Multielectron photoredox chemistry

Example: [Pt₂(μ-P₂O₅H₂)₄]⁴⁻ ("PtPOP")

  • No M−M bond in ground state (d⁸−d⁸)
  • Excitation creates M−M bonding orbital population
  • Excited state lifetime: 9 μs
  • Powerful reducing agent

Grätzel cells (Dye-Sensitized Solar Cells) use Ru(II) complexes like N-3 dye:

cis-[Ru(dcbpy)₂(NCS)₂] (dcbpy = 4,4'-dicarboxylato-2,2'-bipyridyl)

Mechanism:

  1. Light absorption (MLCT): Ru²⁺ → Ru³⁺ + e⁻(ligand)
  2. Electron injection into TiO₂ conduction band (ps timescale)
  3. Electron diffusion through TiO₂ to electrode
  4. Ru³⁺ reduction by I⁻ electrolyte (ns timescale)
  5. I₃⁻ reduced at counter electrode

Efficiency ~11% - limited by recombination reactions

Chapter Summary

Ligand Substitution

  • Lability depends on LFSE, ion size, charge
  • Mechanisms: A, D, I (with a or d activation)
  • Square-planar: associative, trans effect important
  • Octahedral: usually interchange mechanism

Electron Transfer

  • Inner-sphere: bridging ligand required
  • Outer-sphere: electron tunneling
  • Marcus theory: λ controls rates
  • Inverted region at large |ΔrG°|

Photochemistry

  • d−d → photosubstitution
  • CT → photoredox
  • Prompt vs delayed reactions
  • Applications: solar cells, catalysis