4.3 Electron Transfer Reactions

Electron transfer reactions are crucial in coordination chemistry, involving the movement of electrons between metal centers. These reactions can occur through inner-sphere or outer-sphere mechanisms, depending on factors like metal centers, ligands, and solvents.

The rate of electron transfer is influenced by driving force, reorganization energy, distance, and electronic coupling. Understanding these factors helps predict reaction rates and mechanisms, connecting to the broader study of coordination compound reactivity.

Inner-Sphere vs Outer-Sphere Electron Transfer

Mechanisms and Bridging Ligands

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• Inner-sphere electron transfer reactions involve the formation of a bridging ligand between the two metal centers, allowing for direct electron transfer through the bridging ligand
• The inner-sphere mechanism typically involves the formation of a binuclear complex, where the two metal centers are connected by a bridging ligand, followed by electron transfer and dissociation of the complex
• Examples of bridging ligands in inner-sphere electron transfer include chloride (Cl⁻), cyanide (CN⁻), and pyrazine (C₄H₄N₂)

Outer-Sphere Electron Transfer and Encounter Complexes

• Outer-sphere electron transfer reactions do not involve the formation of a bridging ligand, and electron transfer occurs through space or via a solvent molecule
• The outer-sphere mechanism involves the formation of an encounter complex, where the two metal centers are in close proximity, followed by electron transfer and dissociation of the complex
• Examples of outer-sphere electron transfer reactions include the reduction of [Fe(CN)₆]³⁻ by [Ru(NH₃)₆]²⁺ and the oxidation of [Fe(H₂O)₆]²⁺ by [Co(NH₃)₅Cl]²⁺

Factors Influencing the Choice of Mechanism

• The choice between inner-sphere and outer-sphere mechanisms depends on factors such as the nature of the metal centers, ligands, and solvent
• Metal centers with easily exchangeable ligands and the ability to form stable bridged intermediates favor the inner-sphere mechanism
• Bulky or strongly bound ligands that hinder the formation of bridged intermediates favor the outer-sphere mechanism
• Solvents with high dielectric constants and the ability to stabilize charged intermediates favor the outer-sphere mechanism

Factors Influencing Electron Transfer Rates

Driving Force and Reorganization Energy

• The rate of electron transfer reactions is influenced by the driving force of the reaction, which is determined by the difference in reduction potentials of the two metal centers
• A larger difference in reduction potentials leads to a greater driving force and faster electron transfer rates
• The reorganization energy, which is the energy required to adjust the nuclear configurations of the reactants and the solvent to the transition state geometry, also affects the rate of electron transfer reactions
• Higher reorganization energies lead to slower electron transfer rates due to the increased energy barrier for the reaction

Distance and Electronic Coupling

• The distance between the two metal centers plays a crucial role in determining the rate of electron transfer, with the rate decreasing exponentially with increasing distance
• This distance dependence arises from the exponential decay of electronic coupling between the donor and acceptor orbitals as the distance increases
• The nature of the bridging ligand in inner-sphere mechanisms can affect the rate of electron transfer by modulating the electronic coupling between the metal centers
• Conjugated or π-electron-rich bridging ligands can enhance electronic coupling and increase electron transfer rates

Solvent Effects and Spin States

• The solvent can influence the rate and mechanism of electron transfer reactions by affecting the reorganization energy and the stability of the encounter complex
• Polar solvents with high dielectric constants can stabilize charged intermediates and lower the reorganization energy, leading to faster electron transfer rates
• The spin states of the metal centers can also impact the rate and mechanism of electron transfer reactions, with spin-allowed transitions generally being faster than spin-forbidden transitions
• Electron transfer between metal centers with the same spin state (e.g., high-spin Fe²⁺ and high-spin Fe³⁺) is typically faster than between metal centers with different spin states (e.g., low-spin Fe²⁺ and high-spin Fe³⁺)

Thermodynamics and Kinetics of Electron Transfer

Driving Force and Marcus Theory

• The thermodynamic driving force for an electron transfer reaction is determined by the difference in reduction potentials of the two metal centers, with a larger difference leading to a more favorable reaction
• The Marcus theory provides a framework for understanding the relationship between the thermodynamic driving force, reorganization energy, and the rate of electron transfer reactions
• According to Marcus theory, the rate of electron transfer is maximal when the driving force equals the reorganization energy, and decreases when the driving force is either larger or smaller than the reorganization energy

Activation Barrier and Gibbs Free Energy

• The activation barrier for an electron transfer reaction is determined by the reorganization energy and the thermodynamic driving force, with the optimal rate occurring when the driving force equals the reorganization energy
• The Gibbs free energy change for an electron transfer reaction can be calculated using the Nernst equation, which relates the reduction potentials of the metal centers to the concentrations of the reactants and products
• The Nernst equation is given by: $\Delta G = -nFE$, where $\Delta G$ is the Gibbs free energy change, $n$ is the number of electrons transferred, $F$ is the Faraday constant, and $E$ is the cell potential

Rate Constants and Marcus Cross Relation

• The rate constant for an electron transfer reaction can be described by the Arrhenius equation, which relates the rate constant to the activation energy and temperature
• The Arrhenius equation is given by: $k = Ae^{-E_a/RT}$, where $k$ is the rate constant, $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the temperature
• The Marcus cross relation can be used to predict the rate constant for an electron transfer reaction based on the self-exchange rate constants of the individual metal centers and the equilibrium constant for the overall reaction
• The Marcus cross relation is given by: $k_{12} = (k_{11}k_{22}K_{12}f)^{1/2}$, where $k_{12}$ is the rate constant for the cross reaction, $k_{11}$ and $k_{22}$ are the self-exchange rate constants for the individual metal centers, $K_{12}$ is the equilibrium constant for the cross reaction, and $f$ is a factor that depends on the reorganization energy and the driving force