Thermal intramolecular cobalt(III)-iron(II) and cobalt(III)-titanium(III) electron-transfer reactions involving outer-sphere and inner-sphere precursor complexes

1979 ◽  
Vol 18 (7) ◽  
pp. 1799-1807 ◽  
Author(s):  
Horst Bertram ◽  
Karl Wieghardt
Keyword(s):  
Electron Transfer ◽  
Outer Sphere ◽  
Transfer Reactions ◽  
Electron Transfer Reactions ◽  
Inner Sphere

Quantum theory of electron-transfer reactions

1996 ◽  
Author(s):  
Wolfgang Schmickler
Keyword(s):  
Electron Transfer ◽  
Outer Sphere ◽  
Transfer Reactions ◽  
Discrete Energy ◽  
Electron Transfer Reactions ◽  
Inner Sphere ◽  
Oppenheimer Approximation ◽  
Semiconductor Electrode ◽  
The Masses ◽  
Molecular Vibrational Modes

The theory of electron-transfer reactions presented in Chapter 6 was mainly based on classical statistical mechanics. While this treatment is reasonable for the reorganization of the outer sphere, the inner-sphere modes must strictly be treated by quantum mechanics. It is well known from infrared spectroscopy that molecular vibrational modes possess a discrete energy spectrum, and that at room temperature the spacing of these levels is usually larger than the thermal energy kT. Therefore we will reconsider electron-transfer reactions from a quantum-mechanical viewpoint that was first advanced by Levich and Dogonadze. In this course we will rederive several of, the results of Chapter 6, show under which conditions they are valid, and obtain generalizations that account for the quantum nature of the inner-sphere modes. By necessity this chapter contains more mathematics than the others, but the calculations are not particularly difficult. Readers who are not interested in the mathematical details can turn to the summary presented in Section 6. To be specific we consider electron transfer from a reactant in a solution, such as [Fe(H2O)6]2+, to an acceptor, which may be a metal or semiconductor electrode, or another molecule. To obtain wavefunctions for the reactant in its reduced and oxidized state, we rely on the Born-Oppenheimer approximation, which is commonly used for the calculation of molecular properties. This approximation is based on the fact that the masses of the nuclei in a molecule are much larger than the electronic mass. Hence the motion of the nuclei is slow, while the electrons are fast and follow the nuclei almost instantaneously. The mathematical consequences will be described in the following. Let us denote by R the coordinates of all the nuclei involved, those of the central ion, its ligarids, and the surrounding solvation sphere, and by r the coordinates of all electrons.

An insight into the outer- and inner-sphere electrochemistry of oxygenated single-walled carbon nanohorns (o-SWCNHs)

2019 ◽  
Vol 43 (46) ◽  
pp. 18210-18219 ◽  
Author(s):  
Arvind S. Ambolikar ◽  
Saurav K. Guin ◽  
Suman Neogy
Keyword(s):  
Electron Transfer ◽  
Outer Sphere ◽  
Transfer Reactions ◽  
Electron Transfer Reactions ◽  
Carbon Nanohorns ◽  
Single Walled Carbon ◽  
Inner Sphere ◽  
Insight Into

The electrocatalysis/interference of single-walled carbon nanohorns (o-SWCNHs) in relation to outer-sphere and inner-sphere electron transfer reactions.

‘Catalysis’ by anionic and cationic polyelectrolytes on reactions between cationic species: outer and inner sphere electron transfer reactions of Co complexes

1976 ◽  
Vol 351 (1665) ◽  
pp. 233-243 ◽  
Keyword(s):  
Electron Transfer ◽  
Outer Sphere ◽  
Electron Transfer Reaction ◽  
Cationic Polyelectrolyte ◽  
Transfer Reactions ◽  
Electron Transfer Reactions ◽  
Cationic Species ◽  
Enthalpy Of Activation ◽  
Inner Sphere ◽  
Cationic Polyelectrolytes

Electron transfer reactions of Co complexes with Fe 2+ (inner sphere) and with V 2+ (outer sphere) are studied in the presence of polyelectrolytes. Anionic polyelectrolytes accelerate the reactions remarkably, as expected. Two points are noteworthy: (1) the acceleration for the Fe 2+ systems is larger than that for the V 2+ reactions, in spite of the fact that both are divalent, and (2) electron transfer reaction between cationic species (Co(NH 3 ) 4 (N 3 ) 2 + and Fe 2+ ) is accelerated, though slightly, by addition of a cationic polyelectrolyte. This is in qualitative agreement with predictions based on Brönsted-Bjerrum-Manning theory. Temperature dependence study shows that the acceleration observed for the Fe 2+ cases is due to entropic gain whereas that in the case of V 2+ is ascribed to decrease in the enthalpy of activation.

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