Quantum effects in electron-transfer reactions

Siders, Paul; Marcus, R. A.

doi:10.1021/ja00394a003

Cited by 194 publications

(153 citation statements)

References 4 publications

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“…͑39͒, can be considerably simplified by estimating the time-integral in Eq. ͑39͒ using a saddle point method 16,47 and by dividing the whole frequency range of integration into two regions: 10,48 the low frequency region corresponding to Ͻ4k B T/ប and the high frequency region with Ͼ4k B T/ប. 48 We leave this calculation for a future work.…”

Section: E Representation Of ␣ In Terms Of a ''Free Energy'' Differencementioning

confidence: 99%

Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model

Georgievskii

Hsu

Marcus

1999

The Journal of Chemical Physics

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The effect of solvent fluctuations on the rate of electron transfer reactions is considered using linear response theory and a second-order cumulant expansion. An expression is obtained for the rate constant in terms of the dielectric response function of the solvent. It is shown thereby that this expression, which is usually derived using a molecular harmonic oscillator ͑''spin-boson''͒ model, is valid not only for approximately harmonic systems such as solids but also for strongly molecularly anharmonic systems such as polar solvents. The derivation is a relatively simple alternative to one based on quantum field theoretic techniques. The effect of system inhomogeneity due to the presence of the solute molecule is also now included. An expression is given generalizing to frequency space and quantum mechanically the analogue of an electrostatic result relating the reorganization free energy to the free energy difference of two hypothetical systems ͓J. Chem. Phys. 39, 1734 ͑1963͔͒. The latter expression has been useful in adapting specific electrostatic models in the literature to electron transfer problems, and the present extension can be expected to have a similar utility.

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Section: E Representation Of ␣ In Terms Of a ''Free Energy'' Differencementioning

confidence: 99%

Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model

Georgievskii

Hsu

Marcus

1999

The Journal of Chemical Physics

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“…The Franck-Condon term F can be evaluated analytically if the vibrational wave functions are assumed to be displaced harmonic oscillators. In the limit of high temperature, when these oscillators can be treated classically, the Franck-Condon term takes a particularly simple form [34]:…”

Section: General Expression For the Charge Recombination Reaction Ratementioning

confidence: 99%

An expression for the bridge-mediated electron transfer rate in dye-sensitized solar cells

Maggio

Troisi

2014

Phil. Trans. R. Soc. A.

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We have derived an expression for the rate of electron transfer between a semiconductor and a redox centre connected to the semiconductor via a molecular bridge. This model is particularly useful to study the charge recombination (CR) process in dye-sensitized solar cells, where the dye is often connected to the semiconductor by a conjugated bridge. This formalism, designed to be coupled with density functional theory electronic structure calculations, can be used to explore the effect of changing the bridge on the rate of interfacial electron transfer. As an example, we have evaluated the CR rate for a series of systems that differ in the bridge length.

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“…In the harmonic oscillator approach ͑with finite N, which at the end is allowed to become infinite͒, the solvent Hamiltonian H g in the ground electronic state can be written as 54,[56][57][58] …”

Section: The Modelmentioning

confidence: 99%

“…When the resulting change of electronic state after an electronic transition leads only to shifts of the normal modes but not to changes in their frequency, the solvent Hamiltonian H e in the excited electronic state can be written as 54,[56][57][58] …”

Section: The Modelmentioning

confidence: 99%

“…The harmonic approximation for intramolecular modes is often used for electron transfer and other nonadiabatic electronic transitions. 57,58 One can then assume that the sum in Eqs. ͑1͒ and ͑2͒ is not only over the solvent modes but also over the intramolecular solute modes, neglecting any change in their frequencies as a result of the electronic transition.…”

Section: ͑2͒mentioning

confidence: 99%

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Dynamic Stokes shift in solution: Effect of finite pump pulse duration

Georgievskii

Hsu

Marcus

1998

The Journal of Chemical Physics

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The time-evolution of the fluorescence spectrum of a dissolved chromophore excited by an ultrafast pump pulse is considered. The average value of the energy difference of the solute in its excited and ground states is used to describe the relaxation of the maximum of the transient fluorescence spectrum to its equilibrium value ͑dynamic Stokes shift, DSS͒. A simple formula for the normalized DSS is obtained which generalizes an earlier standard classical expression and includes the effect of a pump pulse of finite duration. As an example, dielectric dispersion data are used for a dipolar solute in water to estimate the quantum correction to the standard DSS expression. The correction is negligible when the frequency of the pump pulse is close to the maximum in the absorption spectrum, but a deviation from the standard formula can be expected for the pump pulse tuned to a far wing of the absorption band of the chromophore. An expression is given for this deviation.

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Quantum effects in electron-transfer reactions

Cited by 194 publications

References 4 publications

Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model

Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model

An expression for the bridge-mediated electron transfer rate in dye-sensitized solar cells

Dynamic Stokes shift in solution: Effect of finite pump pulse duration

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