Theory of highly exothermic electron transfer reactions

Marcus, R. A.; Siders, Paul

doi:10.1021/j100394a009

Cited by 180 publications

(129 citation statements)

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“…In this formalism, when the reactants approach each other to some separation distance R, there is a "work term" w r ðRÞ, including any electrostatic interaction and/or structural reorientation. [In the electron transfer theory there is a weighted integral over a separation distance coordinate R involving an electronic transition probability pðRÞ, the pair distribution function of the reactants gðRÞ, and the dependence of ΔG † ðRÞ on R (22)(23)(24).] This work is then, in the theory, followed by the reaction, which includes any chemical or other structural changes, and in turn followed by a separation of the products from R to ∞, involving a work term, −w p ðRÞ (16).…”

Section: Significancementioning

confidence: 99%

Theory for rates, equilibrium constants, and Brønsted slopes in F ₁ -ATPase single molecule imaging experiments

Volkan-Kacso

Marcus

2015

Proc. Natl. Acad. Sci. U.S.A.

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A theoretical model of elastically coupled reactions is proposed for single molecule imaging and rotor manipulation experiments on F 1 -ATPase. Stalling experiments are considered in which rates of individual ligand binding, ligand release, and chemical reaction steps have an exponential dependence on rotor angle. These data are treated in terms of the effect of thermodynamic driving forces on reaction rates, and lead to equations relating rate constants and free energies to the stalling angle. These relations, in turn, are modeled using a formalism originally developed to treat electron and other transfer reactions. During stalling the free energy profile of the enzymatic steps is altered by a work term due to elastic structural twisting. Using biochemical and single molecule data, the dependence of the rate constant and equilibrium constant on the stall angle, as well as the Børnsted slope are predicted and compared with experiment. Reasonable agreement is found with stalling experiments for ATP and GTP binding. The model can be applied to other torque-generating steps of reversible ligand binding, such as ADP and P i release, when sufficient data become available. S ingle molecule imaging directly demonstrated a stepping rotation in F 1 -ATPase (1) that was resolved into ∼ 40°and ∼ 80°s ubsteps (initially reported as ∼ 30°and ∼ 90°; cf. refs. 2 and 3), and much information has been extracted by elaborate techniques at the single molecule level (3-6). Complementing experimental tools such as X-ray spectroscopy (7) and ensemble biochemical methods (8), single molecule experiments reveal key details of the coupling between enzymatic processes and rotation (9-12). A detailed picture of highly coordinated substeps has emerged in which the binding of solution ATP to an empty subunit and release of hydrolyzed ADP from the clockwise neighbor (viewed from the rotor side) occur in concert during the ∼ 80°rotation step (13). As depicted in Fig. 1 and Table 1, the subsequent ∼ 40°r otation is coordinated with the hydrolysis of ATP in the third subunit and the release of P i from the subunit that just released ADP (13).Recent stalling (6,13,14) and controlled rotation (15) experiments provide additional insight into the dynamics of the coupling between the rotation of the central shaft and the reaction steps in the stator ring subunits. These experiments yielded the rate constants of various steps, binding and release of ligands, and hydrolysis/synthesis reaction, as a function of the stalled rotor angle θ. The rates show an exponential dependence on θ over a wide range, such as a range of 80°for ATP binding and 40°for hydrolysis. Free energy profiles for the initial and final dwell angles at a specific 40°or 80°step are given in Fig. 2. For intermediate stalling angles, the profile is intermediate between these two limits.In stalling experiments (14) the freely rotating shaft of the ATPase is stalled by magnetic tweezers upon reaching a dwell angle. Rotation experiments have resolved two dwells: the binding dwell (before...

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Section: Significancementioning

confidence: 99%

Theory for rates, equilibrium constants, and Brønsted slopes in F ₁ -ATPase single molecule imaging experiments

Volkan-Kacso

Marcus

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…11 It has been proposed that such deviations may involve electronically excited states of the product radical anion of para-benzoquinone (pBQ• -), 12 which could provide reaction pathways that bypass the barrier, as shown in Figure 1a with purple arrows. 6,[13][14][15][16][17] At present, very little is known about the excited state dynamics of pBQ• -and, more generally, most radical ions. Here, we take a bottom-up view of electron transfer and consider what happens to the excited states that are initially formed following electron capture by an isolated pBQ molecule.…”

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confidence: 99%

Ultrafast above-threshold dynamics of the radical anion of a prototypical quinone electron-acceptor

et al. 2013

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. (2013) 'Ultrafast above-threshold dynamics of the radical anion of a prototypical quinone electron-acceptor.', Nature chemistry., 5 (8). pp. 711-717. Further information on publisher's website:https://doi.org/10.1038/nchem.1705Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Quinones are found throughout nature as key electron acceptor intermediates, 1,2 with examples including plastoquinone which is involved in the electron transfer chain of photosystem II, and ubiquinone (coenzyme Q10) which plays a key role in aerobic cellular respiration. 3 The central moiety responsible for the electron accepting ability in quinones is para-benzoquinone (pBQ), shown in Figure 1c. Electron transfer reactions involving pBQ can be highly exergonic and are therefore often classed as being in the Marcus inverted region. [4][5][6][7][8][9][10] This is shown schematically by the green path in Figure 1a, where a barrier between the Gibbs free energy of the reactants and products lowers the rates of the electron transfer process. However, even in the earliest experimental verifications of the inverted region for intramolecular electron transfer, several electron acceptors based on pBQ showed marked deviations from the expected behaviour, with transfer rates approaching those of a barrierless reaction. 11 It has been proposed that such deviations may involve electronically excited states of the product radical anion of para-benzoquinone (pBQ• -), 12 which could provide reaction pathways that bypass the barrier, as shown in Figure 1a with purple arrows. Figure 1b shows the location of these resonances.From the point of view of an electron approaching pBQ, these anionic resonances in the detachment continuum can capture an electron. Subsequent formation of the anionic ground state through internal conversion would redistribute the excess internal energy amongst all the vibrational modes. In a condensed-phase environment, this energy will be quenched by the surroundings. However, the initially formed excited states of pBQ• -can be unbound with respect to electron loss. For the above picture to be feasible, internal conversion must be able to compete with autodetachment. Electron attachment spectra suggest that it can, 26-28 but how does this occur given that these resonances are in some cases > 1 eV above the detachment threshold?In order to gain a fundamental understanding of the processes involved following electron capture, it is necessary to observe the relaxation dynamics in real t...

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“…As is shown in the figure, the absorption decay was faster than the bleach recovery. The decay of the absorption band has been [13][14][15] where Vel is the electronic coupling matrix element evaluated at the equilibrium nuclear geometry, oeg the energy difference between the potential minima of the excited and the ground electronic states, and Re signifies the real part of the integral. g(t) is a solvent lineshape function.…”

Section: Resultsmentioning

confidence: 99%

Electron-Transfer Rate in the Charge Transfer Complex in the Supercritical Fluids.

Kimura

Takebayashi

Hirota

1998

THE REVIEW OF HIGH PRESSURE SCIENCE AND TECHNOLOGY

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The back-electron transfer (b-ET) process in the hexamethy]benzene/tetracyanoethylene charge-transfer complex was studied by the transient absorption spectroscopy in several fluids (ethane, nitrous oxide, carbon dioxide, and trifluoromethane) from the critical density to twice of it at 323.2 K. The b-ET rate increased with increasing the solvent density, and also increased in the order of ethane, nitrous oxide, carbon dioxide and trifluoromethane, compared at the similar reduced density divided by the solvent critical density. The b-ET rates in various fluids were well correlated with the theoretical b-ET rates estimated from the analysis of the absorption spectra based on the formulation by Marcus and Jortner.[charge transfer complex, electron transfer rate, supercritical fluid, isotope effect, transient absorption]

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Theory of highly exothermic electron transfer reactions

Cited by 180 publications

References 20 publications

Theory for rates, equilibrium constants, and Brønsted slopes in F ₁ -ATPase single molecule imaging experiments

Theory for rates, equilibrium constants, and Brønsted slopes in F ₁ -ATPase single molecule imaging experiments

Ultrafast above-threshold dynamics of the radical anion of a prototypical quinone electron-acceptor

Electron-Transfer Rate in the Charge Transfer Complex in the Supercritical Fluids.

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Theory of highly exothermic electron transfer reactions

Cited by 180 publications

References 20 publications

Theory for rates, equilibrium constants, and Brønsted slopes in F 1 -ATPase single molecule imaging experiments

Theory for rates, equilibrium constants, and Brønsted slopes in F 1 -ATPase single molecule imaging experiments

Ultrafast above-threshold dynamics of the radical anion of a prototypical quinone electron-acceptor

Electron-Transfer Rate in the Charge Transfer Complex in the Supercritical Fluids.

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Theory for rates, equilibrium constants, and Brønsted slopes in F ₁ -ATPase single molecule imaging experiments

Theory for rates, equilibrium constants, and Brønsted slopes in F ₁ -ATPase single molecule imaging experiments