Marcus Theory of Electron Transfer 4: Classical Marcus Equation in Three Dimensions

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This Demonstration describes the classical Marcus model in three dimensions. The rate is plotted on the
axis as a function of the Gibbs free energy change
and the total reorganization energy
. This is a linear plot; often
is plotted in this application.
Contributed by: René M. Williams (August 2022)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: increasing the solvent reorganization energy makes the curve more broad, lower and shifted to the right
Snapshot 2: note the shaper curve at 77 K. With lower , the maximum attainable rate increases within the classical Marcus model show a sharper, higher peak.
Snapshot 3: in the high temperature limit, the semiclassical Marcus equation reduces to the classical Marcus equation; note the broadening of the curve at 1000 K
The results of this Demonstration were checked against the R-package [10] that runs in the statistical software package R [11] for computing and graphics.
References
[1] R. A. Marcus, "Electron Transfer Reactions in Chemistry: Theory and Experiment (Nobel Lecture)," Angewandte Chemie International Edition, 32(8), 1993 pp. 1111–1121. doi:10.1002/anie.199311113.
[2] S. Chaudhuri, S. Hedström, D. D. Méndez-Hernández, H. P. Hendrickson, K. A. Jung, J. Ho and V. S. Batista, "Electron Transfer Assisted by Vibronic Coupling from Multiple Modes," Journal of Chemical Theory and Computation, 13(12), 2017 pp. 6000–6009. doi:10.1021/acs.jctc.7b00513.
[3] P. F. Barbara, T. J. Meyer and M. A. Ratner, "Contemporary Issues in Electron Transfer Research," Journal of Physical Chemistry, 100(31), 1996 pp. 13148–13168. doi:10.1021/jp9605663.
[4] G. L. Closs and J. R. Miller, "Intramolecular Long-Distance Electron Transfer in Organic Molecules," Science, 240(4851), 1988 pp. 440–447. doi:10.1126/science.240.4851.440.
[5] P. Hudhomme and R. M. Williams, "Energy and Electron Transfer in Photo- and Electro-active Fullerene Dyads," Handbook of Carbon Nano Materials (F. D'Souza and K. M. Kadish, eds.), Hackensack, NJ: World Scientific, 2011 pp. 545–591. doi:10.1142/9789814327824_0017.
[6] R. M. Williams. "Introduction to Electron Transfer." (Nov 11, 2021) doi:10.13140/RG.2.2.16547.30244.
[7] R. M. Williams. Photoinduced Electron Transfer—The Classical Marcus Theory [Video]. (May 17, 2022) youtu.be/YFzeMMOvhl0.
[8] R. M. Williams. Photoinduced Electron Transfer—The Semi-classical Marcus–Levich–Jortner Theory [Video]. (May 17, 2022) youtu.be/GnPIbH6nM9o.
[9] R. M. Williams. University of Amsterdam. (May 17, 2022) www.uva.nl/en/profile/w/i/r.m.williams/r.m.williams.html.
[10] J. Idé and G. Raos. "ChargeTransport: Charge Transfer Rates and Charge Carrier Mobilities." (May 17, 2022) CRAN.R-project.org/package=ChargeTransport.
[11] "What Is R?" The R Foundation. (May 17, 2022) www.r-project.org/about.html.
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