Marcus Theory of Electron Transfer 2: Semiclassical Marcus Equation in Three Dimensions

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This Demonstration describes the semiclassical Marcus model (also called Marcus–Levich–Jortner Theory, MLJ) in three dimensions. The rate on the
axis is plotted as a function of the Gibbs free energy change
and the solvent reorganization energy
on the
and
axes. This is a linear plot; often
plots are used in this application.
Contributed by: René M. Williams (August 2022)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: data based on the work of Closs and Miller (focused here on the isooctane data) at , shifting the
axis to 0.1 eV as the upper limit, highlighting the region with low solvent reorganization energies
Snapshot 2: for , the semiclassical Marcus equation behaves similarly to the classical Marcus equation
Snapshot 3: in the high temperature limit, the semiclassical Marcus equation reduces to the classical Marcus equation
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
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[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]. (Nov 11, 2021) youtu.be/YFzeMMOvhl0.
[8] R. M. Williams. Photoinduced Electron Transfer—The Semi-classical Marcus–Levich–Jortner Theory [Video]. (Nov 11, 2021) youtu.be/GnPIbH6nM9o.
[9] R. M. Williams. University of Amsterdam. (Nov 11, 2021) 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." (Nov 11, 2021) CRAN.R-project.org/package=ChargeTransport.
[11] "What Is R?" The R Foundation. (Nov 11, 2021) www.r-project.org/about.html.
[12] A. Sarai, "Energy-Gap and Temperature Dependence of Electron and Excitation Transfer in Biological Systems," Chemical Physics Letters, 63(2), 1979 pp. 360–366. doi:10.1016/0009-2614(79)87036-0.
[13] J. R. Miller, J. V. Beitz and R. K. Huddleston, "Effect of Free Energy on Rates of Electron Transfer between Molecules," Journal of the American Chemical Society, 106(18), 1984 pp. 5057–5068. doi:10.1021/ja00330a004.
[14] M. R. Gunner, D. E. Robertson and P. L. Dutton, "Kinetic Studies on the Reaction Center Protein from Rhodopseudomonas sphaeroides: The Temperature and Free Energy Dependence of Electron Transfer between Various Quinones in the QA Site and the Oxidized Bacteriochlorophyll Dimer," Journal of Physical Chemistry, 90(16), 1986 pp. 3783–3795. doi:10.1021/j100407a054.
[15] R. Rujkorakarn and F. Tanaka, "Three-Dimensional Representations of Photo-induced Electron Transfer Rates in Pyrene--N,N'-dimethylaniline Systems Obtained by Three Electron Transfer Theories," Journal of Molecular Graphics and Modelling, 27(5), 2009 pp. 571–577. doi:10.1016/j.jmgm.2008.09.008.
[16] T. Unger, S. Wedler, F.-J. Kahle, U. Scherf, H. Bässler and A. Köhler, "The Impact of Driving Force and Temperature on the Electron Transfer in Donor–Acceptor Blend Systems," The Journal of Physical Chemistry C, 121(41), 2017 pp. 22739–22752. doi:10.1021/acs.jpcc.7b09213.
[17] W. W. Parson, "Generalizing the Marcus Equation," The Journal of Chemical Physics, 152(18), 2020 184106. doi:10.1063/5.0007569.
[18] J. B. Kelber, N. A. Panjwani, D. Wu, R. Gómez-Bombarelli, B. W. Lovett, J. J. L. Morton and H. L. Anderson, "Synthesis and Investigation of Donor–Porphyrin–Acceptor Triads with Long-Lived Photo-Induced Charge-Separate States", Chemical Science, 6, 2015, pp. 6468-6481. doi:10.1039/C5SC01830G.
[19] G. Lanzani, "Charge Transfer and Transport," The Photophysics behind Photovoltaics and Photonics, Weinheim: Wiley-VCH, 2012 pp. 145–176. doi:10.1002/9783527645138.ch8.
[20] R. M. Williams. Marcus Waves 5 Fast [Video]. (Nov 30, 2021) youtu.be/xn1_2w6-gqs.
[21] R. M. Williams. Marcus Waves 3 Fast [Video]. (Nov 30, 2021) youtu.be/c_Qb89Zvc3s.
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