Wolfram Demonstrations Project

This Demonstration shows three aspects of solvent reorganization energy: the solvent reorganization as a function of the dielectric constant of the medium; the solvent reorganization energy in one particular solvent; the ionic radius using the density and molar weight. These are done independently. Reorganization energies feature in both the classical and semiclassical versions of the Marcus equation to study the rate of electron transfer (charge separation), influenced by the relevant molecular parameters. The total reorganization energy

is also obtained.

Use the sliders to vary the individual thermodynamic parameters.

The solvent is described by its dielectric constant

, the center-to-center distance is given by

and ionic radii are represented by

and

(in Å). Here

is the internal reorganization energy and

is the refractive index of the solvent. The center-to-center distance can be obtained from molecular modeling.

Nobel Prize winner Rudolph Marcus developed the theory of electron transfer, also for biological systems [1]. The classical Marcus equation (CME) is based on two simultaneous quadratic relations involving the driving force

, the internal and external (solvent) reorganization energies

and

and the electronic coupling

. The CME underestimates the electron transfer rate in the inverted region [2, 3].

The related links contain more information and references.

Starting data is for C60[11]DMA in benzonitrile solvent [4]. See [5, 6] for information on the solvent reorganization.

Some examples of molecules with their density and molecular weight: (C60, 1.65,

); (DMA, 0.956,

); (pyrene, 1.271,

); (perylene bis-dicarboximide, 1.407,

); (DABCO, 1.02,

); (1,8-naphthalimide, 1.4,

); (triethylamine, 0.762,

); (TPP, 1.27,

); (dimethoxynaphthalene, 1.097,

); (TCNE, 1.35,

(DMA = dimethyl aniline, DABCO = 1,4-diazabicyclo[2.2.2]octane, TPP = tetraphenylporphyrin, TCNE = Tetracyanoethylene).

It should be noted that there is a variation of the equation in which the average ionic radius is used [4, 6]. This can be practical and useful, but gives values deviating slightly.

Note that a negative solvent reorganization energy makes no physical sense.

This Demonstration uses the original equation developed by Marcus [5].

Contributed by: René M. Williams

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Snapshot 1: A change to a smaller center to center distance results in lower solvent reorganization energies. Less space to reorganise around dipole created.

Snapshot 2: Delocalization of the positive (or negative) charge over a larger molecular structure leads to lower solvent reorganization.

Snapshot 3: If the ionic radii are too large, relative to the center to center distance, the equations gives useless negative energies.

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] R. M. Williams. "Introduction to Electron Transfer." (Feb 14, 2023) doi:10.13140/RG.2.2.16547.30244.

[5] R. A. Marcus, "Tutorial on Rate Constants and Reorganization Energies," Journal of Electroanalytical Chemistry, 483(1), 2000 pp. 2–6. doi:10.1016/S0022-0728(00)00011-5.

[6] R. M. Williams. "Fullerenes as electron accepting components in supramolecular and covalently linked electron transfer systems" PhD Thesis 1996, University of Amsterdam (March 19, 2023).