Introduction to Marcus Theory of Electron Transfer Reactions

The following sections are included:

• Dedication
• Foreword
• Preface
• Scheme of the Book, Figures, Notes, and Abbreviations
• Acknowledgments
• Contents
• List of 42 Marcus’ Papers Closely Followed, Summarized or Abridged in Chapters 2–11 and of 10 Papers Considered in the Oral Interviews of Chapters 12 and 13
• List of Marcus’ Papers Considered in the Chapters of the Book

Charge transfer is present in the phenomenon of contact electrification at the very beginning of the history of electricity, with Thales of Miletus, as well as at the dawn of electricity as science, with William Gilbert. Triboelectricity, the contact electrification by tribocharging, was first observed, as far as we know, by Thales of Miletus when he rubbed amber with wool, the Greek word for friction being τρι′βος and that for amber η′λεκτρον (or η′λεκτρος). Tribocharging is due, we today know [1], to ions or electrons transferring from one to the other of two surfaces in contact. In a sense, we can consider Thales’ tribocharging also as the first experiment in chemical kinetics because, as Marcus remarked, that rubbing is overcoming the activation energy barrier for transfer of an ion or of an electron…

In this chapter I have summarized the two Marcus’ landmark papers of 1956–Refs. [1] (Part I of the theory) and [2], which laid the foundation of the whole theory. References have been given in keeping with the educational character of this work. The most important results have been emphasized and mathematical proofs have been given in separate starred sections following the results, so they can be omitted by the noninterested reader. In Chapters 5 and 6, the more general and more abstract formulations of the theory in terms of potential energy surfaces and statistical mechanics is dealt with, but the present earlier treatment in terms of the dielectric continuum theory represents an easier introduction to Marcus theory, with its detailed explanation of all the different steps involved in the ET process, and by itself allows an understanding of the applications given by M. in Part II and in Part III. Similarly, one deals with ideal gases before studying the real ones.

After the fundamental results of the wonder year 1955 (published ten months later in 1956), M. developed his theory and applied it to a variety of chemical and electrochemical systems. This chapter is devoted to the description of results mainly reported in Refs. [1–7], which span the years 1956–1964. I have also freely resorted to the reviews in Refs. [8–13], altogether a real “Guide of the Perplexed” [14].Among the early applications are comparisons of calculated and experimental data, examples of how to use the theory to investigate reaction mechanisms and of how to systematize and correlate experimental data. These last characteristics have been typical of chemical theories like, say, the theory of the periodic system of elements or that of electrode potentials.

The first and fundamental formulation of Marcus theory for homogeneous ET reactions (redox reactions) was summarized in Chapter 2. In this chapter, an abridged version is presented of its extension to electrode systems from Refs. [1, 2, and 2a]. The two Office of Naval Research reports were written by Marcus in 1957 but were published in 1977 in a book edited by Peter A. Rock. In the following, the symbol M. is for Marcus.

In this chapter, I have summarized the theory on potential energy expressions, on interparticle interaction energy, and on interactions in polar media which can be found in Refs. [1–5].

In the pivotal paper written for the Discussions of the Faraday Society of 1960 M. introduced for the first time a treatment of his theory in terms of potential energy surfaces and of statistical mechanics. This generalization of the earlier macroscopic treatment in terms of nonequilibrium solvent polarization was needed in order to treat in a consistent manner the contributions of both the inner coordinates of the molecules (in particular of the coordination shells, when present) and the outer solvent coordinates in the electron transfer process. The new concept of equivalent equilibrium distribution (e.e.d.), already briefly mentioned and used in Ref. [5a] (see Chapter 4), was formulated, “inverted free energy effect” was here predicted for the first time and, finally, the contribution of the internal molecular coordinates of the central ions or molecules, in particular that of the coordination shells, to the reaction rates was considered in some detail. Such topics as well as a more rigorous and extensive formulation of the theory were also the object of Marcus’ great paper of 1965, Ref. [6], and they will be dealt with in Chapter 6.

In this chapter, Ref. [1] is summarized in which M. presented a unified treatment for homogeneous and electrode reactions. This Reference is # VI in the series of papers “On the Theory of Electron Transfer Reactions” and is the “summa” of M. theory up to 1965. Many topics dealt with in the preceding chapters are taken up again and more extensively dealt with in the framework of Marcus’ generalization of the activated complex theory of reaction rates. In this theory, generalized coordinates are used in both ordinary and mass-weighted configuration space. The elements of the generalized activated complex theory necessary to understand the application to ET theory are briefly described in Sections 6.4–6.7.

In this chapter is summarized the work of Marcus on the theory of ET reactions of solvated electrons and on the chemiluminescent ET reactions, M61 [1], 55 [2], 57 [3], 57 Erratum [3], 60 [4]. The text, very close to Marcus’ papers, is interspersed with notes and remarks. Marcus’ Notes are collected at the end of the chapter…

In this chapter, I have followed very closely the content of M69, M71, and M77, Refs. [1, 2, and 3]. Notes and remarks are interspersed throughout the text, Marcus’ notes are collected at the end.

M69. Theoretical Relations among Rate Constants, Barriers, and Brønsted Slopes of Chemical Reactions, J. Phys. Chem. 72, 891, (1968).

In this Chapter, M49, M50, M74, M105, M118, M119, and M134 are considered.

In M49 and M50, M. generalizes the activated-complex theory by extending it to curvilinear reaction coordinates. Excerpts from the papers are reproduced here that are of interest for electron transfer (ET) theory. Some concepts, formulas, and symbols appearing here have been used in the fundamental M53. There is an abridged description of M74 with Marcus’ Notes at the end. The Sections of M105 here reproduced are the ones important for ET reactions, Marcus’ Notes are at the end. Oral interviews with Marcus about M118, M119, and M134 are finally presented, each one preceded by a brief presentation of the paper.

Here are considered: M110, M139, M140, M141, M145, M146, M154, M156, M163…

The following sections are included:

• M30a. Discussion Comment on Mixed Reaction-Diffusion Controlled Rates
• NOTES
• M164. Quantum Effects for ET Reactions in the Inverted Region
• Introduction
• Theory
• Appendix. Relation between λ and the Stokes Shift
• NOTES
• M170. On the Frequency Factor in ET Reactions and Its Role in the Highly Exothermic Regime
• Introduction
• Theory
• NOTES
• M173. Further Developments in ET
• Theory
• Results
• Discussion
• Appendix. “Experimental” Rate Constant at ΔG⁰= 0
• NOTES
• M174. Theory of Highly Exothermic ET Reactions
• Introduction
• Theory
• Steady State Results
• Short Time Experiments
• Analogy between Charge-Transfer Spectrum and Plot of k_act versus ΔG⁰= 0
• NOTES
• M177. Electron and Proton Transfer
• “Introduction
• Weak-Overlap Electron Transfers
• Other Classes of Reactions
• Quantum Effects
• The Inverted Region
• Effect of Separation Distance
• NOTES
• M194. Nonadiabatic Processes Involving Quantum-like and Classical-like Coordinates with Applications to Nonadiabatic Electron Transfers
• Introduction
• Theory
• Appendix B: Relation of Eq. (11.104) to the Landau–Zener Formula
• NOTES

In this Chapter and in the following, oral interviews with Marcus are reported on M126, M201, M204, M207, M209, M210. The interviews are presented in the form of NOTES to Marcus’ articles.

In this Chapter, oral interviews with Marcus are reported on M211, M213, M214. The interviews are presented in the form of NOTES to the publications.