Chemical reactivity is currently explained in terms of several diverse scientific traditions and Proton-Coupled Electron Transfer (PCET) is central to these traditions, together with quantum mechanical tunnelling of the electron particle. This book brings together all these traditions through the authors' research and experience. It covers the most recent developments in the field of PCET reactions, from the theoretical and experimental points of view. It concentrates on the importance of PCET in biological systems and for bioenergetic conversion, namely the oxidation of water in Photosystem II, to produce oxygen, and the reduction of protons to hydrogen by hydrogenase, for energy storage. Furthermore, the book also brings together the most important chemical explanations employed in this field.
About the Author
Sebastiao J. Formosinho obtained his Ph.D. from the Royal Institution at the University of London. He later became a Professor of Physical Chemistry, and subsequently the Dean of his Department and of the Faculty of Sciences and Technology at the University of Coimbra. His research interests focus on unidimensional models of chemical reactivity and structure-reactivity relationships. Professor Formosinho has published more than 160 scientific papers and is co-editor / editor of three books and 2 patents. He has also published articles on chemistry teaching and the epistemology of physical sciences. Sebastiao Formosinho is an active member of the Portuguese Academy of Sciences, holds the EUROCHEM title, and is an IUPAC Fellow. He has also been the recipient of a number of professional awards. Mónica Barroso is a postdoctoral researcher at the University of Coimbra, in the group of Photochemistry and Molecular Spectroscopy. Her current research is focused on nanoscale devices for the conversion of solar energy into clean energies. Prior to that, she was based at the EPFL in Switzerland where she started her studies on solar hydrogen generation with nanocrystalline semiconductor photoelectrodes. Other research interests include photochemical reactions in solution, supercritical fluids, proton-coupled electron transfer, and organic-based photovoltaics. She has received 3 research grants from the Portuguese Science Foundation and 2 awards (from Fundação Calouste Gulbenkian and the University of Coimbra).
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Proton-Coupled Electron Transfer
A Carrefour of Chemical Reactivity Traditions
By Sebastião Formosinho, Mónica Barroso
The Royal Society of ChemistryCopyright © 2012 Royal Society of Chemistry
All rights reserved.
Application of the Marcus Cross Relation to Hydrogen Atom Transfer/Proton-Coupled Electron Transfer Reactions
JEFFREY J. WARREN AND JAMES M. MAYER
Department of Chemistry, University of Washington, Box 351700, Seattle, WA 98195-1700, USA
Many important chemical and biological reactions involve transfer of both electrons and protons. This is illustrated, for instance, by Pourbaix's extensive 1963 Atlas of Electrochemical Equilibria. These have come to be called 'proton-coupled electron transfer' (PCET) reactions. Due to the widespread interest in this topic, the term PCET is being used by many authors in a variety of different contexts and with different connotations. As a result, a very broad definition of PCET has taken hold, encompassing any redox process whose rate or energetics are affected by one or more protons. This includes processes in which protons and electrons transfer among one or more reactants, regardless of mechanism, and processes in which protons modulate ET processes even if they do not transfer.
Mechanistic issues are central to PCET. In contrast to electron transfer (ET) and proton transfer (PT), which are two of the most fundamental and well-understood reactions in chemistry, our understanding of how protons and electrons are transferred together is still emerging. The importance of mechanism was emphasized by Njus in a biochemical context almost two decades ago: "Many [biological redox] reactions involve the transfer of hydrogen atoms (or the concerted transfer of H+ and e-) rather than electron transfer alone. This distinction is generally disregarded because H and e- are considered interchangeable in the aqueous milieu of the cell, but the focus on electrons obscures some of the general principles underlying the functioning of redox chains".
This chapter focuses on hydrogen atom transfer (HAT) reactions, which involve concerted transfer of a proton and an electron from a single donor to a single acceptor in one kinetic step (eqn (1.1)). These are one subset of PCET processes and are one type of 'concerted proton-electron transfer' (CPET).
[MATHEMATICAL EXPRESSION OMITTED] (1.1)
"Concerted" implies a single kinetic step for transfer of the two particles, but does not imply synchronous transfer. HAT is a fundamental reaction studied by physical and organic chemists for over a century, critical to combustion and free-radical halogenations, for example. More recently, it has been recognized that transition metal coordination complexes and metalloenzymes can undergo HAT reactions, and the recognition of overlap between traditional HAT reactions and PCET has stimulated much new thinking. Our focus has been to understand the key factors that dictate HAT and PCET reactivity and to build a simple and predictive model that can be used in chemistry and in biology.
In this chapter, we show that the Marcus cross relation holds remarkably well for HAT reactions in most cases. This provides important insights into HAT and allows the prediction of rate constants. We begin with an introduction to Marcus theory and the cross relation. This is followed by applications the cross relation to purely organic reactions (Sections 1.3), and then to HAT reactions involving transition metal complexes (Sections 1.4). Finally, Section 1.5 describes the intuitive picture of HAT derived from the success of the cross relation, and also emphasizes some of the weaknesses of this treatment and the questions that remain.
1.2 An Introduction to Marcus Theory
The Marcus theory of electron transfer has proven invaluable for understanding a variety charge transfer reactions, from simple solution reactions to long-range biological charge transfer. The primary equation of Marcus theory, equation (1.2), is derived from a model of intersecting parabolic free energy surfaces. When the coupling between these diabatic surfaces HAB is small, the reaction is non-adiabatic and the reaction does not always occur
[MATHEMATICAL EXPRESSION OMITTED] (1.2)
[MATHEMATICAL EXPRESSION OMITTED] (1.3)
when the system reaches the intersection (the transition state). When the coupling is sufficiently large the reaction is adiabatic and equation (1.2) reduces to equation (1.3). The pre-exponential factor A in equation (1.3), for a bimolecular reaction, is typically taken as an adjusted collision frequency. The intrinsic barrier λ is the energy required to distort the reactants and their surrounding solvent to the geometry of the products. Because electron transfer occurs over relatively long distances, with little interaction between the reagents, it is typically assumed that λ can be taken as a property of the individual reagents. λ for a reaction is then commonly taken as the average of the individual reagent λ's (the 'additivity postulate,' eqn (1.4)). In the adiabatic limit, λ for an individual reagent can be determined from the rate of the self exchange reaction (eqn (1.5)). Combining equations (1.3) and (1.4) gives the cross relation (eqn (1.6) and (1.7)), which relates the rate constant of a cross reaction, X + Y-, to the self exchange rate constants for reagents X and Y (eqn (1.5)) and the equilibrium constant KXY. The constant f is defined by equation (1.7) and is typically close to unity, unless |ΔG°| ≥ λ/4.
λXY = 1/2 (λXX + λYY) (1.4)
X + X- [??] X- + X (1.5)
kXY = √kXXkYYKXYf (1.6)
ln f = (ln KXY)2/4 ln(kXXkYYZ-2) (1.7)
Theoretical treatments of PCET reactions typically have equation (1.2) as a conceptual starting point. In Hammes–Schiffer's multistate continuum theory for PCET, the pre-exponential factor includes both electronic coupling and vibrational overlaps, and the rate is a sum over initial and final vibrational states integrated over a range of proton-donor acceptor distances. This theory has been elegantly applied to understand the intimate details of a variety of PCET reactions, but many of its parameters are essentially unattainable experimentally.
The cross relation can be written for an HAT reaction (eqn (1.1) and (1.8)). It is a very simplistic model, but it has the advantage that all of the parameters are experimentally accessible (in many cases).
[MATHEMATICAL EXPRESSION OMITTED] (1.8)
It should be emphasized that the cross relation is not a corollary of current PCET theory and that there is little theoretical justification for applying it (although Marcus has briefly discussed this). Still, the cross relation has been successfully applied to group transfer reactions including proton and hydride transfers, and SN2 reactions. While these successes are notable, in each instance the cross relation holds only over a narrow set of reactants and reactions. In contrast, the treatment described here has shown to be a powerful predictor for a wide array of HAT reactions.
Our interest in applying the Marcus cross relation grew out of our finding that the traditional Bell–Evans–Polanyi (BEP) relationship, Ea = α(ΔH) + β, holds well for transition metal complexes abstracting hydrogen atoms from C–H bonds. The BEP equation relates HAT activation energies to the enthalpic driving force (ΔH) (although, as discussed in Section 1.4 below, free energies should be used, as in Marcus theory). The ΔH is typically taken as the difference in bond dissociation enthalpies (BDEs) of X–H and Y–H. The BEP equation has been a cornerstone of organic radical chemistry for many decades, typically holding well for reactions of one type of oxidant Xd with a series of substrates Y–H. The success of this treatment is one reason why organic textbooks list BDEs. We initially found that the rate constants for HAT from C–H bonds to CrO2Cl2 or MnO4- show good BEP correlations with the BDE of the C–H bond. Later, we found an excellent BEP correlation for C–H bond oxidations by [Ru(O)(bpy)2(py)]2+ (Figure 1.1). Such a correlation, with a Brønsted slope ΔΔG/ΔΔH° close to ½, is a strong indicator of an HAT mechanism. Many other groups have also used these correlations to understand the relationship between rate and driving force for HAT reactions of transition metal containing systems. Marcus theory and the cross relation also predict a Brønsted slope (ΔΔG/ΔΔG°) close to ½, for reactions at low driving force (specifically when ΔG° << λ/2).
The BEP correlation between rates and driving force for HAT is very valuable, but it applies only to a specific set of similar reactions, for instance MnO4- abstracting H from hydrocarbons. In addition, the α and β parameters are defined only with the context of the correlation and have no independent meaning. In contrast, cross relation uses three independently measurable parameters: the equilibrium constant KXH/Y (which is equal to [MATHEMATICAL EXPRESSION OMITTED]) and the rate constants for the hydrogen atom self-exchange reactions kXH/X and kYH/Y (eqn 1.9).
XH + X -> X + XH (1.9)
1.3 Predicting Organic Hydrogen Atom Transfer Rate Constants
Hydrogen atom transfer (HAT) reactions of organic compounds are fundamental to combustion, industrial oxidation processes, and biological free radical chemistry, among other areas of chemistry and biology. One important example is the series of H-transfers that is thought to be involved in lipid oxidation. Peroxyl radicals (ROO) abstract H from a lipid to give a lipid radical that adds O2 to form a new peroxyl radical and propagate the radical chain. ROO can also abstract H from [apha]-tocopherol (a component of vitamin E) and the resulting α-tocopheroxyl radical is thought to be regenerated via HAT from ascorbate (vitamin C). Understanding such a web of free radical reactions requires knowledge of the rate constants for each of the steps. To this end, we have developed a predictive model for organic HAT reactions based upon the Marcus cross relation and the kinetic solvent effect model of Ingold et al.
We begin this section discussing the application of the cross relation to real systems, how the needed rate and equilibrium constants can be obtained. These same principles also apply to the metal-mediated HAT reactions discussed in Section 1.4. A set of reactions are used to test the Marcus model, using inputs all obtained in the same solvent. Then we address how to extrapolate rate and equilibrium constants from one solvent to another, using the H-bonding descriptors developed by Abraham and co-workers. Finally, we show that this allows remarkably accurate prediction of a very wide range of HAT cross rate constants.
1.3.1 Obtaining Self-Exchange Rate Constants and Equilibrium Constants
Ideally, all three of the parameters needed for the cross relation, KXH/Y, kXH/X and kYH/Y, are measured in the same medium under the same conditions. When the values are only available in different solvents, solvent corrections must be included, as described in Section 1.3.3 below. The f term can be calculated from the three parameters, with the collision frequency Z typically taken as 1011 M-1 s-1.
The driving force for a HAT reaction, ΔG°XH/Y = -RTln KXH/Y, is best determined by direct equilibrium measurements in the solvent of interest. However, this is typically limited to reactions where |ΔG°XH/Y| is small, less than about 5 kcal mol-1. Also, this is only possible for reactions in which all of the species are fairly stable, which is unusual for organic radical reactions. The ΔG° for a HAT reaction is typically more easily derived as the difference in bond dissociation free energies (BDFEs) of X–H and Y–H in the solvent of interest. We have recently reviewed BDFEs of common organic and biochemical species and how they are obtained, so only an overview is given here.
One powerful method to determine BDFEs uses a solution thermochemical cycle with the reduction potential of XH and the pKa of XH+, or with E°(X-) and pKa(XH). The BDFE in kcal mol-1 is given by 23.1E° + 1.37pKa + CG. Bordwell and others have used this approach to measure many bond dissociation enthalpies (BDEs) but it is more appropriate to use BDFEs because the E° and pKa values are free energies. Determining X–H BDEs from E° and pKa measurements is valid when XH and X have similar absolute entropies, as is typically the case for organic molecules but not for transition metal complexes (see Section 1.4.1 below). Due to the uncertainties in the CG value in thermochemical cycle, and typical uncertainties in the E° and pKa values, this procedure yields BDFEs accurate to no better than ± 1 kcal mol-1. This leads to estimated uncertainties in rate constants calculated from the cross relation of an order of magnitude.
Solution-phase BDFEs can also be obtained from gas-phase BDEs, which are available for many small organic molecules. An extensive tabulation of such BDEs can be found in the recent book by Luo, portions of which are available online. As described in detail elsewhere, a gas-phase BDE can be converted into the corresponding solution-phase BDFE using data from standard tables [S°(H)gas, ΔG°solvation (H)] and an estimate of the difference in the free energies of solvation of XH and X (see below).
Self-exchange rate constants, kXH/X and kYH/Y, are best measured directly when this is possible. NMR line broadening is a powerful technique for degenerate exchange reactions of stable species if the rate constant is ca. 103–106 M-1 s-1; faster reactions can be monitored by EPR methods. In the 1H NMR experiments, typically one reactant is diamagnetic and has a sharp spectrum while the other is paramagnetic. In the slow-exchange limit, addition of the paramagnetic species to the diamagnetic causes broadening of the spectrum but not shifting, and the amount of broadening is directly related to the rate constant. We have used this method to measure a number of kXH/X values for transition metal reagents.
Self-exchange rate constants can also be determined through the use of 'pseudo-self-exchange' reactions, that is H exchange reactions using two very similar reagents X(H) and *X(H) (eqn (1.10)). The reagents can differ in just an isotopic label (e.g. toluene/3-deuterotoluene) or just be chemically similar. For instance, we have examined the pseudo-self-exchange reaction of oxovanadium complexes that differ only in their 4,4'-dimethylbipyridine vs. 4,4'-di-(t-butyl)bipyridine supporting ligands. This reaction has KXH/*X = 1 within experimental error, so it is very close to a true self-exchange reaction. Reaction of the hydroxylamine TEMPO-H (2,2,6,6-tetramethyl-N-hydroxypiperidine) with the aminoxyl radical 4-oxo-TEMPO (eqn (1.11)) has KXH/*X 1/4 4.5 ± 1.8. In such cases the self-exchange rate constant kXH/X is taken to be the geometric mean of the forward (kXH/*X) and reverse (k*XH/X) rate constants (eqn (1.12)).
Excerpted from Proton-Coupled Electron Transfer by Sebastião Formosinho, Mónica Barroso. Copyright © 2012 Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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Table of Contents
Proton-coupled electron transfer: introduction and state-of-the-art; Application of the Marcus Cross Relation to proton-coupled electron transfer/hydrogen atom transfer reactions; Theoretical and experimental criteria for proton-coupled electron transfer; On the solvation of ionic systems; Experimental approaches towards proton-coupled electron transfer reactions in biological redox systems; Metal ion-coupled electron transfer; Electrochemical concerted proton-electron transfers. Comparison with homogeneous processes