Electron-Transfer Reactions in Organic Chemistry

EIect ron-Tra nsf er R ea c t io ns in Organic Chemistry LENNART EBERSON

Chemical Center, University of Lund, Lund, Sweden 1 Introduction 79 2 Classification of organic electron-transfer reactions

86 Mechanistic classification of inorganic redox processes 86 Mechanistic classification of organic redox processes 86 Synthetic classification of organic electron-transfer reactions 90 3 The Marcus theory of adiabatic electron-transfer processes 95 A qualitative overview 95 A molecular orbital picture of electron transfer 97 Quantitative aspects of Marcus theory 98 Kinetic schemes with an initial non-bonded electron-transfer step 106 4 Problems involved in applying the Marcus theory to organic reactions 1 I 3 Calculation of 1 113 Standard electrode potentials and other free energy data for organic redox reactions 5 Experimental tests of the Marcus theory in organic systems 129 The Marcus inverted region 129 The normal region 132 Conclusions 146 6 Examination of certain postulated organic electron-transfer reactions 147 Non-metallic inorganic reagents 15 1 Metallic redox reagents 154 Organic redox reagents 164 7 Concluding remarks 172 Acknowledgements 174 References 174

1

122

Introduction

The simplest elementary act in homogeneous solution chemistry is the exchange of an electron between two chemical entities. No bonds need to be formed or broken in the process, and if the two species are identical, except for a difference in oxidation state, no net chemical change takes place (1). Such self-exchange reactions, although of no chemical consequence, constitute the basis of theoretical treatments of electron transfer. *Ant

+

AO-l)t

*AV-l)+ + An+

n is an integer, usually between -5 and 5 79

(1)

80

LENNART E B E R S O N

A more complex and chemically interesting situation is the electron-transfer reaction between two species of different chemical composition (2). Now a net chemical change occurs (AZ] is reduced, BZ2 is oxidized) and this may be preceded or accompanied by chemical steps involving bond formation or cleavage. If the participants in (2) are both inorganic species we are dealing AZ1 + BZ2

+

A Z l - I + BZ2 f I

Z, = charge on the oxidizing form of species A Z , = charge on the reducing form of species B

with a well-established area of chemical inquiry within inorganic chemistry, characterized by a good theoretical background (for a detailed review, see Schmidt, 1975, 1978) which can adequately guide experimentation and provide the impetus for fast and efficient growth of knowledge. In fact, the predominant theory of electron transfer, the Marcus theory (Marcus, 1964, 1977) has been claimed to predict rate constants for electron transfer between any pair of metal complexes to within an order of magnitude (see, however, Pennington, 1978 for a critical assessment of this claim), using extrakinetic data as input variables. This is no mean achievement as far as theories of chemical dynamics go. A cursory look into textbooks of descriptive as well as mechanistic and theoretical inorganic chemistry (e.g., Basolo and Pearson, 1967; Cotton and Wilkinson, 1972; Purcell and Kotz, 1977; Tobe, 1972; Williams, 1979) and into specialized monographs (e.g., Reynolds and Lumry, 1966; Taube, 1970) attests to the fruitful interplay between theory and experimentation regarding inorganic electron-transfer processes. Now consider the seemingly insignificant change of A or B or both into organic species! A thorough sifting of a considerable number of the most commonly used modern texts of descriptive and mechanistic organic chemistry turned up very little about electron transfer processes: at most a few scattered pages per thousand treat topics like radical ions, dissolving metal reduction, electrochemical oxidation and reduction, and oxidation by metal complexes, no theoretical background being presented. With few exceptions (Dewar and Dougherty, 1975; Alder et al., 1971; Le Noble, 1974; Carey and Sundberg, 1977) textbooks of organic chemistry do not seem to recognize the phenomenon of electron transfer, in spite of the fact that the simple act of removal or addition of an electron brings about a profound qualitative change in the reactivity of an organic compound. Denoting reagents as E+ (electrophiles) or Nu- (nucleophiles), we can immediately see that neutral closed-shell organic substrates R-E (a nucleophile) and R-Nu (an electrophile) undergo reversal of polarity upon electron transfer (3 and 4). In other words, electron transfer is an act of Umpolung, indeed the simplest imaginable one, with great potential synthetic use (see Section 2). Other types of organic

-

ELECTRON-TRANSFER REACTIONS

81

R-E A nucleophile

R-E+' A radical cation, a strong electrophile

(3)

R-NU

R-NU-' A radical anion, a strong nucleophile and base

(4)

-

An electrophile

species are similarly changed; neutral radicals give carbonium ion or carbanions (9,ions give neutral radicals, etc. With the enormous wealth of

redox reagents that is available to the organic chemist, why is the concept of electron transfer not taught and used in contemporary organic chemistry, as it was when physical organic chemistry was in its infancy (Hammett, 1940)? Specialized monographs do treat the topic, at least descriptively, (e.g., see: Walling, 1957; Nonhebel and Walton, 1974; Kochi, 1978) and the current research literature of organic chemistry abounds with suggestions of more or less probable electron-transfer steps, but why has no theory of electron transfer whatsoever been incorporated into the body of organic chemical thinking? From a historical and epistemological point of view-and perhaps even a sociological one-this difference in treatment of a specific area within two fields of chemistry is extremely interesting and thought-provoking. In the Kuhnian (Kuhn, 1962) sense, we would say that the paradigm of organic chemistry, i.e. the set of definitions, concepts, rules, laws, theories, methods and facts that constitutes the science of organic chemistry, as laid down in current texts, is so different from that of inorganic chemistry that it does not recognize an important chemical phenomenon that obviously is common to both sciences. This amounts more or less to saying that the two fields have developed in parallel with little contact and cross-fertilization (for a historical account of chemistry using this line of thought, see Warr, 1976) and with relatively few problems in common. And nowhere is this more apparent than in the treatment of redox processes, a problem common to both fields. Truly, the redox reaction concept in its simplest form, transfer of one or several electrons between two species, is much easier to apply to the central atoms of inorganic complexes and relatively simple covalent inorganic compounds with their well-defined oxidation states than to the carbon atoms of organic molecules. Nevertheless oxidation states of the latter can be defined using very simple rules (see, e.g. Hendrickson et al., 1970) and immediately reveal the possible redox nature of any transformation at a carbon atom. It is also true that redox mechanisms other than electron transfer-hydrogen atom or hydride transfer, oxygen transfer, displacement, etc.-should by their very

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nature be in vogue in organic chemistry with its formal and very strong emphasis on moving electrons two by two in curved arrow schemes. In electron-transfer theory it is an important postulate that electrons are transferred one by one (Semenov, 1958), which does not mix well with the two-electron centered electronic theory of organic molecules. Interestingly enough, a lively Russian school propagates ideas of organic electron-transfer mechanisms, often in contradiction to currently accepted views (for reviews, see Todres, 1978; Blyumenfel’d et af., 1970; Bilevich and Okhlobystin, 1968). This is reminiscent of a period when one-electron oxidants and reductants, e.g. Fe(CN,)3- and metallic sodium, were perfectly acceptable as electrophiles and nucleophiles, respectively (Ingold, 1953). With the present upsurge of research studies that frequently invoke organic electron-transfer steps in mechanistic discussions, there is a great need of a theoretical background applicable to organic species and compatible with the language of physical organic chemistry. Enough work has been carried out to show that the Marcus theory is applicable to a limited number of organic model reactions of both the self-exchange (1) and net chemical change type (2). It remains critically to assess these studies and their applicability in a wider context, above all in experimental situations that organic chemists normally encounter (e.g. testing free energy relationships). Which are then the most common situations in which organic chemists are likely to be confronted with electron-transfer steps? We start with what one is tempted to call compulsory electron-transfer processes. Many electrochemical reactions-and these include dissolving metal reductions-in organic systems must involve initial electron transfer from or to an organic species (for reviews on mechanistic organic electrochemistry, see : Heischmann and Pletcher, 1973; Ross et af., 1975; Eberson and Nyberg, 1976). If the organic species is neutral, we enter the areas of radical-anion and cation chemistry (3, 4), both actively pursued in recent years (Szwarc, 1968, 1969, 1972; Dorfman, 1970; Holy, 1974; Bard et af., 1976), and presenting a host of intriguing problems. Naturally, the sink for, or source of, electrons need not be the anode or cathode of a heterogeneous electrochemical system. In fact, we shall not attempt to discuss heterogeneous electron transfer processes here, unless we can extract useful kinetic and thermodynamic data from studies of organic electrode processes. Instead we shall focus our interest on reactions in homogeneous systems, which conveniently can be classified into two categories, depending on whether the redox reagent is an (a) one-electron or (b) two-electron transfer reagent. Situation (a) is rather unambiguously recognizable and believed to be a very common one. It includes the initial step in redox reactions between neutral or ionic organic molecules or radicals and the typical one-electron redox reagents, e.g., oxidation by Fe(III), Co(III), Mn(III), Tl(III), Ag(II), Ce(IV), Pb(IV),

83

ELECTRON-TRANSFER REACTIONS

SO;' and radical cations, and reduction by Cr(II), halide and pseudohalide ions, and radical anions. Another class of one-electron redox reagents are excited states formed by photoexcitation of organic or inorganic species. Neutral radicals, organic as well as inorganic ones, could in principle act as one-electron transfer reagents, although it is seldom that this has been experimentally verified. However, it is important to note that electron transfer is not the sole process that can take place in case (a); bond formation between the two participating species is a possible competing step, as for example in the reaction between an aromatic radical cation and a nucleophile (6) (Bard et al., 1976; Eberson et al., 1978a,b; Eberson and Nyberg, 1978) and aromatic hydrocarbons and a Pb(1V) species (7) (Norman et al., 1971). This dichotomy poses an interesting and challenging theoretical problem, namely, what are the reactivity rules in reactions such as (6) and (7)? ArH+' + Nu-

+ LArHH Ar

Nu'

(6)

\N" Nu-

= C1-,

Br-, CNArH+' + PbL;-

L = ligand

The same problem is accentuated for case (b) reagents. Many electrophilic and nucleophilic reactions involve what both formally and/or practically are considered to be two-electron redox reagents (such as NO:, NO+, halogen, SO,, I-, sulfur nucleophiles) and indeed lead to a change in oxidation state of the carbon atom involved. These reactions are assumed to follow two-electron mechanisms that are very much part of the paradigm of organic chemistry. And yet, now and then, the paradigm is challenged by suggestions of alternative mechanisms initiated by one-electron transfer (for reviews, see Bilevich and Okhlobystin, 1968; Todres, 1978) and exemplified by aromatic nitration by NO: (8) (Weiss, 1946; Perrin, 1977) and the S,2 reaction between ArH+NO:

ArH+'+NO,

-

/H Ar\N02 +

(8)

species like butyl 4-nitrobenzenesulfonate and benzenethiolate ion (9- 11, NsO = 4-nitrobenzenesulfonyl group) (Bank and Noyd, 1973). It should come as no

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LENNART EBERSON

surprise that the chemical community receives such proposals with somewhat less than enthusiasm; yet, as we shall see, the proposed electron transfer steps are sometimes compatible with current theory and hence the mechanisms cannot be summarily dismissed from this point of view. PhS-

+ RONs

PhS'+R'

-

-

PhS'

RSPh

+ RONs-'

(9)

(1 1)

Summarizing, the main part of this chapter will attempt to apply the Marcus theory to a range of organic processes of the type shown in (2), in which A and/or B are organic (including organometallic) species, and will assess its usefulness in this context. In doing so, the necessary linguistic, conceptual and formal changes in going from a largely inorganic theory to an organic equivalent will be undertaken. We shall start by drawing lines of demarcation around the area to be covered, first by looking briefly at the use of Marcus theory for inorganic redox reactions and then by translating this delimitation to organic ones. This will involve a discussion in terms of outer- and inner-sphere mechanisms and their organic equivalents, following Littler's suggestion (Littler, 1970, 1973) termed non-bonded and bonded mechanisms. The main part of the chapter will discuss the application of Marcus theory to organic electron-transfer processes, both in cases where the electron-transfer character has been established beyond reasonable doubt and in more ambiguous, if not downright controversial ones. It is hoped to demonstrate that Marcus theory can provide an additional tool in the service of physical organic chemistry and guide experimental and theoretical work in new directions.

Relation to topics of practical interest The study of organic electron-transfer processes may superficially seem to be a rather futile academic exercise: two species collide, an electron is transferred between them, and two new species are formed. Naturally, the story does not begin or end here. It is the preceding and subsequent steps that put electron transfer in its correct perspective and determine its usefulness in chemistry, in science as a whole and in society. The following applications of electron transfer processes speak for themselves: 1 New synthetic reaction types (see Section 2). These may either be run heterogeneously at electrodes or via reagents of the type mentioned above. The field of organic electrosynthesis has been thoroughly reviewed (for leading references, see Eberson and Nyberg, 1976; Eberson, 1980a) and current

ELECTRO N-TRAN S FE R R EACTlO N S

85

thinking in the area holds that it should be possible to duplicate almost any type of organic electrode process using a homogeneous redox reagent. This generalization should be valid for both reactions which need stoichiometric withdrawal or removal of electrons, and those which at least formally are electron- or hole-catalyzed. 2 Chemiluminescence.* The mechanisms behind this phenomenon, as induced by the reaction of, e.g. diphenoyl peroxide and an easily oxidized fluorescent molecule has been brilliantly illuminated by Schuster and co-workers (Schuster, 1979b; Koo and Schuster, 1978) who proposed the CIEEL pathway (Chemically Initiated Electron Exchange Luminescence) according to (12). Note that two electron-transfer steps are postulated, the

1-C..

J.

ArH

second one involving electron transfer from a radical anion to the LUMO of a radical cation, thereby generating an excited state [cf. electrochemiluminescence; McCapra, 1973)l. 3 Capture of light energy. Nature captures light energy and uses it for the reduction of carbon dioxide on a colossal scale, albeit with a rather low quantum yield. It is an important objective to find simple chemical systems that can perform similarly; one way to imitate Nature in this respect is to utilize *Editors’ note. Chemiluminescence is the subject of a review by G. B. Schuster and S. P. Schmidt in this Volume

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LENNART EBERSON

molecules or ions in photoexcited states as electron-transfer reagents. This field is rapidly evolving presently (Balzani et al., 1978; Sutin, 1979; Whitten, 1980). 4 Biological electron transfer reactions. In the mechanistic realm, knowledge of organic electron-transfer processes, apart from its intrinsic interest, is likely to influence thinking about electron transfer in biological systems (Haim, 1975), which is still not understood in any detail (Moore and Williams, 1976). In particular, studies of electron transfer through organic structures should be important. This problem has obvious connotations for another promising area of application of organic electron transfer, namely the design of organic metals (Hatfield, 1979). Another biologically important problem is whether the products of one-electron oxidation (radical cations) play a part in the effects on an organism of foreign organic compounds such as drug molecules. There has been much discussion (Tamaru and Ichikawa, 1975) along this and similar lines since Szent-Gyorgyi first drew attention to the possible role of charge-transfer complexes (and by extrapolation, electron transfer) in biology (Szent-Gyorgyi, 1960). 2

Classification of organic electron-transfer processes

Since classification schemes tend to be rather boring, a few words are necessary to explain why this Section has been included. In the first place, the philosophy behind the synthetic use of organic redox processes in which electrons are transferred stoichiometrically is entirely different from that used in conventional synthesis. There is a risk-and anyone who has dealt with the thankless task of propagating the virtues of organic electrosynthesis can attest to it-that a redox reaction is only considered to be a way of transforming diverse functional groups into each other. This is not so! Secondly, a mechanistic classification scheme is necessary to narrow down a vast and ill-defined subject matter to a manageable size with a consistent content. Moreover, we will here have to take the first steps in transferring inorganic concepts into organic ones. Whatever we may think of nomenclature and definitions, science would not exist without them. MECHANISTIC CLASSIFICATION O F INORGANIC R E D O X P R O C E S S E S

Since most inorganic redox processes take place between two metal complexes, they are classified according to the behaviour of the inner (first) co-ordination spheres (shells) in the transition state (Basolo and Pearson, 1967). In the transition state of an outer-sphere mechanism the inner co-ordination spheres of both metal ions are intact, i.e., no ligand to metal bond is broken or formed, whereas in the transition state of an inner-sphere mechanism a bridging ligand,

a7

ELECTRON-TRANSFER REACTIONS

common to both co-ordination shells, connects the two metal ions thus providing a series of continuously overlapping orbitals for efficient electron transfer. The bridging ligand can be an atom or a group (Cl, OH, O H , NJ, sometimes of a rather extended type. An example would be the transition state [ 1I for electron transfer between certain carboxylato complexes of Co(II1) and

Ill

chromous ion in water, in which fumaric acid is the bridging ligand. Since in this case the electron can transfer from Co(II1) to Cr(I1) through a conjugated system, the process is called resonance transfer. It should be remembered that the classification criterion used above has nothing to do with the fact that the composition of the products may indicate that an atom or group has been transferred between the two metal centers. An inner-sphere mechanism may or may not be accompanied by atom or group transfer, and this may either occur as a consequence of the transition state structure or trivially be due to the fact that the complexes involved are substitution labile, i.e. exchange of ligands between themselves or the environment takes place at a rate faster than that of electron transfer. For the latter reason atom or group transfer may sometimes also take place in outer-sphere processes, and it has even been suggested that atom transfer can be part of an outer-sphere mechanism, if only for the case of hydrogen atom transfer. Such a case is the Fe(I1)-Fe(II1) self-exchange reaction in water where hydrogen bonding between two ligands in the transition state 121 would

[21

lead to hydrogen atom transfer. Obviously, such a mechanism is of the outer-sphere variety (since no ligand-to-metal bond is formed or broken) but in the sense of the Marcus theory for outer-sphere reactions, the degree of intraspecies bonding in the transition state is presumably too high to classify the reaction as a true outer-sphere mechanism (see below). MECHANISTIC CLASSIFICATION O F ORGANIC R E D O X PROCESSES

Before we proceed to translate the outer-/inner-sphere concepts to a terminology more suitable for organic molecules and while we still have the

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LENNART EBERSON

1 Reaction coordinate

c

FIG. 1 Potential energy surface for a system going from reactants (curve R)to products (curve P)

hydrogen atom transfer case fresh in mind, the meaning of the terms adiabatic and non-adiabatic, as commonly applied to electron transfer processes, will be explained. The profile of a potential energy surface for a chemical system going from reactants (R, lower curve) to products (P, upper curve) is shown in Fig. 1. In the region where the two curves intersect, i.e. where the distance between the reacting species is small enough, we obtain the usual quantum mechanical splitting between the two surfaces due to electronic interaction (resonance) between the reactants. Normally, depending upon the strength of the interaytion one would distinguish between two cases, namely, an adiabatic case where the interaction is so strong that R will pass over to P along the lower surface (arrowed line) with a probability of z 1, and a non-adiabatic case where the interaction is very weak and hence the transition probability, although finite, is very much less than 1. It is immediately recognized that most organic reactions follow strongly adiabatic mechanisms (bonds are broken and/or formed in the transition states) and that non-adiabatic mechanisms are rare; electron and certain H atom-transfer processes are the most obvious candidates. Now the Marcus theory must tread lightly between the Scylla of adiabaticity and the Charybdis of non-adiabaticity! Since the theory is based on a classical treatment of chemical dynamics, it must assume that the interaction energy (resonance energy) in the transition state is so small that one can neglect its

89

ELECTRON-TRANSFER REACTIONS

influence; otherwise the classical treatment must be replaced or supplemented by a quantum-mechanical one. On the other hand, if the resonance energy is assumed to be z 0, then the transition probability K of eqn (13), where k is the rate constant, Z is the collision frequency, AG* is the free energy of activation, and R and T have their usual meanings, will be 91 by a factor that again requires a quantum-mechanical approach for its calculation. It is an attractive feature of most electron transfers that they are adiabatic to the extent that K can be set equal to one, but not to the extent that it is necessary to consider the resonance energy; the dilemma is thus resolved. Thus for most electron-transfer reactions (even inner-sphere ones) the resonance energy is maximally 1 kcal mol-', more than sufficient to make K z 1 for electron transfer, and accordingly large enough to justify the classification as adiabatic. On the other hand, an energy quantity of gl kcal mol-' is negligible in comparison with the other factors explicitly considered in the Marcus theory. We can now return to the problem of classifying organic electron-transfer mechanisms. Littler (1970, 1973) has advocated the use of the terms non-bonded and bonded instead of outer-sphere and inner-sphere, respectively, when either or both reactants are organic species, since there is no simple, or rather generally acceptable, way of systematizing organic compounds in the same way as co-ordination compounds. Thus, with the use of the new terms for organic electron-transfer processes we arrive at the overall picture of all types of redox processes shown in Table 1. It is the non-bonded, adiabatic type in the upper right corner that we shall concentrate upon in what follows. TABLE1

Analogy between inorganic and organic electron-transfer processes Inorganic Outer-sphere, adiabatic Electron transfer Hydrogen atom transfer Inter-sphere, adiabatic Bridging Atom or group transfer

Organic Non-bonded, adiabatic Electron transfer Hydrogen atom transfer (?) Bonded, adiabatic Ligand oxidation and reduction within a metal complex Atom or group transfer Examples: Hydrogen atom transfer, hydride transfer, oxygen transfer, substitutions and additions with change of oxidation state at the atom(s) involved, etc.

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LENNART EBERSON

Let us see what this demarcation line means in practice! At the outset, we can exclude many reactions between substitution-labile complexes and organic substrates capable of acting as ligands (e.g. alcohols, phenols, amines, carboxylic acids). Generally these would be the majority of the reactions treated under the heading “Metal Ion-Ligand Redox Reactions’’ in, for example, the Specialist Periodical Reports on Inorganic Reaction Mechanisms (Lappin, 1977; Lappin and McAuley, 1979; McAuley, 1972, 1974, 1976; Burgess et al., 1971). We will also have to exercise some care with reactions where both reactants are organic species, since these are often the cases where charge transfer (CT) complexes are formed. Can we use the classical treatment of Marcus in situations like this, in spite of the fact that the electronic interaction energies in the transition state might be 21 kcal mol-’? Finally, it should be stressed that organic electron transfers only rarely occur as isolated steps because of the high chemical reactivity of odd-electron species. Normally, they are part of multi-step mechanisms together with other types of elementary reaction, such as bond forming and breaking. In organic electrochemistry a useful shorthand nomenclature for electrode mechanisms denotes electrochemical (= electron transfer) steps by E and chemical ones by C, and it is appropriate to use the same notation for homogeneous electron-transfer mechanisms too. Thus, an example of a very common mechanism would be the ECEC sequence illustrated below by the Ce(1v) oxidation of an alkylaromatic compound (14-17) (Baciocchi et al., 1976, E: ArCH,

--H1ArCH; ArCH; + Ce(1V) * ArCH: + Ce(II1) ArCHi + NuArCH,Nu

C: ArCH:’ E:

C:

+ Ce(IV) s ArCH:’ + Ce(II1)

-

1977, 1980, 1982). Here a formal two-electron oxidation is initiated by an electron transfer step, and a second electron transfer step involving a neutral radical is interspersed between two chemical ones. As we shall see, such mechanisms are not always easily distinguished from atom-transfer mechanisms.

SYNTHETIC CLASSIFICATION OF ORGANIC ELECTRON-TRANSFER PROCESSES

As mentioned in the preceding section, few organic electron-transfer processes occur alone. It is possible to prepare certain relatively stable radical-ion salts by one-electron oxidation (Bard et al., 1976; Holy, 1974), but by far the greatest

ELECTRON-TRANSFER REACTIONS

91

preparative potential lies in reactions which either are two-electron (or more) redox processes in the formal sense, or are electron- or hole-catalyzed. In the former category a first and trivial class is functional group interconversion. Such reactions are well-established in synthetic practice, and need not be commented upon. Instead we shall emphasize the oxidative and reductive versions of the usual gross synthetic principles: Substitution Addition Elimination Coupling Cleavage The great difference from the conventional meaning of these terms lies in the choice of reactants. Most conventional synthetic steps start from [nucleophile, electrophilel combinations, in the nomenclature of eqns (3) and (4), [R-E, E+l or [R-Nu, Nu-l pairs. Introducing an additional symbol, C=C, for double bonds (and this includes systems of conjugated double bonds) we also have the combinations [C=C(S+), Nu-l and [C=C(S-), E+l, depending upon the electrophilicor nucleophilic nature of C=C. In the oxidative or reductive versions of the reaction types listed above the [nucleophile, electrophilel combination is not allowed; instead we use [nucleophile, nucleophilel combinations oxidatively or [electrophile, electrophilel combinations reductively : [R-E, Nu-l, [C=C(S-), Nu-l, [R-Nu, E+l and [C=C(S+), E+l. This principle (Umpolung! see Section 1) vastly increases the number of choices available for synthetic schemes, and particularly allows for short cuts in conventional ones. Thus, the synthesis of ArOH or ArCN from ArH normally requires four steps (18), whereas the Ar-H

- - ArNO,

ArNH,

ArNl-

ArOH or ArCN

(18)

corresponding oxidative substitutions require two and one step, respectively (19,20). In complex synthetic schemes the savings of steps can be considerable,

-

ArH + AcO--H+ ArH + CN-

+ 2e- + ArOAc

H+ + 2e-

+ ArCN

-

ArOH

(19)

(20)

and in industry the handling of environmentally less acceptable intermediates can be circumvented. We shall not develop this theme further since exhaustive treatments are available, mainly in connection with electro-organic synthesis (Eberson and

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LENNART EBERSON

TABLE2 List of different types of organic redox reactions, emphasizing their synthetic scope Name Oxidative substitution

Oxidative addition

Oxidative cleavage-addition

General formula

+ Nu-

R-E

C=C+2Nu-

+ C=C

2R-E

--

E E

I I

Oxidative elimination

C-C

Oxidative coupling-elimination

2R-E

Oxidative coupling-addition

+ 2Nu-

2C=C

+ 2E+ + 2e-

C=C

Reductive cleavage-addition

2R-Nu Nu

Reductive elimination

C

4

Reductive coupling-elimination

2R-Nu

Reductive cleavage

R R

I I

+ 2E+ + 2e-

C-C

I

+ 2e+ 2e-

Nu

I

I

C-C-C-C

-

-

+ 2C=C + 2e-

Nu

-

+ C=C + 2e-

Nu

2Et

I

C-C+2e-

-

+ Et + 2e-

R-Nu

Reductive addition

Reductive coupling-addition

Nu

I

R-R+2Et+2e-

U

I

Nu

C=C+2E++2e-

Oxidative cleavage Reductive substitution

-

+ Ef + 2e-

R-Nu

--+

+ Nu-

R-E E E

I I

C-C

-

I

C-C

I

C=C

+ 2Nu-

R-R

+ 2Nu-

-

+ 2e-

E

I

C-C-C-C

+ 2Nu-

E

I

a

aDifficult to accommodate with the [Nu-, E+, R, C = Cl formalism because of the vague definition of cleavage processes in general

93

ELECTRON-TRANSFER REACTIONS

Schafer, 1971; Fry, 1972b; Baizer, 1973; Beck, 1974; Weinberg, 1974; Eberson, 1980a). For the sake of completeness, a list of the general types of synthetically useful two-electron redox reactions is given in Table 2. It should be noted that combinations of the simple categories are feasible too, making possible combined carbon-skeleton construction and functionalization in a single step. Electron-catalyzed (or electron-stimulated) processes constitute a relatively new class of reactions of great potential synthetic interest (Zelenin and Khidekel, 1970; Linck, 1971). Foremost among these ranks the S,,1 mechanism, which is an "electron-initiated" radical-chain mechanism of nucleophilic substitution (2 1-24; X- = halide ion) (for reviews, see Kornblum, 1975; Bunnett, 1978, 1982). The initiation step (21) can be performed photochemically, electrochemically, or by adding alkali metal (Pinson and Saveant, 1978; Amatore et al., 1979; van Tilborg et al., 1977, 1978; Saveant, 1980).

Initiation:

R-x R-X-' R'

-

(2 1)

R-X-0

R'

+ Nu-

+ X-

R-Nu-'

+ R-x

(R-NU-.

R - N ~+ R-X-*

(24)

An eliminative mechanism denoted E,,I, has been shown to occur in conjunction with the S,,1 mechanism in certain systems (Norris and Smyth-King, 1979 and references cited therein). It is, however, of a type different in principle from S,,1, being a reductive elimination (see Table 2) which requires a stoichiometric addition of electrons. Oxidative counterparts are the recently proposed S0,2 and So,l mechanisms (Alder, 1980; Eberson and Jonsson, 1980, 1981) which both are initiated by electron transfer oxidation. The S0,2 mechanism is shown in (25)-(28).

Initiation:

R-X

+

-

R-X+'+Nu-

-,x

R,

Nu

-

R-X"

R-Nu+' + R-X

(25)

R-Nu+' ---+

.,x

R,

(26)

Nu

+ XR-X+'

(27)

+ R-Nu

(28)

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LENNART EBERSON

Few leaving groups are available for step (27); so far, only fluoride ion is an unambiguous candidate of the (-1) charge type, since it is hardly possible to assume that it can leave as a fluorine atom (or, even less probably, as fluoronium ion). A good uncharged leaving group is nitrogen, as shown by the electron transfer catalyzed decomposition of diazodiphenylmethane by Cu(I1) or tris(4-bromopheny1)aminiumion (Bethel1 et al., 1979). The So, 1 mechanism (29-32) is an oxidative analogy to the S,,1 mechanism and is probably involved in the peroxydisulfate promoted hydrogen-deuterium exchange cc to nitrogen in certain amines (Alder et al., 1979; see also Gardini and Bargon, 1980). Initiation:

R-E R-E+' R'

-R-E+'

[R-Ell+'

(29)

+ E+

(30)

[R-E']+'

(3 1)

R'

+ E'+

+ e-

+ R-E

R-E'

+ R-E+'

(3 2)

Finally, several cases of electron-transfer catalyzed 271 + 271 cyclodimerizations have been reported and suggested to have chain mechanisms (Ledwith, 1972; Bard et al., 1976; Cedheim and Eberson, 1976). All these mechanisms are non-redox in nature, as is easily found by consideration of the oxidation states of the carbon centers involved. They are furthermore chain reactions, initiated by electron transfer, and the term "electron-transfer chain catalysis" (ETC catalysis) is therefore appropriate (Alder, 1980). Another term is the DAISET (Double Activation Induced by Single Electron Transfer) concept, recently introduced by Chanon and Tobe (198 1). The DAISET (ETC) concept is applicable to inorganic mechanisms too.

Stereochemistry of electron transfer processes Processes involving one or several electron-transfer steps are not likely to preserve the stereochemical integrity of the reactants. As we have seen, we are dealing with multistep mechanisms which involve odd-electron intermediates such as neutral radicals and radical ions. In both cases, the presence of an odd electron has a weakening effect on bonds, so that rotational barriers decrease drastically and exchange reactions, e.g., of the type shown in (33) become possible. This topic has been discussed in detail (Todres, 1974). The rather disappointing results from attempts to run organic electrosyntheses in a stereoselective fashion are an indication of the same factors at work (Eberson, 1980a; Fry, 1972a).

RH+'

R' + H-

(33)

ELECTRON-TRANSFER REACTIONS

3

95

The Marcus theory of adiabatic electron-transfer processes

A QUALITATIVE OVERVIEW

As already mentioned, the Marcus theory is most widely used among several others (Schmidt, 1975, 1978), presumably because it is simple, offers no computational problems ("back-of-an envelope calculations" are sufficient), has reasonably good predictive power and is thus amenable to experimental tests. On the other hand, it uses input data that sometimes are difficult to obtain or estimate, like other kinetic theories of similar character such as the bond energy-bond order (BEBO) method (Johnston and Parr, 1963; Gilliom, 1977). The Marcus treatment is empirical in that it uses extrakinetic experimental data (such as free energy changes, dielectric constants, molecular dimensions, vibrational frequencies, etc.) to calculate kinetic data. This is in a sense a strength, since the insight and understanding provided by a simple and easily comprehended model is sometimes better than something that has to be ground for hours in a computer. Let us first see qualitatively how Marcus attacked the problem of estimating the rate constant for electron transfer (34) between two metal complexes (M = metal ion, L = ligand, Z = charge), approximated as structureless spheres. The

[MIL;Iz1 + [M2Lilz* + [MIL:Iz1-' + [M2L:1'*+'

(34)

primary step is the diffusion together of the two reactants, aided or opposed by electrostatic forces, which can easily be calculated. The second step is the electron-transfer step, assumed to occur at contact distance between the two complexes, and it may at first sight appear strange that the transfer of an electron over such a distance (5-10 A) should experience a barrier of activation. The origin of this barrier stems from the Franck-Condon principle which tells us that the transfer of an electron takes place in such a short time (10-15-10-'6 s) that nuclear motions do not occur (the time of a vibration is 10-13 s).

A thought experiment shows how the Franck-Condon principle can give a hint about the nature of the barrier to transfer of the electron. Let us assume that the electron is transferred between Fe(H,0)2,+ and Fe(H,0)3,+ in their equilibrium configurations (35). We will then end up with Fe(H,O):+ with the

*

Fe(H,O):+

+ Fe(H,O):+

*

*

Fe(H,O):+

+ Fe(H,O):+

(35)

same Fe-0 distance as in Fe(H,O)i+; likewise Fe(H,O)Zgt will have retained the configuation of Fe(H,0)3,+ since no nuclear movements have had time to take place. In other words, two vibrationally activated states have been created, and these will decay to their ground states by giving off heat to the environment. Since the reaction is of the self-exchange type, its A H o = 0 and our imagined process hence has vialated the first law of thermodynamics!

96

LENNART EBERSON

We therefore turn the application of the Franck-Condon principle around, and assume that the co-ordination spheres of M' and MZ (including their surrounding solvent spheres) are distorted (expanded, compressed or asymmetrically rearranged) so as to make the energy of the two species identical (which of course means that they have identical structures in a self-exchange reaction). This corresponds to movement of R and P along their potential energy surfaces up to the intersection point (see Fig. 1). At this point, when exact matching of the energies of the two species has been achieved, the electron jumps from M' to Mz, and now we see that no violation of the First Law is involved. Thus we must consider two forms of the transition state, both with exactly the same nuclear structure but one with the electronic structure of the reactants and the other one of that of the products. These are called the reactants' and products' transition state, respectively. Figure 2 is a pictorial

FIG.2 Schematic representation of the Fe(H,O)~+/Fe(H,O):+reaction

representation of these events for the Fe(II)/Fe(III) reaction (see also Albery and Kreevoy, 1978). This model was used by Marcus and expressions for the inner-sphere (A,) and solvent-reorganization energy (A,) were derived (see below). It should be noted that the transfer of the electron from one metal center to the other in the transition state is associated with an electrostatic effect of sometimes appreciable magnitude. How well can we encompass organic systems within this qualitative model? In fact, this can be done at least as well as for metal complexes and in some respects better. Truly, the shape of many organic molecules deviates severely from a spherical one, and this problem might well be prohibitive for the use of

97

E LECTRO N-TRAN S FE R R EACTlO N S

the simple expression for calculation of A, of certain organic molecules. On the other hand, it is often assumed that Ai can be put equal to 0; we shall scrutinize this assumption later. Thus we would be left with the problem of finding a good computational method for A, with more realistic molecular geometries. Another advantage gained in many organic systems where one component is uncharged is the absence of electrostatic effects; on the other hand, if present, these may be more pronounced than in inorganic reactions due to the prevalent use of solvents of low dielectric constant for experimentation with highly reactive radical ions. Complications due to ion pairing are also to be expected. A MOLECULAR ORBITAL PICTURE O F ELECTRON T R A N S F E R

Before we proceed to the quantitative aspects of Marcus' theory, let us briefly look at an MO description of non-bonded electron transfer (36) between two species each with an even number of electrons. The electron is transferred from the highest occupied MO (HOMO) of the reductant (R) to the lowest

R + R' e R+' + (R')-' (36) unoccupied MO (LUMO) of the oxidant (R'; Fig. 3). Again, we can symbolize the vibrational excitation ( b in Fig. 3) and solvent reorganization (s in Fig. 3) necessary for matching the two energy levels to the same level. In keeping with the assumed very small bond distortion necessary for many organic molecules, solvent reorganization (A,) has been assumed to be the more important factor for R.

E

-

w

-

_c

-

- 0 e =

-

-

HOMO-

88 LUMO R

R(s)

R(s,b)

R'(s,b)

R"5)

R'

FIG. 3 MO diagram of an electron transfer process between the HOMO and LUMO of two = electrons; 0 = vacancies; s and b denote solvent and bond reactants R and R'. reorganization respectively

98

LENNART EBERSON

Symmetry rules for non-bonded electron transfer reactions To complete the M O description, we can quote an authoritative statement on the application of symmetry rules to redox reactions by Pearson (1976):

In any of these kind of redox reactions, orbital symmetry plays a major role, as it must in all chemical reactions. The requirement for a net positive overlap between the electron-donating MO and the electron-accepting orbital is a key part of the general theory of electron transfer. It is, however, not likely that orbital symmetry effects should manifest themselves very strongly in non-bonded processes where by definition the electronic interaction energy between the reactants in the transition state is 1 kcal mol-I (for a discussion, see Burdett, 1978). Search for stereoselectivity in non-bonded processes, which is one possible manifestation of orbital symmetry control has so far shown small, albeit real, effects (Bruning and Weissman, 1966; Chang and Weissman, 1967; Geselowitz and Taube, 1980). An attempt to rationalize the non-bonded redox vs. bond-forming reactivity of nucleophiles toward aromatic radical cations (6) on the basis of the DewarZimmerman rules (Eberson, 1975; Eberson et al., 1978a) was reasonably successful, but was criticized (Evans and Hurysz, 1977; Rozhkov et al., 1976) because of lack of agreement regarding both the mechanisms [how d o we distinguish the two paths of (6)?1 and phenomenology of these reactions (e.g. does ArH react at all with fluoride ion?). A lot of experimental work therefore remains to be done before one can assess properly the validity of the Dewar-Zimmerman rules in this context.

<

QUANT I T A T I VE A S P E C T S O F M A R C U S THEORY

Following the outline given above we shall first present the Marcus theory in its quantitative version and then discuss the various ways in which it can be compared with experimental results. In the original version, (1 3) is the starting point, using a value of Z equal to the normal experimental collision number for a bimolecular reaction in solution at 25OC, loL1M-I s-l, and with K = 1. The AG+ = AG:

+ AG: + AG:

(3 7)

term AG' contains three terms (37) where AG: is the free energy change due t o electrostatic interaction between the reactants in the transition state (equal to the work expended or gained in the process of moving the reactants from infinite distance to the distance in the transition state), AG: is the free energy change upon distorting the inner co-ordination spheres to the nuclear configuration of the transition state (corresponding to skeletal and other bond distortions in species other than metal complexes), and AGZ is the free energy

ELECTRON-TRANSFER REACTIONS

99

change upon rearranging the solvent and ionic atmosphere on going from the reactants’ to the products’ activated complex. We shall discuss these terms in detail separately before we analyse the complete expression for AG*. It is assumed that (2) is the starting point, Azl being the oxidant and BZzthe reductant.

Electrostaticfree energy change The electrostatic free energy change required to bring the two species (regarded as spheres) to their distance (r12)in the collision complex (Fig. 4) is

FIG.4 The colliding-spheremodel of the transition state for an electron-transfer reaction

given by (38) where e is the electronic charge, rI2is the internuclear distance in the transition state (Fig. 4), Nois Avogadro’s number, p is the ionic strength, D

is the static dielectric constant of the solvent and k the Boltzmann constant. With r,2 expressed in A and D as the usual dimensionless unit, (38) reduces to (39), giving AGf in kcal mol-I. For p = 0, (40) results. Table 3 gives values for

AGf =

33 1.3 Z,Z,

Dr12

AGZ at 25 OC, calculated by (40) at typical values of D, rI2and 12,Z , I. With the exponential factor of (39) included, the electrostatic factor decreases strongly with increasing ionic strength. As an example, at p = 1 all values of the column for D = 78.5, r12= 7 A are reduced to one-tenth, whereas in the column for D = 6.2, rI2= 7 A at p = 0.1 the reduction factor is cu. 0.07 (of course neglecting the effect of ion pairing).

100

LENNART EBERSON

TABLE 3 Values of A e for some typical sets of IZ,Z,I, D,and rI2 Acetonitdeb (D = 37.5)

Water (D= 78.5) IZ,Z,l

I 2 3

4

5 6

a

r,;

Acetic acid (D= 6.2)

5

7

9

5

7

9

5

7

9

0.8 1.6 2.5 3.4 4.2 5.1

0.6 1.2 1.8 2.4 3.0 3.6

0.5 0.5 1.4 1.9 2.3 2.8

1.8 3.5 5.3 7.1 8.8 10.6

1.3 2.5 3.8 5.0 6.3 7.6

1.0 2.0 2.9 3.9

10.7 21.4 32.1 43 53 64

7.6 15.3 22.9 31 38 46

5.9 11.9 17.8 24 30 36

4.9

5.9

A@ in kcal mol-I; r I 2in A

* N,N-Dimethylformamide electrostatic properties

(D= 36.7) and methanol ( D = 32.5) have similar

For all reactions (2) with at least one component uncharged, AG: = 0 if, as is normally done, we exclude dipole-dipole interactions. This means that AG$ can be neglected for many organic electron-transfer reactions. Otherwise, in media that are often used for organic redox reactions the electrostatic effects are formally fairly large and certainly not negligible. The effect of cations upon the disproportionation of radical anions (4 1) in ethereal media is an example of ArH-’

+ ArH-’

e Ar2-

+ Ar

(4 1)

the importance of electrostatic interactions (Szwarc, 1972; Levin and Szwarc, 1976).

Thefree energy change due to inner-sphere reorganization (bond distortion) For a reaction between two complexes, AG: expresses the free energy change due to changes in the ligand geometry (bond lengthening, compression, binding, etc.) required to satisfy the Franck-Condon principle. It can be written in terms of vibrational partition functions for the participating species (Ql,Q,” and QY ), as in (42) in which AG is the difference in zero-point energies

,

between the transition state and reactants A and B. The partition functions are set equal to 1, giving (43) from which the final set of eqns (44-48) for AGf

= AU?

(43)

ELECTRON-TRANSFER REACTIONS

101

expressing dG: was derived by a treatment based on statistical mechanics (Marcus, 1963). AG:

AGO’ =AGO

= m2,Ii

(44)

+ ( Z , - Z 2- 1) e2/r12D

(46)

a = ai + a.

(47)

We repeat that 1,is the inner-sphere reorganization energy (44), 1, (47) is the solvent and ionic atmosphere reorganisation energy (to be discussed in the next section) and 1 (45, 47) is the total reorganization energy. AGO’ is introduced to simplify eqn (45) and corresponds to the free-energy change for the reaction in the medium used, AGO (not necessarily equal to the standard free energy change but nevertheless in most cases put equal to it), plus the electrostatic term [the last one in (46)l originating from the change in the charge of the transition state upon electron transfer. Equation (48) contains as the variables kR and kp, the force constants of the jth vibrational co-ordinate in a species participating as reactant and product, respectively, and (4: - qp), the change in the bond lengths and bond angles in going from reactant to product. A simple example will help to clarify the meaning of (44)-(48). For a self-exchange reaction of the type shown in (35) it is an adequate approximation to consider changes in Fe-0 bond distances only (Sutin, 1962). In such a case (48) gives the simplified expression (49) for Ai, in which k , and

k, are the force constants of the Fe-0 bonds of the reactants and q , and q2 their equilibrium distances (remember that there are 2 x 6 = 12 Fe-0 bonds in the transition state). Looking at (45) and (46) our self-exchange reaction is found to have rn = -0.5 [AGO = 0,( Z , - Z , - 1) = 01 as would be demanded for a transition state that must be symmetrical with respect to both ions. Thus (44) becomes (50), and with values for k,, k,, q, and q2 appropriate to

102

LENNART EBERSON

Fe(II)(H,O), and Fe(III)(H,O), of 1.49 x losand 4.16 x lo5dyn cm-', 2.21 and 2.05 A one obtains AG: = 12 kcal mol-'. For organic molecules it is often assumed that the inner-sphere reorganization energy, A,, is equal to 0, which is another way of saying that no bond lengths and angles are changed on electron removal from or addition to an organic species. We shall discuss the validity of this approximation later when we have defined the solvent-reorganization term and have a complete view of the Marcus equation.

Free energy change due to solvent reorganization For two spherical complex ions of radii rl and rz the free energy change required to rearrange the solvent shells of the two ions from the reactant state to the transition state is estimated (Marcus, 1956) from a classical dielectric continuum model of the solvent, giving (51) and (52), in which all quantities A G= ~ m21,

(5 1)

except Do,the optical dielectric constant (the square of the refractive index), have been defined above. Figure 4 shows that r12is usually set equal to rl + r,, i.e. the two ions are assumed to be in van der Waals' contact in the transition state. Table 4 shows calculated values of A, for some typical situations covered by the model. Note that 1/D can be neglected with respect to l/Dofor high-dielectric constant solvents (values of Lo for water, with D = 78.5, are only about 4% higher than those for acetonitrile). TABLE 4 Values of 1, in acetonitrile and acetic acid calculated by (52) for different values of r, and r," Acetic acid (D= 6.2)

Acetonitrile ( D = 37.5) rl

2 3 4 5 6

r , 2 43.7

3

4

5

6

2

3

4

5

6

37.9 29.2

36.4 26.0 21.9

36.2 24.8 19.9 17.5

36.4 24.3 19.0 16.2 14.6

30.7

26.6 20.5

25.6 18.3 15.4

25.4 17.4 14.0 12.3

25.6 17.1 13.3 11.4 10.2

&in kcal mol-I; r,, rI in A

ELECTRON-TRANSFER REACTIONS

103

As already mentioned, one difficulty with this model when applied to organic molecules is their non-spherical shape. Octahedral complexes are reasonably well approximated as structureless spherical objects but what about such species as aromatic hydrocarbons and their radical ions? The problem has been treated in two principal ways. In one the spherical approximation is retained and an “effective” radius of the sphere is estimated from the molecular volume calculated by a simple method, e.g. using (53), in which M is the molecular weight and d is the density (Peover, 1968; Kojima and Bard, 1975). Alternatively a more realistic geometry based on known molecular dimensions is introduced (Suga and Aoyagui, 1973; Suga et al., 1973; Yamagishi, 1976; Kharkats, 1976). We shall discuss this problem in detail in Section 4.

The complete expression for AG’ We can now combine (37), (38, omitting the exponential), (44), (49, and (5 1) and after some rearrangement obtain the complete expression (54) for AG+.

For a reaction involving at least one uncharged species, as many organic electron transfers are, we can omit the electrostatic term and, putting 1 = ,Ii + 1, we obtain the simplified expression ( 5 5 ) which is the form normally employed. One often also sees the alternative form (56) in which AG+(O)

replaces 1/4. A G s ( 0 ) is then simply the change in the free energy of activation for a process with AGO’ = 0. We immediately realize that it is possible to determine 1 = 1,+ A,, experimentally from the rate constants of self-exchange reactions. By definition these must have AGO‘ = 0. As we shall see later, it has often been the practice to assume that AG*(O) is a constant for a whole series of closely related electron-transfer reactions. As an example, a value of 2.4 kcal mol-’ has been used for fluorescence quenching of excited states by electron donors (57, 58) (Rehm and Weller, 1969; 1970). Values of AGP(0) of 15 kcal

104

LENNART EBERSON

mol-’ or higher have been proposed (see, e.g., Fukuzumi et al., 1980; see also Section 4). A

r

ArH*

H

-

(57)

h ArH*

+ Ar’H

ArH-’

+ Ar’H+’

(58)

Plots of AG’ vs. AGO’ for different values of AG*(O) are shown in Fig. 5 in order to illustrate the relative simplicity of (56). We shall later show other types of plots (log kobsvs. AGO’) in which the electron-transfer step is part of a kinetic scheme.

-40

- 20

0

AGO) kcal mol-’

20

40

FIG.5 Plots of AC* vs. AGO’ according to (56) for dG*(O) equal to 2.4 (I), 4.8 (2). 7.2 (3) and 9.6 (4) kcal mol-I. The enclosed areas on the curves indicate the region from -AG*(O) to +AG*(O) around AGO’ = 0

The Marcus cross relations Thus the Marcus theory gives rise to a free energy relationship of a type similar to those commonly used in physical organic chemistry. It can be transformed into other relationships (see below) which can easily be subjected to experimental tests. Foremost among these are the remarkably simple relationships that were developed (Marcus, 1963) for what have been denoted “cross” reactions. All non-bonded electron-transfer processes between two different species can actually be formulated as cross reactions of two self-exchange reactions. Thus the cross reaction of (59) and (60) is (61), and, neglecting a small electrostatic effect, the relationship between kll, k,, and k , ,

105

ELECTRON-TRANSFER REACTIONS

is given by (62) and (63), where K,, is the equilibrium constant of (61). are the Recasting (63) in free energy terms, it becomes (64), where All and ,Izz

k

*All+ + A(n-l)+l:*A(ll-l)+

+

An+

kll *B/+ + B(/-l)++ *B(/-l)+ + B/+

An+ + B(/-l)+3A(ll-l)++ B/+

logs=-

1

(AG?;)'

2.303 RT

+

(59) (60) (6 1)

reorganization energies of the two self-exchange reactions. Finally (62) and (63) can be combined and rewritten to give (65). This useful relation tells us that a plot of the left hand side vs. AGY,' should be a straight line with slope 0.5. AG:,

+ (0.5)(2.303)RTlogf = 0.5 (AG:, + AG:,) + 0.5 AG;;'

(65)

Another useful outcome of the derivation of (62) is that A,, is approximately equal to (All + A,,)/2. Thus we can estimate A ] , from experimentally accessible values of 3, for self-exchange reactions (see discussion in Section 4). Finally we also see from (65) and (64) that, for the case when IAG&' I g (,Ill + A,*), the left-hand side of (65) is simplified to AG:,. Usually, one formulates this condition as a requirement for IAGYi I to be
106

LENNART EBERSON

non-adiabatic. Thus the cause of failure of (62),f= 1, must be that assumption (1) or (2) is not valid: none of the assumptions (3)-(7) will cause failure of the cross-relation. KINETIC S C H E M E S WITH A N INITIAL N O N - B O N D E D ELECTRON TRANSFER STEP

Electron transfer steps seldom occur in isolation, and it is therefore necessary to deal briefly with the relation between observed rate constants and rate constants for electron transfer in a few common kinetic situations. The simplest case of a kinetic scheme with an initial electron transfer is the one shown in (66). Here the two reactants diffuse together with rate constant kd k

kd

A + B +[A...Bl-products

(66)

k-d

to form an encounter complex which undergoes the electron transfer step with rate constant k,,. If we apply the steady state approximation to [A...BI we obtain the usual expression (67) for the observed rate coefficient, kobs. To k obs =--

kd

I+-

-

k-d

kd kd

k-d

kel

kd

1+--.-

'el

simplify this expression, it is common to put k,/k-, = 1 M-' (Marcus, 1960). If we want to be more accurate, the equilibrium constant for formation of the encounter complex, with distance a (in cm) between the two particles, is given (Eigen, 1954) by (68) in which y is a symmetry factor (1 for unlike species, f kd

-=k-d

y4nn3N0

exp

3000

[

for like species). U(a)is a potential function; if the reactants are ionic a simple coulombic potential (40) or a Debye-Hiickel potential (39) is used. Assuming that U(a) is approximately equal to 0, as it would be if one or both reactants were uncharged, k,/k-, is estimated to be 0.32,0.86, and 1.84 M-I for a = 5, 7 and 9 A. Introducing (13) for k,, and (54) and (56) to express AG*, we arrive at the kinetic expression (69), the starting point for many discussions of the kd

kobs =

kd

+ A@(O)

(I +

(69)

c ) ] / R T ) 4 AG+(O)

ELECTRO N-TRAN S FE R R EACTlO N S

107

application of Marcus theory. If it looks rather formidable we should remember the approximations that are possible when one reactant is uncharged. In order to show how different variables influence kobs,(69) is written in the abbreviated form (70). Since we are interested in free energy quantities, one normally plots

log kobsvs. AGO'; families of such curves are shown in Fig. 6 for changes in each of A, W, and A@(O) while the others are kept constant. In all cases k, is assumed to be 2 x 1O'O M-I s-l, which happens to be the diffusion-controlled bimolecular rate constant at 2 5 O C in acetonitrile, and Z = 10" M-'s-'. A change of A from 1 to l o 2 lowers the maximum by ca. 2 logarithmic units; since A is likely to vary over a rather small interval, the model is not very sensitive for changes in A. On the other hand changes in the electrostatic term Win the range from -10 to + 10 kcal mol-I strongly influence the shape of the curves and the value of (log kobs)max. Since at least formally I WI can have appreciable values in solvents of low dielectric constant, the work gained or expended in bringing two highly charged ions to their encounter distance can have a profound effect upon the rate. Luckily, most organic electron-transfer processes are not influenced by this particular problem. The electrostatic effect does, however, often appear in the estimate of AGO' (46) since the product of electron transfer from a neutral molecule is an ion; strict avoidance of all electrostatic effects in the Marcus theory is only possible for reactions of the type A + B* -,A* + B. Increases in the value of dG*(O) have the effect of flattening the curves (Fig. 6 4 and moving the maxima towards lower values of AGO'. The effect on the shape of the curve is marked over the interval in which AG*(O) values normally appear [see Tables 5 and 7 which give examples of A = 4 AG"(0)I. A second kinetic scheme of interest is the slightly more complex one used in studies of the kinetics of fluorescence quenching by electron transfer (Rehm and Weller, 1969, 1970). In such investigations an aromatic hydrocarbon or heteroaromatic compound (A) is promoted by light to its lowest excited singlet state ('A*) in a polar medium (acetonitrile or DMF). The fluorescence of the species is quenched in the presence of electron donors (easily oxidizable aromatic compounds such as substituted anilines, polymethoxybenzenes, etc.). The quenching rate constant is then the observed rate constant, and is connected to k,, using kinetic scheme (71) where 'A* and ID diffuse together to give the encounter complex as usual but the k,, step is now reversible with k-,, as the rate constant for the reverse step. The ion pair .2D+),still with the two species at encounter distance, can also react irreversibly with internal

.

108

LENNART EBERSON

electron transfer (annihilate) to give back eventually A and D with rate constant kann(estimated at 2 10" s-I). Using the steady state approximation, expression (72) can be derived and this can then be combined with (13), (54), and (56) in the same way as before, yielding a similar although more complex equation. In order to illustrate another aspect of the Marcus theory, this exercise is however left to the reader. Instead, we shall briefly touch upon the

TABLE5 Calculated values of AGf, Lo and I , for some inorganic self-exchange reactions in aqueous solution

r,/A

Reduced form

r,/A

AGY Lob/ AIC'I kcal mol-' kcal mol-l kcal mol-'

AGAl,d

AG&

Ref.

~~~

Co(H,O)i+

3.56

3.40

3.6

26.3

48.4

22.3

14.3

e

Fe(H,O):+

3.59

3.43

3.6

26. I

48.4

22.2

14.2

e

Mn(H,O)it

3.66

3.46

3.6

25.1

15.2

28.8

19.8

e

Cr(H,O)Y

3.58

3.40

3.6

26.2

60.4

25.3

)2 1.4

e

V(H,O)i+

3.56

3.41

3.1

26.2

12.0

13.3

17.6

e

Ti(H,O);+

3.56

3.45

3.6

26. I

22.8

15.8

11.7

e J

18.3

11.0

20.0

16.7

g

9.0

0

2.3

4.0

i

(C0"lW ,zo40)J-

5.0

5.0

12.7

IRu3O(CH3CO0),(py),Ih

7.0

7.0

0

' Equation (40) Equation (52) Equation (48)

AGf + (1, + LJI4 Recalculated from data given by Sutin (1962) 'Brunschwig and Sutin (1979) Rasmussen and Brubaker (1964) Solvent, dichloromethane i Walsh

el a/. (1980)

FIG.6 Plots of log k vs. AGO' according to eqn (70). (a) W = 0, AC'(0) = 2.4 kcal mol-' and A = 1.0 (1); 10 (2) and 100 (3); (b) A = 1.0, AG*(O) = 2.4 kcal mol-' and W = 10 (l), 0 (2), and -10 (3) kcal mol-I: (c) A = 1.0, W = 0 and AC*(O) = 2.4 (1). 4.8 (2), 7.2 (3) and 9.6 (4) kcal mol-'. The enclosed areas on the curves indicate the region from -AC*(O) to +AG*(O) around AGO' = 0

ELECTRON-TRANSFER REACTIONS

(FIG.6 )

109

110

LENNART EBERSON

problem of applying the theory to strongly exergonic reactions (i.e., with AGO' < 0). 'A*

k

+ ID

] A * . . .ID

k-d

41

A-.

k-d

. . . D+

(71)

Ik.""

A+D kobs

=

kd

As shown by Fig. 6, the Marcus theory predicts a parabolic shape for log kobs vs. AGO' in situations like those depicted in (71). The molecules are uncharged, and AG'(0) is small (2.4 kcal mol-' according to Rehm and Weller). However, for reactions with AGO' values as low as -60 kcal mol-' (Rehm and Weller, 1970) the rate constant for fluorescence quenching was still diffusion-controlled. In other words, Marcus theory seems correctly to predict k,, for slightly exergonic and endergonic processes only, and the remarkable prediction that k,, should decrease with decreasing AGO ' is refuted (see also Ballardini et al., 1978; van Duyne and Fischer, 1974; Scandola and Balzani, 1979). This is the problem of the Marcus "inverted region". In view of this difficulty, Rehm and Weller proposed an empirical relationship (73) between AG and AGO' for the k,, step which gives virtually the

same values as the Marcus equation in the endergonic and slightly exergonic regions but a plateau value equal to log k, in the highly exergonic region. By suitable manipulation of (72) with the aid of (13) one obtains (74) finally l+kd

L

k, gave a value of 0.25, and (Rehm and Weller, 1969). Estimates of kd k-d/kann with the AG' given by (73) log kobsvs. AGO' plots can be obtained. Figure 7 shows two curves [AG*(O)= 2.4 and 7.2 kcal mol-'I of this type together with two curves calculated from (74) using the Marcus expression for AG* instead, but with all variables identical. The similarities and differences commented upon already are clearly visible. It has been pointed out (Indelli and Scandola, 1978) that neither the Marcus nor the Rehm-Weller expressions for AG* should be introduced into (74) since

ELECTRON-TRANSFER REACTIONS

-40

111

-20

0

20

AGo?kcol mol-’

FIG. 7 Rehm-Weller (-) and 4) kcal mo1-l

and Marcus (---)

plots for dC’(0) = 2.4 (1 and 3) and 7.2 (2

its derivation is based upon the simplification that k,,, is extremely large,’ 210’’ M-’ s-l. Rather, one should use the complete equation obtained by substituting into (72) the AG* expression (13) for all three electron transfers (k,,, k-,,, k,,,) of kinetic scheme (71). In doing this, Indelli and Scandola (1978) found that the Rehm-Weller curve is hardly changed at all but the Marcus curve undergoes drastic changes (see Fig. 8). Thus it was claimed that the Marcus model for correlation of log kobswith AGO’ for excited state electron-transfer quenching leads to an appreciable disagreement with experimental results also in the region where AGO‘ > 0. Noting that the origin of the Rehm-Weller equation (73) is entirely empirical, Scandola and Balzani (1979) sought to develop a function with the same general properties but with a better theoretical background. Thus it was proposed that the bond energy-bond order (BEBO) method, used to develop a free energy relationship for atom-transfer reactions (Marcus, 1968; cf. Agmon and Levine, 1977; Levine, 1979) could provide such a background. The expression obtained by this treatment (75) in conjunction with (72) gives almost the same log k vs. AGO’ plot as (73). According to Scandola and I

This assumption implies “anti-Marcus” behaviour for the /c-~, step

112

LENNART EBERSON

3

AGO) kcal rn01-l

FIG. 8 Rehm-Weller (1 and 3) and Marcus (2 and 4) plots, using the treatment proposed by Indelli and Scandola (1978). - , A = 0.0043 1, dCC(0) = 3 kcal mol-', Eo-,, = 70 kcal mo1-I; _ _ _ , A = 0.25, dC=(O)= 2.4 kcal mol-l, Eo-,, = 70 kcal mol-'

Balzani (75) should be the preferred choice in the treatment of non-bonded electron-transfer processes. AC'

= AGO'

+

AG+(O) ~

In 2

AGO' In 2

(75)

The Rehm-Weller equation has an interesting property which we shall have occasion to return to later. For AGO' 0, AG*(O) can be neglected in (73) and thus the plot of log k vs. AGO' is approximated as a straight line with slope 1/2.303 RT (= -0.73 kcal mol-I or -17 V-I) in the region of high AGO'. This is valid with good precision for AGO' > 4 AG*(O). Fortuitously, one can of course obtain plots of the same slope using the Marcus model in the region of AGO' B 0, depending on which interval of log k-values one works in; for example the slopes of the tangents of the Marcus curve, AG'(0) = 2.4 kcal mol-', in Fig. 7 has the values -0.74, -1.1 3 and -1.5 1 mol kcal-' for AGO' = 10, 20 and 3 0 kcal mol-'. The Scandola-Balzani equation (75) behaves similarly to the Rehm-Weller equation for AGO' 2 4 x AG*(O), being approximately a straight line in this region. Summarizing, the Marcus model for non-bonded electron-transfer mechanisms provides several types of predictions that can be tested experimentally:

ELECTRON-TRANSFER REACTIONS

113

(a) Rate constants for single reactions can be estimated from extrakinetic data (molecular dimensions, vibrational frequencies, dielectric constants and change in standard free energy) according to (56) and (13). (b) Rate constants for single reactions can be estimated from kinetic data pertaining to the self-exchange reactions and equilibrium constants (62,63). (c) A log k vs. AGO' plot in the region IAGO'I < AG*(O) should be approximately a straight line with slope -0.5/2.303 RT. Outside this interval, (65) applies. (d) For the region AGO 2 4 AG'(0) a log k vs. AGO' plot should be approximately linear with slope < -1/2.303 RT. If the Rehm-Weller or Scandola-Balzani approach is used, the prediction is a slope of -1/2.303 RT. The Marcus parabola can of course be approximated as a straight line in any range of AGO' and slopes can then be calculated for that range. (e) Finally, for the sake of completeness it should be mentioned that the rate constant of a homogeneous self-exchange reaction (k,,,,,,) is predicted to be related to its heterogeneous electrochemical counterpart (kWhJ through (76), (khom/Zhom)t

kechern/Zechem

(76)

assuming that the electrostatic terms can be neglected. Here frequencies are normally taken to be 10" M-' s-l and lo4 cm s-l, respectively, for the homogeneous and heterogeneous reaction (Marcus, 1965). It has, however, been argued (Hush, 1968) that a slightly different model of the electrochemical exchange reaction should be used, and then the modified correlation of (77) khomlZhom

= kechem/zechem

(77)

results. Experimental data are in better accordance with the latter treatment (for a detailed discussion of the problem, see Kojima and Bard, 1975). 4

Problems involved in applying the Marcus theory to organic reactions

CALCULATION OF

1

For inorganic species, the application of Marcus theory involves an estimate of

A = A, + 1, using (48) and (52), the latter usually based on the model depicted

in Fig. 4. Table 5 shows some typical results for calculations of 1 for inorganic self-exchange reactions and the corresponding experimentally derived values. According to the calculations A, and A, make comparable contributions to 1, but it is to be noted that the agreement between calculated and experimental values is not very good. For organic systems, it was early assumed that Ai can be neglected in comparison with 1, (Marcus, 1957). This was substantiated by theoretical

114

LENNART EBERSON

TABLE 6 Estimates of 2 s for alkylmetals Compound Et,Si Et,Ge Me,Sn Me,Et,Sn Et,Sn Pr,Sn secBu,Sn isoBu,Sn neoPe,Sn Me,Pb Me2Et2Pb

Radius/A"

kcal mol-l

kcal mol-I

Aid/ kcal mol-'

5.59 5.68 4.38 5.14 5.90 5.90-7.31 5.90-7.37 5.9Ck7.37 7.37 4.52 5.28

15.7 15.4 20.0 11.0 14.8 14.8-1 1.9 14.8-1 1.9 14.8-1 1.9 11.9 19.4 16.6

70 62 52 58 66 58 48 60 48 60 40

54 47 32 41 51 43-46 43-46 43-46 36 41 23

(4Jcal:/

AexpCI

Estimated from the geometry of the molecule Equation (52); rI2= rl + r2 Calculated from I values for reactions between Fe(II1) complexes and alkylmetals (Table 13), assuming dlFe(III)/Fe(II)l = 16 kcal mol-' Obtained as the difference between A,,, and (I,),,,,

calculations (Hale, 1971), showing that in almost all cases I i is less than 5% of I,. Exceptions were found in systems that required a large bond andlor

conformational energy change in the transition state. As an example, the cyclo-octatetraene/cyclo-octatetraene- system involves a flattening of the neutral molecule in the transition state, and this energy (ca. 14 kcal mol-I of a total I of 36 kcal mol-I) cannot be neglected. X-ray crystallographic studies on radical cations and anions (Kistenmacher et al., 1974; Fritz et al., 1978; Galigne et al., 1979; Herbstein, 1971) have since shown that the bondreorganization energy must be small compared to Lo in radical ions with extensive delocalization of charge. Species with more localized charge, e.g., tetraalkylhydrazine radical cations, show large differences in geometry from that of the neutral molecules (Nelsen et af., 1978). Alkylmetals which exhibit very large I values (Table 6) in all probability undergo extensive bond changes upon one-electron oxidation. One can estimate I, for these compounds-well approximated as spheres for the tetrahedral molecules-from (52) to fall in the range of 12-20 kcal mol-I, putting the value of I i between 25 and 55 kcal mol-', a very high proportion indeed of A. Noting cases of such behaviour, we shall nevertheless adopt the approximation that I i = 0 for purely organic redox systems, unless otherwise noted.

ELECTRON-TRANSFER REACTIONS

115

Before we can discuss the different approaches available for estimating A0 for organic self-exchange reactions we need to have a look at the pertinent experimental material. Table 7 contains a collection of rate data for many different types of organic self-exchange reactions. In selecting these reactions, care has been taken to include only such processes which involve free radical anions, since ion pairing exerts an appreciable rate-retarding influence. This is especially pronounced for radical anions, presumably due to metal atom transfer in the transition state (Adam and Weissman, 1958), but should be kept in mind for radical cations too (Ocasio and Sullivan, 1979). A few cases (nos. 18,20, 38) have been included to show this effect; in general a “loose ion pair” reacts ca. 100 times slower than the free ion whereas a “tight ion pair” reacts slower still (Hirota et al., 1968). Sometimes it was not possible to find data for the free ions, and it should always be kept in mind that radical anion reactions are especially sensitive to ion-pairing effects (Szwarc, 1968). The rate constants of Table 7, in the appropriate cases corrected for diffusion (67), were then used to calculate Aexp = 4 x dG*(O), using (13) with 2 = 10” M-’ s-’ (column 5 in Table 6). The problem of estimating A. for organic species is not trivial, since their molecular shapes differ appreciably from the spherical one assumed by the Marcus model. In addition, the charge of an organic anion may be strongly localized, as for example in the radical anion of a nitroalkane (Peover and Powell, 1969); and this is not taken into account by the Marcus model either. The simplest approach (Kowert et al., 1972; Kojima and Bard, 1975) is to assume that any organic molecule can be approximated as a sphere, using, e.g. (53) or any equivalent method to estimate the “effective” radius of the sphere. Table 7 lists A values calculated by this method. Instead of using (53) directly for determining the radius of the sphere, Traube’s rule (Wiberg, 1964) was employed for estimating the molar volume [= M / d in (53)l. This treatment avoids the necessity of finding the densities of organic solids (which are not always available) but gives almost the same results as (53). The structure of the transition state was approximated as two colliding spheres (Fig. 4) and rl was set equal to r,. With rl2 = rl + rz a set of 1 values was calculated (column 6 of Table 7). A comparison between experimental and calculated 1 values immediately shows that with few exceptions the spherical model predicts 1 values that are far too large. It is gratifying, however, to find that molecules of approximately spherical shape (nos. 11,24,25,74) do fit reasonably well with the model. A way of checking the possible physical reality behind the overestimated 1 values of the spherical model is to keep rl = r, = the estimated radius of the sphere and instead evaluate the value of rl, = r* which corresponds to the experimental A. Column 7 of Table 7 shows r* of the spherical model; we now see that in the majority of cases r* < rl + r,, i.e., it seems as if the colliding

TABLE 7 Experimentally determined rate constants and 2 values for organic self-exchange reactions, together with estimates of 1 and r* according to a spherical model and an ellipsoidal model Spherical model' Reaction no. 1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18

Solventb

Parent compound" Radical cations: Dibenzo-p-dioxin Phenoxazine Phenoxathiin Phenothiazine 9,lO-Diphenylanthracene 10-Methylphenothiazine Tri-p-tolylamine N,N-Dimethyl-p-phenylenediamine

N,N,N',N'-Tetramethyl-pphenylenediamine N,N,N',N'-Tetramethyl-pphenylenediamine Ferrocene Bisarenechromium(0)'

R,Sn, R,Pb, R,Hg" Radical anions:" Benzene" Toluene" p-Xylene Naphthalene Naphthalene"

AN AN AN AN CH,CI, AN AN AN AN

Propanol-water (1 : 1) Benzene-d,

kexchC~~O0 Lexpd/ kcal mol-l M-I s-I

kcal mol-l

rc+a,c/A

Ellipsoidal modele

r&JA

25 55 44 101 3.4 25 6.8 7.8

8.8 6.9 7.4 5.4 7.0 8.8 11.8 11.5

21.6 21.4 21.3 21.1 21.1 20.5 18.0 23.0

5.10 4.85 4.95 4.75 7.00 5.45 7.25 5.05

5.65 5.65 5.68 5.68 8.71 5.70 9.25 5.01

10.5

10.8

21.4

5.45

5.72

0.00025

36

22.4

0.057 2.3-3.7

23.1 14.3-13.2

22.0 .2

40-70

AN DME DME DME THF THF

2catc/

0.36 0.45 0.43 3.3 0.6

18.8 18.3 18.4 8. I 17.6

>20.0

8.70

8.40 Calculation not possible See Tables 6 and 13 19.4 18.4 17.6 17.0 16.2

6.35 6.90 7.65 5.05 8.25

4.78 5.02 5.38 4.88 5.73

Ref.

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Naphthalene Naphthalene" Naphthalene Naphthalene Naphthalene I-( I-Naphthyl). l-phenylethane, (+)-form with (+)-ion I-( I-Naphthy1)-1-phenylethane, (-)-form with (+)-ion Anthracene Pyrene Tetracene Perylene Hexahelicene, (+)-form with (+)-ion Hexahelicene, (-)-form with (+)-ion Cyclo-octatetraene (Cyclo-0ctatetraene)-'/ (cyclo-octatetraene)*trans-Stilbene trans- 1,2-Diphenyl-1methylethylene

2,4,6,2',4',6'-Hexamethyltrans-stilbene Dibenzofuran 2.2'-Bipyridinen Dibenzothiophene Benzonitrile Benzonitrile

DME DME DME/THF DMF HMPA DME' DME'

13 6.7 4.7 0.68

8.2 16.3 10.3 11.9 12.7 17.3

20.3 19.2 14.0

5.00 7.25 5.35 5.65 11.85

1.1

16.1

14.0

10.65

3.2

1.o

17.0 17.0

4.87 5.50 -

4.98 5.06 -

p p

4 r

S

U

rn r rn

0 --I

n

0

5n b

DMF DME DME DME THF

24 28 26 30 200

8.8 8.5 8.7 8.3 3.8

18.4 14.9 14.3 13.9 12.2

5.45 6.00 6.45 6.66 5.95

5.70 6.22 6.81 6.27 6.96

X

n rn D 0 =!

y

v)

THF

33

8.1

12.2

7.50

7.87

Y

> 38.2

10.8

17.1 17.1

>20.0 5.25

10.3; 10.7 15.6

18.2 17.8

5.90 7.65

6.72 7.64

g, r

8.68

r

5.73

g

5.72 4.89 4.98

g g g

THF THF

<0.0001 %I02

DMF DMF

13; 1 1 1.4

DMF

0.6 1

17.5

15.9

10.80

DMF DME DMF AN DMF

20 0.0 12 14 6.8 6.0

9.3 27.6 10.1

19.2 16.6 18.8 25.6 22.5

5.30 >20.0 5.60 4.45 4.70

11.8

12.1

> 18.6

4.20

> 20.0

U X

x

all

aa

r

bb

g

TABLE7 (continued) Spherical model' Reaction no.

Parent compound"

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Benzonitrile Benzonitrile o-Tolunitrile m-Tolunitrile p-Tolunitrile m-Nitrobenzonitrile Phthalonitrile Terephthalonitrile Pyromellitonitrile Pyridine-2-carbonitrile Tetracy anoethylene Tetracy anoquinodimethane Nitrobenzene Nitrobenzene m-Chloronitrobenzene p-Chloronitrobenzene

61 62 63 64 65

Acetone Benzophenone Benzoquinone Benzoquinone Benzoquinone

66 67

2,5-Dimethylbenzoquinone 2,6-Dirnethylbenzoquinone

3,5-Dichloronitrobenzene

m-Dinitrobenzene p-Dinitrobenzene

L P d /

Solventb Dimethyl sulfoxide Propylene carbonate DMF DMF DMF DMF DMF DMF DMF DMF AN AN DMF DMF-water (9: 1) DMF DMF DMF DMF DMF Water DME" DMF DMF-water (9: 1) Water (5Min isopropyl alcohol, 1M in acetone) As for no. 65 As for no. 65

4.4 2.8 9.5 6.0 8.5 1.7 14 16 10 7.3 40;25 40 0.3 0.0032 0.88 0.80 1.6 6;55 7.2; 6.0;6.3 d.1 1.1; 20.5 4.0 0.56 0.62 0.55 1.7

cad

Ellipsoidal model'

kcal mol-I

kcal mol-I

rfalc/A

12.9 13.9 11.0 12.1 11.3 15.1 10.2 9.7 10.9 11.6 7.6;8.8 7.7 19.2 30 16.7 16.9 15.2 12.1;12.3 11.7; 12.0;11.9 21.8 16.1;18.0 13.1 17.7 17.5

21.3 23.4 21.3 21.3 21.3 21.5 21.7 21.7 21.6 23.1 27.0 22.0 22.1 22.7 21.5 21.5 20.9 21.4 21.4

4.90 4.85 4.85 5.00 4.90 5.50 4.60 4.55 5.10 4.45 3.80 4.80 6.10 10.20 5.80 5.85 5.75 5.00 4.95

5.06 5.05 5.18 5.21 5.26 4.81 4.67 5.74 5.58 5.20 4.78 6.00 5.09 6.23 5.52 5.52 6.09 5.68 5.16

g g g g g

32.4 15.5 22.9 23.3 26.4

4.25 8.55

4.02 8.50

if .ii,kk

4.70 5.35 5.00

4.65 4.89 4.76

gg gg 11

17.9 15.1

23.9 23.9

5.90 5.40

4.99 5.37

11

Ref.

CC

g g

g g dd,ee

%ff

CCYgg

gg gg gg gg

r

CGgg m cC,gg,hh 9 zu

5

11

--I

m W

m

a

cn

0 Z

68

69 70 71 72 73 74 75 76

Tetramethylbenzoquinone Tetrameth ylbenzoquinone I&Naphthoquinone Fluorenone Xanthone N-Butylphthalimide Neutral radicals: Ph3C'/Ph,C + (4-02NC,H4)3C'/ (4-02NC ,H,),C9-Phenylacridinyl radical/9Phenylacridinyl cation

As for no. 65

DMF DMF THF AN DMF

Trifluoroacetic acid-acetic acid (30 :70) AN Methanol

5.60 1.75 6.00 6.80

5.35 5.73 5.40 6.77 5.85 7.42

14.7

9.90

10.90

PP

z i

18.1

5.50

6.80

44

v)

7.16

rr

- 2.6""

14.7 17.5 12.8 14.3 10.6 13.9

22.2 19.3 20.1 15.1 16.8 18.2

1.3

15.7 4.3

2.0 0.62 4.6 2.4

10

163 34

8.0

35.7

5.95

,7.30

5.85

II gg

cc

mm

ii 00

rn r rn

2

a'

0

Fz

n

rn D

n rn D

0

The neutral species of the self-exchange reaction is given, unless specifically noted -r Abbreviations: AN, acetonitrile; DME, 1,2-dimethoxyethane; DMF, N,N-dimethylformamide; HMPA, hexamethylphosphortriamide; THF, 0 z tetrahydrofuran v) In most cases measured at or around 25OC: all rate constants have been measured in the range 15-30°C. In the appropriate cases, kexchhas been corrected for the diffusion-controlled term according to (67), assuming that k , / k - , = 1 M-'. Rate constants for diffusion-controlled processes were obtained from Ridd (1978) and Kowert et al. (1972). For DME, k, was set to 7.2 x lo9M-' s-I Calculated as 4 x dGf (O), which is estimated from (13) with K = 1 and Z = 10" M-' s-I For the calcdation of A,,,, of the spherical model (Kojima and Bard, 1975), rl = r2 of (52) was estimated from Traube's rule (Wiberg, 1964). AS shown in Fig. 4, r,2 was set equal to rl + rz' The calculation of 6of the spherical model is based upon rl = r2 (from Traube's rule) and is obtained as the value of rI2which makes I,,, =I,,,, For the calculation of f i of the ellipsoidal model (Kharkats, 1976) the following procedure was used: (1) The molecular dimensions of the species involved were estimated by measurements on CPK models; (2) the axes of the triaxial ellipsoids were taken to be half the measured lengths; (3) the ellipsoids were assumed to be oriented with their "flat" faces parallel to each other; and (4) the value of r* was obtained as the distance between the centers of the ellipsoids that makes A,, =A,,,,. See also text. Data for solvents were obtained from Riddick and Bunger (1970): for solvent mixtures it was assumed that n and D vary linearly with composition. 'Sorensen and Bruning, 1973 Kowert et al., 1972 Pladziewicz and Espenson, 1973 Arene = toluene, p-xylene, mesitylene and durene j Elschenbroich and Zenneck, 1978

TABLE 7 (continued) A large number of symmetrical and unsymmetrical tetraalkylmetals Fukuzumi et al., 1980 Unless otherwise noted, rate constants for reaction of the free radical anion have been listed. See text " Ion pair Malinoski et al., 1970 PChang and Johnson, 1966 4 Hirota et al., 1968 'Forno et al., 1970 Hofelman et al., 1969 ' In tetrahydrofuran the rate constants were almost identical (0.19 and 0.20 x los M-' s-I 1 " Bruning and Weissmann, 1966 " Suga and Aoyagui, 1973 Suga et al., 1973 Chang and Weissman, 1967 The same value was found in liquid ammonia at O°C (Smentowski and Stevenson. 1969) O0 Katz, 1960; Strauss et al., 1963 bb Reynolds, 1963 w Malachesky et al., 1965 dd Watts el al., 1973a,b; see also Eastman et al., 1977 p p Komarynsky and Wahl, 1975 "Haran et at., 1974 I R Layloff et al., 1965 hh Miller et al., 1966 Ii Voiculescu and Fessenden, 1975: quoted from Meisel, 1975 ij Hirota and Weissman, I964 Irk Adam and Weissman, 1958 Meisel and Fessenden, 1976 Wong and Hirota, 1972 "" Practically identical values were found in HMPA, N,N-dimethylacetamide, DME and propionitrile "O Shimozato et al., 1975 pp Lown, 1963 qq Jones and Weissman, 1962 "Castellano et al., 1976

m Z Z

9 a

--I

rn

m

m R

v, 0 Z

ELECTRO N-TRAN S FE R R EACTlO N S

121

spheres penetrate each other to a considerable extent. For all compounds except nos. 10-16, 18, 20, 21, 24,25,32, 36, 38, 55, 62,64-68, 74, r’is 30 & 8% shorter than ( r , + r2).In other words one may say that the molecules must approach each other more closely in the transition state than their effective radii allow for. This is not a surprising result in view of the elongated shape of most of the systems listed in Table 7. The reactions left out in the calculation of the percentage penetration fall into four distinct categories: (1) reactions involving spherical molecules; (2) reactions in water or water-containing solvents; (3) reactions influenced by ion pairing: and (4) reactions involving appreciable changes in molecular shape. If all cases are included, r* comes out as 15 & 41% shorter than rl + r2 which clearly shows that the reactions excepted display strongly deviant behaviour of some kind or other. Spherical models with slightly differing methods of estimating radii were tested on a limited number of aromatic radical anions, but showed basically the same weakness as the one used above (Kojima and Bard, 1975; Suga et al., 1973; Suga and Aoyagui, 1972). A non-spherical model, in which both reactants were represented as oblate ellipsoids (Kharkats, 1974; Yamagishi, 1976), showed some improvement but at the price of a certain ambiguity in the choice of r12’The most elaborate model is that given by Kharkats (1976) and depicts the reactants of a self-exchange reaction as two identical triaxial ellipsoids with semiaxes a, b and c (a b > c); these are located either with the b axes and ab planes coinciding, or with the c axes and ac planes coinciding. The latter arrangement, which corresponds to a configuration of two planar molecules parallel to each other, gives rise to the complex expression for lo given in (78), where F(plm) is an elliptic integral of the first kind (79). Column

>

+

4(Sc4

+ 3(a4 + b4) - S C ’ ( U ~ + b2)+ 2 ~ c’’) 1% B

F(plm) = j’ (1 - m sin’ 0

p = arcsin [(az- c2)/u2l1/’;

J

d0

(78)

(79)

m = [(a’ - b2)/(az- c2)11/z

8 gives r* values determined from (78) using the same basic approach as for the spherical model. We now see that 6 is longer than the distance of closest approach, 2c, in all cases except one (no. 75). If we denote such a transition state an “expanded one”, the percentage expansion, 100 x (6- 2c)/c, for all reactions except nos. 10-13, 24, 25, 32, 36, 38 and 75, is 63 k 21%; with all reactions included,

122

LENNART E B E R S O N

except the spherical cases, it becomes 72 -C 66%, again showing that these few reactions represent strongly deviating behaviour. The triaxial ellipsoidal model creates fewer aberrant cases than the simple spherical one, however, and thus constitutes a certain improvement. Both treatments in essence lead to the conclusion that electron transfer takes place via a transition state where the distance, r*, between the reacting species is determined by the shortest contact possible in the system, i.e. for a triaxial ellipsoid along the c axis. Still the r* values obtained show that the molecules need not be in direct contact with each other for electron transfer to occur. Whether we interpret this as an effect of solvation (Meisel and Fessenden, 1976) or as an appreciable allowed variation of f l in a transition state with parallel planar molecules (Weller, 1967) is a moot point at present. It appears necessary first to find better methods for the calculation of Lo. This might for example be approached in the same way as in the calculation of the effective dielectric constant in the Kirkwood-Westheimer treatment, namely by using the finite element method for the integration of the Poisson equation (Orttung, 1977, 1978). Another refinement in the estimation of Lo was introduced by Peover (Peover, 1968, 197 1; Peover and and Powell, 1969) who treated species with non-uniformly distributed charge, e.g. radical anions of nitro compounds, as two or more spheres of different charges. The charge density distribution was estimated from esr data, e.g. for nitro compounds the value of the coupling constant at the nitrogen atom (aN).This model was tested with fair success on the heterogeneous rate constants obtained for the cathodic reduction of nitro compounds of different types (log k,,, correlated linearly with a function of aN). A slightly different treatment along the same lines has also appeared (Fawcett and Kharkats, 1973). S T A N D A R D ELECTRODE POTENTIALS A N D OTHER FREE ENERGY D A T A FOR ORGANIC REDOX REACTIONS

At a given value of L and hence AG*(O), AGO' is the variable that determines the free energy of activation of a non-bonded electron-transfer process through eqns ( 5 5 ) and (56). As shown by (46), AGO' is equal to AGO plus an electrostatic correction term for the change of charge in going from the reactants' to the products' transition state. We therefore need access to data for AGO (or E O , the standard electrode potential, related to AGO via the expression AGO = - n x 23.06 E o where n is the number of electrons transferred and AGO and E o are expressed in kcal mol-' and V respectively) for organic redox reactions; also, in the appropriate cases we need AGO or E o values for inorganic redox couples in non-aqueous media. It should be strongly emphasized that the need is for data pertaining to one-electron transfer processes, and that therefore many data on inorganic

123

ELECTRO N-TRAN S FE R R EACTl 0 N S

redox processes must be modified accordingly. To quote an example, if we want to estimate d E o for reaction (go), we need E o for (81) and not for (82) which is the one commonly found in electrode-potential tables (Milazzo and Caroli, 1978; Clark, 1960; Latimer, 1952). E o values for a number of such

-

ArH+' + CICI'

+ e-

C1,

+ 2e-

ArH

+ CI'

CI-

2C1-

one-electron oxidations of inorganic species have been estimated (Table 8) in aqueous as well as non-aqueous medium (Berdnikov and Bazhin, 1970; Eberson and Nyberg, 1978). In addition, Table 8 lists E o values for the oxidation of carboxylate ions, estimated by consideration of thermochemical cycles (Eberson, 1963; Eberson et al., 1978b) and the reduction of methyl halides (Hush, 1957). A further point to consider is the need for AGO or E o values for reactions under the actual conditions used. As an example, a large number of so-called E , values for one-electron processes (nitro compounds semiquinones) have been determined in aqueous solution at pH 7 using a pulse radiolytic method (see, e.g. Meisel and Neta, 1975; Rao and Hayon, 1975; Wardman and Clarke, 1976b). Such values may differ somewhat from strictly defined AGO (EO) values listed in standard tables. The problem of determining AGO for organic redox couples can usually be attacked experimentally by either electrochemical methods or gas-phase measurements of ionization potentials and electron affinities. In both approaches, we can in principle determine thermochemical parameters for one-electron oxidation (83) and reduction (84) of an organic species. RH RH

--

+ e-

RH+' + e-

(83)

RH-'

(84)

To start with gas-phase data, ionization potentials (ZP)and the derived heats of formation of radical cations are available for a large number of organic species (Franklin et al., 1969; Gutmann and Lyons, 1967; Turner, 1966), whereas electron affinities ( E A ) are far more scarce (for a recent review, see Janousek and Brauman, 1979). For both types of data one has to estimate heats of solvation for participating species in order to obtain E o in solution, and this is known to be an uncertain procedure (Mortimer, 1962). An alternative is to use the rather good correlations that are available between gas phase and solution data for estimating unknown solution values (see below). The most direct way of determining E O and hence dG O for an organic redox couple is by voltammetric methods, such as single-sweep voltammetry

LENNART EBERSON

I24

TABLE8 Estimated standard electrode potentials, E o , for a number of one electron redox processes Eo/V"

Redox couple

F'/FCI./CIBr'/Br-

r/1-

SCN '/SCNNO;/NO; NO;/NO; CN'/CNHO'/HOCH,COO '/CH,COOEtCOO ./EtCOOPrCOO '/PrCOOCF,COO '/CF,COOPhCOO '/PhCOOCH,CI/CH; + ClCH,Br/CH; + BrCH,I/CH; + I-

In water

In CH,CN

Ref.

3.6 2.55 2.0 1.4: 1.33d 1.66 1 .o 2.3 1.9 0.8 2.4 1 2.23 2.23 2.0 1.66 -0.17 -0.74 -0.77

3.0 2.1 1.71 1.2 1.4 0.7 1.6 1.8 1.7 1.7 1.8 1.1

b. c b, c b. c b. c d b, c b b. c b e e e f;g e h

-

-

h h

vs. the normal hydrogen electrode (NHE) Berdnikov and Bazhin, 1970 Eberson and Nyberg, 1978 Stanbury et al., 1980 Eberson, 1963 'This value is inaccurate due to uncertainties in the thermochemical data for trifluoroacetyl peroxide; one would expect that this E o value should be higher than that of the AcO'/AcO-couple because of the higher resistance of trifluoroacetate ion to anodic oxidation Eberson et al., 1978b Hush, 1957

(determination of E 1,2, the half-wave potential) or cyclic voltammetry (determination of E,, the peak potential) (for references, see Ahlberg and Parker, 1980). The latter method is to be preferred since it is fast, can be made very accurate (Ahlberg et al., 1980), and provides an automatic check on the reversibility of the electrode reaction. By electrochemical reversibility we mean that (a) the electron exchange between RH or RH+' (or RH-') and the electrode should be fast (khet > 0.1 cm s-l) and (b) none of the organic components should be consumed by chemical reactions during the time-scale of

ELECTRON-TRANSFER REACTIONS

125

the sweep. If the latter requirement is not fulfilled, the measured E , value will be numerically smaller than E o due to interference from the coupled chemical reaction (Mark, 1968). For a radical cation, this reaction is often with a nucleophile and for a radical anion the reaction is with an electrophile. Requirement (a) is most often met in organic systems. The more reactive the radical ion is, the larger will be the displacement of E,. Thus the standard potential of benzene/[benzenel+ ' in acetonitrile under the best possible conditions is 3.03 V vs. NHE (Jensen and Parker, 1975; Parker, 1976), whereas its E , comes out around 2.6 V (Osa et al., 1969). Thus we would expect that E , values of organic redox systems with very reactive radical ions ought to show the largest deviations from EO,whereas those with stable radical ions would give E , values close to or identical with EO. Thus a linear correlation between E O and E, (or E1,J with a slope > 1 V is to be expected. This has partly been shown to be valid for a limited series of aromatic redox couples (Eberson and Wistrand, 1980). A third electrochemical technique, phase selective second harmonic AC voltammetry has recently been successfully used for determining reversible redox potentials for systems where species formed undergo fast follow-up reactions (Ahlberg et al., 1978; Ahlberg and Parker, 1980; Jaun et al., 1980). Table 9 lists E O values for organic redox couples of different types, together with the corresponding ionization potentials. Most cases belong to the category where one of the two components of the couple can undergo rapid follow-up reactions with nucleophiles or electrophiles present, intentionally or accidentally. Table 10 shows the results of correlating E o values from Table 9 with a number of experimentally consistent electrochemical data sets. Among the oxidation reactions, nos. 1 - 4 have been measured in the weakly nucleophilic electrolyte, acetonitrile/perchlorate ion, whereas no. 5 refers to a moderately nucleophilic medium. As predicted above, the slopes in all these cases are > 1, the weighted average being 1.12 for all five correlations. For the reduction reactions (nos. 6-9) we can note that the two more electrophilic media (nos. 6 and 9) give slightly higher slopes than the less electrophilic ones (7 and 8). The deviation from a slope of 1 is, however, small in all four cases. It should be mentioned that two other sets of E o values for RH/RH-' have been reported, namely for THF (Jagur-Grodzinski et al., 1965) and TME (Hoijtink et al., 1956). If these are correlated instead with the data set of entry no. 6, slopes of 1.04 (0.989) and 1.18 (0.989), respectively, are obtained. We thus see that E o / E l , 2or E , correlations have slopes of 1 or slightly larger. We can use such slopes to correct Marcus-type log k / E correlations for which we do not have access to experimental values of E O but have available El,, or E , values that we suspect to be influenced by rapid follow-up reactions. With some care we can also use correlations of the type listed in Table 10 to estimate E o (and hence AGO) for individual redox couples.

LENNART EBERSON

126

TABLE 9

E o (in acetonitrile) and IP values for organic redox couples

Redox couplen Benzene Toluene Triphenylene Naphthalene Phenanthrene Durene Chrysene Hexamethylbenzene 4-Methoxytoluene Dibenzo- 1,4-dioxin 1,2-Benzanthracene Anthracene Pyrene 1,12-Benzoperylene Thianthrene Phenoxathiin 4,4'-Dimethoxybiphenyl 9,lO-Diphen ylanthracened 3,4-Benzopyrene Perylenee Tri-(p-toly l)amine' Ferrocene Cobaltocene [Perylene)- ' [Benzo(e)pyrenel-' [ Anthracenel- ' [Benz(a)anthracenel- ' [Pyrenel - ' [Chrysenel - * [Triphenylenel - * [Phenanthrenel- ' [Naphthalene]-' [Biphenyl]- '

E OIVb

IP/eVC

3.03 2.61 2.12 2.08 2.07 2.03 1.88 1.85 1.82 1.70 1.68 1.61 1.60 1.59 1.52 1.50 1.49 1.44 1.40 1.30 0.9V 0.60 -0.60' -1.44j -1.60 -1.74 -1.78 -1.80 -2.03 -2.24 -2.25 -2.26 -2.35

9.245 8.81 8.08 8.12 7.85 8.025 7.79 7.85 -

7.56 7.40 7.55 -

8.14 -

7.19 7.14 6.86'' -

-

-

The reduced form of the redox couple is given bvs. NHE. Taken from Hammerich and Parker, 1973; Svanholm and Parker, 1973; Parker, 1976; Eberson and Nyberg, 1978; and Eberson et al. 1978b, unless otherwise noted Taken from Gutmann and Lyons, 1967 Kakutani et al. (1978) give 1.46 V Kakutani el al. (1978) give 1.25 V 'Hagopian et al., 1967 A value of 0.92 V was reported in PhCN/Bu,NBF, (Tachikawa and Faulkner, 1976) Value for triphenylamine Kakutani et al., 1978 'Measured in DMF (Ahlberg et al., 1978)

'

ELECTRO N-T RAN S FE R R EACTlO N S

127

TABLE10 Correlations of E o (see Table 9) with voltammetric data for aromatic hydrocarbons under different conditions No.

. -

Solvent/supporting electrolyte

Intercept on y-axis

Slope

0.62b 0.32d 0.79b 0.45K 0.3 Id -0.27d -0.35k 0.19 -0.10

1.13 1.17 1.05 1.18 1.05 0.99 0.86 0.98 1.09

l a CH,CN/NaCIO, 2c CH,CN/NaCIO, 3e CH,CN/NaCIO, 4f CH,CN/Et,NCIO, 5h HOAc/NaOAc 6' Dioxan/H,O (75%) 71 DMF 8' DMF 9" 2-Methoxyethanol

No. of data points 9

12

7 7 1 1 7 4 9

Correlation coefficient 0.983 0.997 0.98 1 0.943 0.994 0.99 1 0.959 0.998 0.994

Lund, 1957 Reference electrode: Ag/Ag+ (0.1 M) Pysh and Yang, 1963 Reference electrode: Saturated calomel electrode (SCE) Neikam and Desmond, 1964; Neikam et al., 1964 'Peover and White, 1967 Reference electrode: Ag/Ag+ (0.01 M) Eberson and Nyberg, 1966 Hoijtink et al., 1954 Streitwieser and Schwager, 1962 Reference electrode: Hg Pool Aten et al., 1959 Bergman, 1954

' '

As already mentioned, ionization potentials have often been correlated with electrochemical ones, most often with E,,,. Here one finds correlations covering both a limited range of compounds, such as aromatic hydrocarbons I(85), Pysh and Yang, 1964; (86), Neikam and Desmond, 19641 bicycle[ l.l.0lbutane derivatives [(87), Gassman et al., 197912, and homoleptic alkylmetals 1(88), Klingler and Kochi, 19801 and a very extended range of different types of aliphatic and aromatic compounds [(89), Miller et al., 19721. For the E OIIP set E,,, = 0.68 x IP - 3.95

(85)

E l , , = 0.83 x IP

5.50

(86)

E l , , = 0.86 x IP - 5.98

(87)

-

x IP - 4.92

(88)

E l , , = 0.92 x IP - 6.20

(89)

E,

= 0.76

These IP values were calculated by the PRDDO method

128

LENNART EBERSON

of Table 9, one obtains the regression line (90) with a correlation coefficient of 0.943. This equation represents yet another possibility of estimating E o for Eo= 0.78 x

IP - 4.26

(90)

processes that are difficult or impossible to deal with using electrochemical techniques. Unfortunately, the same type of treatment is not available for redox couples with negative E o due to the lack of experimental electron affinities (Janousek and Brauman, 1979). It is possible to use instead semi-empirical (Briegleb, 1964) or theoretically calculated values. As an example, Dewar et al. (1970) calculated electron affinities by the variable# S C F M O method for an extensive series of aromatic hydrocarbons: the correlation (correlation coefficient 0.952) between these and the E o values of Table 9 is given in f91). The same authors also calculated ionization potentials which correlate well (correlation coefficient 0.996) with E O using (92). Eo(red) = 1.04 EA,,,, EO (OX) = 1.02

= 2.44

(9 1)

IP,,,,- 6.50

(92)

Finally, the possibility exists to estimate E o values via the excellent correlations that exist (Streitwieser, 196 1) between oxidation potentials and HOMO energy coefficients or reduction potentials and LUMO energy coefficients. Both simple Huckel and S C F MO calculations have been performed, the latter ones giving a small, but real improvement over the former (Gleicher and Gleicher, 1967). The main advantage of the S C F method was the feasibility of treating alternant and non-alternant hydrocarbons within the same correlation. The E o values of Table 9 have been correlated with energy coefficients (taken from Streitwieser, 1961) of the HOMO'S and LUMO's of aromatic hydrocarbons in (93) and (94) respectively (correlation coefficients Eo(ox) = 2.31 mHOMO + 0.62

(93)

Eo(red) = 2.58 rnLUMO - 0.63

(94)

0.989 and 0.980). These correlations provide yet another method of estimating

E O , even if its use so far has been limited to aromatic hydrocarbons. It would be interesting to have the general problem of correlating electrochemical potentials with MO parameters reconsidered using modern quantum chemical methods, now capable of determining even absolute values of IP to within ? 0.1 eV. Concluding, we have now demonstrated several possibilities for estimating E O for organic one-electron redox couples using electrochemical data of different types (for extensive tabulations, see Mann and Barnes, 1970; Siegerman, 1975; Meites and Zuman, 1977; Bard and Lund, 1978), ionization

ELECTRON-TRANSFER REACTIONS

129

potentials, electron affinities and quantum chemical methods. The reader should be warned, however, that electrochemical data should be critically examined before use in order to ascertain that they are compatible. If possible, only experimentally consistent data sets should be used; if not, care should be exercized that all potentials are converted to a common scale (for conversion terms for reference electrodes, see Mann and Barnes, 1970; Siegerman, 1975) in a common solvent. Luckily, electrochemical potentials do not differ much from solvent to solvent (Hammerich and Parker, 1973; Parker and Lines, 1980), so that this aspect can be neglected in the first approximation. 5

Experimental tests of the Marcus theory in organic systems

Even in the domain of inorganic redox chemistry relatively little use has been made of the full potential of the Marcus theory, i.e. calculation of Ai and 1, according to (48) and (52) and subsequent use of (54) and (13) to obtain the rate constant (for examples, see Table 5). Instead the majority of published studies are confined to tests of the Marcus cross-relations, as given in (62)-(65) (see e.g. Pennington, 1978), or what amounts to the same type of test, analysis of log k vs. AGO’ relationships. The hesitation to try calculations of 1 is no doubt due to the inadequacy of the simple collision model of Fig. 4, which is difficult to apply even to species of approximately spherical shape. As we have seen in connection with the discussion of the data in Table 7, organic systems are even less well-behaved than inorganic ones due to their non-spherical shape. Assumptions of an ad hoc character can, at least for the time being, permit limited application of the spherical model to non-spherical molecules, and non-spherical models show a certain improvement, albeit with loss of computational simplicity. It is therefore hardly surprising that most organic redox systems have been analyzed in terms of log k vs. AGO’ plots (to evaluate their general appearance, the 1value, and slopes in different regions of AGO’). THE M A R C U S INVERTED REGION

We have already touched upon the failure of the Marcus model to predict correctly the parabolic decrease in log k with decreasing AGO‘ in the strongly exergonic region, the so-called “Marcus inverted region”. Even if the shape of Marcus plots can in principle be adjusted to produce a linear horizontal portion down to very low AGO’ values (see Fig. 6), it is not possible to reconcile such plots with any physically realistic model, or for that matter in many cases with the behaviour in the region where AGO’ > -10 kcal mol-’. It is large values of 1 that produce such an effect (Fig. 6), but then the curve shape is entirely different in the “normal region” (see below and Fig. 9).

130

LENNART EBERSON

The classical study by Rehm and Weller (1969, 1970) on the kinetics of fluorescence quenching of excited states (for a description of the kinetic scheme, see Section 3) illustrates most features of the theoretical analysis of organic electron-transfer processes. Rate constants for quenching in the range of 106-10'o M-I s-l were measured in acetonitrile for the excited states of a number of fluorescing compounds (mostly acting as oxidants but also with a few reducing systems) and a large number of quenchers (aromatic amines and ethers were used as reductants, nitriles as oxidants). The free energy change of the electron transfer step (71) in this case is given by ( 9 9 , where AE,,, is the electronic excitation energy of the fluorescent compound and the half-wave potentials for oxidation of donors and reduction of acceptors are used due to the lack of standard potential data. As we have seen in Section 4, this is a reasonable approximation for this type of analysis. AGO' = 23.06[E,,,(D/Dt') - EI,,(A/A-')l

- e2/Dr- LIE,,,

(95)

Figure 9 shows the log klAGO' plot based on the data given by Rehm and Weller (1970) for more than 60 systems. The solid line is calculated using (73) and (74), the former one being the so-called Rehm-Weller equation, whereas the broken line is based on (56) and (74), i.e. the Marcus model; in both cases a AG'(0) of 2.4 kcal mol-I (A = 9.6 kcal mol-I) is used. The dotted line is again based on the Marcus equation (56) but with a large value of AG*(O), 9.6 kcal mol-I (A = 38.4 kcal mol-I). It is immediately noticeable that the Marcus

10

*

F8

6

4

AGO/ kcal mol-'

FIG. 9 Plots of log k for fluorescence quenching of excited states (Rehm and Weller, 1970). The solid curve is a Rehm-Weller plot and the broken one a Marcus plot, both with AG' (0) = 2.4 kcal mol-I. The dotted line corresponds to a Marcus plot with AG'(0) = 9.6 kcal mol-'

ELECTRON-TRANSFER REACTIONS

131

model cannot possibly be fitted to the experimental data over the whole region. A reasonable adherence in the normal region leads to complete breakdown in the inverted one, and vice versa. Rehm and Weller therefore designed (74) to produce a good fit over the whole range of AGO' values and at the same time to be closely similar to the Marcus equation (56) for the region of AGO' > -10 kcal mol-'. For AGO' > 4 AG*(O), the Rehm-Weller equation approximates a straight line with slope 1/2.303 RT = -0.74 mol kcal-', whereas the parabolic Marcus plot over narrow intervals, if approximated as a straight line, gives slopes < -0.74 mol kcal-'. No distinction between the two equations can be made on the basis of the data of Fig. 9. Although it has been claimed that rate constants are slightly diminished in the inverted region (Creutz and Sutin, 1977), most studies so far have yielded the same conclusion as that of Rehm and Weller, namely that no such rate decrease is discernible. Examples of such investigations are quenching of excited ruthenium complexes by substituted pyridinium ions and back electron transfer between the species formed (Nagle et al., 1979), quenching of excited chromium and iridium complexes (Ballardini et al., 1978), and electron transfer between triplet dyes and aromatic compounds (Tamura et al., 1978). A brief review is available (Balzani et al., 1979; see also Sutin, 1979). Several explanations have been put forward to account for this discrepancy within the framework of the Marcus theory (Efrima and Bixon, 1974, 1976). One is the assumption that exothermic processes take place over larger distances than the collision model implies. This is claimed to make L larger and hence AG+ smaller (see, however, Table 4 for the sometimes contrary effect upon A of increasing r J . Anyway, this explanation neglects the very strong decrease of K in (13) with increasing rI2, which would make the reaction nonadiabatic. A second explanation is that for strongly exothermic processes electron transfer to an electronically excited state is feasible; this explanation is disfavoured somewhat by the scarcity of electronic levels and the rather high excitation energy required for transitions from the ground to excited state. A third and provisionally accepted explanation is that electron transfer can take place to vibrationally excited states of the products, i.e. nuclear tunnelling of the reactants to vibrationally excited states of the products takes place (Efrima and Bixon, 1974, 1976). The potential surfaces depicted in Fig. 10 show the rationale behind this mechanism. For AGO' > -A (Fig. 1Oa) we have the normal situation with an activation barrier for electron transfer. At AGO' = -A (Fig. lob) the maximum rate for an activationless process has been reached, whereas for AGO' < -A an activation barrier appears again (Fig. lOc, representing the inverted region). With electron transfer allowed to an excited vibrational level (dotted line in Fig. 106) we have once again an activationless reaction proceeding at the maximum rate. For large molecules there is a

132

LENNART E B E R S O N

4

4

9

FIG. 10 Potential energy surfaces of electron-transfer reactions for (a), AGO' > - I ; (b), AGO' = - I ; (c) and (d), AGO' < -I. U = potential energy, q = reaction coordinate, R = reactants and P = products

continuum of vibrational levels from 10 kcal mol-I above the ground state, so there will always be such levels available for the reaction to proceed at maximum rate. THE NORMAL REGION

We shall now continue to examine critically the validity of the Marcus theory for organic electron-transfer reactions in the normal region, defined as the range where AGO' > - 4,4G*(O). Many studies have been devoted to this task and unfortunately the methodology of comparing experiment with theory is rather varied and difficult to compare between different investigations. It has therefore been necessary here to adopt a consistent series of criteria for assessing the agreement between experiment and theory and sometimes the published procedures have had to be modified to a considerable extent. Without this re-evaluation it is not possible to get a total view of the validity of the Marcus theory in the context of this review. First a word of caution against the possibility of generating perfect, but trivial Marcus or Rehm-Weller plots (log k vs. AGO' or the equivalent). Since the

133

ELECTRON-TRANSFER REACTIONS

TABLE1 1 Simulated data for the Rehm-Weller plot of Fig. 1 Iu K

AGo/kcal mol-I

log k

10’0

-13.6 -12.2 -10.9 -9.5 -8.2 -6.8 -5.4 -4.1 -2.1 -1.4

10 10 10 10 10 10 10 9.8 9.7 9.4 8.9 8.4 1.1 6.8 6.0 5.0 4.0

I0 9 108 107 106 105 104 103 102 10’ 100 10-1 10-2 10-3 10-4 10-5 10-6 10-1 10-8 10-9 10-’0

0.0 1.4 2.1 4.1 5.4 6.8 8.2 9.5 10.9 12.2 13.6

3.0 2.0 1 .O

0.0

The “experimental” values are those corresponding to AGO < 0, whereas the remaining ones have been calculated from the expression k-, =k l / K

Marcus treatment requires the determination of (1) a series of rate constants (k,) and (2) the corresponding series of equilibrium constants (K), it is tempting to double the data set by calculating a series of rate constants for the back reactions ( k - ] ) from the relation k - , = k , / K . However, this procedure merely consists of “mirroring” the log k data in a plane and can be shown to give perfect Marcus or Rehm-Weller behaviour in the appropriate regions. Thus, if we for example choose a case with a Rehm-Weller type appearance, the slope of the regression line in the range -AG*(O) < AGO’ < AG*(O) must be 112 x 2.303RT and the slope at high AGO‘ must be 112.303RT. Table 11 and Fig. 1 1 show the mechanics behind this trivial outcome of the Marcus treatment in a simulated case where the data for AGO’ < 0 kcal mol-’ can be thought of as the experimentally determined ones. The criteria that have been adopted here to evaluate a wide variety of proposed corroborations of Marcus theory are:

134

LENNART EBERSON

-10

0 AGO’Ikcal mol-‘

10

FIG.1 1 Simulated Rehm-Weller plot, based on “data” from Table 1 1. 0.“experimental” data: 0,calculated from k - , = k , / K

( 1 ) The value of the slope (‘slope 1’) in the region -AG*(O) < AGO ’ < AG+(O) which ideally should be -112 x 2.303RT = -0.365 mol kcal-I at 25OC in both the Marcus and Rehm-Weller treatment. ( 2 ) The value of the slope (‘‘slope 11”) in the region of high AGo’(AGo’>, 4 AG*(O)) which should be -112.303RT = -0.73 mol kcal-I in the Marcus theory (the exact value to be expected can be calculated for any value of AG*(O) in any desired region) and equal to this value in the Rehm-Weller treatment. ( 3 ) Calculation of A for a reaction series or for individual reactions from the log k vs. AGO’ plot. (4) Calculation of rate constants for cross reactions from known data on self-exchange reactions. Table 12 lists a number of organic reactions which have been examined in the light of Marcus theory or the Rehm-Weller modification. We have chosen to use the Rehm-Weller treatment for those cases where rate data far into the inverted region are available. These cases largely coincide with the excited state quenching investigations: as already shown (Fig. 9) the deviation between the two types of formalism is practically negligible in the normal region and hence ,I values are not affected by this choice. The ,I values were evaluated by non-linear regression analysis using Marquart’s method. Slopes were calculated by the least squares method. Since most studies are confined to a range of log k values between 6 and 10 it turned out to be impossible to estimate “slope 11” values except in a few cases.

<

TABLE 12. Experimental tests of the Marcus" and Rehm-Wellerb treatments

rn r rn

0 --I

Reaction no. 1

2 3 4 5

6 7

8 9 10

Reaction type Quenching and back electron transfer of excited Ru(bpy),(CN), and Ru(phen),(CN), and different types of pyridinium ions8 Quenching of excited Cr(bpy):+, Ru(bpy):+ and Ir(Me,phen),CI: by aromatic amines and methoxybenzenesg Quenching of excited Cr(bpy):+ and Ir(Meghen),CI: by aliphatic aminesg Quenching of excited Ru(bpy):+ by aromatic aminesg Quenching of excited Ru(bpy):+ by bipyridinium ions8 Quenching of excited Ru(bpy):+ by nitroaromatics8 Quenching of triplet states of aromatic hydrocarbons and carbonyl compounds by inorganic anions (I-, Br-, NO;, CI-) Quenching of excited aromatic molecules by aromatic hydrocarbons, nitriles, methoxy- and amino-aromatics Quenching of excited aromatic molecules by methoxy and amino-aromatics Quenching of excited cyanoanthracenes, by aromatic hydrocarbons, methoxyaromatics and sulfides

Medium (temp./OC; ionic strength/M) CH,CN (25; 0.001-0.5)

I

valuec/

kcal mol-' 9.7

n

Slope/mol kcal-I Id -0.36

IIP

0

Remarks

-0.65

Ref.

f

2 --I

n

2 L

v,

n a

rn

a

rn

CH,CN (22; 0.02-0.1)

12.0

-0.37

See Fig. 12

h

> n 0

2

CH,CN (22; 0.02-0.1)

20.7

-0.30

CH,CN (22; 0.1)

10.7

-0.35

CH,CN (22; 0.1)

23.3

CHJN (22; 0. I )

13

HzO (-22; 0) CH,CN (-22; 0)

See Fig. 12

Too few points -0.46

0.74 0.74

9.6"

-0.4"

CH,CN (-22; 0)

9.3

-0.45

I

i,j, k

-0.4 1

CH,CN (-22; 0)

v,

i

5.2 10.7

h

Too few data

I

See Fig. 9

m

P 4 2

W

rJl

W

0

TABLE 12 (continued) Reaction no.

II 12 13 14

15 16 17

18

19 20

Reaction type Quenching of triplet states of aromatic hydrocarbons by quinones Quenching of triplet dyes by aromatic hydrocarbons and amines Quenching of triplet dyes by aromatic hydrocarbons, methoxy- and aminoaromatics Electron transfer between semiquinone radical ions and quinones Electron transfer between substituted phenoxy radicals and phenolate ions, aromatic amines, etc. Electron transfer between oxygen and nitro-substituted radical anions Electron transfer between oxygen and semiquinone radical anions, duroquinone and nitro-substituted radical anions, and two identical semiquinone radical anions Electron transfer between tetracyanoquinodimethane anion radical and quinones Electron transfer between aromatic radical anions and chlorobenzene Electron transfer between aromatic radical anions and bromobenzene

Medium (temp./"C: ionic strength/M)

A value'/ kcal molPl

Slope/mol kcal-I 1"

Ile

Remarks

Ref.

Benzene (-22; 0)

12.7

r

CH,CN (-22; 0)

19.8

1, u

CH,OH (-22:O-O.l)

15.5

-0.43

H,O, 5M in 2-propanol and I M in 15.2 acetone at pH 7 (22: -0) H,O at pH 13 16.8

See Fig. 13

v

X

SeeFig. 14

v

H,O (22: 0.2)

31.7

-0.28

2

H,O (22: -0)

14.8

-0.35

aa, bb rm

CH,CN (-25; -0)

- 10

Too few data

cc, dd

z z > a

--I

m W

rn

DMF (25: 0.1)

28.1

DMF (22; 0.1)

24.1

ee,B -0.39

ff

W

cn 0 Z

21 22 23 24

25 26 27 28 29

Electron transfer between aromatic radical anions and aromatic hydrocarbons Electron transfer between aromatic radical anions Electron transfer between radical cations of aromatic amines and heteroaromatic and aromatic amines Electron transfer between the radical cation of tri-(4-methoxyphenyl)amine and dimethylphenazine and ferrocene derivatives Electron transfer between nitroxyl radicals and semiquinone radical anions and bipyridinium radical cations Electron transfer between homoleptic alkylmetals and iron(II1) complexes

2-PrOH (25; -0)

Electron transfer between e;,, and aromatic and aliphatic halides Electron transfer between benzenediols and halogenoiridates(1V) Electron transfer between Cr(I1) and organic cations

H,O (22; 0)

12.5

l,2-C,H4C12(25; -0) 1 :3 v/v ethanol-water (25; 0.01)

18.6

CH,CN (25; 0.22)

18.1

-0.28

H,O at pH 7 (21; -0)

21.3

-0.35

CH,CN (25; 0.1)

Too few data

See text, Table 13 and rnm Fig. 15 See text nn

34,35,35 8.4

H,O (25; 1.0)

23.4; 17.1

-0.43

00

75% EtOH/H,O (25; 2.0)

41.4

-0.37

PP

The kinetic scheme of (70) with A = 0.2 was used in the analysis of ground state reactions The kinetic scheme of (74) with k, k-,/ KannKd= 0.25 was used in the analysis of excited state reactions Obtained by Marquardt's non-linear regression method, unless otherwise stated This slope should theoretically be -0.367 mol kcal-I at 25OC; see text This slope should theoretically be <-0.733 mol kcal-' at 25OC; see text 'Nagle el al., 1979 8 Abbreviations: bpy = 2,2'-bipyridine, phen = 1,lO-phenanthroline, Meghen = 5,6-dimethyl-l,lO-phenanthroline 4

W

U

TABLE 12 (continued) Ballardini et al., 1978. It should be noted that quenching of triplet methylene blue by aliphatic amines has quite different characteristics (Kayser and Young, 1976) and cannot be reconciled with a non-bonded electron-transfer mechanism Bock et al.. 1979a Meisel, 1975 j Bock et al., 1979b bb Meisel and Neta, 1975 Bock et a/., 1975 "Yamagishi, 1975a 'Treinin and Hayon, 1976 dd Yamagishi, 1976 Rehm and Weller, 1970 pe Andrieux et al., 1978 " Estimate given in the paper "Andrieux et a/., 1979 " Crude estimate from diagram in the paper Dorfman, 1970 Rehm and Weller, 1969 hh Yarnagishi, 1975b Eriksen and Foote, 1978 ii Winograd and Kuwana, 1971 'Wilkinson and Schroeder, 1979 "O'Neill and Jenkins, 1979 ' Tamura et a/., 1978 " Wong and Kochi, 1979 " Kikuchi ef a/., 1977 Fukuzumi et al., 1980 " Vogelrnann et al., 1976 mm Klinger and Kochi, 1980 Meisel and Fessenden, 1976 "" Rate data, efc., see Hart and Anbar, 1970 Steenken and Neta, 1979 "'Pelizzetti et al.. 1978b ' Wardman and Clarke. 1976a,b. Ilan ef al., 1976 pp Bowie and Feldrnan. 1977

''

r rn Z

Z

P a --I

rn m

m

W

cn 0 Z

139

ELECTRON-TRANSFER REACTIONS

What first strikes the eye in Table 12 is the variation in 1,which is to be expected from an inspection of the individual values of for self-exchange reactions that are listed in Table 6. No doubt the considerable scatter of data points in the Marcus plots reflects to a large extent this variation in 1. It is therefore important to study series of closely similar compounds to test the theory, as was indeed pointed out very early by Marcus (1964). Preferably, one should work with compounds of known 1, determined by independent measurements of self-exchange rate constants. It is difficult to discern any pattern in the variation of 1,except that 1for reactions involving charge delocalized systems tend t o be smaller than those involving molecules where delocalization of charge is not possible. Thus there is a distinct difference between reactions of aromatic and aliphatic amines (nos. 2 and 3, see Fig. 12); for the latter type of compound this may indicate that 1, cannot be neglected due to relatively large, charge-induced geometrical changes around the nitrogen atom. Few data are available to support this assumption, but one can mention here the rather drastic geometrical changes that occur in going from a tetraalkylhydrazine to its radical cation (Nelsen et al., 1978). The same effect has been suggested (Andrieux et al., 1978, 1979) t o account for the high 1values of reactions 19 and 20 of Table 12, i.e. 1,would be > O due to a significant change in the C-halogen bond length in going from the neutral molecule to the radical anion. High 1 values also seem to be prevalent for reactions in aqueous medium, as was already noticed for self-exchange reactions (Table 7).

L

I

-20

I -10 AGO'/ kcal mol-'

I 0

FIG. 12 Plots of log k vs. AGO' from entries nos. 2 (aromatic amines and ethers; open and filled circles, triangles) and 3 (aliphatic amines; semi-filled circles, squares) of Table 12. The upper and lower curve have been drawn with AG*(O) = 3 and 5 kcal mol-'

140

LENNART EBERSON

<

Generally, in the range AG*(O) AGO’ < AG*(O) slopes turn out to be in reasonable agreement with the theoretically calculated value, -0.37 mol kcal-’ [corresponding to the slope of 0.5 predicted by (65)l. Due to the experimental difficulties in obtaining accurate rate data in this region one should not, however, place too much reliance on this particular test. To illustrate some of the salient features of Marcus plots a few of the studies in Table 12 have been singled out for a more detailed presentation. Figure 12 shows log k/AGo’ plots of reaction series 2 and 3; it is clearly seen that aliphatic amines follow a different correlation from that which aromatic amines and methoxybenzenes do, corresponding to different values of A. Figure 13 demonstrates a Rehm-Weller plot from reaction series 13; again we notice a fairly large scatter of the data, giving 1= 4 kcal mol-I. Figure 14 is a good demonstration of how important electrostatic effects can be. The authors in this case rightly concluded that the log k / A G o ’ plot shows a large scatter (Fig. 14a), but this can largely be eliminated by including electrostatic terms in the proper places (Fig. 14b). Reaction series 26, electron transfer between alkylmetals and iron(II1) complexes (Fukuzumi et al., 1980; Wong and Kochi, 1979) merits special attention since it represents a huge volume of rate data in a region of higher AGO’ than all the others. Rate constants for a large number of alkylmetals were determined, each compound being allowed to react with five different complexes (with E o values between 1.155 and 1.417 V vs. NHE). It was therefore possible to estimate EO’ for the alkylmetals by extrapolation of linear @/E:e(III) plots.3 These standard potentials are not experimentally accessible (Klingler and Kochi, 1980) because of the total irreversibility of their electrochemical oxidation (“total” meaning that these electrode reactions exhibit both slow electron transfer kinetics and have very fast chemical follow-up reactions). E o ’ values, estimated by extrapolation to E;e(I,I)= 0 of the F / E ; e ( I I I ) regression line for each alkylmetal and log k for three of the five reaction series studied are given in Table 13. The corresponding Marcus plots are shown in Fig. 15; they have slopes of -0.52 f 0.07, -0.56 k 0.05, and -0.5 1 f 0.05 mol kcal-’, which should be compared with those calculated for Marcus parabolas with A’s according to the caption of Fig. 15, approximated as straight lines in the same ranges of AGO‘, namely, -0.52, -0.50, and -0.44 mol kcal-’. The agreement is satisfactory. The A values (see Table 13) for all of the alkylmetal reactions with Fe(II1) complexes are high, 28 to 43 kcal mol-’, and with the assumption that the self-exchange reactions of the Fe(II1) complexes have rate constants lo8 M-l s-’ (1 16 kcal mol-’ (Pennington, 1978), for self-exchange reactions of alkylmetals values turn out to be very high, 40-70 N

-

E o ’ also contains the electrostatic work term; cf. AGO’ as defined by (46)

ELECTRO N - l

141

10-

-

0 -

i

0

8z m

-

6-

4

I

AG0)kcol mol-'

FIG. 13 Plot of log k vs. AGO' from entry no. 13 of Table 12. The curve was drawn with AG*(O) = 4 kcal rnol-I

-5

0

AGo'/kcol mol-'

FIG. 14 Plot of log k vs. AGO' from entry no. 15 of Table 12; (a) data plotted without correcting for electrostatic effects: (b) after correction for electrostatic effects. A,Q; + Qi-: 0. Q;* + Qi-;0,Q;-*+ Q;-; 0,Q;-- + Qi-;A, N,N,N',N'-tetramethyl-p-phenylenediamine reactions

142

LENNART EBERSON

TABLE13 Rate and Eo'data for reactions between alkylmetals and Fe(II1) complexes" log k and AG'" for: Alkylmetal (A/ kcal mol-')g Et,Si (43) Et,Ge (39) Me4% (34) Et,Me,Sn (37) Et,Sn (4 1) Pr,Sn (37) secBu,Sn (32) isoBu,Sn (38) neoPe,Sn (32) Me4Pb (38) Et,Me,Pb (28) EtMeHg (32) Et,Hg (29)

E ' O

b/V

1.890 1.767 1.948 1.602 1.490 1.516 1.4 11 1.418 1.521 1.522 1.486 1.561 1.409

Fe(III)(4,7-diPh-phen),'"

-3.78 0.09 0.538 1.03 2.94 1.64 1.72 0.704 2.75 1.30 3.36

18.3 10.3 7.7 8.3 5.9 6.1 8.4 8.5 7.6 9.4 5.9

Fe(III)(phen),e -3.49 -1.55 -2.81 0.754 1.12 1.66 3.65 2.4 1 2.55 1.41 3.55 2.06 4.04

15.4 12.6 16.8 8.8 6.2 6.8 4.4 4.6 6.9 7.0 6.1 7.9 4.4

Fe(III)(S-NO,-phen)/ -1.31 0.559 -0.592 2.65 2.89 3.5 5.21 3.96 4.25 3.17 5.29 3.87 5.7

10.9 8. I 12.2 4.3 1.7 2.3 -0.14 0.05 2.4 2.4 1.6 3.3 -0.2

Wong and Kochi, 1979; Fukuzumi ef al., 1980 Obtained by extrapolation to AGO' = 0 of the @/AGO' regression line. Standard deviations 3-8%. The Eo' value contains a small work term (-0.01 V) which can be neglected in this context 'Phen = 1,lO-phenanthroline " E o= 1.155Vvs.NHE E o = 1.220 V VS. NHE 'Eo = 1.417 V VS. NHE regression line. Standard deviations, 10-20% Obtained from the slope of the @/AGO'

kcal mol-'. This is most probably due to a large contribution of Ai to A for these compounds. There is no obvious steric influence on the A values (Table 13). Reactions 28 and 29 are examples of mixed organic-inorganic electrontransfer processes, of which the former is representative of a large number of studies of metal-ion oxidation of aromatic diols in aqueous acidic medium. In general, the Marcus treatment can be applied successfully to such systems (Pelizzetti et al., 1978a,c, 1976a,b; Pelizzetti and Mentasti, 1977a,b, 1976; Mentasti et al., 1977; for similar investigations on other types of organic compounds, see: Ng and Henry, 1976; Kustin et al., 1974). Finally, reaction no. 27, electron transfer from eiq to aromatic and aliphatic halides, presents us with a puzzling problem. From the high 2 s of reaction 19 and 20, with consequently high values of A for the self-exchange reactions of aromatic halides, one would expect high A values for their reaction with eiqtoo. Instead, an unusually low A value is obtained. The cause of this anomaly may

ELECTRO N - T R A NS FE R R EACTlO N S

143

AGo>kcol mol-’

FIG. 15 Plot of log k vs. AGO‘ from data given in Table 13. Curve I (a), Fe(II1) (4,7-diphenyl- 1,lO-phenanthroline), reactions; curve 2 (A),Fe(III)( 1, 10-phenanthroline),; curve 3 (W), Fe(III)(5-nitro-l,lO-phenanthroline),. The broken lines correspond to Marcus plots with AG*(O) = 6 (upper) and 11 kcal mol-’ respectively

be that the reactivity of eiq is not compatible with the theoretical framework of Marcus’ theory, or, less probably, that a faulty E O value was used for eiq.The problem has been discussed in detail (Hart and Anbar, 1970) and it was suggested that electron transfer from eiq should generally follow a nonadiabatic pathway. To complete the picture of the usefulness of Marcus’ theory with respect to organic electron transfer processes, Table 14 lists some 30 cases to which the cross relations (62) and (63) have been applied: both purely organic and organic-inorganic reactions are included. With the exclusion of reactions nos. 28 and 32 [Co(III) oxidations, see comment below1 and no. 30 [(k,2)ohsdonly known as the lower limit1 a log (k,2)ca,c/log(k12)ohsdplot fits a regression line with slope 0.98 & 0.04, y-axis intercept -0.2 t 0.3 log units, and correlation coefficient 0.974. Considering the wide variety of reactions, the widely differing reaction conditions, and the large variations in K , , ( > 20 orders of magnitude) and k,, and k,, (> 10 orders of magnitude), this is a very satisfactory result. Reactions with C0(111)~~ and other Co(II1) species often do not conform to the Marcus theory (for a summary, see Pennington, 1978) and reactions nos. 28 and 32 thus constitute “expected” cases of deviation. The reason for this discrepancy is not known. It should be noted that experimentally determined self-exchange rate constants and AG*(O) values derived therefrom must be corrected for the electrostatic term when used in conjunction with another self-exchange rate

P P

TABLE14 Calculation of rate constants (k12)for organic electron transfer processes. using the Marcus cross relations (62)and (63) Reaction Reaction

no. 1

2 3 4 5 6 7

8 9 10 11

12 13 14 15 16 17 18

N.N.N.N-Tetrameth ylphenylenediamine and tetracyanoquinodirnethane 12.5-Dimethylbenzoquinone)-' + benzoquinone 12.6-DimethylbenzoquinoneI-. + benzoquinone [Duroquinonel- + benzoquinone IDuroquinonel-' + 2.5-dimethylbenzoquinone IDuroquinone I-' + 2,6-dimethylbenzoquinone 0;' + 2,6-dimethylbenzoquinone 0;' + 2.5-dimethylbenzoquinone 0;' + duroquinone PhNO;' + 0, [Biphenyl]-' + PhCl INaphthalenel-' + PhCl IDibenzothiophenel-' + PhCl Ip-Tolunitrilel-' + PhCl [m-TolunitrileI-' + PhCl [Benzonitrilel-' + PhCl [Benzonitrilel-' + PhBr Im-Tolunitrilel-' + PhBr

.

k,,lM-'s-l

k,,lM-' s-'

1.05 x 10'

4 x 109

5.5 x 10' 1.7 x 10' 2.0 x lo9 2.0 x 10'

2.0 x 108 1.4 x 107 1.4 x 107 1.4 x 10'

3.2 x 105 4 x 107 6.7 x 1.4 x 8.5 x 6.0x 6.8 x 6.8 x

10'

lo8 lo8 10' 10'

loR

6.0 x 10'

6.2 x 6.2 x 6.2 x 5.5 x 1.7 x

1.7 x 5.5 x 2x 1.4 x 4.7 x 4.7 x 4.7 x 4.7 x 4.7 x 4.7 x 4.7 x 4.7 x

10' 10' 10' 10' 10' 10' 107 105 10' 10" 103 103 103

103 103 103e

103

K,,

(kl,),,,,d

7 x 10-2

4.8 x loR

(kIZ),>h\d

5.9 x 1.06 x 4.43 x 7.5 x 4.2 x 25 6.9 x

102

1.0 x lo9 2.2 x loy

102

3.9 x 1.56 x 9.5 x 4.5 x

10s lo-'

1.6 x 1.9 x 2.6 x 2.3 x 5.3 x I x 5x 1.4 x 1.1 x 3.2 x 4.9 x

lo3 102

lo2 10,

4.6 x lo-,

10-5 10-5 6.4 x 10-7 4.6 x lo-' 1.61 x 4.16 x 1.33 x 10-3

109

10' loy 10' 108

10'

lo* 104 104

10' 102

71

35 2.6 x 1 0 4 4.8 x 1 0 4

4 x 108 6.5 x 1.0 x 1.1 x 1.0 x 9.6 x 2.2 x

loR 109

109 109

loR 108

1.7 x loR I x 107

8 x lo6 1.6 x lo4 2.5 x 10' 2.5 x lo3 1.3 x 10, 10

4

2.0 x 1 0 4 3.2 x 1 0 4

Ref-.

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Ip-Tolunitrilel-' + PhBr

[Anthracenel-' + PhBr IAnthracenel-' + pyrene

[N,N,N,N-Tetramethylphenylenediaminel+ * +

phenothiazine Catechol + IrCliCatechol + ICoW,,O,, IsHydroquinone + Mo(CN)iHydroquinone + Fe(CN):Hydroquinone + IrBriHydroquinone + C0(111)~~ Catechol + Fe(III)(phen), 4,4'-Dihydroxybiphenyl + Ag(II)aq 4,4'-Dihydroxybiphenyl + Ce(Iv),, 4,4'-DihydroxybiphenyI + Co(III),, + Co(III)(phen), Ferrocytochrome cSfll

Yamagishi el al., 1977 Meisel and Fessenden, 1976 Meisel, 1975 Wardman and Clarke, 1976 Assuming a value of dG)(O) = 10 kcal mol-' f Andrieux el al., 1978 Andrieux et al., 1978 Dorfman, 1970 Yamagishi, 1975b a

8.5 2.4 2.4 3

4.7 x 103 4.7 x 10' 2.8 x lo8

x lo8 x lo8 x lo8 x 104

6x 6x 6x 6x 6x 6x 6x 1.7 x 1.7 x 1.7 x 1.4 x

1 x 10'0

lo7 lo7 lo7 lo7 lo7 lo7 lo7 lo6 lo6 106 107

1.7 0.55 7.7 5.9 1.2 7.6 1.5 8.6 0.19 7.6 45

x 106 x 107 x 104 x 108 x 109 x lo2

2.03 x lo-' 5 x 10-10 1.2 X lo-* 1.91 x

2.6 x lo5 19 2.3 x l o 7 6.9 x 10'

1.6 x los 2.5 2.1 x 10' 8 x 10'

g

7.4 x 2.9 x lo-' 1.9 x 10-6

1 . 1 x lo4 2.7 x 10' 2.1 x 1 0 4

2.7 x 10' 1.2 x lo4 1.1 x 1 0 4

j

k I

2

5.5 4.3 6.4 5 5.8 4.3 3.7 1.3

89 2.3 x 8.4 x 3.6 x 1.1 x 1.6 x 6.2 x 2.6 x

12 7.4 x 3.3 x 1.7 x >5 x 2.4 x 1.2 x 5.3 x

1 rn

%

x lo-* x lo-' x 10" x 10-4 x 1015 x

1010

x 10"

x 10-2

JMentasti et al., 1977 Amjad el al., 1977 Pelizzetti et al., 1978a Pelizzetti et al., 1978b " Pelizzetti and Mentasti, 1976 Pelizzetti and Mentasti, 1977a P Pelizzetti and Mentasti, 1977b 9 McArdle et al., 1977

'

los

lon 106

1010

107 10'

103

lo4 lo2 10' 107

g

h i

n

o

r rn

2

I]

0

f

%

g

;

0

106

10' 104

rn

p

5

-.

146

LENNART EBERSON

constant with a different value of Z , Z , . This is a very common situation for organic-inorganic electron-transfer processes. As an example, k , for IrCIZ,-/ IrCli- was determined experimentally at I = 0.1 M to be 2.3 x los M-’ s-’, corresponding to AGt(0) = 7.7 kcal mol-I. The electrostatic work to bring the two ions together ( Z , Z , = 6) at I = 0.1 M in water and with rI2= 8.6 A was estimated to be 1.2 kcal mol-’ (Pelizzetti et al., 1978a; (39) with the same parameters gives 2.1 kcal mol-I) and thus the “intrinsic” ,Ivalue is 7.7-1.2 = 6.5 kcal mol-I. Such intrinsic parameters were worked out for a number of metal-ion redox systems (Pelizzetti et al., 1978a and references quoted therein).

,

CONCLUSIONS

We now have surveyed a number of studies which have aimed explicitly at testing various aspects of Marcus theory as applied to organic systems. We have seen that it fails on one important point, namely to predict rates correctly in the inverted region, and that other equations have been put forward to resolve this problem. In the normal region all three equations predict practically the same log k/AGo’ behaviour, and lead to reasonably good agreement with experimental data. Great care must however be exercised to find reaction series with identical or nearly identical 4, values for all compounds. The early assumption that the self-exchange rate constant of most, if not all, organic redox systems are identical has definitely been proved wrong. In many cases the contribution from ,Iito A cannot be ignored either. Estimates of ,I (i.e. when ,Iiis assumed to be 0) using eqn ( 5 2 ) or more complicated versions thereof (78) have turned out to be somewhat less than successful. It is usually difficult to use the spherical approximation (Fig. 4) for the shape of organic molecules. and other, more complex treatments produce problems of their own. Thus the intuitively satisfying model for electron transfer between two aromatic species, parallel orientation of the molecular planes at collision distance, cannot be fitted to the triaxial ellipsoidal model discussed in Section 4. Instead, one has to assume that electron transfer takes place over a considerably larger distance. This expansion of the transition state seems to be fairly constant for different compounds and can be included as an ad hoc (at least at present) parameter in the calculation of A. As for estimates of individual rate constants via the cross relations, this procedure seems to work well for organic electron-transfer processes. and the few existing limitations are of the same kind as those encountered for inorganic redox processes. Concluding, the Marcus theory and related treatments can be applied to organic systems with some confidence and should be useful as one tool among others to distinguish non-bonded electron transfer mechanisms from other

ELECTRON-TRANSFER R E A C T I O N S

147

types in unknown or uncertain cases. We shall deal with this problem in the next Section. 6

Examination of certain postulated organic electron-transfer reactions

In this Section we shall discuss certain aspects of the problem illustrated at the very beginning of this chapter by (6) and (7), and now presented in its most general form in (96). Two species, A and B, one electrophilic and one

A+B<

(b)

A-B

nucleophilic, charged or uncharged, either or both organic, with one- or two-electron redox properties, meet and either exchange an electron by a nonbonded mechanism [path (a)] or form a bond directly [path (b)].Path (a) can be followed by bond formation between A+ and B-, and path (b) can have a subsequent bond-dissociation step of A-B. This reaction scheme applies to any imaginable [electrophile, nucleophile] combination, and our task here will be to examine the feasibility of path (a) for a number of typical cases where electron-transfer mechanisms either have been proposed or preferably could be exploited. Note, however, that we shall not always try to establish which actual route a given reaction might follow; although tempting to undertake, such an endeavour would be far too space-consuming. To exemplify, it is rather easy to show that the electron-transfer step of (97) ArH

+ NO:

-

ArH+' + NO,

(97)

should be a very fast one for easily oxidized aromatic compounds (Perrin, 1977; see below), but it is extremely difficult to ascertain if this step precedes the formation of the Wheland intermediate or if the latter is formed directly (Eberson et al., 1 9 7 8 ~ ;Eberson and Radner, 1980; Pedersen et al., 1973; Nagakura and Tanaka, 1954; Weiss, 1946). A thorough discussion of this problem alone would require a chapter of its own! Following our initial, loose classification of redox reagents as belonging to either the one- or two-electron variety, we now proceed to examine a wide range of suspected cases of nonbonded electron transfer mechanisms in the light of the Marcus theory. We shall use an approach similar to the one developed in Section 5 , namely, to see if Marcus theory can predict rate constants or other rate parameters that are in reasonable agreement with experimentally determined ones or otherwise are compatible with known facts.

TABLE15 Marcus analysis of organic reactions of certain non-metallic inorganic redox reagents

Reaction no.

Reactiona

Lsbf

kcal mol-'

4a,,el

kOb,dl

kcal mol-'

M-ls-'

kc,,,'/ M-l s-I

CommentYon electron Slope' (calcd) transfer mol kcal-I step Ref.*

~

I 2 3 4

9 10 11

12 13

SO;' (2.52') + ArHj SO;' (2.52') + ArCH,' SO;' (2.52') + pyridine (2.37') SO;' (2.52') + CHICOO- (2.41: see Table 7) SO;' (2.52') + CHIOH (4.19) COT' (2.144) + ArH HO' (2.02") + PhH NO: (1.57x) + Cl0H8(2.08: see Table 8) NO; (1.57x) + C,H, (3.03: see Table 8) CIO, (0.95") + aliphatic amines Br, (0.5 I d d ) + alkylmetalsee I, (0.1 I d d ) + alkylmetals" DPA+' kk (1.44") + iodide, rhodanide, bromide and cyanide ionmmin acetonitrile

14

Pe+'OO(1.30") + iodide, rhodanide and bromide ionmmin acetonitrile

15

Pe+*O"(1.30") + chloride ionmmin acetonitrile 1.4- and 1.2-dinitrobenzene + hydroxide ion'"'" in aqueous DMSO

16

8.0

9.0

-0.52 (-0.47) -0.17 (-0.20)

1 -10'0

21 x 1 0 8

-109

2.5 x 10' 3 x 10'' 3.5 x 109

< I x 10-8 .lo-'r
-109

32 68

200" 3W

3 x 10'' 2 x 105bb O.025OR 1.5 x 1 0 7 5.5 x 1 0 6 6.9 x 105 6.3 x 10, 2.1 x 10'0 1.6 x 10, 2.7 x 10, 6.3 x 10' -5 -1

-0.14'

10-24

2.5 x 103 1.63 x lo3 1.6 3.4 9 9.2 1.7 3.4

x lo8 x

-0.31 (-0.49) -0.20 (-0.46) 0.1-0.2

F(?); see text F(?); see text F F

k rn n

NF NF NF (see text) NF (see text)

P t

NF B B (see text) N F (see text)

J'

cc hh jj

NF

94

0

1)

y

106

x 103 x 104 x 10' x 10' 1 x 106 1.6 x 10-3

17

18 19

20

Diphenyliodiniurn ion (0.0)+ nitrite,

rhodanide and cyanide ionmmin aqueous dioxane at 100°C SbCI,- (0.54”) + triphenylamine in dichloromethane Tropylium ion (0.06”’) + iodide and nitrite ion in acetonitrile

Flourescence quenching of aromatic compounds by iodide, rhodanide, azide bromide. hydroxide and chloride ion in aqueous ethanol

>80

26

10-2-10-5

-1

F

rr


-

F

uu

NF

.Vl’ .

no electron transfer no electron transfer

-10-5 .10-6

103

5 x 10-9 0.3

a 0.10 (-0.6)

P

2 n

cn rn

ln

2J

F

0

The number given in parentheses refers to the E ” (or sometimes E l , , ) values vs. NHE for the corresponding redox couple 5 0 *Estimated from the Marcus plot z ‘Estimated from A values of the self-exchange reactions involved v) Experimental value, in appropriate cases corrected for diffusion according to (67), with k,/k-d = 1 ~ - 1 From the Marcus cross relations (62) and (63) ’Experimental slope is given first; the calculated one (within parentheses) is based on the Marcus parabola, approximated as a straight line in the AG”‘ region involved F = feasible; N F = not feasible; B = borderline case (ix. not possible to decide) References are sometimes given both to data sources and to pertinent discussions of the problem of electron transfer vs. other types of mechanism Estimate for aqueous medium; see text jEo values were either estimated from (90). Table 9 or E,,, values were used Neta el al., 1977; O’Neill et al., 1975 Relative rate constants were determined Jonsson and Wistrand, 1979 “ Ledwith and Russell, 1974 “Ashworth el al., 1978; Steenken et al., 1977; Vasudeva, 1975; Walling and Camaioni, 1975; Norman el a/., 1970; Snook and Hamilton, 1974; Norman and Storey, 1970; Anderson and Kochi, 1970; Tanner and Osman, 1968; Eberson el al., 1968 Dogliotti and Hayon, 1967 Calculated in the same way as for SO;/SO:-; see text For benzene a

‘

TABLE15 (continued) AGO' range, 10-18 kcal mol-I

' Chen et al..

2

m 0

1975 " Milazzo and Caroli, 1978 " Ingold, 1973 In acetonitrile (Bontempelli et al., 1974); a value of 1.53 V was obtained in nitromethane (Cauquis and Serve, 1968a) Y For references, see text Estimated from a value given by Ridd (1978) Estimated from data regarding reaction no. 3 in Table 12; I values for Cr(bpy), and Ir(Me,phen),CI: are 12 and 8 kcal mol-' respectively, and from the mean value, 10 kcal mol-1 and I for reaction no. 3, 20 kcal mol-l, A for aliphatic amines can be estimated at 30 kcal mol-l. I for CIO,/CIO,- was set equal to 10 kcal mol-' bb For triethylamine cr Rosenblatt et al., 1967; Hull el al., 1967, 1969 dd In water: Woodruff and Margerum, 1973 ee In CCI, "Calculated from an average I for alkylmetal self-exchange reactions of 57 kcal mol-I and an estimated I for Br2/Bry' of <20 kcal mol-l For Et,Sn hh Fukuzumi and Kochi, 1980a ii In CH,CN j j Fukuzumi and Kochi, 1980b kk 9,IO-Diphenylanthracene radical cation ' I Table 8 mm For E O , see Table 8; for the anions I was set equal to 40 kcal mo1-l nn Evans and Blount, 1978 "" Perylene radical cation r m p p Evans and Hurysz, 1977 2 Z qq Abe and Ikegami 1976, 1978 9 a Lubinkowski et al., 1978 --I Is Estimated value; for SbCI;/SbCI:was set equal to 26 kcal mol-' m m This value was estimated from the instantaneous appearance of the end product m n "" Cowell et al., 1970 v) "" Wasielewski and Breslow, 1980; see also Ahlberg and Parker, 1980 0 Z Cf. Ledwith and Sambhi, 1965; Kessler and Walter, 1973 yy Shizuka el al., 1978

ELECTRON-TRANSFER REACTIONS

151

In some cases, data are available to evaluate slopes of the log k/AGo'regression line, and then this approach will be used in addition. NON-METALLIC I N O R G A N I C R E D O X R E A G E N T S

In this category we find a number of neutral and charged species with mainly one-electron redox properties such as O,, O;', O,, O;', HO', CO;', CO;', SO;', NO+, NO:, CIO,, the halogens, etc. The organic reactions of the inorganic radical anions included have been reviewed (Morkovnik and Okhlobystin, 1979). Following a descending order of redox potential of the inorganic component, a number of reactions of these species are listed in Table 15, together with a quantitative evaluation of rate parameters according to Marcus theory. Unfortunately, it is not always possible due to limitations of space to give a complete account of data sources and methods for the estimation of data in the Table, so the reader in many cases must accept the numbers given and be assured that they have been obtained by the most appropriate methods and approximations available. In important cases, comments have been made in the text; as seen for example in the case of sulfate radical anion, even a description of how to calculate its E o value occupies almost one third of a page. Sulfate radical anion

This species is generated thermally, photochemically or pulse radiolytically from peroxydisulfate ion, and is one of the strongest oxidants known. Its standard potential in water can be estimated from A H ; [(SOi-)aQl= -216.9 kcal mol-I and AH,? [(HSO;),,] = -21 1.7 kcal mol-I (Rossini et al., 1952) by assuming that the bond-dissociation energy of the 0-H bond in HS0;lsee (98)1 is normal for such a bond, ca. 105 kcal mol-' (Mortimer, 1962). With AH,O(H') = 52.1 kcal mol-' (Benson, 1976), AH,O(SO;'),, is estimated to be -158.8 kcal mol-I. With the assumption that the S o terms cancel. Eo(SO;'/SOi-) is then calculated to be 2.52 V vs. NHE. -0,SO-H

-,SO;' + H'

(98)

However, with this E o value it is impossible to fit the data of entry no. 1 of Table 15 to the Marcus relation. Only by using a considerably higher E o for the SOa'/SO',- couple, 3.08 V (or, of course, a set of lower values for ArH), can any reasonable fit be obtained. We then also have to postulate a rather small A value, 8.0 kcal mol, for the reaction. Knowing that A for self-exchange reactions of the compound types involved is around 10 kcal mol-I (see Table 7) and assuming it to be small, 10 kcal mol-I, for SO;'/SO2,- too we can "calculate" A to be 9.0 kcal mol-I.

152

LENNART EBERSON

Entry no. 2 presents another problem in that the electrostatic correction term for AGO in the solvent used, acetic acid, is very large, -15.3 kcal mol-' (see Table 3: Z , Z , = -2, r I 2= 7 A). Again, E o = 2.52 V is far too small to give any reasonable fit to the Marcus relation. With E o = 3.08 V, the result is at least consistent with that of entry no. 1. Entries nos. 3 and 4 have been treated with A values for self-exchange reactions of pyridine and acetate equal to 10 and 20 kcal mol-' respectively: k,,,, comes out at loLoM-' s-' irrespective of the choice of E o = 2.52 or 3.08 V. For entry no. 5 il(CH,OH) was assumed to be > 20 kcal mol-' and the quoted value of k,,,, is estimated with E o = 3.08 V. It thus represents a maximum value and the reaction is certainly not feasible as an electron-transfer step.

Hvdroxvl radical From its E o value, 2.02 V, hydroxyl radical would be expected to show strongly oxidizing properties. It sometimes does, but the major pathway for its reactions with organic compounds is bond formation, either by addition or hydrogen-atom abstraction. The calculation for benzene assumes A(OH '/ OH-) 20 kcal mol-' and A(PhH+ '/PhH) = 10 kcal mol-' both of which are probably maximum values. Clearly, nonbonded electron transfer is not feasible in this case.

<

Nitronium ion Entry nos. 8 and 9 of Table 15 deal with the possible role of electron transfer as the initial step of electrophilic aromatic nitration (97) (Perrin, 1977: Eberson et al., 1978c; Eberson and Radner, 1980). Conflicting data with respect to the E o value of the NO:/NO, couple make estimates of the feasibility of the electron-transfer mechanism somewhat ambiguous. Table 15 uses a value of 1.57 V, obtained by cyclic voltammetry from both the NO, and the NO: side (quasi-reversible process), and then a rather low value of k,,,, is predicted for naphthalene (entry no. 8). Another E o value, 2.3 V (Perrin, 1977), obtained from the NO, side only, gives k,,,, as ca. lo9 M-' s-I. Since a low E o value, 1.53 V, is obtained in nitromethane too, starting from both sides, we now favor the lower k,,,,. Thus the electron-transfer mechanism must be deemed not feasible in solution (see also Eberson and Radner, 1980), at least not with substrates which are difficult to oxidize (say, with E o > 1.6 V). In the gas phase, electron transfer to NO: even from benzene is highly exergonic (Nagakura and Tanaka, 1954): experimentally one finds that electron transfer is ca. 100 times faster than bond formation (Jalonen et al., 1978). Much the same discussion applies to the nitrosonium ion (Reents and Freiser, 1980) which is an oxidant of the same strength (EO 5 1.5 V) as nitronium ion (Cauquis and Serve, 1968b: Bontempelli et al., 1974).

ELECTRON-TRANS F E R REACTIONS

153

Halogens Entry no. 1 1 of Table 15 illustrates many of the difficulties involved in judging the feasibility of a slow electron-transfer step, in this case further complicated by the assumption that it takes place within a pre-formed charge-transfer complex (99). Taking for granted that Marcus theory can be applied to such a R,M

+ Br, t I R , M . . .Br,] = [R, M+' Br;']

(99)

situation we see from Table 15 that no clearcut decision can be made on this basis. In the first place, it is necessary to apply a very large electrostatic correction term to AGO in a solvent of such low dielectric constant as carbon tetrachloride (for D = 2.23, r I 2= 9 A, this term is -16.5 kcal mol-'). To fit the resulting data set (the AGO' values were calculated using the E O values given in Table 13) a very large 1 (ca. 70 kcal mol-') must be used, whereas the calculated 1 value comes out at 38 kcal mol-'. This is also reflected in the large discrepancies between experimental and estimated k values and slopes. However, the rather extreme nature of the solvent system warrants caution in deeming electron transfer not feasible. For reaction no. 12,iodinolysis of alkylmetals in acetonitrile, the situation is more clearcut. The slope even has a positive sign, and no fit to a Marcus-type relation is possible. It was suggested at one time that the chlorination of polymethyl-substituted aromatic hydrocarbons might proceed by a non-bonded electron-transfer mechanism (for arguments for and against, see Kochi, 1975; Baciocchi and Illuminati, 1975; Hart et al., 1977). The low value of E o for the C12/Cl;* couple, 0.6 V (Malone and Endicott, 1972), makes this suggestion rather unlikely ( E O of, e.g. hexamethylbenzene is 1.85 V).

Radical cations Radical cations act both as electrophiles and one-electron oxidants toward nucleophiles (Eberson, 1975;Bard et al., 1976;Eberson et al., 1978a,b;Evans and Blount, 1978) as shown in (6), and it is therefore important to find out which factors govern the competitition between these reaction modes. Evans and Blount (1978) measured rate constants and products for a number of [9,10-diphenylanthracene)+'/nucleophile reactions and found that iodide, rhodanide, bromide and cyanide undergo oxidation, whereas nucleophiles that are more difficult to oxidize form a C-NU bond directly. Entry no. 13 of Table 15 shows non-bonded electron transfer to be feasible for these ions, and the reactions of [perylenel+' with iodide, rhodanide and bromide (entry no. 14) presumably can be classified in the same way. The reaction with chloride ion

154

L E N N A R T EBERSON

(entry no. 15) is definitely much too fast to be compatible with the Marcus theory. The reaction between different types of radical cation and nitrite ion (EO = 0.7 V in acetonitrile) has been extensively studied (Ristagno and Shine, 1971; Johnson and Dolphin, 1976; Shine et al., 1979; Smith et al., 1979; Eberson and Radner, 1980). Generally, one obtains nitration products from this reaction, and in view of its exergonic nature the mechanism most probably consists of an initial, very fast electron-transfer step, followed by a slower nitration reaction, caused by NO, (N,O,) from the first step.

Hexachloroantimonate( V ) SbCI, has been claimed to act as an electron-transfer oxidant toward a number of reagents, such as N,N,N',N'-tetramethylphenylenediamine. triphenylamine, 2,4,6-tri-t-butylphenolate ion, ferrocene, and N-vinylcarbazole. Among these, triphenylamine is the most difficult to oxidize, and was therefore chosen as a model compound in entry no. 18. By matching the lowest possible experimental rate constant, l o 3 M-' s-', with rate constants calculated as a function of E o for the SbCl;/SbCI2,- couple, the latter was estimated to be 0.54 V. This is an entirely reasonable value (see Cowell et a/., 1970).

Trop-vlium ion Tropylium ion is a weak oxidant, and it is interesting to ponder on why it does not oxidize nitrite ion, in principle a feasible electron-transfer step (entry no. 19). METALLIC REDOX REAGENTS

Under this heading we can easily include dozens of redox reagents and literally thousands of individual reactions, but, as before, we shall limit ourselves to suspected or postulated non-bonded electron-transfer steps. The reagents are mostly oxidants, such as Co(III), Mn(III), Ag(II), Ir(IV), Ce(IV), and Fe(III), and the substrates mostly of a type that does not make ligand attachment to the metal ion possible. Again, accurate or sometimes even approximate E o data are not always available for the systems studied, so that one has to rely on data pertaining to aqueous solution for estimates of rate constants in non-aqueous systems.

Cobalt(ZZZ)

Co(II1) oxidation is important in organic chemistry, not least in its industrial practice, and it has been the subject of many studies (for a review. see Sheldon

ELECTRON-TRANSFER REACTIONS

155

and Kochi, 1973). We have already noted (Table 14, entries nos. 28 and 30, and text) that Co(II1) reactions often do not conform to Marcus theory: entry no. 1 of Table 16 serves to reiterate this fact. Only by assuming that one or more of the underlying principles of the theory breaks down for C0(111)~~ can one fit these data to (56); this is then most simply done by putting K of (13) equal to 10-5-10-6. Entry no. 2 of Table 16 introduces the most remarkable aspect of Co(II1) chemistry, namely its ability to oxidize nonactivated C-H bonds (for a recent study, see Jones and Mellor, 1977) and we immediately see that Marcus theory here completely rules out the possibility of an initial electron-transfer step. This is predicted to be ca. 1OI6 times slower than what is actually observed. On the other hand, the theory correctly predicts the rate constant for oxidation of naphthalene under the same conditions, and the postulated “direct abstraction of a n-electron” is thus feasible (Cooper and Waters, 1967). The Co(II1) trifluoroacetate study of entry no. 3, including only substrates without an alkyl side-chain, however, cannot be fitted to any physically realistic set of E O , 1 parameters. With E o = 1.83 V (value in 1.0 M HClO,) 1 ought to be ca. 40 kcal mol-I and the slope of the log k/AGo’ regression line ca. -0.6; the 1 value is then in reasonable agreement with the estimated one but not the slope. With E o = 3.2 V (clearly not a physically very realistic standard potential) a 1 value of ca. 80 kcal mol-’ is required. This seems to be far too large for such a system. Generally, it is a serious problem for this type of analysis that standard potentials for metallic reagents are seldom known in non-aqueous systems. Thus, it would be of great help to have such values for TFA in view of its great popularity as a solvent for metal-ion oxidations. The Co(1II) case discussed above is typical: in TFA Co(II1) is presumably bonded to six trifluoroacetate ligands and one then wonders what effect this might have upon E O . In water, E o is lowered considerably by carboxylate ligands, e.g. from 1.83 V to 0.74 V in changing from C0(111)~~ to Co(malonate)3,- (Al-Obadie, 1980). Electrochemical measurements of the simplest variety, such as cyclic voltammetry, are not useful in this context since these reactions are electrochemically irreversible due to slow electron transfer to and from the electrode (as is also reflected in the large 1 values of these reactions in homogeneous medium). Hence they require a considerable overpotential to proceed at a measurable rate, and E , values, if at all measurable, will thus correspond to the maximum possible values of E O. As an example, the Ag(II)/Ag(I) couple, which has the relatively low 1 value of 44 kcal mol-I in water, displays in TFA an oxidation peak in the region of 2.0-2.4 V (reduction takes place at potentials < O V) showing that its E o is probably lower than 2.0 V (Eberson. 1980b). Similarly, Cu(III)/Cu(II) in the form of its Cu(II1) (H-, biuret); complex displays an oxidation peak with E , z

TABLE16 Marcus analysis of organic reactions of certain metallic redox reagents

Reaction no. 1

2 3 4 5

6 7 8 9 10 11

12

Reaction" C0(111)~~ (1.83') + benzenediols in aqueous acidic (HC10,) medium Co(II1) (1.83') + aromatics in 50% waterlacetonitrile (1.0 M HCIO,) Co(II1) trifluoroacetate (1.83'*") + aromatics in CF,COOHP Co(II1) acetate + alkylaromatics in HOAc at 65OCS ICo(II1) Wl,0401s- (1.00) + alkylaromatics in HOAc at 102OC Mn(III)aQ(1.5 1') + 4,4'-dihydroxybiphenyl and hydroquinone Mn(OAc), (0.79Y) + 4-methoxytoluene in HOAc at 70°C Mn(OAc), (0.79"") + activated toluenes in HOAc at 7OoC Ag(IOa,, (2.0k) + 4,4'-dihydroxybiphenyl and hydroquinone Ag(II),,(2.0k) + CH,COO-, C,H,COO- and C,H,COOAg(II), (2.0') + methoxybenzenes Ag(I1) (bpy), + 4-substituted anisoles in H O A g

L21

kcal mol-I

Comment8 on electron Slope' (calcd) transfer mol kcal-' step Ref.h

M-'S-'

kcalcel M-I s-I

41

9.3 x 10"

3.5 x 10'

-0.27 (-0.29)

B

k

33

50' 4 x 10-3"

5 x 10-19

66

-0.27 (-0.46)

m

-0.16 (-0.60)

F NF NF

-0.10

NF

t

NF

X

F

k

F

z

F

cc

F

k z

F

dd

&a,cCI

kcal mol-l

kObsdl

33 33

-

-

36 53 45

9 x 103 4.8 x 103 5 x 10-5

4.5 x 104 3.8 x 104 5 x 10-5 -0.32''

35 32 27 27

>s x

107

very fast 1.9 7.5 17 4.5 x 10'

1.1 x 1010 I .O x 1 0 ' O 14 103 103 6.7 x loae'

(-0.55)

r

r m

z

Z 9

rn

a

(n

-0.02 (-0.30) -0.26'' (-0.37)

F F

dd hh

0

13 14 15

16 17 18

19 20 21 22

Ce(IV) (NO,):- (1.3k) + alkylaromatics in HOAc Ir(IV) Cli- (0.67kk)+ alkyltins in CH3CN Ir(IV) Cli- (0.67kk)+ alkylmercurysSs in CH3CN Tl(II1) (OCOCF,), (1.25k.UU)+ naphthalene in TFA Fe(CN):- (0.36k+) + aliphatic amines in 30% MeOH/H,O Cu(II1) (H_,biuret); (l.Oddd) + chlorobenzene in TFA at 80°C + Pb(IV) trifluoroacetate (1.67k*hhh) anisole and/or methylbenzenes in TFA/CH,CI, at 0°C Co(1) (salen)- (-0.84) + t-butyl bromide in DMF Bu,P-cobaloxime (-0.7mmm)+ methyl chloride, bromide and iodide in methanol cr(I1Iaq(-0.41) + benzyl bromide

32 -40

32

41

1.8"

42"

5.2 x

36PP

32"""

0.4 3 x lo-"

244 2 x 10-9 48" 6x 10-3 (10-2)Vv 10-4-10-6" 2.8 x 10-3bbb0.4

-0.59 (-0.54)

F

ji

-0.07 (-0.58)

NF

nn

-0.26

NF

rr

F

YY

F

ccc

NF

ggg

-0.52 (-0.54)

F

Sn

0

f

n

D z

cn n

g

n D

urn 0

i

1 . 1 x 103

0.85 2.2 x lo2 2.3 x 103 0.4 1

104kkk

F

111

0.25-103"nn

F

000

54.005~PP

F

444

5 x

The number given in parentheses refers to the E" (or sometimes E l , , ) value vs. NHE for the corresponding redox couple Estimated from the Marcus plot Estimated from A's of the self-exchangereactions involved ,IExperimental value, in appropriate cases corrected for diffusion according to (67), with kd/k-d = 1 ~ - 1 From the Marcus cross relations (62) and (63) 'Experimental slope is given first; the calculated one (within parentheses) is based on the Marcus parabola, approximated as a straight line in the AGO' region involved 8 F = feasible; NF = not feasible; B = borderline case (is., not possible to decide) References are sometimes given both to data sources and to pertinent discussions of the problem of electron transfer vs. other types of mechanism Milazzo and Caroli, 1978 a

rn r rn

5 0

TABLE 16 (continued) For hydroquinone Pelizzetti and Mentasti, 1976 For naphthalene; I is assumed to be 10 kcal mol-' (cf. Table 7) Cooper and Waters, 1967 " For cyclohexane; I is assumed to be 40 kcal mol-1 The value for 1 M aqueous HCIO, was used Relative values were measured; from the information given the rate constant for benzene was estimated to be -0.2 M-' s-' This data set cannot be fitted to any physically realistic set of EO, 1pairs ' Kochi et al., 1973 Relative rates were measured; the rate constant for p-methoxytoluene is of the order of 2 M-' s-l ' Heiba et al., 1969 " For toluene " Calculated with the assumption that the electrostatic term in AGO' contributes fully (ZIZ,= -6). The value given within parentheses corresponds to z,z, = 0 Eberson and Wistrand, 1980 Y Value adjusted (Marcus' cross relations) to make k,,,, = kobs Andrulis et al., 1966 From entry no. 7 bb Read off a plot in the paper rc Gilmore and Mellor, 1970 dd O'NeiU er al., 1975 ee For 1,4-dimethoxybenzene ff Relative rates were determined Eg Based on an E o value for Ag(II)/Ag(I) = 2.0 V; only two data pairs were usable due to the lack of potential data ** Nyberg and Wistrand, 1978 ii For hexamethylbenzene j j Baciocchi et al., 1976, 1977, 1980, 1981; Eberson and Oberrauch 1979 kk Value measured in acetonitrile An average value of for alkylmetals of 57 kcal mol-I (Table 6) was used; A(Ir*-'3-) = 26 kcal mol-' m m For tetramethyltin "" Wong and Kochi, 1979; Fukuzumi etal., 1980; see also Chen et al., 1976 j

Ir

r m

Z Z

D

n

4

rn

m rn

a

v,

0

Z

For tetra-(s-butyl)tin

pp

I for R,Hg was set equal to 45 kcal mol-'

For ethylmethylmercury Chen ef al., 1976 Is I for EtMeHg and Et,Hg was estimated to be 48 and 42 kcal mol-' respectively (see Table 13) '' For diethylmercury "" For the TI(III)/TI(I) couple in aqueous solution "" Semiquantitative estimate, probably lower limit, from data in the referenceYY;the reaction seems to be over within 60 s. The value in parentheses refers to experiments with boron trifluoride etherate present xx Calculated for the following sets of I~Tl(lIl)/Tl(Il)l,I[naph+/naphl, AGO': 10, 2.5, 20; 10, 5, 20; 15,5,20 yy McKillop el al., 1980; Elson and Kochi, 1973; for a discussion of similar problems, see Torssell, 1969) IZ A value of O.71V (Pelizzetti et al., 1978a) gives a Jobs of ca. 55 kcal mol-' and a smaller observed slope From I = 8.5 kcal mol-' for Fe(CN):-/Fe(CN):- and 7.5 kcal mol-' for R,N+'/R,N (see Table 15, entry No 10) bbb For N,N-dimethylbenzylamine ccc Audeh and Smith, 1971; Smith and Mead, 1973; Smith and Masheder, 1976 ddd Estimated value, based on published E o values for Cu(II1) peptide complexes (Bossu el al., 1977; see also text) eep Crude estimate mBased on I for Cu(III)/Cu(II) = 17 kcal mol-I (De Korte et al., 1979), 1 for PhCI+/PhCl = 10 and 60 kcal mol-I and AGO' = 41.7 kcal mol-I, all at 25 OC ggg Eberson and Jonsson, 1980 hhh For Pb(IV)/Pb(II) in aqueous solution iii Based on I for anisole/methylbenzenes = 10 kcal mol-l, I for Pb(IV)/Pb(III) = 40 and 60 kcal mol-', and AGO' = 11.5 kcal mol-' (corresponds to compounds like anisole and mesitylene) .O'Norman et al., 1973 lrkk Based on I for Co(II)salen/Co(I)salen = 16 kcal mol-l, for t-BuBr 60 kcal mol-l, and AGO' = -1.8 kcal mol-I (see text) Puxeddu et al., 1980 mmm Schrauzer er al., 1965 """ See text Oo0 Schrauzer and Deutsch, 1969 ppp Based on I for Cr(III)/Cr(II) in water = 84 kcal mol-l (cf. Tables 5 and 12, entry no. 29), for PhCH,Br 20 and 60 kcal mol-', and AGO' = 2.1 kcal mol-' qqq Davis and Kochi, 1964 qq

f f f

rn r

rn

7 II

0

7 z

v,

n

rn

n

II rn

D A

0

0

z v)

160

LENNART EBERSON

1.2 V in TFA (reduction takes place at potentials < O V), whereas different Cu(III)/Cu(II) peptide complexes have E o values between 0.5 and 1.0 V in water (Youngblood and Margerum, 1980). Co(II1) acetate oxidation of alkylaromatics (entry no. 4) displays the same characteristics as those of entry no. 3, and, as concluded by several groups (Cooper and Waters, 1967; Hanotier and Hanotier-Bridoux, 1973), this reaction cannot be initiated by electron transfer. The 12-tungstocobalt(III)ate oxidation of alkylaromatics (entry no. 5 of Table 16) is also difficult to reconcile with the assumption of an initial non-bonded electron-transfer step. There is unfortunately a considerable ambiguity with respect to the magnitude of the electrostatic work term which makes quantitative estimates difficult. (Is it reasonable to assume the existence of free, even mononegative, let alone hexanegative, ions in acetic acid?) Assuming this electrostatic work term to be 0, the estimated rate constant is ca. 10l5times smaller than the observed one, whereas the estimated one for Z , Z , - 1 = -6 [see (46)1 gives an estimated value ca. lo4 times larger than the observed one. We deem the former possibility closer to physical reality since equilibrium constants for ionization of, e.g. alkali metal acetates in HOAc are generally very small (Martin, 1962) and hence an electron-transfer step is not feasible. Instead, hydrogen-atom transfer from the @carbon atom to one of the oxygens of the tungstate cage (a “synchronous proton-electron transfer”) was postulated, in line with the observation of a large k,/k, of ca. 6 (Eberson and Wistrand, 1980). Clearly, to clarify Co(II1) oxidation mechanisms a great deal of further work is needed e.g. looking for organometallic intermediates and elucidating the role of charge-transfer complexes between Co(II1) and aromatics (SzymanskaBuzar and Ziolkowski, 1979).

Manganese( ZZZ) Mn(II1) is formally a weaker oxidant than Co(III), yet it oxidizes aromatic diols faster than Co(II1) in aqueous HClO, (entry no. 6). Rate constants calculated using the Marcus cross relations agree well with the observed ones. For the oxidation of 4-methoxytoluene by Mn(II1) acetate in HOAc, kobswas used to estimate E o for Mn(II1) acetate (entry no. 7) in this particular medium and this value was then used for estimating the log k/AGo’ slope for the data set of entry no. 8, dealing with Mn(II1) acetate oxidation of activated toluenes under similar conditions. The agreement between the calculated and observed slope is far from good, but yet an electron-transfer step is deemed feasible. It would be interesting to have data on even more activated aromatics, since the slower reactions are complicated by a characteristic side-reaction in Mn(II1) oxidations, production of radicals formally obtained by homolysis of a solvent

ELECTRON-TRAN S FER REACTIONS

161

C-H bond, in HOAc the carboxymethyl radical. This type of reaction occurs by rate-determining enolization of the radical-producing species (de Klein, 1977; Southwick, 1970; van der Ploeg et al., 1968). Mn(II1) oxidation of olefins in the allylic position (Gilmore and Mellor, 1971) and saturated hydrocarbons (Jones and Mellor, 1977) is considered to take place by attack on a C-H bond, indeed very likely in view of the high oxidation potentials of such compounds.

Silver(Zl) Ag(I1) is formally one of the strongest oxidants known, and from the cases shown in Table 16 (entries nos. 9-12) it can be seen to possess the characteristics of an electron-transfer reagent.

Cerium( I V ) The Ce(1V) oxidation of alkylaromatic hydrocarbons has been extensively studied in recent years, and entry no. 13 indicates that this reagent should be a well-behaved electron-transfer reagent, in line with other kinetic evidence (Baciocchi et al., 1980, 1981).

Iridium(ZV) Hexachloroiridate ion, IrCli-, is a complex inert to substitution and is known to undergo outer-sphere electron transfer with other inorganic species (cf. Cecil and Littler, 1968). Some of its reactions have been treated in Tables 12 and 14 and shown to be of the non-bonded electron-transfer type. Its reaction with various alkylmetals has been thoroughly studied, and some results are shown in Table 16 (entries nos. 14 and 15). Except for sterically hindered tetralkyltins the Marcus theory makes incorrect predictions for these reactions, and non-bonded electron transfer does not appear to be feasible.

Thallium(ZZZ) Tl(II1) trifluoroacetate, sometimes with the requirement that boron trifluoride etherate should be present, causes fast dehydrodimerization of many aromatic compounds to give biaryls and/or diphenylmethanes in competition with thallation (McKillop et al., 1980). This system thus seems to be a typical exponent of (96). Table 16, entry no. 16, presents a crude estimate of the possibility of non-bonded electron transfer between Tl(II1) trifluoroacetate and naphthalene, showing that it indeed appears to be feasible. Note however that both observed and estimated rate constants are based upon rather uncertain

162

LENNART EBERSON

assumptions and that more accurate kinetic and thermodynamic data are needed for a correct appraisal. The reaction is of great interest, since it should be suitable for quantitative studies of the factors which determine the outcome of the competitition between electron transfer and metalation (96), if these steps are at all competitive.

Iron( ZZZ) We have already discussed several cases of fast Fe(II1) oxidations which occur by a non-bonded electron-transfer mechanism (Tables 13 and 14). One case of a relatively slow reaction, involving the substitution-inert hexacyanoferrate(II1) ion, is shown in Table 14 (entry no. 17) and clearly demonstrates the electron-transfer oxidizing properties of this species with respect to easily oxidized aliphatic amines. Whether the same mechanism holds for compounds more resistant to oxidation, such as methylnaphthalenes (Andrulis et al., 1966) remains to be seen (the estimated rate constant at 25OC is ca. lo-' M-' s-I ). Generally, hexacyanoferrate(II1) seems to be a good non-bonded electrontransfer reagent (for a review, see Rotermund, 1975).

Copper( ZZZ) Cu(II1) peptide complexes have been extensively studied by Margerum and co-workers (for references to this work, see Rybka et al., 1980), and their redox properties with respect to both inorganic and organic species have been elucidated. A remarkable property is the ability of Cu(II1) to promote the hydrolysis of fluoro- and chlorobenzene in TFA (in competition with trifluoroacetoxylation of free ring positions) with a low concentration of water present (Eberson and Jonsson, 1980). It was suggested that this reaction might be initiated by an electron-transfer step between Cu(II1) and the halogenobenzene [the S,,2 mechanism: see (29)-(32)l. This step (Table 16, entry no. 18) does not however seem feasible, unless one is prepared to accept a considerably higher value of E O , ca. 1.8 V, for the Cu(III)/Cu(II) ~ o u p l e At . ~ present, such a value is too far out of the range expected for a Cu(II1) peptide-type complex, with reservations for the general ability of TFA to promote oxidation.

Lead(ZV) Pb(1V) oxidations mostly seem to proceed via aryllead intermediates, but it has been suggested that a non-bonded electron-transfer mechanism might operate in TFA (Norman et al., 1973) where methyl-substituted benzenoid compounds The value for CU(III)~,JCU(II)~~ is given as > 1.8 V (Latimer, 1952)

E LECTRO N-TRA N S F E R R EACTl 0N S

163

are converted to biaryls and diphenylmethanes (see also McKillop et al., 1980). This electron-transfer step is certainly feasible (entry no. 19 of Table 16), although it should be noted that much the same uncertainty pertains to this judgement as for the Tl(II1) reaction. Since biaryls can be made in high yields by reacting preformed aryllead(1V) tricarboxylates with aromatic substrates in TFA (Bell et al., 1974a,b), more work is needed to distinguish between the possible mechanisms. Like Tl(III), Pb(IV) ought to be a good candidate for a quantitative study of the problem posed by (96).

Cobaft(1) We now enter the field of metal ion reductions, where Co(1) reduction of alkyl halides (entries nos. 20 and 21 of Table 15) raises several important and difficult problems. Alkyl halides are difficult to reduce electrochemically (at -2 V or lower), but their E o values (Table 8), estimated for reaction (loo), are considerably higher, around -0.75 V for the methyl halides. Thus alkyl halide reductions should be classified as electrochemically irreversible just as, e.g., the tetralkylmetals discussed before. It is, however, to be noted that E o for (100) refers to a final system where the C-X bond has been broken: what we actually want to know is the E o of reaction (101).

The problem of the stability (or, rather, instability) of alkyl halide anions (for a discussion, see Kochi, 1978) has not yet been settled experimentally, but ab initio calculations (Canadell et al., 1980) on the C-CI bond cleavage of hydrated (CH,Cl)-' indicate that there is a barrier to dissociation of < 16 kcal mol-' and that the energy difference between (CH,CI)-' and CH; + C1- is very small. In the transition state the C-C1 bond is stretched considerably, from 2.05 to ca. 2.5 A. In terms of Marcus theory this amounts to a large for the self-exchange reaction, similar to those of self-exchange reactions for aryl halides (Table 12). The calculation also justifies the use of E o values for (100) in estimating rate constants. For entry no. 21 of Table 16 we used II for Co(II)/Co(I) = 5 and 10 kcal mol-I and II for CH,CI/(CH,Cl)-' = 60 and 80 kcal mol-' in order to estimate the possible range of non-bonded electron-transfer rate constants. This almost coincides with the range of experimentally determined rate constants. Thus, supernucleophilicity (for a review, see Schrauzer, 1976; see also Pearson and Figdore, 1980) might well reflect the reducing properties of the Co(1) species; much the same can be said about the reduction of alkyl halides by Cr(I1) (entry

164

LENNART EBERSON

no. 22 of Tables 5 and 16) and possibly Fe(I1) porphyrins (Wade and Castro, 1973) and V(1I) (Cooper, 1973; Olah, 1980) as well.

ORGANIC REDOX REAGENTS

This class of reagents includes many cases of possibly ambiguous chemical behaviour in the sense of (96), and it is often not even recognized that non-bonded electron-transfer mechanisms can be viable alternatives to conventional ones. As we shall see, it is always necessary to be watchful for electron-transfer steps when one of the components contains electronwithdrawing groups (like C=O, C=N, N=N, halogen, NO,, cationic centers, etc.) and the other one electron-repelling ones (e.g., alkyl, amino, alkoxy and anionic centers). Table 17 lists some 30 reactions of this type for which non-bonded electron transfer mechanisms have been discussed at one time or another. As noted before, good values of the pertinent equilibrium constants are not always accessible, so that we again have to accept a good deal of guess-work on this point. Entries nos. 1 and 2 deal with a very common type of oxidant in organic chemistry, the so-called high-potential quinones (for a review, see Becker, 1974) which are normally considered to act as hydride-transfer reagents. Entry no. 1 is, however, unique in the sense that all substrates contain aromatic C-H bonds only, the strength of which precludes the operation of a hydride-transfer mechanism. Consequently, we see almost ideal electron-transfer behaviour, provided that E o(DDQH+/DDQH') in TFA is set equal to 0.87 V. This value is entirely in line with those reported for other media (Becker, 1974). As we go to entry no. 2, where the substrate is difficult to oxidize and has at least one weak C-H bond, electron transfer is not feasible and hydride transfer takes place. The same holds for DDQ oxidation of substituted toluenes (Eberson et al., 1979). The next three entries (3-5) of Table 17 concern highly cyanated unsaturated compounds with weakly oxidizing properties, in fact so weak that only easily oxidizable compounds can undergo electron transfer. The same conclusion applies to acyl peroxides which are weak oxidants, seemingly not capable of undergoing non-bonded electron transfer from, e.g., aromatic compounds (entries nos. 9 and 10). Schuster (1979a) has discussed this situation in detail, and concluded that concerted 0-0 bond cleavage/electron transfer might take place instead. However, it would appear that this possibility is equivalent to assuming a very large A value for the (RCOO),/[(RCOO);'I reaction (in fact a value so large that it implies almost complete breaking of the 0-0 bond in the transition state) and then one is back at the Marcus treatment. Why should it not work in such a situation?

TABLE 17 Marcus analysis of possible non-bonded electron transfer reactions between organic species

Reaction no.

Reactiona

LPl

kcal mol-’

Ll,El

kcal mol-I

k0bPl M-’s-I

rn r rn

0 -I

k,,,P/ M-I s-l

Slope’(calcd) mol kcal-’

Comment8 on electron transfer step Ref!

a

:

0

a

v)

-n

1

2

3 4 5

6 7

8 9 10 11

2,3-Dichloro-5,6-dicyanobenzoquinone 10 (0.87’)+ aromatic hydrocarbons in TFA Tetrachlorobenzoquinone (0.23)+ 1-benzyl-1,4-dihydronicotinamidein acetonitrile 7,7,8,8-Tetracyanoquinodimethane (0.11) + mesitylene at 165OC 7,7,8,8-Tetracyanoquinodimethane (0.11,0.36) + benzoate ion” in acetone Tetracyanoethylene (0.46)+ alkyltins 33 Benzoyl peroxide (0.Is) + N,Ndimethylaniline in toluene at 35OC Benzoyl peroxide (0.Is) + dimethyl sulfide in carbon tetrachloride Benzoyl peroxide (0.1’) + dibenzenesulfenimide (0.54.8”)in benzene at 35°C Diphenoyl peroxide (O.Iy)+ aromatic >80 compounds in dichloromethane Phthaloyl peroxide (O.ly)+ aromatic >80 compounds in benzonitrile Triphenylmethyl cation (0.45dd)+ perylene and tetracene in T F A/dichloromethane

12 j

6.9 x 103k

4 x 103

-0.83 (-0.85)

F

I

rri R

a

m

1.9 x lo3

NF

-10-3

m

> o 2

0 Z

-10-4

-

10-4

10-39 1.1 x 10-3

1 x 10-2

< 10-32

- 10-2-10-6 -10-8

-0.20 (-0.56)

8x
NF

n

F

P

NF F

r t

NF

U

F

X

6x

2-1 x 10-3

25

1.45‘

1.2 x 10-6

-0.21 (-0.73)

NF

nu

25

5Ibb

4 x 10-8

-0.37 (-0.88)

NF

CC

F

ee

1 x 10-4 2 x 10-2

r n

2

a

ul

TABLE17 (continued)

Reaction no. 12 I3 14 15 16 17

18 19 20 21

Reaction"

kcal mol-'

L1,'l

kcal mol-I

Tropylium ion (0.06dd*ll)+ N-methylcarbazole in acetonitrile Tropylium ion (0.06ddtf/) +

>10-4

N,N,N',N'-tetramethylphenylenediamine in

acetonitrile Tris-(4-bromophenyl)aminiumion (1.30"") + pelargonate iono in C H J N Tris-(2.4-dibrornophenyl)aminiumion (1.74"")+ benzyl octyl ether in CH3CN Phenothiazine radical cations + 26 dopamine in 0.1 M aqueous perchloric acid 4-Methoxybenzenediazonium (0.12) ion + N-methylphenothiazine in acidic acetonitrile Cyclopentadienide (-0.06dd) ion + 1.3-dinitrobenzene in ethanol Alkanide (-2.09 ions + alkyl halides (-0.75) in benzene 1 -Acetonyl-2,4,6-trinitrocyclohexadienide ion (1.07") + tropylium ion (0.06dd)in water Benzenethiolate ion (-0.85"") + butyl nosylate (-0.6 1) and bromide (-0.74) in 87% ethanol/water

Commentg on electron Slopef(ca1cd) transfer mol kcal-' step Ref.*

2x

NF

io-i8

fast

1.6 x 1 0 7

F

-

103

2 x 102

F

ii

- 10-2

2 x 102

F

ii

F

11

F

nn

-0.41 (-0.44)

1Zkk

3 x 10-3

2 x 10-3""

r-

PP

uu

5

m

i n

a

v)

10-2-10-3; 2 x 10-2

5.5 x lo3: 3 x 102: 7 x lO-'OXX

B

0

.. vv

Z

22

23 24 25 26 27 28 29 30 31

-

Benzenethiolate ion (-0.85"") + 4-chloronitrobenzene (-0.76) in D M F I-Nitroalkanide (0.6-0.9cc') ions + 4-nitrobenzyl chloride (-0.25') at O°C in DMF t-Butoxide ion (1.0') + 4-nitrobenzyl chloride (-0.25') in t-butyl alcohol Triphenylmethanide ion (-0.88dd) + triphenylmethyl chloride (0.0') in T H F Succinimide anion + N-bromosuccinimide in acetonitrile Alkyl iodidefl(-O.77) + radical anions in T H F Alkyl bromide@ (-0.74) + radical anions in T H F Alkyl chlorides"' (-0.77) + radical anions in T H F Hexyl fluoride (< -3.1°") + [naphthalene]-' in DME Cyclopentyl bromide (-0.74) + Ibenzophenonel-' in T H F

relatively fastaaR 2.3 x Relatively fast fast

B

bbb

3x

N F (?)

eee

7 x 10-'lf/l

NF(?)

ggg

10'0

F

hhh

<10-2

F

iii

6 x lo4

8x 70

38

1.2 x 106"k

0 -I

m 9

z v)

-n rn

F(?)

111

a a

0

38

0.58"""

5 x 108

-0.28 (0.0)

NF

Ill

>80

38

0.13"""

2 x 10'0

-0.30 (0.0)

NF

Ill

F 5

0

z

v)

2 x 10-4

-10-4

NF

PPP

1 x 10-4

6 x lo8

NF

444

Estimated from the Marcus plot

'Estimated from I values of the self-exchange reactions involved

=

1 M-'

'Experimental slope is given first; the calculated one (within parentheses) is based on the Marcus parabola, approximated as a straight line in the AGO' region involved F = feasible; N F = not feasible; B = borderline case (i.e. not possible to decide) References are sometimes given both to data sources and to pertinent discussions of the problem of electron transfer vs. other types of mechanism Estimated value; see text

'

f--I

-0.28 (-0.24)

>80

Experimental value, in appropriate cases corrected for diffusion according to (67). with k , / k - ,

a 0

2 x 10'0

'A number given in parentheses refers to the E D (or sometimes E1,Jvalues vs. N H E for the corresponding redox couple

' From the Marcus cross relations (62) and (63)

rn r rn

TABLE17 (continued) Table 6 For perylene 'Sep et a/.. 1979 Martens et a/., 1978 Yamasaki et al., 1975; Inagaki et al., 1975 " See Table 8; 1 was taken to be 40 kcal rno1-l p Farcasiu and Russell, 1976 For tetraethyltin Fukuzumi et a/., 1980; see also Eaton, 1980a,b Values between 0.0 and 0.2 V have been given (Kuta and Quackenbush, 1960; Willits eta/., 1952); 1 was taken to be 40 kcal rno1-l ' Graham and Mesrobian, 1963; Horner and Schwenk, 1950 Pryor and Brickley, 1972 " This value is not known, but an estimate based on E l , , for similar compounds indicates that it should be in the range of 0.5 to 0.8 V Church and Pryor, 1980; cf. Pryor and Hendrickson, 1975 This is not known but is taken to be the same as that of benzoyl peroxide: 1 was set equal to 40 kcal mol-I For perylene Koo and Schuster, 1978 bb For tetracene cc Zupancic et a/., 1980; see also Schuster, 1979b dd Wasielewski and Breslow, 1976; Jaun et al., 1980 '* Dauben and Wilson, 1968 "See also Ahlberg and Parker, 1980 RR Ledwith and Sambhi, 1965 hh Schmidt and Steckhan, 1980 l i Schmidt and Steckhan, 1978 Schmidt and Steckhan, 1979 k k Based on 1 for [phenothiazine]+'/phenothiazine = 5.4 kcal mol-I and for [dopamineHl+/ldopamineH]' = 18 kcal mol-' (Tables 7 and 14) "Gasco and Carlotti, 1979 mm See Table 7: for ArN,+/ArN; A . was set equal to 10 kcal mol-' "" Bisson el al., 1978 O0 for C,H;/C,H; was set equal to 10 kcal mol-I; see also Table 7

r

m

z z

> a 4

rn W

rn

n

ffl

0

z

rn

Russell ef al., 1964 99 Taken to be equal to that of t-C,Hb/t-C,H; in 1,2-dimethoxyethane (Breslow and Grant, 1977) l r Due to the high exergonicity of this reaction the magnitude of the 1 values plays no role in determining k,,,, Is See, e.g. Ward ef al., 1969; Lepley and Landau, 1969; Russell and Lamson, 1969 " In acetone; Sosonkin and Kolb, 1974 "" Kalinkin ef al., 1973 "" Dessy ef al., 1966 xx The first value refers to E o (RBr/R' + Br-) = 4 . 7 4 V and the latter to -1.9 V yy Bank and Noyd, 1973; Noyd, 1972 According to esr experiments bbb Sosonkin ef al., 1975 ccc Schafer, 1969 ddd I for I-nitroalkanide ions and 4-nitrobenzyl chloride were taken to be 20 kcal mol-' eee Kerber el al., 1965; Kornblum, 1975 m L for t-BuO- and 4-nitrobenzyl chloride were taken to be 40 and 20 kcal mol-', respectively Bethell and Bird, 1977 hhh Zieger et al., 1973 iii Ross et al., 1982 M Composite of rate constants of various alkyl halides kkk For butyl iodide + [pyrenel-' For a summary of kinetic data, see Bank and Juckett, 1976; Garst, 1971 "-For hexyl bromide + [perylenel-' """ For hexyl chloride + lanthracenel-' Oo0 Assumed value, see text ppp Garst and Barton, 1974 9~ Barber and Whitesides, 1980 PP

r

rn r)

--I

a

0

f--I a D Z

v)

n

rn

a a m D

c)

2

0

z

v)

170

L E N N A R T EBERSON

Carbonium ions, radical cations and diazonium ions are oxidants of widely differing strength, and entries nos. 11-17, except no. 12, show the feasibility of a number of electron-transfer reactions involving such species. In most reactions involving organic cations the possibility of competition according to (96) always exists (Eberson et al., 1978a,b; Eberson and Nyberg, 1978; Bard et al., 1976) and rules for distinguishing between these pathways are not easily discernible at the present state of knowledge. Carbanions and other even-electron organic anions act as reductants toward a wide variety of species that are so weak as oxidants that they normally are not thought of as such. A classical study by Russell et al. (1964) delineated the enormous scope of this at that time rather diffuse area of chemistry (Russell, 1978) and has since then guided much work and thought, e.g. in connection with the development of the S,,1 mechanism. Many of the cases studied by Russell et al. (1964) can now be analyzed quantitatively, as for example entry no. 18 of Table 17 shows. Entry no. 20, oxidation of a Meisenheimer complex by tropylium ion in aqueous solution, is analogous to a large number of similar electron-transfer oxidations (Kalinkin et al., 1973) and all the experimental evidence points in the direction of a non-bonded electron-transfer mechanism. The discrepancy between kcalcand kohsmay be ascribed to too low a value of E o for C,HT/C,H; (the value given is for the solvent 30% HMPA/THF). Entry no. 20 is furthermore representative of a large number of what are formally nucleophilic substitutions of hydrogen in aromatic systems (for a review, see Chupakhin and Postovskii, 1976). Since hydrogen is very unlikely to leave as hydride ion in such situations, most if not all of these reactions must be examples of oxidative substitutions, offering a rich variety of objects for future studies of non-bonded electron transfer. The generality of electron-transfer reduction by carbanions and other anionic species has been amply demonstrated. Apart from halide reductions, to be discussed in more detail below, one can mention, e.g., reduction of & m a t u r a t e d ketones by trimethylsilyl anion (Russell et al., 1979), of benzophenone by di-isopropylamide ion (Scott et al., 1978), of flavine by fluorenyl anions (Novak and Bruice, 1977; Bruice 1980), of model flavin I0-(2,6-dimethylphenyl)isoalloxazine by the anion of methyl 2-methoxy2-phenylacetate (Novak and Bruice, 1980), of aromatic nitro compounds by fluorenyl anions (Guthrie et al., 1976). of peroxides by organolithium and Grignard reagents (Nugent et al., 1974), of ketones by Grignard reagents (for recent studies with leading references, see Holm and Crossland, 1979; Ashby and Wiesemann, 19781, and addition of lithium organocuprates to rxpunsaturated carbonyl compounds (House, 1976). An interesting case of a catalyzed electron-transfer process, reduction of fluorenone by butyllithium in the presence of a ferredoxine model compound (an iron-sulfur cluster) was recently described (Inoue et al., 1977); the catalyst presumably serves to

E LECTR 0 N -T RAN S FE R R EACTlO N S

171

transfer electrons from BuLi to the ketone, thus suppressing the normal addition reactions that otherwise predominates. Entry no. 19 of Table 16 introduces one of the most important and perplexing problems of organic electron-transfer chemistry, namely the reaction between alkyl halides and carbanions or other organic anions (0-,S-, metal-centered). We have already discussed three cases of halide reductions in connection with metallic redox reagents (entries nos. 20-22 of Table 16) and found them compatible with Marcus theory, provided that the transition state was described as in (102) with the C-X bond stretched to the point of almost being broken. The latter requirement is manifested in a high A value for

+ RCH,X = [Co---L RCH,---X * Co---L RCH; X-1* (102) RCH,X/RCH,X-' self-exchange (60-80 kcal mol-I) and an E o pertaining to (loo), and not (101). Thus, calculated E o values of methyl halides (Hush, Co-L

1957) are around -0.75 V, far above experimental El,, around or below -1.8 V. This behavior would of course be expected for an electrochemically irreversible process, as alkyl halide reduction indeed is found to be experimentally (Mann and Barnes, 1970), and hence the above assumptions are self-consistent. In the following discussion, we shall use E o values for reaction (100) for alkyl and aralkyl halides, with suitable corrections for the formation of resonance-stabilized radicals like benzyl and 4-nitrobenzyl. With an E o value of -0.75 V, entry no. 19 of Table 17, reaction between alkyl halides and alkyllithium compounds, represents a strongly exergonic electron-transfer reaction which is expected to proceed at a diffusion-controlled tate. Experimental rate constants are not available, but such reactions are qualitatively known to be very fast. As we proceed to entry no. 21, two model cases of the nucleophilic displacement mechanism, it can first be noted that the nosylate/[nosylatel- ' couple is electrochemically reversible: the radical anion can be generated cathodically and is easily detected by esr spectroscopy (Maki and Geske, 196 1). Hence its E O = -0.6 1 V is a reasonably accurate value. E O (PhS'/PhS-) is known with considerably less accuracy since it refers to an electrochemically irreversible process (Dessy et al., 1966). The calculated rate constant is therefore subject to considerable uncertainty and it cannot at present be decided whether the Marcus theory is compatible with this type of electron-transfer step. In the absence of quantitative experimental data, the same applies to entry no. 22 of Table 17. For the PhS-/BuBr reaction we again suffer from the inaccuracy of E o (PhS'/PhS-); what can be concluded is that for an electron-transfer step to be feasible the higher E o value (-0.74 V) should be the preferred one. The reality of an electron-transfer mechanism has certainly been strongly disputed, however (Kornblum, 1975). Entry no. 23 of Table 17 represents an electron-transfer step typical of the S,,1 mechanism. Again we are hampered by the lack of accurate E o values;

172

LENNART EBERSON

the reported E, for reduction of 4-nitrobenzyl chloride is -0.73 V (Lawless et al., 1969) which is far too low as an approximate E o value compared with E o (CH,Cl/CH; + el-),-0.77 V (Table 8). Instead, it is appropriate to correct for the resonance stabilization of the 4-nitrobenzyl radical on the right-hand side of (98), and this results in the estimate of -0.25 V of entry no. 23 of Table 17 (and likewise the E" of 0.0 V for triphenylmethyl chloride in entry no. 25). Even so, the assumed E o values of 1-nitroalkanide ions are too uncertain to allow us to decide about the feasibility of the electron-transfer step on theoretical grounds. The same conclusion applies to entry no. 24 where E o (t-BuO'/t-BuO-) is a very crude estimate. Entry no. 25, dealing with triphenylmethanide ion as a reductant, with an accurate value of E O , is exergonic even if we allow for an (improbably low) E o of triphenylmethyl chloride at -0.9 V, and hence the feasibility of this electron-transfer step can hardly be doubted. Entry no. 26, reaction between succinimide anion (S-) and Nbromosuccinimide (SBr) to produce eventually succinimide and bromide ion, is most probably an electron-transfer step. The calculated rate constant represents a maximum value and could, depending on certain factors influencing E o (S./S-), be up to lo5times smaller (for a discussion, see Ross et al., 1982). The last five entries (nos. 27-31) of Table 17, dealing with the seemingly well-established electron-transfer reduction of alkyl halides by radical anions of high reducing power (Garst, 1971, 1973) present certain anomalous features, in that, starting from the same assumptions as before, they do not conform to Marcus theory. With E o (RX/R' + X-) ardund -0.75 V, all these reactions are predicted to proceed with rates at or close to diffusion control: attempts to accommodate them within the Marcus formalism leads to physically impossible L value^.^ On the other hand, attempts to fit experimental rate constants to theoretical ones by changing E o (already done in Table 17 for entry no. 30) leads to the following E O values : E O (RI/RI- *) = - 1.54 V, E O (RBr/RBr- ') = -1.79 V, and E o (RCl/RCl-') = -2.24 V. The problem with these is that they imply that the cathodic reduction of alkyl halides be classified as an electrochemically reversible process and that alkyl halide anion radicals should have a certain stability. Both conclusions are contradicted by almost all experimental evidence available. 7

Concluding remarks

We have now surveyed the use of Marcus theory for organic processes of many different kinds. With a few notable exceptions, the agreement between 'Unless we have here an actual case of parabolic behaviour in the inverted region (see Section 5).

ELECTRON-TRANSFER REACTIONS

173

theory and experiment is satisfactory, considering the uncertainty of many E O values and the frequent need of pure guesswork on this point. Thus the Marcus theory should be a useful tool in organic chemistry for recognizing electron-transfer steps in reaction mechanisms. To be true, dubious applications exist (at least until further studies have proved differently) and these involve especially those cases where bond lengthening to the point of bond-breaking is required in the transition state (e.g. alkyl halides, acyl peroxides, and perhaps alkanecarboxylates). Here more refined studies will be necessary for a firm decision to be reached about their feasibility. As a starting point for a summary of the effects of structure upon electron-transfer processes, we concentrate again upon (55) which tells us that AG' of such a reaction depends upon A, the bond and solvent reorganization energy parameter, and AGO', the standard free energy of the reaction after the appropriate correction for electrostatic effects. AGO is obtained as the difference between the E o of the two redox couples involved, and we reiterate below the key principles behind the influence of substitutents upon E o values of organic redox couples of the general type A + e- ?;r A-, irrespective of the charge type of A:

Electron-withdrawing substitutents increase E O Electron-repelling substituents decrease Eo In order to show the influence of AEO (EEd- E&) as a function of dG'(0) A/4, we have defined a very slow bimolecular reaction as having a rate constant of M-I ssl (equivalent to a halving of concentrations in ca. 2500 h, starting from components with initial concentrations of 0.1 M). Rate constants of lo-*, and lo2 M-' ssl similarly correspond to halving of concentrations in 25, 0.25, and 2.5 x lop5h, respectively. Figure 16 shows AEo/AG*(O) = A/4 profiles for these four rate constants; these divide the diagram into regions where non-bonded electron transfer is predicted to be relatively fast or faster, and relatively slow or slower. Each curve has a maximum, indicating that any reaction with a given AEO can be made to correspond to an optimal rate constant. The influence of structural and other factors upon the rates of non-bonded electron-transfer reactions can be summarized in the following way : The value of A will be kept small by arranging for good possibilities to delocalize the electron to be transferred, i.e., in conjugated systems (also as ligands to metal centers) which results in smaller changes in local charge on transfer, smaller changes in bond lengths, and better possibilities for electron transfer over a longer distance. Easily polarizable groups (also as ligands) have the same effect. On the contrary, A will be large in systems where charge must be localized on transfer (in for example a single bond, as in the reduction of alkyl halides) and =

LENNART EBERSON

174

4 I

0

FIG. 16

10 AG*(O)/kcal mol-'

I

20

Plots of AEO vs. dG*(O) (= 1/4)for electron-transfer rate constants of 10-6(1), 10-2(3) and 102(4)M-' s-I

in those having groups that are difficult to polarize. Thus, a hydration shell has a deleterious effect on 1 for both organic and inorganic species. Unfortunately, factors which decrease A have a tendency to increase A E O and vice versa, so that fine-tuning of electron-transfer redox properties requires a fair amount of purely empirical work. As nearly always true for organic reactions, we shall perhaps do best by imitating the ways biological electron-transfer systems work (Moore and Williams, 1976)! Acknowledgements

I thank Dr Svante Wold, University of Umei. for stimulating discussions and the Swedish Natural Science Research Council for financial support. I also thank Professors M. Chanon (Marseilles) and V. D. Parker (Trondheim) for giving me access to unpublished results and for their kind criticism of the manuscript.

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