J. Phys. Chem. 1986, 90, 3141-3156 (NH3)J2+,15392-08-2;CO(NH~)~N:+,14403-83-9;CO(NH~)~NO~Z+, 14482-68-9;cis-Co(en),(cha)CI2+,28 121-20-2; cis-Co(en)2(aniline)C12+, 46753-03-1; ci~-Co(en)~(benzylamine)C1~+, 19306-83-3; cis-Co(en),(CN)Cl+, 75364-94-2; ci~-Co(phen),(CN)~+, 22806-53-7; C ~ ( p h e n ) ~ ~ + , 18581-79-8;Co([ 14]aneN4)(NH3)23+, 53176-75-3; Co(Me4[141tetraeneN,)(NH3)2+,36452-45-6;co( [ 14]aneN4)(OH2)2+,46750-08-7; co(Me,[ 14]aneN4)(OH2)2+, 36452-48-9; meso-Co(bzo3[12]hexaeneN3)~+, 47872-01-5; rac-Co(bzo,[ 12]he~aeneN,)~~+, 47872-04-8; [Co(en),-
3747
(NH3)cha]C13,93966-10-0. Supplementary Material Available: Details of parameters used in calculations Of perturbational effects, and the quality of fit of Co(NH~)SX2+-Co(sep)*+reactions data to the correlation parameters (3 pages). Ordering information is given on any current masthead page.
Marcus Theory in Organic Chemistry. Mechanisms of Electron Transfer and Proton Transfer from Aromatics and Their Cation Radicals C.J. Schlesener, C.Amatore,' and J. K. Kochi*+ Chemistry Department, University of Houston, University Park, Houston, Texas 77004 (Received: January 15. 1986; In Final Form: March 18, 1986)
Methylarenes (ArCH3) undergo electron transfer to tris( 1,lO-phenanthroline)iron(III) complexes (FeL33+)to afford the metastable cation radical ArCH3*+.The rigorous analysis of the kinetics allows the second-order rate constant k , for electron transfer to be evaluated together with the rate constant k2 for the subsequent proton transfer from the various cation radicals ArCH3*+to different pyridines. The energetics of electron detachment from these ArCH3 in solution (EAr')and in the gas phase (Ip)are measured by a novel microvoltammetric technique and from their photoelectron spectra, respectively. The applicability of the Marcus theory in the correlation of the electron-transferrates (log k , ) with the driving force for methylarene oxidation (EAI0)and FeL33+reduction (EFeo)is established for the endergonic region, and the dichotomy between activation and diffusional contributions is discussed. The Marcus evaluation of the inner- and outer-sphere reorganization energies accords with theoretical and experimental models of the structure and solvation of ArCH3*+. The Marcus equation also provides a viable free energy relationship for proton transfer from the methylarene cation radicals to widely different pyridine bases. The driving force includes the acidity constants pKaAfor the methylarene cation radical and pKaBfor the pyridine conjugate acid pyH+, together with the work terms wp and w,. The evaluations of the work terms wp and w, with the aid of the Marcus equation are discussed in the context of the transition state for proton transfer. Marcus theory thus provides a unifying basis for electron transfer and proton transfer in a single chemical system.
Introduction Mechanisms in organic chemistry remain in a rather rudimentary state of development insofar as any unifying theory exists to allow the prediction of reaction rates. Heretofore the quantitative means to examine organic reaction mechanisms have largely depended on the use of various types of linear free energy correlations such as the Hammett and B r ~ n s t e drelationships which are limited by the necessity of employing empirical constants.*~~This situation is understandable if one considers that most organic reactions involve inner-sphere processes in which the activated complex is highly constrained! A conceptually more straightforward situation is represented by outer-sphere reactions, of which electron transfer is the simplest form. The development of Marcus theory of outer-sphere electron transfer thus provides the theoretical basis to potentially consider this class of organic reaction mechanisms in a quantitative, predictive way.s,6 Unfortunately the thorough application of Marcus theory to organic systems has been limited.' The problem arises largely from the experimental difficulty of evaluating the standard electrode potentials E o of the usual diamagnetic organic compounds, owing to the metastability of the associated cation and anion radicals. We believe that aromatic systems offer an excellent opportunity to apply Marcus theory to organic chemistry since electron detachment or accession generates aromatic cation and anion radicals of which a wide variety have been identified.* For our purposes, the methylarenes ArCH3 are useful electron donors because they are known to undergo oxidative substitution reactions via the arene cation radical formed by either chemical or electrochemical methods9 In particular, these arenes are subject to oxidative
degradation of the methyl side chain, as in the industrially important cobalt-catalyzed conversion of p-xylene to terephthalic acid.1° The results of numerous chemical and electrochemical studies are compatible with the initial steps which can be outlined
'Dedicated to Rudy Marcus for his seminal contributions to the understanding of reaction dynamics.
1981.
~~~~~~~
(1) Present address: Laboratorie de Chimie, Ecole Normale Superieure, Paris, 75231. (2) Lowry, T. H.; Richardson, K. S.Mechanism and Theory in Organic Chemistry, 2nd ed.; Harper and Row: New York, 1981. (3) (a) Hammett, L. P. Physical Organic Chemistry, 2nd ed.; McGrawHill: New York, 1970. (b) Kosower, E. M . Physical Organic Chemistry;
Wiley: New York, 1968. (4) See, e.g.: Fukuzumi, S.; Wong, C. L.; Kochi, J. K. J . Am. Chem. SOC. 1980, 102, 2928. ( 5 ) Marcus, R. J.; Zwolinski, B. J.; Eyring, H. J . Phys. Chem. 1954, 58, 432. Marcus. R. A. J. Chem. Phvs. 1956. 24.4966. J . Chem. Phvs. 1957. 26, 867; 1965, 43, 679; Discuss. Faraday Soc: 1960; 29, 21. (6) For reviews, see: (a) Sutin, N. In Inorganic Biochemistry; Eichhorn, G. L., Ed.; Elsevier: Amsterdam. 1973, Vol. 2, p 611. (b) Reynold, W. L.; Lumry, R. W. Mechanism of Electron Transfer; Ronald Press: New York, 1965. (c) Cannon, R. D. Electron Transfer Reactions; Butterworths: London, 1980. (7) See: (a) Pelizzetti, E.; Mentasti, E.; Praumauro, E. Inorg. Chem. 1978, 17, 1181. (b) Pelizzetti, E.; Mentasti, E.; Barni, E. J . Chem. SOC.,Perkin Trans. 2 1978,623. (c) Eberson, L. J . Am. Chem. SOC.1983,105,3192. (d) Pelizzetti, E.;Mentasti, E.; Praumauro, E. Ibid. 1978, 620. (e) Ng, F. T.; Henry, P. M. J . Am. Chem. SOC.1976, 98, 3606. (f) Cecil, R.; Littler, J. S., J. Chem. Soc. B 1968,1420; 1970,626,632. See also: Eberson, L. Adv. Phys. Org. Chem. 1982, 18, 29. (8) See,e.g.: (a) Kaiser, E. T.; Kevan, L. Radical Ions; Wiley: New York, 1968. (b) Parker. V. D. J . Am. Chem. SOC.1976, 98, 98. (c) Masnovi, J. M.; Seddon, E. A.; Kochi, J. K. Can. J . Chem. 1984, 62, 2552. (9) For a review, see: (a) Yoshida, K. Electrooxidation in Organic Chemistry; Wiley: New York, 1984. (b) Sheldon, R. A.; Kochi, J. K. Metal-Catalyzed Oxidation of Organic Compounds; Academic: New York, (10) Landau, R.; Saffer, A. Chem. Eng. Prog. 1968, 64, 20.
0022-3654/86/2090-3147$01.50/0 0 1986 American Chemical Society
3'748 The Journal of Physical Chemistry, Vol. 90, No. 16, 1986
Schlesener et al.
in general form as in Scheme 1. SCHEME I
ArCH,
* ArCH3*++ [e]
(1)
* ArCH2' + H +
(2)
ArCH3'+ ArCH,'
-
[e]
+ ArCHzf, etc.
(3)
-
4
In Scheme I [e] represents the redox couple, Le., either the electrode or the reduced oxidant such as C O " ~ Co". Scheme I is a classical example of an ECE process commonly encountered in the electrochemical literature." As such, the degradation of the methyl side chain commences by prior electron transfer in eq 1, followed by the loss of an a-proton from the radical cation ArCH3'+ in eq 2. Thus the mechanism in Scheme I presents the opportunity to apply simultaneously Marcus theory to organic electron transfer as well as to proton transfer in a single system. We describe how a series of tris( 1,lO-phenanthro1ine)iron complexes FeL,3+ FeL32+can be exploited as [e] for the study of initial electron transfer from aromatic hydrocarbons in Scheme I. The outer-sphere iron(II1) oxidants FeL33+are particularly suited for mechanistic studies since they are well-behaved in solution to allow for meaningful kinetics (i.e., they are substitution inert) and their reversible potentials EFeocan be varied systematically by nuclear substitution of the phenanthroline ligand12 (e.g., for X-phen with X = H, 5-C1, and 5-N02,EFeo= 1.09, 1.19, and 1.29 V vs. SCE, re~pectively).'~
-
&
Fe(X-phen)3z+----
Fe(X-~hen)~~+
(4)
Electrochemical methods offer the most direct access to oxidation potentials of methylarenes, and among the readily available techniques, cyclic voltammetry (CV) is the simplest and the most convenient to use, particularly in organic solvents. Unfortunately with the exception of highly condensed polycyclic and very electron-rich systems, the cyclic voltammograms of most aromatic compounds exhibit irreversible behavior at sweep rates < 100 V s-].l4 This is shown by the absence of the cathodic component on the return potential sweep, largely owing to competition from fast followup reactions of the metastable arene cation radicals. However, the recent development of microvoltammetric electrodes has allowed cyclic voltammograms to be recorded at sweep rates exceeding 10000 V s-I.l5 Reversible Oxidation Potentials of Methylarenes
The application of the microvoltammetric technique to methylarenes was carried out in trifluoroacetic acid with gold microelectrodes.I6 The optimum sweep rates to obtain chemically reversible cyclic voltammograms are included in Figure 1, and the values of the reversible potential EA: for the homologous series from toluene to hexamethylbenzene are listed in Table I. ArCH3 ----
ArCH,"
(5)
The table also includes the vertical ionization potentials I,, of the (1 1) Bewick, A.; Edwards, G. J.; Mellor, J. M.; Pons, B. S . J. Chem. Sot., Perkin Trans. 2 1977, 1952. Bewick, A,; Mellor, J. M.; Pons, B. S. Electrochim. Acta 1980, 25, 931. (12) (a) Schilt, A. A. Analytical Applicatiom of IJ0-Phenanthroline and Related Compounds; Pergamon: Oxford, 1969. (b) Dulz, G.; Sutin, N. Inorg. Chem. 1963, 2, 917. Diebler, H.; Sutin, N. J . Phys. Chem. 1964, 68, 174. (c) Wilkins, R. G.; Yelin, R. E. Inorg. Chem. 1968, 7, 2667. (d) Wong, C. L.; Kochi, J. K. J . Am. Chem. SOC.1980, 101, 5593. (13) Schlesener, C. J.; Amatore, C.; Kochi, J. K. J. Am. Chem. SOC.1984, 106, 3567. (14) Meites, L.; Zuman, P. CRC Handbook Series in Organic Electrochemistry; CRC Press: Cleveland, OH, 1981; Vol I and 11. Meites, L.; Zuman, P.; Rupp, E. B. Ibid. Vol. 111-V. (15) For a background review, see: Wightman, R. M. Anal. Chem. 1981, 53, 1125A. ( 1 6) Howell, J. 0.; Goncalves, J. M.; Amatore, C.; Klasinc, L.; Wightman, R. M.; Kochi, J . K. J . Am. Chem. SOC.1984, 106, 3968.
2.
2
I.
2.
I.
.
I.
:
2.
I.
/ j l . I I I I -
,
,:E
V v s Ag/AgC104
Figure 1. Cyclic voltammograms at a gold microelectrode of methylarenes in trifluoroacetic acid at the sweep rates indicated.
t'
E,: V v 5 NHE
'
2'1
'
'
'
I
,
' '
'
'
'h '
I
,
I
'1
2.0
,
,
,
I
1
8.5
8.0 Ip,
eV
Figure 2. Correlation of the reversible oxidation potentials and the vertical ionization potentials of the methylarenes identified in Table 1.
same series of methylarenes from their He( I) photoelectron spectra. The examination of these cyclic voltammograms shows that the values of Eko progressively decrease with increasing numbers of methyl substituentsI8-the difference between hexamethylbenzene and toluene being more than 700 mV. Furthermore, the chemical reversibility of the cyclic voltammograms (as indicated at by the ratios of the cathodic and anodic peak currents i;/i: a given scan rate), generally parallels the magnitude of Eke, being the most reversible for the highly methylated benzenes. The correlation of the reversible oxidation potentials of the methylarenes in solution with the ionization potentials in the gas phase is shown in Figure 2. The line in the graph describes the relationship EA,.'
= 0.711, - 3.67
(6)
when EAr' is given in V vs. the Ag/AgCIO, standard electrode and I , is given in eV. The slope of considerably less than unity indicates that the energetics of the gas-phase ionization are not completely mirrored in the solution oxidation. In particular, the contribution from solvation is implicit in the values of Ek0 whereas it is not in the values of I,. The difference in the free energy (AG,') associated with solvation changes can be expressed as
(17) (a) Kimura, K.; Katsumata, S.; Achiba, Y.; Yamazaki, T.; Iwata, S. Handbook of He(l) Photoelectron Spectra of Fundamental Organic Molecules; Halstead: New York, 1981. (b) Klasinc, L.; Kovac, B.; Gusten, H. Pure Appl. Chem. 1983, 55, 289. (18) When both the anodic and cathodic CV waves are visible as in Figure 1, the standard oxidation potential Eo must lie within the interval: ( E + 30 mV) < Eo < (E; - 30 mV). See: Nicholson, R. S. Anal. Chem. 1665, 37, 1351.
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3749
Marcus Theory in Organic Chemistry TABLE I: Ionization Potentials and Reversible Oxidation Potentials of Methylarenes
I."
ArCH2'+
7.85 (7.83)'
1.20 (1.50)d
7.92
1.33 (1.63)d
8.06
1.41 (1.71)c
8.14
1.40 (1.71)d
8.03
1.41 (1.70)d
8.27
1.47
8.42
1.57
+
AC,") decreases by about 10 kcal mol-' in covering the gamut of aromatic hydrocarbons from hexamethylbenzene to toluene at the extremes.19 Interestingly this trend also parallels the structural changes of increasing size of the arene moiety resulting from polymethylsubstitution. Since size is an important factor in solvation energies, the deviation of the slope in Figure 2 from unity may well represent variations of mainly AG,o.20 Kinetics of Oxidative Substitution of Methylarenes with Iron(II1) Oxidants
When a solution of tris(phenanthroline)iron(III) is mixed with hexamethylbenzene in either trifluoroacetic acid or acetonitrile, there is a color change from blue to red diagnostic of the reduction to iron(II).l2 Side-chain substitution results since pentamethylbenzyl trifluoroacetate and acetamide can be isolated in essentially quantitative yields in CF3COOH and CH3CN, re~pective1y.I~Furthermore in anhydrous acetonitrile containing pyridine, the N-benzylpyridinium salt is obtained with the following stoichiometry: /PY+
(12)
8.40
1.69
8.56
1.72
8.56
1.71
8.44
1.64
8.76
1.93
The kinetics of the oxidative substitution in eq 12 were followed by measuring either the disappearance of FeL33+at 6 5 0 nm (t = 540 M-' cm-I) or the appearance of FeL$+ at 510 nm (e = 1.1 X lo4 M-I cm-' ). In the presence of excess hexamethylbenzene (HMB), the rate varied strongly with the amount of pyridine added. The dependence on pyridine derives from the general mechanism in Scheme I for which the deprotonation step (eq 2) is forced to be undirectional by mass action. Accordingly, the mechanism for iron(II1) reduction is as shown in Scheme 11.
SCHEME I1 ArCH3
From photoelectron spectra in eV. In trifluoroacetic acid containing 7 vol % trifluoroacetic anhydride and 0.1 M tetra-n-butylammonium perchlorate at 25 "C. Potentials in V vs. Ag/AgClO, at a gold microelectrode. E(V vs. Ag/AgClO,) = E(V vs. SCE) - 0.42. Hexamethylbenzene-d18. In acetonitrile vs. SCE.13 e Estimated from the data in ref 13 and 16.
where the subscripts g and s refer to the gas-phase and solvation states. Correspondingly, the standard oxidation potential is EAr" = (1/3)(Acs0
+ (GAr+o)g - (GAro)g) +
+ FeLj3+
ArCH3'+ ArCH2'
+ py
+ FeL33+
k k-1
kl
ArCH3'+ ArCH2'
+ FeL3,+
+ Hpy'
FeL3,++ ArCH2+, etc.
(1 3)
(14)
(1 5)
Since the oxidation of benzyl radicals in eq 15 is rapid,21 the consideration of the steady-state behaviors of [ArCH3'+] and [ArCH,'] in Scheme I1 leads to the rate law for the disappearance of iron(II1) as
(8)
where 3 is the Faraday constant and C i s a constant determined by the particular working electrode and reference electrode. Under the same circumstances, the vertical ionization potential is Ip
= (1/3)i(GAr+*')g - (GAr')gl
(9)
where (GAr+.o)gis the free energy of formation of the arene cation radical in the unrelaxed state in which is has the same nuclear coordinates as those in the neutral arene. The combination of eq I and 8 yields
EA^' = Ip+ (AGP + AGso)/9 + c
(10)
where AG,", the reorganization energy of ArH", represents the Comparison of eq 10 with the difference: (GAr+'& experimental relationship in eq 6 indicates that (AG,' + AG,') cannot be considered as a constant term for the series of arenes under consideration. Instead it varies with Ipor EA,", as given by the combination of eq 6 and 10; Le. AG,' + AC,' = -0.2931, C' (1 1)
+
where C' = (4.1
+ C).
Such a relationship implies that (AG,'
where [Fe(III)lo and [Fe(III)] represents the concentrations of tris(phenanthroline)iron(III) initially and at time t , respectively, and [ArCH310is the concentration of methylarene in >lO-fold excess. The general rate expression in eq 16 thus contains three rate constants which are relevant to this study, namely, k , and k q for (19) The effect is largely due to contributions from the arene cation radicals since solvation energies of the neutral species are small. See: Lofti, M.; Roberts, R. M. G . Tetrahedron 1979, 35, 2137. Abraham, M. H. J . Am. Chem. SOC.1982,104, 2085. (20) (a) For example, consider the evaluation of solvation energies using the Born model: Bockris, J. OM.; Ready, A. K. N. Modern Electrochemistry; Plenum: New York, 1970: Vol. 1, p 56ff. (b) The reorganization energy for benzene is estimated to be only 2.7 kcal mol" [See: Salem, L. The Molecular Orbital Theory in Conjugated Systems; Benjamin: New York, 1966; pp 467-85.1 Thus, AGr is unlikely to be a large factor in affecting the slope. (21) Rollick, K. L.; Kochi, J. K. J . Am. Chem. SOC.1982, 104, 1319.
3750 The Journal of Physical Chemistry, Vol. 90, No. 16, 1986
b.
a.
Schlesener et al. TABLE II: Second-Order Rate Constants k I for Electron Transfer for Methylarenea to Iron(II1) Oxidants" (5-X~hen)~Fe~+~ y-PY' methvlarene X kt Y k, 14 14 (38)" 4-CN 3-c1 15 IHMB) I{' NO2 52 1300
$
iO'[Fe(lll)].
/ [Base]
Figure 3. Dependence of the experimental rate constant k, for the oxidative substitution of (a) hexamethylbenzene and (b) pentamethylbenzene by FeL?+ on the concentration of pyridine ( 0 )and 2,6- lutidine (0). The effect of 0.1 M tetramethylammonium perchlorate is shown in (a).
2,6-Me2
14
13
H
15
2,6-Me2
H
c1
0.28 5.3
0.23
NO2
75
H
0.04
4-CN 3-CI 2,6-Me2 4-CN 3-CI 2,6-Me2 3-c1 4-CN 3-c1
0.0045 0.0041
2,6-Me2
0.0055
4-CN 3-CI 2,6-Me2
0.04 0.06 0.028
0.30 0.33 0.025 0.036 0.026 0.04
-dia
electron transfer and k z for proton transfer. Let us now consider how each of these rate constants can be extracted from the experimental data. A . The electron-transfer rate constant k, is obtained at sufficiently high pyridine concentrations such that k2[py] is fast relative to back electron transfer, k-l [Fe(III)Io. Under these conditions, the rate of iron(II1) disappearance obeys first-order kinetics, i.e.
H
0.058
(PREI
In acetonitrile containing 0.1 M tetraethylammonium or lithium perchlorate at 22 OC. With substituted phenanthroline complexes and substituted and pyridine. With (~hen)~Fe'+ (5-X-~hen)~Fe~+ pyridines Y-py. k , in M-I s-l. "No added salt.
A typical experimental dependence of this rate constant on the iron(II1) and pyridine is shown in Figure 3, in which the intercept yields the rate constant k l directly. The values of k l determined in this way for the oxidation of various methylarenes by several substituted phenanthrolineiron(II1) oxidants are listed in Table 11. Since the electron-transfer rate constant listed for the first entry in the table was subject to a small negative salt effect, all kinetic measurements were carried out at constant ionic strength with either 0.1 M tetraethylammonium or lithium perchlorate. Two criteria were used to evaluate the validity of this measure of the electron-transfer rate constants. First, the value of k, in Table I1 was within experimental error found to be the same for the deuterated methylarenes (compare entries 1 and 4 or 8 or 11). Such a result accords with the mechanism in Scheme I1 since only a small secondary kinetic isotope effect is expected for electron detachment. Indeed the absence of a deuterium isotope effect for electron transfer under these conditions coincides with the results of the photoionization measurements in Table I. Second, the use of substituted pyridine bases allowed the experimental rates to be varied over a wide range. Despite a -3000-fold variation, the evaluated k l was independent of the structural effects of the pyridine bases, as shown in Table 11, column 5 . B. The rate constant kWlfor back electron transfer derives from the measured value of k l . Since the ratio of rate constants represents the equilibrium constant for the electron exchange in eq 13, it is related to the overall free energy change and can be expressed as K- I
where EFeoand E A r ' are the standard oxidation potentials of FeL32+and ArCH3 in eq 4 and 5 , respectively, and 9 is the Faraday constant. This relationship provides the rate constant k-, for back electron transfer listed in Table I11 from the values
TABLE III: Second-Order Rate Constants k-,for Back Electron Transfer from Methylarene Cation Radicals to Iron(I1)" methylarene (5-X-~hen)~Fe~+, X kI! M-l s-' H 1 x 108 1 x 107 5 x 106
IHMBI
I
H
{ {
H :02 H
1 x 108
5 x 108
2 x 108 5 x 107 1
x 109
:02
3 x 109 2 x 108
H
1 x 109
H
1 x 108 1 x 109 4 x 107
{go2 H
2 x 109
In acetonitrile containing 0.1 M tetramethylammonium or lithium perchlorate at 22 OC with (5-X-phen),Fe3+and pyridine. bThe rate constant k-, was evaluated from EAloin acetonitrile (Table I).
of k , in Table I1 together with the reversible potentials E A r ' in Table I and Ea' in eq 4. C. The proton-transfer rate constant k2 can also be obtained from the data of the type illustrated in Figure 3. Thus it follows from eq 18 that the slope represents the ratio of the rate constants k-,/klk2. This together with the relationship in eq 19 yields the value of k2 for the deprotonation of the cation radical ArCH3*+.
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3751
Marcus Theory in Organic Chemistry TABLE I V Kinetic Acidity of Various Methylarew Cation Radicals with Different Substituted Pyridine Basesa
TABLE V: Free Energy Change, Activation Free Energy, and Intrinsic Barrier for Electron Transfer from MethylarenesO methylarene
deprotonation rate (log k2) Y
pKaB 4.2 6.3 7.0 8.0 9.0 9.4 12.3 14.0 14.3 15.0 15.4 11.8
HMB'+ PMB+ DUR" TMB" 2.56 3.42 3.62 3.89 (3.26) 4.87 5.08 5.31 4.36 (3.68) 5.27 5.41 (4.87) 5.68 4.40 5.29 (4.72) 6.13 6.60 (6.18) 6.61 5.69 5.67 5.77 5.64 (5.04) 6.68 7.10 7.34 3.55
2-fluor0 2-chloro 3-cyano 4-cyano 3-chloro 3-flUOrO hydrogen 2-methyl 4-methyl 4-methoxy 2,6-dimethyl 2,6-di-tertbutyl 2,4,6-trimethyl 16.8 5.99
&
PRE"
(5-X-~hen)~Fe'+, AGdb X
I{' NO*
LHMBI
a
H
(DURI
9.30
I
H
13.4
6.61 1
10.7 12.6
7.04
7.521
::::z::;}
14.2 11.9 9.55
6.34 6.92 9.30
AG"
11.2 8.86 6.55
12.4
6.78
16.0 13.7 11.4
13.3
6.31
15.8 13.5 11.2
18.0 14.0 14.0
7.33
7.1
6.6
::;:}
6.8
In acetonitrile containing 0.1 M tetramethylammonium or lithium perchlorate at 22 oC.22 Numbers in the parentheses are the perdeuterated methylarene. k , in M-' s-'.
Energies in kcal mol-'. Experimental uncertainty is *OS. Experimental uncertainty is *0.1. dMarcus eq 25. CAG,,' is not evaluated since AGd > AG'.
For the more reactive methylarenes-pyridine systems, we also developed a slightly modified, alternative procedure for the kinetics analysis which is applicable over a wide range of pyridine concentrations.22 The analysis by multiple linear regression leads directly to the values of the electron-transfer rate constant k , and to the ratio of rate constants k - , / k 2 . As expected, the values of k l are the same as those obtained from eq 18 and are included among those in Table 11. Since the quotient of k - , / k 2 and kl is equivalent to the slope in Figure 2, it also provides for the evaluation of the proton-transfer rate constant k2 with the aid of eq 19. The values of k2 for the deprotonation of hexamethylbenzene cation radical by various pyridine bases are listed in Table IV. It is noteworthy that these deprotonation rate constants range from -4 X lo2 M-I S-I for the weakest base 2-fluoropyridine to more than 9 X lo5 M-l s-I for the strongest base, 2,4,6-trimethylpyridine examined in this system. The same procedure was used to determine values of k2 for the other methylarene cation radicals which are also included in Table IV.
from the overall electron transfer in eq 21 considered in terms of the three successive elementary steps outlined in Scheme III.25
Application of Marcus Theory to Electron-Transfer Rates from Methylarenes The oxidative substitution of arenes offers an unique opportunity to examine the quantitative relationship between the rate and the driving force for electron transfer, since it is one of the few organic systems in which values of both the intrinsic rate constants [k,,k-,] and the free energy changes [ 3 ( E A / for electron transfer have been rigorously established. It is noteworthy that the rate constants k-, for back electron transfer listed in Table 111 fall in the range closely approaching the diffusion-controlled limit of 109-1010M-' s-1.23As such, neither k-, nor k , can be considered to represent only a purely activation process for electron transfer; but they must also include diffusional processes. Let us therefore consider the general case in which the measured rate constant kl for electron transfer takes into account both contributions; i.e. 1 _ki1 -- -k*1 + + -1 exp[Y(E,,O k, kp
- E F e o ) / R T ] (20)
where k* represents the true activation rate constant for electron transfer and k, and k , are the diffusion rate constants for the formation of the precursor complex and the dissociation of the successor complex, r e ~ p e c t i v e l y . ~Such ~ a formulation derives (22) Schlesener, C. J.; Amatore, C.; Kochi, J. K.J. Am. Chem. Soc. 1984, 106,1412. (23) See e.&: Moore, J. W.; Pearson, R. G. Kinetics and Mechanism;
Wiley Interscience: New York, 1981. Cannon, R. D. Electron Transfer Reactions; Butterworths: London, 1980. (24) Cf.: Scandola, F.; Balzani, V.; Schuster, G. B. J. Am. Chem. Soc. 1981, 103, 2519. Andrieux, C. P.; Blocman, C.; Dumas-Bouchiat, J. M.; Saveant, J. M.J. Am. Chem. SOC.1979, 101, 3431.
SCHEME 111
overall: diffusion: activation:
Ar
+ Fel" 2Ar" + Fe" 11 Wr
[Ar, Fe"']
(21)
li WP AGd
e[Ar",
Fe"]
In Scheme 111the diffusion rate constants k, and k , refer to the precursor and successor complexes (see brackets) in steady state, and the free energy change for the activation process in eq 22 is then given by AG; = AGO+ wP- w,. Since the arene is uncharged, we consider the reactant work time w, to be nil. Accordingly the free energy change from the precursor to the successor complex in eq 22 is
AGO' = 3(EAr0 - EFeo) + Wp
(23)
where w, is the work term of the ion pair. The computed values of AG,,' are listed in Table V. The free energy of activation AG* for electron transfer in eq 22 is evaluated from the rate constant by AG* = -RT In ( k * / Z ) - w, (24) where the collision frequency 2 and the adiabaticity coefficient are taken to be 10" M-' s-l and unity, respectively. The values of AG* computed with the aid of eq 20 and 24 are also listed in Table V. The Marcus equation relates the activation free energy AG* to the free energy change AGd in electron-transfer reactions as
in which the intrinsic barrier AGO' represents the activation free energy for electron transfer when the driving force is zero: i.e., AG* = AGO*at As,' = 0. The last column in Table V lists the values of the intrinsic barriers for electron transfer computed from eq 25.26 Since the electron exchange in the tris(phenanthroline)iron(III,II) redox (25) See e.g.: Marcus, R. A. Faraday Discuss. Chem. SOC. 1960,29,129. Marcus, R. A.; Siders, P. In 'Mechanistic Aspects of Inorgranic Reactions; Rorabacher, D. B. Endicott, J. F., Eds.; ACS Symp. Ser. American Chemical Society: Washington, 1982; Chapter 10, pp 235-238. (26) For the computations: (a) The diffusion rate constants k and k, for eq 20 were taken to be 2 X 1O'O and 3 X lo9 M-I s-' re s p e c t i ~ e l y ? ~(b) ? ~The ~ work term w, # 0; and wp # 1.7 kcal mol-' was obtained from an electrostatic model of ArCH;+ and FeL3*+at a distanced' = r,, + rFc= 3.5 + 7.0 = 10.5
A.
3752
Thr Journal of Physical Chemistry, Vol. 90,
11
16. 1986
M a r c u s eqn
Schlesener et al.
Lsy
ki
AG*-~,
A d iav.?
AGd
n G:
A G: (av.~ Figure 4. Fit of the measured rate constants k , for HMB ( O ) ,PMB (O), DER (e).and TMB (a) to the Marcus equation (full line). The dashed curve is the fit to the polynomial espression in eq 26. /
couple is known to be very rapid,2' the variations of AGO*in Table V largely reflect the changes associated with the conversion of the arene to its cation radical. Indeed for a given arene, the value of AGO*is found to be relatively invariant with the nature of the iron(II1) oxidant. A close inspection of the values tabulated in Table V shows no consistent trend in AGO*of any significance. Moreover. a n average estimatc of AGO*taking into account all the redox systems affords AGO*= 6.7 kcal mol-' with a standard deviation of only 0.3 kcal mol-'. which is clearly within the experimental accuracy of the data. The experimental results thus confirm the validity of eq 25 to describe the free energy relationship for electron transfer. This conclusion is graphically illustrated in Figure 4 by the fit of the points to the predicted relationship. [Note the free energy plots are normalized to the intrinsic barrier AGO*.] In order to evaluate the experimental slope (Y of the free energy relationship, the data points in Figure 4 were fitted to the polynomial expansion in eq 26. The form of this polynomial is dictated
(26) by the boundary conditions that at the isergonic point of AGo/ = 0, the activation free energy is AG* = AGO*+ w, and the slope is dAG*/dAGo/ = 0.5, both of which are inherent to the symmetry about this point in the model considered here. The coefficients obtained from a polynomial regression analysis2*of the data in Table V from the Marcus equation was a = 0.0626 ( u = 0.051) when the polynomial was truncated after the second-order term (i.e,, b = 0) to accord with the quadratic nature of eq 25. The polynomial expression which represents the best fit to the experimental data is nearly coincident (dashed line) with the Marcus line in Figure 4. The experimental variations of the Brmsted N were thus calculated from the optimized polynomial in the range of the extant data and compared with the predictions of the Marcus equation. lndeed the relative large values of the Bransted slopes in the range of CY 0.8 for electron transfer from arenes are clearly associated with driving froces in the endergonic region.29 It is noteworthy that the Marcus relationship is quite effective in predicting the absolute magnitudes of the activation free energy as well as its variation with changes in the driving force for electron transfer. Central to the relationship is its ability to afford a reasonably consistent measure of the intrinsic barrier AGO*for electron transfer.
-
(27) Brunschwig, B. S.; Creutz, C.; Macartney. D. H.; Sham, T.-K.: Sutin, 1982. 74, 113. (28) Bevington. P. R. Data Reduction and Error Ana1,vsis for the Physical Sciences; McGraw-Hill: New York, 1969; pp 137 ff. (29) See: Kiingler. R. J.: Kochi, J. K. J . Am. Chem. SOC.1982, 104, 4186. For highly endergonic reaction.;. k can approach the diffusion-controlled limit of I ( P ' 0 hI i
Figure 5. Functional forms of the free energy relationships for the rate constants (a) k', (b) kd, and (c) k , : (a) theoretical curves drawn according to Marcus eq 25 at various values of AGO'; (b) hypothetical curve drawn according to eq 28; (c) curves drawn with various AGOtaccording to eq 20 and 25. The heavy solid curve represents the fit to the experimental data for HMB ( O ) , PMB (O), DUR (e), and TMB (a) with AGO' = 6.7 kcal mol-'. The dashed line is the free energy relationship drawn according to Marcus eq 25 only, with AGO' = 6.7 kcal mol-'. [1C( and AGO*are given in units of RT In IO.]
Owing to its theoretical significance, we now wish to interpret the magnitude of the intrinsic barrier AGO*for electron transfer from arenes within the context of the Marcus rate theory. An important feature of Marcus theory is that it allows the prediction of the intrinsic barrier in terms of the reorganization energy; i.e., h = 4AG0*. For outer-sphere electron transfer, A can be regarded simply as the sum of two contributions: A = A, X., The inner-sphere reorganization energy Xi includes both reactants and takes into account the variations in their bond lengths, bond angles, and any specific interactions attendant upon electron transfer. Since there are no appreciable differences in the experimental bond lengths and angles in tris(phenanthr0l i n e ) i r ~ n ( I I I , I I )hi , ~can ~ be regarded as negligible for the iron moiety. However, it is known that benzene undergoes a geometric change arising from the Jahn-Teller distortion in the cation radical which is generated upon electron transfer.30 An estimate of Xi for the methylarenes examined in this study can thus be obtained from the value of the stabilization energy of C6H6'+ relative to the hypothetical cation radical in the nuclear configuration of benzene. Such a reorganization energy has been reported by Salem to be -2.7 kcal mol-'.20b The outer-sphere reorganization energy A, arises mainly from the changes in solvation (see eq l l ) , and it is evaluated from Marcus theory as
+
where rArand rFeare the radii of the reactants considered as hard spheres, and d* N (rAr rFe). The index of refraction 7 and the static dielectric constant D of the solvent acetonitrile are 1.344 and 37.5, respectively. Taking rFe = 7 8, for tris(phenanthr0line)iron(III) complexes3' and rAr N 3.5 8, for the benzene derivatives, we calculate A, from eq 27 to be 21 kcal mol-'. The results illustrated in Figure 1 indicate that solvation energies are constant for the methylarene cation radicals examined in this study. The total reorganization energy obtained as the sum of the inner- and outer-sphere contributions can thus be estimated as 24 kcal mol-'. The resulting predicted value of the intrinsic barrier AGO*is 6 kcal mol-', which is in remarkable agreement with the measured value of 6.7 k 0.3 evaluated from eq 25 (vide supra). In order to relate the experimental free energy relationship for
+
N.Faraday Discuss. Chem. Soc.
(30) (a) Nakajima, T.; Toyota, A.; Kataoka, M . J . Am. Chem. SOC.1982, 104, 5610 and references therein. (b) Iwasaki, M.; Toriyama, K.; Nunome, K. J . Chem. SOC.,Chem. Commun. 1983, 320. (31) Dickens, J. E.: Basolo, F.; Neumann, H. M.J . Am. Chem. SOC.1957, 79. 1289.
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3753
Marcus Theory in Organic Chemistry
20
AGd
AGO'
Figure 6. The location of the endergonic region as a function of the intrinsic barrier. The curve is arbitrarily chosen to consist of equal activation ( k ' ) and diffusion ( k d )components. R and P in the reaction diagrams shown in the inset refer to the reactants and products, respectively.
electron transfer to the theoretical relationship developed by Marcus, the diffusion rate constants must be explicitly included, as in eq 20. In particular, for endergonic processes of the magnitude encountered in this study, the diffusion rate constant k, of the product pair can contribute as much as 25% to the measured rate constant k, for electron transfer. Therefore let us consider the general description of the rate constant k l when the driving force AGOis zero to the endergonic limits in terms of contributions from the activation rate constant k* and the diffusion rate constant kd. Figure 5a shows the variation of k* with the driving force AG,' according to Marcus theory (eq 25) for various values of AGO*. Figure 5b represents the corresponding variations of the diffusion rate constant kd obtained from eq 20 when k* >> k, = k,; i.e.
kd-' = k;' [ 1 + exp(AGo/RT)]
(28)
Figure 5c illustrates how the measured rate constant kl (where I l k l = l / k * l / k d )varies with the driving force, the various values of AGO*. To stress the importance of the diffusional contribution in our system, we have represented the kl relationship as the heavy line and the corresponding k* relationship as the dashed line. In each case we employed the average AGO*= 6.7 kcal mol-' from data as deduced from the Marcus equation. The diffusional contribution, represented by the gap between k* and k l , is clearly seen to increase as one proceeds in our system into 7 kcal mol-'. It is therefore endergonic region beyond AG,' necessary to develop some operational criteria to determine when the diffusional contribution must be explicitly taken into account in the rate process for electron transfer. An endergonic system (e.g., as applied in the Hammond postulate) is a thermodynamic concept and is of only limited utility in the context of the rate processes of importance here. Let us therefore refer to the endergonic limits of the kinetics, at which the rates of electron transfer are diffusion controlled. In this context, the endergonic region refers to driving forces at which the measured rate constant k, contains diffusion components ( k , and k,) in addition to the activation component ( k * ) . The driving forces with AG; >> 0 as the only criterion of endergonicity is inadequate, since the family of curves in Figure 5c clearly shows that the approach of k l to the diffusion limits is also strongly dependent on the magnitude of the intrinsic barrier AGO*for the particular system. For example, the endergonic limit is reached at AG,' E 5 kcal mol-' when AGO*= 2 kcal mol-', but the same limit is reached later at 12 kcal mol-' when AGO*is doubled. In fact, Figure 6 illustrates how the magnitude of the intrinsic barrier determines the location of the endergonic region. [The curve represents systems with rate constants calculated from eq 20 to consist of (arbitrarily) equal contributions from diffusion and activation. As the systems are displaced above this line, they are increasingly activation controlled, and those below the line are increasingly dominated by diffusion.] Since the curve in Figure 6 beyond JAG,,'l > 1 kcal mol-' is reasonably straight, we can conclude that the location of the endergonic region varies more or less linearly with the magnitude of (AG{/AG0*), Le., the driving force normalized to the intrinsic barrier. Unfortunately such a
+
-
,
0 k c a l mole'
Figure 7. Discrepancy between the measured ( a l )and the theoretical (a*)Bransted slopes as a function of the driving force for electron transfer. The values of a I were derived from eq 20, and a* values were computed from Marcus eq 25 with AGO*= 6.7 kcal mol-'.
criterion is not easy to apply in practice. Accordingly, let us consider an alternative description of the endergonic limits in terms of rate-limiting diffusional processes k , and k, with a Brernsted slope of 1 (see Figure 5b). The endergonic region is then defined as that in which the Brernsted slope is l.29 In order to apply Brernsted slopes as a quantitative criterion, the dependence of the experimental rate constant k , (which includes diffusion) on the driving force, Le., a In k/aAG{, must be evaluated separately from that involving the activation (theoretical) rate constant k * . The corresponding values of the experimental and theoretical Brernsted slopes a1and a*,respectively, are plotted as a function of the driving force for arene oxidations in Figure 7. The theoretical Brernsted slopes a* were computed from the Marcus eq 25 since it provides a reasonable fit to the experimental data (vide supra). The junction at which the a1and a* curves diverge shows that complete activation control of the electron-transfer rates is observed only within a rather narrow window of the driving force, AG,' E f5 kcal mol-', in the endergonic region. The widening gap beyond this point represents increasing control of the electron-transfer rate by diffusional processes. Since the marked discrepancies between the experimental a1and the theoretical a* characterize the endergonic region, we propose the magnitude of the Brernsted slope to be a useful indicator for rate processes in which diffusion must be explicitly taken into account. At this juncture however we must clearly emphasize that any theoretical argument which relates the magnitude of the Brernsted slope to transition-state structures or diagrams (such as those represented in Figure 6 ) refers specifically to values of a* and not a'. Since only a1is accessible by experiment, it is important to take explicit cognizance of diffusional contributions when the experimental results are r a t i ~ n a l i z e d . This ~ ~ caveat is particularly pertinent to organic systems in which rates of electron transfer are likely to lie in the endergonic region owing to limiting values of the standard redox potentials and reorganization energies.
-
Application of the Marcus Equation to Proton-Transfer Rates from Methylarene Cation Radicals
The extensive set of kinetic data in Table IV for the various methylarene cation radicals ArCH," with different substituted pyridine bases Y-py offers the opportunity to examine the quantitative relationship between the rate and the driving force for proton transfer from a carbon acid; i.e. ArCH3*'
+ Y-py
kl
ArCH,'
+ Y-pyHt
Thus for a particular methylarene cation radical, the activation free energy for proton transfer to various pyridine bases as given by AG* = -RT In ( k 2 / Z )in Table VI follows the monotonic trend shown by the family of curves in Figure 8.33 As in Scheme 111, (32) We are actually faced with a conundrum here, since arguments such as those based on the Hammond postulate are most applicable at the endergonic and exergonic limits where the contribution from activation (AG* or AH*) is minor, and the rate is controlled by diffusion. Furthermore, most kinetic measurements are not carried out at the diffusion limits.
3754 The Journal of Physical Chemistry, Vol. 90, No. 16, 1986
Schlesener et al.
e
TABLE VI: Kinetic Acidity of Methylarene Cation Radicals with Different Pyridine Baseso
-@-
u. V
2-4 2-c1 3-CN 4-CN 3-CI 3-F H 2-Me 4-Me 4-Me0 2,6-(Me)2 2,6-(t-B~), 2,4,6-(Me),
/
v K , ~ log k,b 4.2 6.3 7.0 8.0 9.0 9.6 12.3 14.0 14.3 15.0 15.6 11.8 16.8
2.56 3.62 3.62 3.89 4.36 4.40 5.29 5.69 5.67 5.77 5.66 3.55 5.99
\
AC*' 11.6 10.2 9.96 9.60 8.96 8.90 7.70 7.16 7.20 7.06 7.23 10.1 6.75
"For the data in Table IV. b k 2 in M-'
AG* l - 1O ' 5
/
AG'dlAGn* 1.78 1.59 1.56 1.50 1.60 1.39 1.20 1.12 1.12 1.10 1.13 1.58 1.06 s-I.
10
AG*dlACn* IOP.
AG"
AG*dlAGn* IOP. k,b
log kTb
AG*'
4.87 5.27
8.27 7.73
1.29 1.21
5.08 5.61
7.99 7.56
1.25 1.18
6.13
6.57
1.03
6.60
5.96
6.68
5.83
0.9
7.10
5.26
kqb
AG*'
AGtdlAGn*
5.31 5.68
7.68 7.18
1.20 1.12
0.93
6.61
5.92
0.92
0.82
1.36
6.93
0.77
'In kcal mol-'. dAGo' = 6.4 kcal mol-' for all the methylarenes.
TABLE VII: Marcus Parameters for the Deprotonation of Methylarene Cation Radicals by Pyridine Bases ArCH?" w,,kcal mol-l pKnJA w , , ~kcal mol''
5
/
\
15
6.45
2.0
6.7
5.20
2.0
8.6
4.20
3.8
10.7
B PK,
Figure 8. Relationship of the free energy of activation for proton transfer to the pKae of the pyridine base for H M B (O), PMB ( O ) , DUR (0),and TMB (0).
+
the corrected driving force AGd = AGO- w, wp with AGO = -RT In 10(pKaB- pKaA). The acidity constants pKaAand pKaB refer to the methylarene cation radical ArCH3'+and the pyridine conjugate acid pyH+, re~pectively.~~ In order to collect the work terms, a corrected acidity constant can be defined as pK,.* = pKaA (wp - w , ) / R T In 10, so that AGd = RT In 10(pKatA- pKaB). The application of the Marcus eq 25 to proton transfer requires a knowledge of three unknowns, namely, pKarA,w,,and AGO*.35,36 Let us therefore reformulate it in the form
+
+ B(pKaB)+ C ( P K , ~ ) ~ + AGO* + RT In 10[1 + RT In
AG* = A
+
"Evaluated from the relationship: wp = w, RT In 10(pKarApKaA),where the pKaAvalues are derived from thermochemical calculations (see t e ~ t ) . ~ ? ~ '
I
7
(29)
where A = w, 10(pKalA/ 8AGo*)](pKa,A/2),B = -RT In lo['/, + RT In 10(pKarA/8AGo*)], and C = ( R T In 10)2/(16AGo*). Considered in this way, the curvatures of the plots in Figure 8 are only dependent on the value of the intrinsic barrier AGO*for proton transfer. The treatment of the data in Table IV for hexamethylbenzene cation radical by a quadratic regression analysis affords AGO*= 6.4 kcal mol-] (not including the datum for 2,6-di-tert-butylpyridine). Indeed the similarity of the plots in Figure 8 to the curvature for HMB" (33) 2 is taken as 10" M-I s-I and K = 1. (34) (a) Note many of the values of pKaBin Tables IV and VI refer to the acid dissociation constants of the pyridinium ions determined in acetonitrile solution by: Cauquis, G.; Deronzier, A,; Serve, D.; Vieil, E. J . Electroanal. Chem. Interfacial Electrochem. 1975,60,205. (b) Others were obtained from a correlation of the pKaBvalue in water [Perrin, D. D.; Dempsey, B.; Serjeant, E. P. p K , Prediction from Organic Acids and Bases; Chapman and Hall: London, 19811 with that in acetonitrile (vide supra). (c) The value of 2,6di-tert-butylpyridinewas from: Brown, H. C.; Kanner, B. J . Am. Chem. SOC. 1966,88, 986, determined with others in 50% aqueous ethanol, and correlated against those in water. (35) (a) Marcus, R. A. J . Phys. Chem. 1968, 72, 891. (b) Cohen, A. 0.; Marcus, R. A. J . Phys. Chem. 1968, 72, 4249. (c) Marcus, R. A. J . Am. Chem. Soc. 1969, 91, 1224. ( 3 6 ) For the application of the Marcus equation to proton transfer, see: (a) Kreevoy, M. M.; Konasewich, D. E. Adu. Chem. Phys. 1972, 21, 243. (b) Hupe, D. J.; Wu,D. J . Am. Chem. Soc. 1977.99.7653. (c) Kreevoy, M. M.; Oh, S.-W. J. Am. Chem. SOC.1973, 95, 4805. (d) Toullec, J . Adu. Phys. Chem. 1982, 18. 5 .
Figure 9. Unified correlation of the activation free energy and the corrected free energy change for the deprotonation of the cation radicals for
H M B (0),PMB (e),DUR (O), and TMB ( 0 ) .The theoretical variation calculated by the Marcus equation is indicated by the line.
suggests that AGO*is rather constant for the series of methylarene cation radicals in Table VI. The Marcus equation also leads to an evaluation of the acidity constants pKarAfor the various methylarene cation radicals by the introduction of the value for the intrinsic barrier AGO*in the coefficient B, as obtained from the quadratic regression analysis of eq 29. Moreover, the introduction of the values of both AGO* and pKafAin the coefficient A leads to a value for the work term w, = 6.45 kcal mol-' for HMB. These are collected in Table VI1 for the series of methylarene cation radicals examined in this study. Figure 9 shows the fit of the experimental data in Table IV (ordinate) with the parameters in T a b l e VI1 (abscissa) as they are related by the Marcus equation (normalized to the intrinsic
The Journal of Physical Chemistry, Vo1. 90, No. 16, 1986 3755
Marcus Theory in Organic Chemistry TABLE VIII. Deuterium Kinetic Isotope Effects k2(H)/k2(D) for the Deprotonation of Methylarene Cation Radicals by Different Substituted Pyridine Baseso
I.
pY u/)
[ A t D] PGB 8.0
Y
4-cyano 3-chloro hydrogen 2.6-dimethyl
k2(H)/kz(D)
k2(H)l k2(D)
4.4 4.7 3.6 3.9
3.5 2.6
9.0 12.3 15.4
From the data in Table IV.
k
[D. A']
that the magnitudes of the work terms w, and wp in this system are comparable. Under these conditions, the value of AG; could be approximated by 2.3RT[pKaA- pKaB]. As successful as the Marcus equation is in correlating all the rates of proton transfer in Figure 9 it does not yield directly a n independent value for the acidity constant pKaA. In order to evaluate the acidity of methylarene cation radicals, we rely on the thermochemical calculations by Arnold and Nicholas4 which leads to the general relationship: pKaA= -(SEA,' + AGoCH)/RT In 10 constant, where AGOCHis the relevant C-H bond energy in the methylarene cation radical. In the series of cation radicals examined in this study, the variation in AGOCHis minor, and we take pKaA= -(S/RT In 10)EhO constant. An estimate of pKaA = 1 for HMB'+ is obtained from this relationship and the data in Table I, if the acidity constant is taken as -12 for the toluene cation radical, as evaluated by Arnold and N i c h ~ l a s . ~ ~In-~' terestingly, the value compares with pKarA= 2 for HMB" from the Marcus relationship expressed as eq 29.
+
'-1
*t IO A PK,
15
-
B PK,
Figure 10. Deuterium kinetic isotope effect as a function of the driving force for proton transfer from the cation radicals of HMB ( 0 )and DUR (0).
barrier.)37 It is interesting to note the trend in Table VI1 for the value of the work term w, to decrease with the number of methyl substitutents in ArCH3. Furthermore the magnitude of the variation in the work terms, Le., ( w p - w,)/RT In 10, largely overwhelms the variation in the acidity constant pKaA. As a result, the corrected acidity constant pK8tAactually follows a trend opposite to that of acidity constant pKaA (vide infra). The plot in Figure 9 shows a Bransted slope varying between a = 0.30 and 0.15 for the proton transfer from various methylarene cation radicals to the different pyridine bases. Slopes of such magnitudes correspond to an overall free energy change lying in the exergonic region.29 This is in agreement with the values of pKaTAin Table VII. Indeed the kinetics result of the deuterium isotope effect in Table VI11 lead to the same conclusion. Thus Figure 10 shows the deuterium kinetic isotope effect for proton transfer to decrease with an increasing driving force. We interpret the magnitude of the Bransted slope and the trend in the kinetic isotope effect to reflect an early transition state in which proton transfer has not proceeded beyond the symmetrical situation. Such a qualitative description of methylarenes as acids accords with the relatively low sensitivity of proton-transfer rates in Figure 9 to the steric effects of the pyridine bases. Thus a pair of ortho or 2,6-di-tert-butyl substituents as in 2,6-di-tert-butylpyridineare required to significantly perturb the Bransted correlations of various pyridine bases (see Figure 8). Furthermore the analysis from the Marcus approach reveals the high degree to which the work terms w, and wpcontribute to the rates of proton transfer in comparison with electron transfer in which their neglect does not materially affect the correlation (see Figure 4). W e hasten to add however that the theoretical basis for w, and wp in proton transfer is complex. Indeed the proton transfer between methylarene cation radicals and pyridine bases represents a rather unusual situation insofar as acid-base reactions are concerned. Thus the reactant pair is strikingly akin to the product pair, especially if viewed in terms of charge-transfer interactions shown in eq 30. Thus proton transfer within the encounter complex is accompanied by an interchange of the ?r-donor (D) and s-acceptor (A) capacities of the methylarene and pyridine moieties on conversion to the successor complex in eq 30.39 As such, it is possible ~~
~
~
~~
~~
~~~
(37) A statistical correction for the number of available protons is not included.38 (38) (a) Bell, R. P. The Proton in Chemistry, 2nd ed.; Cornel1 University Press: Ithaca, NY 1973. (b) Caldin, E., Gold, V., Eds. Proton Transfer Reactions; Chapman and Hall: London, 1975.
+
Summary and Conclusions Transient electrochemical techniques employing microvoltammetric gold electrodes establish the reversible oxidation potentials EA,' of a series of methylarenes ArCH,. This measure of the energetics of electron detachment in solution is compared directly with the ionization potentials Zpin the gas phase from the photoelectron spectra of the same series of methylarenes. The difference is analyzed in terms of the solvation of the methylarene cation radicals. The corresponding rates of chemical oxidation of the methylarenes by iron(II1) complexes FeL33+in solution are regulated by the concentrations of added pyridine bases. This control allows the complete analysis of the kinetics for iron(II1) disappearance according to the oxidation mechanism in Scheme 11. Experimentally reliable values of the rate constant k , for the formation of methylarene cation radicals and the rate constant k2 for their deprotonation can thus be evaluated for a variety of pyridine bases. Electron transfer from methylarenes to iron(II1) is unique among organic oxidations in that the free energy change AGOfor the metastable redox equilibrium in eq 13 can be quantitatively evaluated directly from independent measurements of the standard oxidation potentials Eho and EFcofor the methylarenes and iron complexes, respectively. This knowledge allows the free energy relationship between the rate of electron transfer (log k , ) and the driving force 3(EAr0- EFeo)to be established experimentally. Marcus theory is effective in the prediction of the absolute magnitudes of the activation free energy as well as its variation (a)with change in the driving force for electron transfer according to eq 25. Central to the free energy correlation is its ability to provide a reasonably consistent measure of the intrinsic barrier AGO' for electron transfer. Inner-sphere and outer-sphere components of the latter accord with the theoretical calculations of the Jahn-Teller distortion of arene cation radicals as well as with the experimental measures of their solvation, respectively. Since the rates of electron transfer lie in the limits of the endergonic region of the driving force, specific considerations must be paid to the diffusional contribution. Analysis of the Bransted slopes (39) Arene cation radicals ArH'* are known to form r-complexes with arenw in the form of dimer cation radicals [ArH];* [See: Edlund, 0.; Kinell, P.-0.; Lund, A.; Shimizu, A. J. Chem. Phys. 1967, 46, 3679. Badger, B.; Brocklehurst, B. Trans. Faraday SOC.1969, 65, 25821. For the structural effects of donor-acceptor complexes between aromatic moieties, see: Foster, R. Organic Charge Transfer Complexes; Academic: New York, 1969. (40) Nicholas, A. M. P.; Arnold, D. R. Can. J. Chem. 1982, 60, 2165. (41) The values of pKaAfor the radicals of PMB, DUR, and TMB are evaluated by this method as -1, -2, and -2, respectively.
J . Phys. Chem. 1986, 90, 3156-3159
3756
(a)provide a useful guide to those rate processes in which diffusion must be included. The rates of proton transfer ( k 2 )from various methylarene cation radicals follow a general Brernsted relationship with the series of substituted pyridine bases included in Figure 8. For the deprotonation of a particular methylarene cation radical by different pyridine bases, the driving force can be expressed in terms of the acidity constant pKaBof the pyridine base (conjugate acid). The Marcus equations reformulated in this manner (eq 29) yields a consistent value of the intrinsic barrier of proton transfer from various ArCH," to different pyridines. The unified correlation of activation free energies for proton transfer in Figure 9 provides the work terms w,and wp. The magnitudes of these (inner-sphere) work terms are such as to strongly influence the evaluation of the acidity constant pKaAof the methylarene cation radical-a situation which strongly contrasts with that for outer-sphere electron transfer from uncharged ArCH,. The magnitude of the deuterium kinetic isotope effect can be interpreted in terms of a transition state in which proton transfer from the methylarene cation radical
has only progressed partially. The limited hydrogen bonding to the base in the activated complex is supported by the small steric effects of ortho-substituted pyridines. Such an early transition state is consistent with the magnitude of the B r ~ n s t e dslope as interpreted by the Marcus formulation of proton transfer. Acknowledgment. We thank the National Science Foundation and the R. A. Welch Foundation for financial support. Registry NO. Me&,, 87-85-4;Me5C6H,700-12-9; 1,2,3,5-Me&,H~, 527-53-7; 1 ,2,3,4-Me4C,H2, 488-23-3; 1 ,2,4,5-Me4C6H2, 95-93-2; 1,2,4Me3C6H3,95-63-6; 1,2,3-M&,H3,526-73-8; 1,3,5-Me$&,, 108-67-8; 1,3-Me2C6H4, 108-38-3;1,2-Me2C6H4, 95-47-6; I ,4-Me2C&, 106-42-3; PhMe, 108-88-3; (5-H-~hen)~Fe'+, 13479-49-7; (5-C1-phen),Fe3+, 22327-23-7; (5-N02-phen),Fe3+, 22327-24-8;2-fluoropyridine,372-48-5; 2-chloropyridine, 109-09-1 ; 3-cyanopyridine, 100-54-9;4-cyanopyridine, 100-48-1 ; 3-chloropyridine,626-60-8; 3-fluoropyridine,372-47-4;pyridine, 110-86-1; 2-methylpyridine, 109-06-8;4-methylpyridine, 108-89-4; 4-methoxypyridine, 620-08-6; 2,6-dimethylpyridine, 108-48-5; 2,6-ditert-butylpyridine, 585-48-8; 2,4,6-trimethylpyridine, 108-75-8; D2, 7782-39-0.
Application of the Marcus Equation to Methyl Transfers' Edward S . Lewis Department of Chemistry, Rice University, Houston, Texas 77251 (Received: January 15, 1986)
The transfer of methyl between two nucleophiles is used as an example of the application of the Marcus equation to group transfers. The direct measurement of equilibria and identity rates allows prediction of unsymmetrical reaction rates over a wide range, which are in good agreement with experiment. Some of the identity rates, measured to test the equation, contain previously unknown information about the charge distribution in the transition state. The quadratic Marcus term is shown to be negligible (by virtue of the rather high intrinsic barriers for methyl transfer); as a consequence, the effect of the leaving group can be separated from that of the attacking nucleophile, leading to a useful scale of nucleophilic and leaving group character. In some cases the quadratic term may become important, but it is unlikely that an experimental distinction can be made between various nonlinear rate-equilibrium relations which behave the same with equilibrium constants near unity.
Introduction
This paper is concerned with the uses of the Marcus equation by organic chemists. The impact in organic chemistry is as a way of thinking, rather than merely a method to calculate reaction rates. Initially organic chemists did not take much notice of electron-transfer reactions, the origin of the Marcus equation.2 However, electron-transfer processes have since become such a familiar part of organic chemistry that the acronym SET (single electron transfer) is now in accepted use. Nevertheless, electron transfer was considered a narrow area of interest and the Marcus equation was not widely used. The extension of the equation to proton transfers by Marcus3 and other^,^.^ to hydrogen atom transfers (using a somewhat different analytical form) also by M a r c ~ s and , ~ later to methyl transfer by Albery and Kreevoy6 and in the gas phase by Pellerite and Brauman' has brought this approach to the SN2reaction, a center of mechanistic organic chemistry. The essential new addition of the Marcus treatment is the idea of an intrinsic barrier, the average of the two identity barriers, which is considered separately from the thermodynamic driving force. In this way it allowed an understanding of the fact that all proton-transfer rates do not fall on the same Bronsted plot when (1) This paper is Methyl Transfers, 12; paper 11 is ref 24. (2) Marcus, R. A. J . Pfiys. Cfiem.1956, 24,966. Throughout this paper reference is made to the Marcus equation rather than Marcus theory. This is deliberate because the applications covered are remote enough from the original derivations to remove much semblance of theoretical justification; it is used here primarily as a plausible empirical relation. (3) Marcus, R. A. J . Pfiys. Chem. 1968, 72, 891. (4) Kreevoy, M. M.; Oh, S.-W. J . Am. Chem. SOC.1973, 95, 4805 (5) Kresge, A.J. Chem. SOC.Reu. 1974, 2, 475. (6) Albery, W. J.; Kreevoy, M. M. Ado. Phys. Org. Chem. 1978, 16, 87. (7) Pellerite. M. J.; Brauman, J. I. J . Am. Chem. SOC.1980, 102, 5993.
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log k is plotted against log K for the same reaction rather than against pK,, because the intrinsic barriers differ. It also allows an understanding of curvature in Bronsted plots; curvature is an essential feature of the Marcus equation as well as the widely accepted ideas such as the Hammond postulate,8 the variable transition state, and the reactivity-selectivity principle. These curvatures, it must be stated, are more often talked about than seen in unequivocal experimental results.9 The analytical separation of the thermodynamics from some independent purely kinetic factor, now expressible as the intrinsic barrier, is particularly attractive to those aware of the absence of generality of rate-equilibrium relations, while at the same time seeing many of these. The application of this idea is only beginning to find interested users. Methyl Transfer Reactions
The Fit to the Marcus Equation. Methyl-transfer reactions were first considered as an appropriate subject for consideration using the Marcus equation by Albery and Kreevof who assembled data from the literature on a number of reactions of nucleophiles with methyl halides in predominantly aqueous media. Thermodynamic data from several sources were combined with this, the applicability of the Marcus equation was assumed, and a series of identity barriers was fitted. The result was a plausible and internally consistent set of numbers allowing the calculation of a large number of cross reaction barriers. Among the interesting conclusions was a clear understanding of observations such as why some nucleophiles, such as the halides, were practical leaving groups (having relatively low intrinsic barriers), while other quite (8) Hammond, G. S.J . Am. Chem. SOC.1955, 77, 334. (9) Johnson, C. D. Cfiem. Rev. 1975, 75, 755.
0 1986 American Chemical Society
