2152
J . Phys. Chem. 1989, 93, 2152-2157
Solvent and Electrolyte Effects on the Kinetics of Ferrocenlum-Ferrocene Self-Exchange: A Reevaluation Roger M. Nielson, George E. McManis, Lance K. Safford, and Michael J. Weaver* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: July 6, 1988) Rate constants, k,, for ferrocenium-ferrocene self-exchange have been evaluated by using the proton NMR line-broadening technique as a function of added electrolyte in acetonitrile, acetone, nitrobenzene, and methanol. Increasing the ionic strength over the range ca. 2 X lo4 -0.25 M by adding tetraethylammonium hexafluorophosphate, tetrafluoroborate, or perchlorate salts yielded monotonic decreases in kex. These rate variations are relatively modest, typically 30% or less, and are substantially smaller than are anticipated on the basis of thermodynamic ion-pairing effects. Similar results were also obtained for cobaltocenium-cobaltocene and decamethyl(ferrocenium-ferrocene) self-exchangeand for the addition of chloride and bromide anions in the latter case. However, the ferrocenium-ferrocene k , values themselves deviate substantially (up to ca. 10-fold), particularly in nitrobenzene, methanol, and also dimethyl sulfoxide, from earlier published values obtained by using the same technique. These disparities are traced to systematic errors in the earlier measurements associated with uncertainties in the paramagnetic line widths. The new solvent-dependent k , data lead to a significant reevaluation of the factors controlling the electron-transfer dynamics for the ferrocenium-ferrocene system. They suggest that the barrier-crossing frequency is limited by donor-acceptor electronic coupling in addition to solvent polarization dynamics. This behavior is briefly compared and contrasted with that for other, more facile, metallocene redox couples. As part of a systematic exploration of solvent dynamical and related effects in electron-transfer processes, we recently reported a detailed examination of solvent-dependent self-exchange kinetics / ~ = cyclopentadienyl) for cobaltocenium-cobaltocene, C P ~ C O +(Cp and its decamethyl derivative, C P ’ ~ C O +(Cp’ / ~ = pentamethylcyclopentadienyl) using the proton N M R line-broadening technique.] One facet of that study utilized comparisons with corresponding self-exchange rate parameters for ferrocenium-ferrocene, Cp2Fe+/0, reported earlier by Wahl and co-workers.2 Apart from the solvent sensitivity of the self-exchange rate constants, k,,, for a given metallocene couple, of primary concern in ref 1, interesting and unexpected differences were observed in the k , values between the various metallocene couples in a given ~ o l v e n t . ~Specifically, the k , values for CP,CO+/~and CP’~CO+/~ were ascertained to be about 10- and 100-fold larger, respectively, than for Cp2Fe+/0. These rate differences were identified with dissimilarities in the nature and extent of donoracceptor electronic coupling, consistent with expectations from orbital symmetry considerations3 and also from optical electron-transfer measurements for related bimetallocene cations., Recent optical measurements for biferrocene and related cations by Lowery et aL5 and Blackbourn and Hupp6 indicate the presence of significant ion-pairing effects upon the electron-exchange energetics on the basis of increases in the intervalence band energy, Eop, with increasing biferrocene cation concentration or ionic strength. These results have implications for the kinetics of corresponding thermal electron-transfer processes (vide infra).6 Especially given that the proton N M R line-broadening measurements utilized to evaluate the metallocene self-exchange kinetics typically refer to significant ionic strengths (0.01 C h 5 0.2),1.2these findings prompted us to undertake further kinetic measurements for Cp2Fe+/0to examine more fully the sensitivity of k,, to the presence of added electrolyte. The salient findings from this study are reported in the present article, specifically for additions of hexafluorophosphate, tetrafluoroborate, and perchlorate (as the tetraethylammonium salts) up to = 0.25 M in acetonitrile, acetone, nitrobenzene, and (1) Nielson, R. M.; McManis, G. E.; Golovin, M. N.; Weaver, M. J. J. Phys. Chem. 1988, 92, 3441, (2) (a) Yang, E. S.;Chan, M.-S.; Wahl, A. C. J . Phys. Chem. 1980, 84, 3094. (b) Yang, E. S.; Chan, M.-S.; Wahl, A. C. J . Phys. Chem. 1975, 79, 2049. (3) Nielson, R. M.; Golovin, M. N.; McManis, G. E.; Weaver, M. J. J. A m . Chem. SOC.1988, 110, 1745. (4) McManis, G. E.; Nielson, R. M.; Weaver, M. J. Inorg. Chem. 1988, 27, 1827. ( 5 ) Lowery, M. D.; Hammack, W. S.; Drickamer, H. G.; Hendrickson, D. N. J. A m . Chem. SOC.1987, 109, 8019. (6) (a) Blackbourn, R. L.; Hupp, J. T. Chem. Phys. Lett. 1988, 150,399. (b) Blackbourn, R. L.; Hupp, J. T., to be published.
0022-3654/89/2093-2152$01.50/0
methanol. These solvents were selected not only in view of the variations in the extent of ion pairing apparent from the optical data5p6but also because they span a substantial range of dynamical behavior.’ In addition to Cp2Fe+/0, some related results for Cp’2Fe+/o and C P ~ C O +self-exchange /~ are presented for comparison purposes. Although k,, was found to be surprisingly insensitive to ionic strength under most conditions, these measurements uncovered some substantial errors in the k,, values reported by Wahl et While these new findings do not, broadly speaking, alter the conclusions reached in ref 1 and 3, they nevertheless provide some new insight into solvent-dependent reaction dynamics for the ferrocenium-ferrocene and related systems. Experimental Section
Ferrocenium tetrafluoroborate was prepared by oxidizing ferrocene with nitrosonium tetrafluoroborate (Lancaster Synthesis, Ltd.) in dichloromethane; the decamethylferrocenium salt was synthesized similarly. The corresponding hexafluorophosphate salts were prepared as described in ref 2b. (Note: The corresponding perchlorate salts are extremely explosive in dry form and therefore were not isolated here.) Ferrocene and decamethylferrocene (Strem Chemicals) were sublimed prior to use. Cobaltocenium tetrafluoroborate was prepared by oxidation of cobaltocene (Strem) with tetrafluoroboric acid (Alfa). Acetonitrile, acetone, nitrobenzene, methanol, and dimethyl sulfoxide (DMSO) were in fully deuterated form (Aldrich Co.); benzonitrile (Fluka) was purified by passing through alumina. Tetraethylammonium perchlorate (GFS Chemicals) was recrystallized from hot methanol. The corresponding BF4- and PF6- salts were prepared by adding HBF, or NH4PF6, respectively, to a water solution of Et,NBr. The precipitate was then recrystallized twice from hot ethanol. Tetrabutylammonium chloride and bromide (Aldrich) were recrystallized from dry acetone under nitrogen. Biferrocenylacetylene (BFA) was synthesized as described in ref 7. The corresponding mixed-valence cation was usually generated in the desired solvent by adding an equimolar amount of Fe( b ~ y ) ~ ( p F(bpy ~ ) , = bipyridyl) to a solution containing BFA. For methanol, Fe(bpy),(PF6), and BFA were reacted in acetone, the solvent was removed, the residue was mixed with methanol, and the solution was filtered. The near-infrared spectra were recorded with a Cary Model 17D spectrophotometer, with use of around 1 mM BFA+. Most details of the N M R sample preparation are given in ref 1 (also see the Results and Discussion). Proton N M R spectra were collected on Nicolet N T 200 and 470 instruments and a (7) Rosenblum, M.; Brown, N.; Papenmeier, J.; Applebaum, M. J. Orgunomet. Chem. 1966, 6, 173.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 2153
Ferrocenium-Ferrocene Self-Exchange Kinetics
TABLE I: Rate Constants, k.v, at 25 "C for Ferrocenium-Ferrocene Self-Exchange and Relevant Proton NMR Line-Broadening Parametersa
solvent acetonitrile
electrolyte
[ C P ~ F ~ ' mM ],~ 0.65
C,,: mM
11.9
Wp," Hz 639
Et4NPF6 20.6 128
acetone
0.21
11.0
726
Et4NCIO4
0.83 0.86 3.0
13.7 40.9 19
726
Et4NBF4
0.30
10.9
726
0.40
25
1070
0.93 0.8 0.94 0.86 2.1 1.2
20.9 13 20.0 44.7 25.8 93
853* 853'
0.54 0.46 0.45 0.43
11.6
762
Et4NPF6
nitrobenzene EtdNPF,
methanol Et4NBF4
104 102 105 111 124 230 49.4 540 581 598 68 1 142 162
5706
0.85 0.86 0.88 0.88 0.89 0.81 0.69 0.79 0.81 0.81 0.83 0.86 0.88
26.3 27.4 27.8 28.0 81.5 133 95.0 37.5 279; 23.8*
5784
0.35 0.38 0.38 0.39 0.42 0.52 0.47 0.45 0.75* 0.52*
Ci? mM 0.65 25 71 25 1 38 38 0.2 8.1 32.4 50.5 229 0.83 0.86 19.4 47.6 85 119 8.5 33 0.4 33.1 50.1 215 35 0.8 0.94 0.86 2.1 1.2
0.70 0.72 0.74 0.77
0.54 8.4 42 203
WDpa*eHz 235 243 257 272 144 308
116 108 113 122
Av,f Hz 5734
13600* 5556
Apg
0.85 0.86 0.87 0.88 0.8 1 0.38
kc,,' M-I s-I 9.1 8.5 8.0 7.1 7.0 5.8
X X X X X X
lo6 lo6 lo6 lo6 lo6
8.7 X 8.0 X 7.6 X 7.0 X 6.2 X 9.0 X 6.3 X 6.5 X 6.0 X 5.7 x 5.0 X 8.5 X 6.7 X
lo6 lo6 lo6 lo6 lo6 lo6 lo6 lo6 lo6 106 lo6 lo6 lo6
lo6
3.0 x 107 2.8 x 107 2.55 x 107 2.5 x 107 2.6 x 107 2.5 x 107 2.15 x 107 1.1 x 107 3.3 x 107* 2.9 x 107* 1.85 x 1.65 x 1.50 x 1.25 x
107 107 107 107
"NMR data obtained at 200-MHz field strength except where noted by an asterisk, which were obtained at 469.6 MHz. All solvents were fully deuterated. Ferrocenium concentration (added as Cp2Fe.PF6or Cp2Fe.BF4) in mixture employed for NMR measurement, as determined from chemical shift by using eq 2 (see text). cTotal concentration of ferrocenium + ferrocene. dNMR line width (at half-height) for the pure paramagnetic species (Le,, ferrocenium). eNMR line width (at half-height) for the ferrocenium-ferrocene mixture fDifference in resonance frequency (contact shift) between the pure diamagnetic and paramagnetic samples. ZFractional contribution to observed line width from electron exchange, equal to (WDp- xpWp)/WDp(see text). "Total anion concentration. 'Evaluated according to eq 1. Varian FT 80 A, operated at 200.0, 469.6, and 79.6 MHz, respectively. Unless noted otherwise, spectra were obtained at 200 MHz. All kinetic data were obtained at 25 f 0.5 "C. Results and Discussion
Table I contains a summary of some representative rate constants measured by N M R line broadening for Cp2Fe+l0self-exchange in acetonitrile, acetone, nitrobenzene, and methanol, each for several concentrations of added electrolyte up to 0.25 M. The lower limit of anion concentration is determined by the minimum quantity of Cp2Fe-PF6(or Cp2Fe-BF4)required to yield satisfactory N M R spectra, typically about 0.1 mM. For convenience, [Cp2Fe+] was usually around 0.2-2 mM. The rate constants were determined by using the relation2,*
Here xD and xp are the mole fractions of diamagnetic and paramagnetic species (in this case Cp,Fe and Cp2Fe+), respectively, Av is the difference in resonance frequency (hertz) between the pure diamagnetic and paramagnetic samples, WDp,Wp, and WD are the N M R line widths (hertz) at half-height for the corresponding mixed and pure paramagnetic and diamagnetic samples, and C,,,is the total (paramagnetic + diamagnetic) concentration. Equation 1 is appropriate in the so-called "fastexchange" region where a single resonance peak is obtained for the paramagnetic-diamagnetic mixture. The line widths WDpand Wp were determined from the spectra by using a Lorentzian (8) Chan, M.-S.; DeRoos, J. B.; Wahl, A. C. J . Phys. Chem. 1973, 77, 2163.
least-squares-minimizing program available on the Nicolet instruments employed here. Since the amounts of paramagnetic species (Cp2Fe+)present in each sample were typically small, xp was in practice most accurately determined from the chemical shift data by using where vDP and vD are the resonant frequencies of the diamagnetic-paramagnetic mixture and the pure diamagnetic species, respectively. Two features of the kinetic data in Table I are most pertinent to the present discussion. First, while the k,, values for Cp2Fe+/0 self-exchange in a given solvent uniformly exhibit monotonic decreases as the ionic strength is increased, these variations are relatively small in all four of the solvents examined here. Thus k,, decreases typically by only ca. 30% or less as p is increased from ca. 0 to 0.25 M. This finding is discussed further below. Second, the absolute k,, values in each solvent are significantly larger than those reported by Wahl et al. under ostensibly similar conditions.2 This discrepancy is most marked in nitrobenzene, where the present values are around 10-fold larger than that [2.3 (f0.2) X lo6 M-' s-' ] r eported in ref 2a. Since these latter rate disparities are disturbingly large, it is desirable to examine possible contributing factors with the aim of identifying the most appropriate conditions for which reliable kinetic data can be obtained. To this end, we evaluated k,, values in each solvent for a range of Cp2Fe+ and especially Cp2Fe concentrations; some of these data are included in Table I. In acetone and especially acetonitrile, the present k,, values do not differ greatly (less than a factor of 2) from the results of Wahl et al. These authors employed relatively high total reactant concentrations, ca. 0.03-0.1 M (with the diamagnetic species,
Nielson et al.
2154 The Journal of Physical Chemistry, Vol. 93, No. 5, 1989
ferrocene, in excess), presumably because of signal-to-noise constraints with the continuous-wave N M R instrument emp l ~ y e d . ~The . ~ FT-NMR spectrometers utilized in the present study allowed us to obtain high-quality spectra over a wider range of reactant concentrations. Nevertheless, k , values obtained here in acetonitrile, and particularly in acetone, for ferrocene concentrations in the range employed by Wahl et al. approach (within ca. 20%) the rate constants reported by the latter authors (5.3 X lo6 and 4.6 X lo6 M-l s-l in acetonitrile and acetone, respectively,), at least when [Cp2Fe] 0.054.01 M (Table I). Although these apparent decreases in k,, with increasing [Cp2Fe] may reflect an actual (albeit minor) deviation from second-order kinetics, we suspect that they arise at least partly from systematic errors in the data analysis embodied in eq 1. Examination of this equation shows that to evaluate k,, the line width of the diamagnetic-paramagnetic mixture, WDp,needs to be corrected for the ”contributions” from the pure diamagnetic and paramagnetic species, x DWD and xpWp,respectively. While the former contribution is usually negligible (since WD 5 1 Hz), the influence of the latter can often be large. As a measure of the extent of this paramagnetic correction in the N M R analysis, Table I also contains values of the fractional parameter ( WDPxpWp)/ WDp,labeled Ap. The occurrence of a larger paramagnetic correction (corresponding to a smaller Ap value) does not necessarily imply a greater unreliability of the resulting k,, value. This circumstance does, however, carry the burden that any uncertainty in the evaluation of Wp will result in a correspondingly greater potential error in k,. Although the presence of clearcut trends is difficult to discern, inspection of the data obtained in acetonitrile and acetone (Table I) reveals that smaller values of k,, a t a given ionic strength tend to be associated with larger paramagnetic corrections to WDp,along with smaller WDp values themselves. Turning now to the results obtained in nitrobenzene, the greater Wp value for Cp2Fe+ together with the larger k,, values in this solvent conspire to yield relatively large paramagnetic corrections when evaluating k , from WDp. Although the apparent k , values in some cases are systematically diminished for smaller WDpand Ap, the variations in k,, are again relatively small (Table I). Our reliance on these results was aided by further measurements using a 470-MHz instrument. (Representative data thus obtained are marked with asterisks in Table I.) Use of the higher magnetic field offers the dual benefit of increasing WDpand decreasing Wp, thus substantially decreasing the magnitude of the paramagnetic correction. These data again yield k,, values for Cp2Fe+/0 in nitrobenzene around 2.5 X lo7 to 3 X IO7 M-l s-l, depending on the solution conditions employed. The self-consistency of these results led us to scrutinize the conditions employed by Wahl et al. in order to pinpoint likely reasons for the 10-fold smaller apparent k,, value reported in nitrobenzene by these authors.2a One feature of concern is the surprisingly small Wp value, 540 Hz, for Cp2Fe+in nitrobenzene utilized in ref 2a. There are several lines of evidence that indicate that Wp at the field strength, 100 MHz, used by these authorsh is actually substantially larger than this estimate. Most directly, we measured Wp for this system at 80 MHz (using a Varian FT 80A spectrometer) and obtained a value of 1000 f 200 Hz. Given that the corresponding line widths at 200- and 470-MHz field strength are 1070 and 853 Hz, respectively (Table I), a Wp value of at least 1000 Hz at 100-MHz field strength appears reasonable. A comparable estimate of Wp, around 1200 Hz, under these conditions in nitrobenzene is also indicated by two other pieces of evidence. First, Wp for a given species is often found to increase linearly with the solvent viscosity.Io (Indeed, a consistent correlation of this type is obtained by using the Wp values of CpzCo from ref 1.) Employing the Wp values given in ref 2a for Cp,Fe+
-
(9) Yang, E. S. Ph.D. Dissertation, Washington University, St. Louis,MO, 1976. (10) For example: (a) McGarvey, B. R. J . Phys. Chem. 1957,61, 1232. (b) Swift, T. J. In NMR of Paramagnetic Molecules; LaMar, G. N., Horrocks, W. Dew., Jr., Holm, R. H., Eds.; Academic Press: New York, 1973; Chapter 2.
in other solvents (except for dimethyl sulfoxide, vide infra) in such a correlation leads to an estimate of Wp in nitrobenzene of ca. 1300-1400 Hz. Second, on the basis of eq 1 a plot of WDPversus C,-I for a series of mixtures with constant xpwill yield an intercept of (xDWD xpWp),from which Wp can readily be extracted. Using data obtained by Yang and Wahl (p 132 of ref 9), we again obtain W, = 1200-1300 Hz for Cp2Fe+ in nitrobenzene. Inserting such larger values of Wp into eq 1 along with the WDP values given in ref 9 yields markedly larger k,, values than are reported in ref 2a and 9 and indeed approach the value, ca. 2.5 X IO7 M-’ s-’, obtained in the present work (Table I). Unfortunately, however, under the lower field (100 h. 3 z ) conditions employed in ref 2a and 9, the extent of the params ietic correction is sufficiently large (Ap 5 0.2) so as to vitiate t , extraction of reliable k , values from these measurements. Similar difficulties associated with signal-to-noise restrictions and paramagnetic line-width corrections are probably also responsible for the similar, albeit smaller (ca. 2.5-fold) discrepancy between the present kinetic results in methanol with that reported in ref 2a. These difficulties originate in the experimental restrictions imposed upon Wahl et al. by the use of a low-field continuous-wave N M R spectrometer (Varian HA-100). The utilization of higher field Fourier transform spectrometers in the present work, which have become widely available in the intervening years, enables us to extract inherently more reliable kinetic data for this system. Due to our interest in the comparative kinetic behavior of different metallocene redox couples, we have also examined the influence of added electrolyte upon the rate constants for CObaltocenium-cobaltocene (Cp2Co+/O) and decamethyl(ferr0cenium-ferrocene) (CP’~F~+/O) self-exchange. Although the results of some of these N M R line-broadening experiments are noted qualitatively in ref I , for convenience we include some representative additional data in Table 11, employing the same format as for Table I. Since it is desirable to use an excess of the diamagnetic constituent in the N M R line-broadening measurements and given that this component is the cationic species in the C ~ , C O +system, /~ it is less straightforward to maintain the ionic strength at very small values than for ferrocenium-ferrocene systems. Nevertheless, similarly to Cp,Fe+/O only small decreases in k,, were typically observed for Cp2Co+/oself-exchange upon the addition of inert electrolyte (Table 11). Thus for acetonitrile, keXfor C P ~ C O +self-exchange /~ decreases by only ca. 15% and 30% upon increasing the ionic strength from 0.01 to 0.14 and 0.55, respectively. Roughly similar results are also obtained for Cp’,Fe+l0 selfexchange (Table 11). These include k , measurements in acetone for the addition of chloride and bromide anions. (Attempts to make corresponding measurements for CpzFe+/Oself-exchange were thwarted by reaction between Cp,Fe+ and the added halide ions.) Interestingly, the present k,, values for Cp’,Fe+/O in acetonitrile and acetone are comparable to that reported by Wahl et a1.;2ait is worth noting that the latter data were obtained by using a Fourier transform 100-MHz instrument. Implications of Solvent-Dependent Ferrocenium-Ferrocene Kinetics. Given that the kinetic data for Cp2Fe+ioself-exchange of Wahl et were utilized in our recent discussions of the solvent1 and reactant structural dependence3 of metallocene self-exchange kinetics, it is appropriate to reexamine these findings in the light of the new kinetic information reported here. To this end, Table I11 contains k,, values in five solvents for Cp,Fe+/O and Cp’,Fe+l0, obtained in the present work, together with corresponding data for C P ~ C O +and / ~ Cp’2Co+/o taken from ref 1. Since most of the latter measurements employed ionic strengths around 0.15 M with BF4- as the electrolyte anion, the k,, values for Cp,Fe+/O and Cp’,Fe+/O listed are adjusted slightly so to refer to comparable electrolyte conditions. In each solvent, the rate constants for C ~ , C O +are / ~ 3 to 5-fold larger than for Cp2Fe+/0self-exchange (Table I). In a previous discussion3 we presumed the former reaction to be about IO-fold faster, based in part on the k , values for the latter in acetonitrile and dimethyl sulfoxide (DMSO) given in ref 2a. The k,, value for Cp,Fe+/O self-exchange in DMSO listed in Table I11 was also
+
Ferrocenium-Ferrocene Self-Exchange Kinetics
The Journal of Physical Chemistry, Vol. 93, No. 5, 1989 2155
TABLE 11: Representative Effects of Added Electrolyte upon Rate Constants, k , at 25 OC for Cobaltocenium-Cobaltocene and &camethyl( ferrocenium-ferrocene) Self-Exchange and Relevant Proton NMR Line-Broadening Parameters"
acetonitrile Et4N BF4 acetone Et4NBF4 benzonitrile Et4NBF4 methanol E t4N B F4 acetonitrile Et4NBF4 acetone Bu4NBr Bu~NCI benzonitrile Et,N BF4
x 107 x 107 x 107
12.9 41.7 40.7 53.0
16.5 55.7 50.7 65.0
117
370 149 154 136
11210
0.93 0.80 0.85 0.84
12.9 41.7 141 552
4.6 4.5 3.8 3.2
34.6 50.3
39.1 65.3
80'
960' 254
26 380' 11 240
0.99 0.89
34.6 152
2.4 x 107; 1.9 x 107
40.3 40.3 40.3 30.6 45.0
41.1 46.3 56.8 45.1 60.4
133
14.0 80.5 123 155 127
11 220
0.82 0.79 0.69 0.72 0.73
40.3 40.3 40.3 140 149
6.7 6.2 6.8 6.8 5.5
34.3 46.8
44.6 55.7
86' 126
377' 71
25 980* 10830
0.95 0.72
34.3 133
9.5 x 107' 7.3 x 107
7 687
0.86 0.94
1.54 93
3.8 x 107 2.5 x 107
562 633 665 675 648 688
7671
0.83 0.85 0.85 0.86 0.85 0.86
2.7 6.9 27.4 57.4 15.9 59.7
2.4 2.2 2.1 2.0 2.1 2.0
883 704
7 665
0.69 0.53
1.53 92
6.1 x 107 5.6 x 107
1.54 1.45
4.07 3.98
2.7 2.2 2.2 2.2 2.2 2.2
11.7 10.5 10.5 10.5 10.5 10.5
1.53 3.54
4.47 8.54
117
Cp,'Fetlo Self-Exchange 472 1308 2673 464
800
x 107
x 107
x 107 lo7 IO7 x 107 X X
x 107
x 107 x 107 x 107
x 107 x 107
" N M R data obtained at 200-MHz field strength except where noted by an asterisk, which were obtained at 469.6 MHz. All solvents were fully deuterated, except for benzonitrile. Cobaltocenium (Cp2Co') or decamethylferrocenium (Cp,'Fe+) concentration (added as Cp2Co.PF6 or Cp,'Fe.PF6) in mixture employed for N M R measurement, determined from chemical shift by using eq 2 (see text). CTotalconcentration of oxidized and reduced forms in mixture. d N M R line width (at half-height) for the pure paramagnetic species. e N M R line width (at half-height) for the paramagnetic-diamagnetic mixture. /Difference in resonance frequency (contact shift) between the pure diamagnetic and paramagnetic samples. EFractional contribution to observed line width from electron exchange, equal to (WDp - x,WP)/WDp (see text). "Total anion concentration. 'Evaluated according to eq 1. TABLE 111: Comparison between Self-Exchange Rate Constants, k,,, for Metallocene Redox Couples
-
solvent' acetonitrile acetone methanol benzonitrile DMSO"
k,,, M-I s-l (at p 0.15*.') Cp,Fetlo Cp,'Fe+lof C~,CO'/~E C ~ , ' C O ' / ~ ~ 7.5 X lo6 2.5 X lo7 3.8 X lo7 4.3 X lo8 6 X IO6 1.8 x 107 2.0 x 107 2.3 x 108 1.35 X l o 7 7.2 x 107 2.0 X l o 7 5.0 X lo7 6.1 X lo7 2.5 X lo8 7.5 X 106d,r 2.4 X lo7 1.85 X IO8
" All solvents, except for benzonitrile and DMSO (dimethyl sulfoxide), employed in fully deuterated form. Cp = cyclopentadienyl, Cp' = pentamethylcyclopentadienyl. Measured or extrapolated to ionic strength p = 0.15, using either PF, or BF,. dExtracted from data obtained in this work. CObtainedas described in footnote 1 1. (A value of 9.5 X lo6 M-l s-' was obtained for Cp2Fet/0 self-exchange in D M S O in the absence of added electrolyte, corresponding to p 0.01 M.) /Obtained in this work, except for acetone, which was estimated from data in ref 2a. EFrom ref 1. obtained in the present work and is about 5-fold larger than that reported in ref 2a.l' As already mentioned, we have traced the differences in k,, between CpzFe+/O and C P ~ C O + as / ~ ,well as between Cp'zFe+/o and Cp'zCot/o, in each solvent to an enhanced degree of donoracceptor orbital overlap for the cobaltocene versus the analogous ferrocene exchange processes.3 This effect is consistent with the ( 1 1) As for Cp,Fetlo self-exchange in nitrobenzene, the Wp value in DMSO, 660 Hz (at 100-MHz field strength) quoted in ref 2a, appears too small on the basis of solvent viscosity-Wp correlations (see text). In our experience, direct measurement of W, for Cp2Fe+in DMSO is complicated by slight decomposition. A reliable estimate of Wp for this system, 1320 Hz, under our conditions (200-MHz field strength) was, nevertheless, obtained by measuring WDpfor a series of Cp2Fe+/Cp2Femixtures having a fixed xp, 0.15 (adjusted to a constant ionic strength, 0.10 M, with KPF,). A plot of WDpversus C,-I enabled Wp to be extracted from the intercept (cf. discussion for Wp in nitrobenzene described in the text).
ligand-delocalized character of the 4el, orbital involved in the former, as compared with the metal-centered 4e2 or Sal, orbital for the latter reactions. Under suitable circumstances, this can yield an increased degree of adiabaticity and/or a larger effective precursor stability constant, as is apparently the case for the cobaltocene relative to the ferrocene exchange proce~ses.~ While the present results indicate that the magnitude of this effect for Cp2Fe+loversus C P ~ C O +(but / ~ not for Cp',Fe+l0 versus Cp'2Co+/o) is somewhat smaller than appeared originally, the validity of the major interpretations given in ref 3 remains intact. One noteworthy feature of the rate data assembled in Table I11 concerns the solvent dependence of the k,, values observed for Cp2Fe+/0 self-exchange in comparison with that for the other metallocene redox couples. As we have outlined in detail elsethis solvent dependence is expected to be determined not only by variations in the free-energy barrier, AG*, but also by the nuclear frequency factor, v,, according to
k,, = Kp~,p,exp(-AG*/RT)
(3) where Kp is the equilibrium constant for forming the precursor complex and K , ~is the electronic transmission coefficient. In a number of cases, the solvent dependencies of AG* and v, are anticipated to provide offsetting contributions to k,, such that the additional presence of the latter, solvent dynamical, contribution can yield qualitatively different solvent dependencies of k,, than are obtained in its absence.lq'2C One simple illustration of these factors can be ascertained by comparing the ratio of rate constants in acetonitrile versus that in benzonitrile, keXAN/kexBN, for each metallocene redox couple. Inspection of Table I11 shows that this ratio increases monotonically in the sequence Cp2Fe+/0 < Cp',Fe+/O e C P ~ C O +
