126
J. Phys. Chem. 1982, 86, 126-130
would be observed. In the limiting case where k f f y d for H203 is effectively zero compared to &lared, the overall expression for kl becomes k i = kzz + kz3(kz4 -t k26[Ml)/(kz.i -I-k-23 + kz,[MI) (27) It is possible to indicate the broad ranges of parameters in eq 27 required for consistency with the observed rateconstant magnitude and apparent pressure enhancement. As previously mentioned, kzz is not expected to be greater than about 1 X 10-l’ cm3s-l, so that the quantity k23k24/(k24 k-%) must be at least 5 X lo-” cm3s-l to account for the total low-pressure observed kl. To explain a pressure enhancement of kl, one must place further constraints on the individual values of k23, k24, kZ3, and kzs. The data cm38, k24 are well fitted by the values k23 = 1.5 X = 1.5 X lo8 s-l, k-23 = 3 X lo8 s-l, and k26 = 2 X lo-” cm3 s-l. Small variations within this set of values would also fit the observations. The consistency of these rate constants with theoretical expectation is difficult to evaluate.
+
The most critical unknown factor is the entropy of the intermediate [H203]*, which determines the equilibrium constant k23/k-23. The high value of k23lk-23 implied by the individual rate constants quoted above requires postulation of an extremely “loose” structure for [H20,]*. Acknowledgment. This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. “7-100, sponsored by the National Aeronautics and Space Administration. I thank several members of the JPL Chemical Kinetics and Photochemistry Group for assistance with this work, including especially Drs. S. P. Sander, J. J. Margitan, R. T. Watson, M. Patapoff, and M. T. Leu. Very helpful advice on the resonance fluorescence method was provided by Dr. I. A. McDermid. Professor R. H. Smith, who was on study leave from MacQuarie University, New South Wales, Australia, aided in the development of the OH calibration procedure.
Electron Exchange between Tris(hexafluoroacetylacetonato)ruthenium(I I ) and -(I I I ) and between Related Compounds. Effects of Solvent on the Rates‘ ManSheung Chan and Arthur C. Wahl’ Department of Chemistry. Washington Universiw, St. Louis, Missouri 63 130 (Received: August 1 1, 198 I; In Final Form: September 2 1, 198 1)
The rate constants for electron exchange between Ru(hfac); and R ~ ( h f a c )between ~, Ru(mezbpy)(hfac)zand R~(me~bpy)(hfac)~+, and between R~(me~bpy)(acac)~ and R~(me~bpy)(acac)~+ have been measured by the NMR linebroadening method, hfac representingthe hexailuoroacetylacetonate ion, acac representingthe acetylacetonate ion, and melbpy representing 4,4’-dimethyL2,2’-bipyridyl. The rote constants at 25 “C in acetonitrile are 5.0 X lo6, 4.5 X lo6, and 1.4 X lo8 M-’ s-l, respectively. The rate constants for the first two reactions vary with solvent dielectric properties about as predicted by the Marcus theoretical model; however, the preexponential coefficient, K ~ Zis ,1order of magnitude smaller than the value of -loll M-’ s-l generally assumed, possibly due to steric effects of the CF3 groups. Measured temperature dependences of rate constants are small.
Introduction The rates of electron exchange between Ru(hfacI3 and Ru(hafc)y, hfac representing the hexafluoroacetylacetonate ion, and between other neutral and singly charged complexes in various solvents are of interest because the main deterrent to electron transfer is probably the necessity for solvent reorganization.2 There is no Coulombic repulsion between reactants, so the work required to bring them together is minimal, the standard free-energy change is zero for exchange reactions, and, for the exchange systems considered, the structures of the reactants are similar, so the energy required for internal rearrangement should be small and essentially the same for exchange in different solvents. Therefore, investigations of the rates of electron-exchange reactions in various solvents should increase our understanding of solvent-reorganizational requirements. For exchange between ferrocene and ferrocenium ion, and also for several other systems, there is little dependence on solvent proper tie^.^ For several other systems, ~
(1) Supported by the National Science Foundation under Grants
CHE-76-02473and CHE-80-03325. (2) Marcus, R. A. J . Chem. Phys. 1966,43,679. (3) Yang, E. S.;Chan, M.-S.; Wahl, A. C. J. Phys. Chem. 1980,84, 3094. 0022-3654/82/2086-0126$01.25/0
exchange rates do vary with solvent dielectric properties. These systems include those described in this article, Ru(hfac)$- and Ru(me2bpy)(hfac)2v+, mezbpyrepresenting 4,4’-dimethyl-2,2’-bipyridyl, and the recently reported4 exchange between Cr(biph)$+, biph representing biphenyl. Experimental Section R ~ ( h f a cwas ) ~ purchased from Strem Chemicals, Inc., and it was purified by vacuum sublimation. Solutions of R ~ ( h f a c ) salts ~ - in ethanol were prepared by reducing Ru(hfad3with potassium iodide, tetramethylammonium iodide, or tetra-n-butylammonium iodide following the procedure by Patterson and Holm.5 Solid products were obtained from the ethanolic solutions by addition of water. The salts K[Ru(hfac),] and Me,N[Ru(hfac),] were purified by recrystallization from ethanol-water solutions. Bu4N[Ru(hfac),] was purified by reprecipitation from acetonitrile by addition of carbon tetrachloride. Analyses for carbon, hydrogen, and nitrogen, as well as analysis by spectrophotometric methods, indicated that these compounds were >-99% pure. Ru(meZbpy)(hfac)2 was synthesized from Ru(me2bpy)(H20)Cl3,which was prepared by the method (4)Li, T.T.-T.; Brubaker, C.H., Jr. J. Organomet. Chem. 1981,216, 223. (5) Patterson, G. S.; Holm, R. H. Inorg. Chem. 1972,11, 2285.
0 1982 American Chemical Society
Electron Exchange between Ru(hfacb- and Ru(hfac):,
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982 127
reported by Dwyer et al.6 for Ru(bpy)(H20)Cla. One gram of Ru(me2bpy)(H20)C13was partially dissolved in 3 mL of dimethylformamide (DMF) and 5 mL of hexafluoroacetylacetone. The mixture was refluxed for -24 h, during which time the color of the solution changed slowly from yellow to wine red, and gradually a dark red precipitate formed. The precipitate was collected by filtration and washed several times with water. The solid was purified by recrystallizing twice from large volumes of acetone. (Anal. Calcd C, 37.75; H, 2.00; N, 4.00. Found C, 37.93; H, 2.09; N, 4.07.) [Ru(me2bpy)(hfac),]PF6was prepared by partially dissolving 0.7 g of Ru(m+bpy)(hfac), in 10 mL of glacial acetic acid and adding a solution of 0.7 g of Ce(NH4)2(N03)6 in 2 mL of ice-cold formic acid dropwise with vigorous stirring. The solution quickly turned red in color, and the solid gradually dissolved. A clear red solution formed after addition of all of the Ce(NH4),(N03)& The red complex was precipitated by addition of aqueous D F 6 , and the red precipitate was colleded by filtration, washed several times with ice-cold doubly distilled water, and then dried under vacuum over P206. The dried solid was redissolved in CH3CN, centrifuged to remove insoluble materials, and reprecipitated by addition of CHC13. The precipitate was collected by filtration and dried under vacuum overnight. (Anal. Calcd C, 31.27;H, 1.66;N, 3.31. Found C, 31.28; H, 1.82; N, 3.31.) [Ru(me,bpy)(a~ac)~]PF, was precipitated by addition of aqueous KPF6 to a solution of [Ru(me,bpy)(acac),]Cl, prepared from Ru(me2bpy)C14and acetylacetone following the method of Dwyer et a1,,6and the precipitate was purified by the procedure described for [Ru(mezbpy)(hfac),]PF& (Anal. Calcd: C, 42.00; H, 4.14; N, 4.45. Found: C, 42.08; H, 4.17; N, 4.58.) Ru(me2bpy)(acac), was prepared from an aqueous solution of [Ru(me2bpy)(acac),]Cl by reduction with sodium dithionite according to the method of Dwyer et al.6 The intensely green-colored Ru(me,bpy)(acac), was extracted into benzene, and a dark solid was obtained by removal of benzene by evaporation under vacuum. The solid was dried under vacuum overnight and kept under nitrogen. The NMR spectrum of a sample dissolved in CD3CN gave seven broad peaks,however, in the presence of NaBH4,the NMR spectrum showed seven sets of narrow peaks, some split due to coupling, expected for the diamagnetic Ru(me&py)(acac)2. All deuterated solvents were purchased from Stohler and were used without further purification, except CDQCNand C6D5NO2were dried over and distilled from P206. NMR spectra for 'H and leF were obtained with a JEOL FX-100FT NMR spectrometer. Electron-exchange rates were determined from NMR spectra recorded for samples of Ru(I1) complexes, of Ru(1II) complexes, and of mixtures of the two in the desired deuterated solvent. Solutions were prepared from weighed amounts of the pure compounds, except as described below. The sample of Ru(mezbpy)(acac)zfor NMR measurements was prepared from [ R ~ ( m e ~ b p y ) ( a c a c ) ~by ] PreF~ duction with NaBH4 in the following way. Deuterated acetonitrile was degassed and kept under nitrogen. About 6 mg of [ R ~ ( m e ~ b p y ) ( a c a c ) ~and ] P F-10 ~ mg of NaBH, were weighed into a 3-mL test tube. After Nz was passed through the test tube for 10 min, -0.05 mL of CD30D was added to the sample. The test tube was capped and shaken vigorously for -20 min, and the color of the solution gradually changed from purple to an intense green.
About 1 mL of CD3CN was added under nitrogen, the sample was centrifuged, and the resultant green solution was transferred under nitrogen to a 5-mm NMR tube, which was capped. The NMR spectrum of the sample showed seven sets of narrow peaks indicating the formation of the diamagnetic Ru(mezbpy)(acac), complex. Samples of Ru(me,bpy)(acac)$+ mixtures for NMR measurements were prepared by dissolving weighed amounts of Ru(meZbpy)(acac),and [ R ~ ( m e ~ b p y ) ( a c a c ) ~in] PCD3CN F~ under nitrogen. Total concentrations of these solutions were determined spectrophotometrically after oxidation of Ru(me,bpy)(acac), to Ru(me,bpy)(acac),+ by a (NH4)2Ce(N03)6solution. NMR spectra of R ~ ( h f a c ) ~ in- acetonitrile showed a proton peak at 623 Hz downfield from tetramethylsilane (Me4Si) and a 19Fpeak at 237 Hz downfield from an external standard of CF3C02D;the line widths (WD) of these peaks were determined to be 1.7 and 0.9 Hz,respectively. A small coupling constant ( J F - H ) of -0.4 Hz was observed for the 19Fpeak. The proton NMR spectrum of Ru(mezbpy)(hfac)z showed five sets of peaks with the following peak positions in Hz downfield from Me4Si (line widths, fwhm in Hz): two doublets with coupling constants of 5.7 Hz at 859 (1.5) and 763 (-2.5) and three singlets at 866 (-2.5), 290 (1.7), and 632 (1.8). The peaks were assigned, respectively, to the (6,6'), (5,5'), (3,3'), and CH3 protons of mezbpy, and the CH proton of hfac. The proton spectrum of Ru(me2bpy)lacac), showed seven sets of peaks with the following peak positions in Hz downfield from MelSi (line width, fwhm in Hz): two doublets at 847 (1.6) and 701 (-2.5) with coupling constants of 5.7 Hz and five singlets at 795 (-2.5), 252 (1.7), 527 (1.3), 205 (0.9), and 152 (0.9). These peaks were assigned respectively to the (6,6'), (5,5'), (3,3'), and CH, protons of me2bpy,the CH proton of acac, and the CH3 protons of acac for the last two peaks, the two CH3groups in the acac ligands being nonequivalent in the complex. N M R spectra of Ru(hfacI3,[Ru(me2bpy)(hfac),lPF6,and [Ru(me,bpy)(a~ac)~]PF~ in various organic solvents were recorded over the temperature range of 5-35 "C. The contact shifts (6v) and paramagnetic line widths ( Wp) for the several proton peaks used for rate measurements, namely, the methine peaks of R ~ ( h f a cand ) ~ the me2bpy methyl peaks of [Ru(me,bpy)(hfa~)~]PF~ and [Ru(mezbpy)(acac)z]PF6,are listed in Table 11. The methyl peaks were easily identified by their downfield paramagnetic shifts. Other proton peaks of [Ru(me,bpy)(hfac),]PF6 and [Ru(me2bpy)(acac),]PF6gave overlapping broad peaks, and no attempt was made to resolve and identify them. For the '!F peak of Ru(hfa& in CD3CN,the 6v and W at 25 "C are 911 and 25.5 Hz, respectively. hectron-exchange rate data were obtained from NMR spectra of samples containing mixtures of neutral and singly charged reactants by determination of peak positions and line widths ( WDp) at half-maximum. For most measurements rates were large, and the fast-exchange approximation (kc >> 2a6v) was valid, so the exchangebroadened peaks were analyzed by using the line-width eq~ation.~ WDP = (1 - f p ) W ~+ f p w p + 4rfp (1 - fp)(Sv)'/(kc) (1) The symbol f p is the fraction of reactants in the paramagnetic form, k is the second-order rate constant, and c is the total reactant concentration. The fraction, fp, was generally determined from the relationship f p = Avo/(6v),
(6) Dwyer, F.D.;Goodwin, H.A,; Gyarfas, E.C. Aust. J. Chem. 1963, 16, 43.
2163.
-
(7) Chan, M.S.;DeRoos, J. B.;Wahl, A. C . J.Phys. Chem. 1973, 77,
128
Chan and Wahl
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
TABLE I: Rates of Electron Exchange between Ru(I1) and Ru(II1) Complexes in Acetonitrile exchange system Ru(hfac),O?-
Ru(me,bpy) (hfac) o * Ru(me,bpy) ( acac) 2 ° *
total counter- 1 0 - 6 k a t 25 concn, hl ion C, M-I s-l
0.20 0.05 0.02 0.05 0.05 0.04 0.05 0.00134
Me,N+ Me,N+ Me,N+
K+ Bu,N+ Bu,N+ Bu,N+ PF,-
4.8 i 0.5 4.4 i 0.4 4.3 i 0.2 4.8 * 0.4 4.9 + 0.4 5.0 i 0.4 5.4 i l . O Q 4.5 f 1.0b
Eact, kcal mol-' 7.0
?:
1.0
6.3
?:
1.0
4.6 4.2
i
1.0
i
1.5"
3.3
i
1.5
+
+
0.0021 0.0033 0.0094
PF,PF,PF,-
1 4 0 t 30 140 i 30 1 2 0 i 30
a The data were calculated from the results of I9F NMR The rate constant was calculated from measurement. the line width of the methine-proton peak and e q 2, as discussed in the text.
where Auo is the frequency difference between the NMR peak of the diamagnetic species and the corresponding peak observed for the mixture. The solubility of R~(me~bpy)(hfac)~ in acetonitrile was only -1.5 X M at room temperature, so only low concentrations could be used for the exchange reaction. Since, under these conditions, the methyl proton peak was in the intermediate-exchange region (kc/ [2a(6u)]N 0.51, for which eq 1 is not applicable, exchange-rate data were deduced from the width of the methine proton peak, which was near ( k c / [ 2 a ( 6 u ) ]1~ 0.2) the slow-exchange limit.* WDp = WD + f p k c / a
(2)
The value of f p was deduced from the position of the (5,5') proton peak, which was near (kc/[2a(6v)] N 3) the fastexchange limit.
Results Table I summarizes the rate constants and the activation energies determined for the electron-exchange systems, Ru (hfac)3°*-, Ru(me2bpy)(hfac)2°,+, and Ru(me2bpy)(a~ac)~O,+ in acetonitrile. For both the Ru(hfa~)~O~and Ru(mezbpy)(acac),O~+systems, the rate constants for electron exchange were measured at various reactant concentrations and were found to be constant. The rate constant for the Ru(hfac)$- exchange was also found to be independent of the type of counterion present, K+, Me4N+,or Bu4N+. These results are similar to those obtained for the ferrocene-ferrocenium ion e x ~ h a n g e . ~ Both 'H and 19Fpeaks were used to measure the electron-exchange rate for the Ru(hfac)$- system, and, as illustrated in Table I, the two types of measurements gave consistent values for rate constants and for activation energies. Uncertainties in activation energies, E,, calculated from the Arrhenius equation, were estimated from the maximum and minimum slopes of lines drawn to be reasonably consistent with the data and associated uncertainties on a log ( k ) vs. 1 / T plot. Uncertainties were usually about 1.0 kcal mol-' because the temperature range was only -30 "C (usually 5-35 "C)and uncertainties in rate constants were -10%. The very large values of the rate constant determined for the Ru(me,bpy)(acac),O*+exchange are associated with ( 8 ) For example, see: Emsley, J. W.; Feeney, J.; Sutcliffe, L. H. *High Fholution Nuclear Magnetic Resonance Spectroscopy"; Pergamon Press: Oxford, 1965; Vol. 1, p 484.
Flgurr 1. Varlatlon of the exchange rate constant, k (log scale), at 25 "C wtth the d l 8 k M e " t a n t term for different solvents, numbered as designated in Table 11: (0)measured for the Ru(hfacho*-exchange; (0)measured for the Ru(me,bpy)(hfac)$+ exchange; (0) measured for the Ru(me,bpy)(acac)$+ exchange. Lines are calculated from eq 3and4: ( - ) R * = 1 0 A , ~ p Z = 8 X109M-'s-'; ( - - - ) R ' = 7 A, ~ p =z 1 X 10'' M-' S-'; 0 . s ) R' = 10 A, K ~ Z 1=X 10" M-' S-1.
the small exchange broadening that was observed. The large experimental uncertainty in k is the result of a relatively large uncertainty in the f p W p term.
Discussion The results of the effects of different solvents on exchange rates are summarized in Table I1 along with measured activation energies (Eae) and NMR parameters (6u and W,) for the paramagnetic species. Figure 1shows that the measured rate constants for both the Ru(hfac)$and Ru(me2bpy)(hfac)$+exchange reactions increase with decreasing values of the dielectric-constant term, 1/D, l/D,,9 for a number of solvents, except for CDC13, approximately as predicted by the Marcus theoretical mode1.2J0 k = ~p2[exp(-AG*/RT)]
+
AG* = W , + AGO* AGi*
N
(3)
AGO*=
The work of bringing reactants together, w,,and the free energy of activation for internal rearrangement, AGi*, should both be small, as discussed in the Introduction, and are assumed to be approximately zero. Other symbols have their conventional meaning and are defined in footnate 9. The solid line in Figure 1calculated from eq 3 and 4 with R* = 10 A and K ~=Z8 X lo9 M-l s-l represents most data reasonably well. A reaction distance, R*, of 10 A is reasonable, but K ~=Z8 X log M-l s-l is l order of magnitude less than the value of -10" usually assumed.2J0 The dashed line calculated for KPZ= 10" M-' s-l and R* = 7 A represents the data less well, and 7 A is somewhat less than the 10 A value estimated for the reaction distance
-
(9) D, and D,represent the optical and static dielectric constants, respectively, D, being equal to the square of the refractive index; the symbol 2 represents the bimolecular collision number, usually assumed to be 10" M-I s-l;e represents the electronic charge; and R* represents the distance between reactant centers in a transitions state composed of touching spheres. The symbol K represents the transmission coefficient, which is usually assumed to be -1, Le., unit probability for electron transfer when other conditions are appropriate, an adiabatic reaction; p represents the square root of the ratio of the mean square deviation in reaction distance to the mean square deviation in perpendicular distance above the reaction hypersurface and is usually assumed to be -I.* (IO) Marcus, R. A. J. Chem. Phys. 1956,24, 966.
-
The Journal of Physical Chemistry, Vol. 86,No. 1, 7982
Electron Exchange between Ru(hfac),- and Ru(hfac),
129
TABLE 11: Effect of Solvent on Electron-Exchange Rates for the Systems Ru(hfac),'*- and Ru(me,bpy)(hfac),o~' exchange system (counterion) Ru(hfac),'?' (Bu,")
Ru( me 2 b??' Wac), (PF, -1 Ru(me 2 b t y ) ( acac1 (PF,-)
solvent (no. in Figure 1)
l/Dopa1 ID,
CD,ODC (1) CD,CN ( 2 ) CD,NO,C (CD,),COC (4) (CD,),COC ( 4 ) (CD,),COC ( 4 ) C,D,NO, ( 5 ) CD,C1, ( 6 ) CD,CO,D ( 7 ) CDCl, (8) CD,CN ( 2 ) (CD,),COC ( 4 ) CD,Cl, ( 6 ) CD,CN ( 2 )
0.5377 0.5283 0.4981 0.4956 0.4956 0.4956 0.3875 0.3831 0.3713 0.2720 0.5283 0.4956 0.3831 0.5283
wz
611 at 25
atb 25 C,
'Clb Hz
Hz
4890
240
4830 4860 4810 4910 -1920
300 225 305 225 290
-1940 -1230
305 120
reactant concn, M
10-6hat 25
0.05 0.04 0.02 0.04 0.05 0 05 0.01 0.02 0.01 0.014or0.005 0.00134 0.0124 0.00153 0.0033
6.8 t 1.0 5.0 t 0.5 8.3 t 1.0 9.8 1.0 10.1 f 1.0 8.7 t l . O d 33 t 5 23 t 4 80 f 20 11 t 1 4 . 5 t 1.0 2.6 t l . O e 35 f 5e 140 t 30e
'C, M-' s - l
+_
EaCt,kfal mol 4.6
+_
1.0
t
1.0
6.7 t 3.6 t 3.4 t 1.2 t
1.5 1.0 1.0 1.0
4.8
2.9 t 1.0 3.3 t 1.5
a Do, = n,, n being the refractive index, and D s is the static dielectric constant; values of n and D, are from ref 11 and are The values of S U and Wp are for the methine protons of Ru(hfac), and for the me,bpy methyl for protonated solvents. Wp and 6 u could not be measured in these solvents protons of [Ru(me,bpy)(hfac),]PF, and [Ru(me,bpy)(acac),]PF,. because of small amounts of reduction of the Ru(II1) complexes, so Wp and 6 v values for CD,CN were used for calculations. The cation was Me,N+. e The rate constant was obtained from the line width of the me,bpy methyl peak and eq 1. WD for the methyl peak is 1.7 Hz.
from examination of models of the reactants in contact. The rate constant for the Ru(hfac)$- exchange in CDC13 is 1order of magnitude less than would be estimated from the general trend observed for exchange in other solvents. The small static dielectric constant of 4.72 for chloroform" could lead to extensive ion association, which could reduce the exchange rate, since ion association reduced the rate of exchange between ferrocene and ferrocenium ion about a factor of 2.3 However, large exchange rates were observed for acetic acid and methylene chloride as solvents, which also have small static dielectric constants" of 6.19 and 8.89, respectively, which could lead to some ion association. Ru(me,bpy)(acac), was too unstable (easily oxidized) for exchange experiments in solvents other than acetonitrile, but in this solvent the rate for the Ru(me,bpy)(acac)$+ exchange reaction is -30 times the rate for the Ru(me2bpy)(hfac)?+ exchange reaction and is nearer the theoretically predicted rate (dotted line, Figure 1,R* = 10 A, KPZ= 10'l M-' s?). Also, it has been observed', that the electron-exchange rate for the R~(bpy),(acac)+.~+ system is -5 times larger than it is for the Ru(bpy),(hfac)+$+system at 25 "C in acetonitrile and is close to the theoretically predicted value. The presence of CF3 instead of CH3 groups on an acetylacetonate ligand reduces the ease of oxidation of the reduced forms of the metal complexes investigated as well as the exchange rates. The effect of CF3on exchange rates may indicate that CF, is a better electrical insulator than CH3, a steric effect that could cause K to be
