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Electron Exchange Reactions of Ammine Complexes of R u ( I 1 ) and - ( I l l )
(20) Churchill. M. R.; Wormald, J. Inorg. Chem. 1970, 9,2430-2436. (21) Graziani, M.; Bibler, J. P.; Montesano, R. M.; Wojcicki, A. J. Organornet. Chem. 1969, 76, 507-5 11. (22) Severson, R. G.; Wojcicki, A . Inorg. Chim. Acta 1975, 74, L7-L8. (23) Kroll. J. 0.;Wojcicki, A. J. Organornet. Chem. 1974, 66, 95-101. (24) Jacobson, S. E.; Reich-Rohrwig, P.; Wojcicki, A. Inorg. Chem. 1973, 72, 717-723. (25) Lalancette, J. M. US. Patent 3 950 262, April 13, 1976. Lalancette, J. M.; Lafontaine, J. J. Chem. SOC.,Chem. Commun. 1973, 815. (26) Byler, D. M.; Shriver, D. F. Inorg. Chem. 1976, 75,32-35. (27) Aynsley, E. E.; Peacock, R. D.; Robinson, P. L. Chem. Ind. (London)1951, 1117. (28) Nowak, P.; Saure. M., Kunststoffe 1964, 54, 557-564. (29) Satchell, R. S.; Satchell, D. P. N. Chem. Ind. (London)1965, 35, 1520. (30) Wojcicki. A. Acc. Chem. Res. 1971, 4, 344-352.
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(31) Waddington, T. C.; Kianberg, F. J. Chem. SOC.1960, 2339-2343. (32) ROSS,D. A.; Wojcicki, A. Inorg. Chim. Acta 1971, 5, 6-8. (33) Severson, R. E.; Wojcicki, A. J. Organornet. Chern. 1978, 749, C66C70. (34) Su, S . 4 . H.; Wojcicki, A . To be submitted for publication. (35) Jacobson, S. E.; Wojcicki, A. J. Am. Chem. SOC. 1973, 95, 69626970. (36) Severson, R. E.; Wojcicki, A. To be submitted for publication. (37) Shriver. D. F. "The Manipulation of Air-Sensitive Compounds", McGraw-Hill: New York, N.Y., 1969. (38) Piper, T. S.; Wilkinson. G. J. Inorg. NucI. Chem. 1956, 3, 104-124. (39) Severson, R. E.; Wojcicki, A. J. Organornet. Chem., 1978, f57, 173185. (40) Laubengayer, A. W.; Condike, G. F. J. Am. Chem. SOC. 1948, 70, 2274-2276.
A Comparison of the Rates of Electron Exchange Reactions of Ammine Complexes of Ruthenium( 11) and -(111) with the Predictions of Adiabatic, Outer-Sphere Electron Transfer Models Gilbert M. Brown and Norman Sutin* Contribution f r o m the Chemistry Department, Brookhasen National Laboratory, Upton, New York 1 1973. Received June 22, I978
Abstract: The rate constants for the R u ( N H ~ ) ~ ~ +R~(NH3)4(bpy)~+/*+, /~+, and R ~ ( N H 3 ) 2 ( b p y ) 2 ~ +electron /~+ exchange reactions have been measured by a technique involving subtle modifications of the ligands. The rate constants (M-' s-l, medi+ / ~ + 7.7 X IO5, 0.1 M CF3SO3H, and 2.2 X 106, um) at 25 OC are 3.2 X lo3, 0.1 M CF3S03H, for the R u ( N H ~ ) ~ ~exchange; 0.1 M HC104, for the R ~ ( N H 3 ) 4 ( b p y ) ~ +exchange; /~+ 8.4 X lo7,0.1 M HC104, for the R~(NH3)2(bpy)2~+/*+ exchange. The
rate constants and activation parameters for the R ~ ( N H 3 ) 4 ( b p y ) ~ +exchange /~+ reaction were determined as a function of ionic strength ( k = 4.1 X lo4 M-I s-I, AH* = 4.0 kcal mol-], and AS* = -24 cal deg-' mol-' at zero ionic strength and 25 " C ) .The rate constants determined in this work together with those for the analogous R ~ ( N H 3 ) j p y ~ +and / ~ +R ~ ( b p y ) 3 ~ + / 2 + exchange reactions are compared with the predictions of theoretical models. Good linearity was found for a plot of log k,, vs. 1/T, where 7 is the mean separation of the ruthenium centers in the activated complex. The Marcus model derived on the basis of a reactive collision formulation gives better agreement with the observed rate constants and activation parameters at zero ionic strength than the conventional ion-pair preequilibrium model. Contrary to prediction, the increase in exchange rate with increasing ionic strength is reflected primarily in a decreased enthalpy of activation.
Introduction Outer-sphere electron exchange reactions constitute the simplest class of electron transfer reactions.' The rates and activation energetics of such reactions a r e therefore of considerable interest. T h e currently accepted model for bimolecular electron exchange between M(r11)L63+and M(11)L62+ involves the reaction sequence2 M(III)L63+ + M(11)L62+
ki
[M(III)L61M(II)L6]5+ (1)
k-1
In this scheme the reactants first form a precursor complex (eq 1). T h e electron transfer takes place within this complex to form a successor complex (eq 2). Dissociation of the successor complex yields the observed electron transfer products (eq 3). In this paper we treat the case in which precursor complex formation is a rapidly established preequilibrium with the subsequent electron transfer within this complex being rate determining (k-1 >> ket). Under these conditions the observed second-order rate constant is equal to Kok,, where K O = k l / k - l . W e will also assume that the electron transfer is adiabatic, that is, that the interaction between the reactants is
large enough for the electron transfer to occur with unit probability in the activated complex. In other words, we assume for the time being that the probability factor ( K ) in t h e expression
is equal to unity. Under these circumstances the FranckCondon barrier to electron transfer should account for AGx*. For a M ( I I ) / M ( I I I ) exchange reaction, the Franck-Condon barrier arises because the metal-ligand bond lengths must rearrange to some common value intermediate between that characteristic for the metal ion in oxidation states I1 and I11 before electron transfer can occur. Likewise, the solvent polarization around the reactants, which is sensitive to the charge of the reactant, must rearrange prior to electron transfer. These rearrangements a r e required to satisfy conservation of energy. 1,3-10 Therefore if the equilibrium constants for precursor complex formation ( k I / k - , ) and the Franck-Condon rearrangement barriers a r e known, t h e rate constants for electron-exchange reactions can be calculated. In this paper the exchange rate constants of the R u ( I I I ) / Ru(I1) redox couple in a series of ruthenium ammine complexes a r e compared with t h e predictions of various models. The exchange rate constants for the ruthenium complexes were
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determined by using subtle modifications of ligands which allowed t h e true exchange rate constant t o be approximated by a net electron transfer reaction rate constant. T h e rate constants t o be compared with theory were either measured in this work or taken from t h e literature. T h e use of t h e Ru(III)/Ru(II) couple allows a n evaluation of the inner-sphere rearrangement energy. T h e differences in t h e metal-ligand bond distances of t h e ruthenium(I1) and ruthenium(II1) complexes used in this work are known to be small either from X-ray crystallographic determinations of t h e structures of the complexes or from extrapolations from similar complexes. Ruthenium complexes also have t h e advantage of being inert t o substitution in both t h e I1 a n d I11 oxidation states. As a consequence the reactions discussed in this work are known to be outer sphere. Furthermore, t h e ruthenium complexes used are not susceptible to hydrolysis in aqueous solution a n d can be employed a t low acidity a n d hence a t low ionic strength. We have also studied t h e temperature dependence of one of these exchange reactions as a function of ionic strength. From a comparison of t h e observed a n d calculated activation parameters w e show under what conditions this simple semiclassical model is applicable and present some possible reasons for deviations from t h e predicted behavior.
perchlorate trihydrate, [Ru(bpy)2(NH3)2](CIO4)2.3H20, and cisdiamminebis( 1 , I 0-phenanthroline)ruthenium( 11) perchlorate, [Ru(phen)2(NH3)2](C104)2, were prepared from Ru(bpy)2Cl~2H20 and Ru(phen)2Cl2-3H20, respectively, by the literature procedure.I6 Tris(ethylenediamine)ruthenium(III) bromide, Ru(en)3Br3, was also prepared by the literature procedure.17 Hexaammineruthenium(II1) chloride [Ru(NH3)6]C13 (Matthey-Bishop), was purified by recrystallization.’* CF3S03H (3 M) was purified by reduced-pressure distillation. Dilute aqueous solutions of CF3CO3H and HC104 were standardized by titration with base. R~(NH3)4(phen)~+ was generated in HC104 or CF3SO3H solution by oxidation of the ruthenium(I1) complex with a stoichiometric amount of cerium(1V) in 1 N H2SO4, followed by dilution until the M). Solutions concentration of H2SO4 was insignificant ( < I X of R~(NH3)4(bpy)~+ were prepared from the solid or by in situ oxidation with cerium(1V) as described above. R~(phen)2(NH3)2~+ was also generated in solution by stoichiometric cerium(1V) oxidation. Solutions of R~(bpy)z(NH3)2~+ were generated by oxidation of an acidic solution of the ruthenium(I1) complex with excess PbO2 followed by filtration through a bed of glass wool to remove the excess oxidant. PbO2 was unsatisfactory as an oxidant for Ru(phen)~(NH,)2~+. Reduction of ruthenium(Il1) solutions of this complex by excess iron(I1) failed to reproduce quantitatively the exRu(NH3)s2+ was generated pected spectrum of R~(phen)2(NH3)2~+. under an argon atmosphere by Zn(Hg) amalgam reduction of a solution of the ruthenium(II1) complex which was kept in an ice-water Experimental Section” bath. These solutions were stored at an acidity of 10-3-10-2 M to Chemicals and Solutions. The preparation of salts of tetraamprevent hydrolysis of NH3 and were used within 1 h of generation. mine-2,2’-bipyridineruthenium(Il),R~(NH3)4(bpy)~+, and of teSolutions of R ~ ( e n ) 3 were ~ + kept in IO-’ M acid to suppress autoxtraammine-1,IO-phenanthrolineruthenium(lI), R~(NH3)4(phen)~+, idation of the coordinated ethylenediamine and were used within 1 have been previously reported.12The procedure reported here repreday of preparation. sents a significant improvement since the starting material is the Kinetic Apparatus and Methods. Rate constants were determined readily prepared and air-stable salt [RU(NH~)~(H~O)](CF~SO~)~.~~ by the stopped-flow method using a Durrum-Gibson instrument which [Ru(NH3)4(bpy)](C104)2 was prepared by reduction of [Ruwas modified as previously described.lg This spectrometer employed ( N H ~ ) s ( H ~ O ) ] ( C F ~with S O ~Zn(Hg) )~ amalgam in C2HsOH conTeflon-covered drive syringes and a 2-cm path length cuvette. Temtaining a tenfold molar excess of 2,2’-bipyridine under an argon atperature determinations were made with a calibrated thermometer mosphere for 1 h. The product was precipitated from solution by adby measuring the temperature of the thermostating liquid in the drive dition to (CzH5)20, and the solid was collected by filtration, dissolved syringe trough and are accurate to within 0.2 OC. Exchange reactions in a minimum volume of H20, and extracted with CHCI3 to remove which involved the substitution of phenanthroline for bipyridine were any residual free bipyridine. The perchlorate salt of the desired monitored at 290-295 or at 265 nm (the rate constants were indecomplex was obtained by adding several milliliters of saturated pendent of the monitoring wavelength). The R U ( ~ ~ ) ~ ~ + - R U ( N H ~ ) ~ ~ + aqueous NaC104 to the solution. The reddish-purple salt was collected reaction was followed at 300 nm. by filtration, washed with 1:1 (v/v) C2HsOH-(C2H&O and then Kinetic Data Treatment. The rate of the R~(en)3~+-Ru(NH3)6~+ (CzH5)20, and air dried, The complex was characterized by UV-vis reaction was measured under conditions such that the concentration spectra (A,,,, nm (e, M-’cm-I) H2O: 522 (3.31 X IO3), 366 (5.51 of R ~ ( e n ) 3 was ~ + in a tenfold or greater excess over the concentration X IO3), 295 (3.2 X lo4)) and ruthenium analysis. Anal. Calcd: Ru, of Ru(NH3)h2+ and the reaction obeyed first-order kinetics. The rewas 19.2. Found: Ru, 18.6. [RLI(IVH~)~(~~~~)](CF~SO~)~.~H~O action systems R~(NH3)4(bpy)~+/~+-Ru(NHj)4(phen)~+/~+ and prepared in an analogous manner. [Ru(NH3)5(H20)] (CF3S03)3 was R u ( ~ P Y ) ~ ( N H ~ ) ~ ~ + / ~ + - R u (were P ~ ~studied ~ ) ~under (NH~)~~+/~+ reduced over Zn(Hg) amalgam in CH30H in the presence of a tenfold conditions such that a rate of approach to equilibrium was measured. excess of phenanthroline monohydrate under argon. After 1 h the For these reactions absorbance-time data were fit to the reaction reaction mixture was filtered to remove the Zn and diluted fivefold scheme with CH2C12, and the flask was sealed and placed in a refrigerator for A+B=C+D 2 days to allow the product to crystallize. The red-black crystals were collected by filtration, washed with CH2C12, and air dried in the filter --d[A1 - kf[A] [B] - k,[C] [D] funnel. The spectrum in H 2 0 and analysis of the solid for ruthenium dt show that the salt is best characterized as a trihydrate. A,, nm (e, M-1 cm-1): 471 (6.68 X IO3), 265 (3.5 X IO4). Anal. Calcd: Ru, 14.4. The R~(NH3)4(bpy)~+/~+-Ru(NH3)4(phen)~+/~+ and Ru(bpy)zFound: Ru, 14.3. [Ru(NH3)d(bpy)](C104)3 was prepared by dis(NH3)23+/2+-Ru(phen)2(NH3)23+/2+ reactions both have equilibsolving the Ru(I1) salt in a minimum volume of CH3CN (MCB rium constants near unity. Under these conditions kf = k , = k and spectrograde) and oxidizing with a 10% excess of Br2 in CH3CN.I4 the rate law for this reaction scheme reduces to a simple expression. There was some precipitate present at this point and the complex was When C and Dare absent at time zero, the integrated rate expression completely precipitated from solution by the addition of several drops is20 of concentrated HCI. The solid was collected by filtration and immediately dissolved in a minimum volume of 0.1 M HCI. The perIn (x, - x ) - In xe = -k([A]o [B]o)t chlorate salt of the desired complex was obtained by dropwise addition where x and x, are the extent of reaction at time t and at equilibrium, of concentrated “ 2 1 0 4 until a purple solid appeared. After the flask respectively, and [AI0 and [B]o are the concentrations of A and B at was cooled in an ice bath the solid was collected by filtration. The time zero. For spectrophotometric monitoring where OD,, ODo, and crystals were washed with several milliliters of ice-cold 2 M HC104, ODr are the optical densities at equilibrium, time zero, and at any time air dried, and then dried in a vacuum desiccator overnight. The solid t , respectively, the integrated rate expression becomes lost it5 crystalline appearance and became powdery as it dried. The complex was analyzed by reducing it to ruthenium(I1) over Zn(Hg) In (OD, - OD,) - In (OD0 - OD,) = - k ( [ A ] o t [B]o)t amalgam in 0.1 M HC1 and comparing the spectrum of the reduced For these reactions the observed first-order rate constant is related product with that of the pure ruthenium(I1) complex. The salt was found to be anhydrous. Ru(bpy)zC12*2H20 and Ru(phen)2C12*3H20 to the exchange rate constant by the expression were prepared by a procedure devised by Weaver and reported by kobsd = kex([Ru(II)lo [Ru(III)lo) (4) Sprintschnik et a1.Is cis-Diamminebis(2,2’-bipyridine)ruthenium(II)
+
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885
Table I. Experimental Data for the [Ru(Ntl3)4(bpy)-Ru(Nt-13)4(phen)l3+I2+ Reaction at 25.0 "C in 0.10 M HC104
kex,
kobsd?'
[Ru(lll)lo, M
[Ru(ll)lo, M
0.50 X
1.01 x 10-5 1.01 x
2.01 x 10-5
c
1.00 X a
30.3 0.2 62 f 1
c
39.7 f 0.1
1.01 X
The errors in
kobsd
M-I
S-1
s-l
2.01 x 106 2.05 X loh 1.97 X I O 6
are average deviations. The rate constant
k,, is calculated from eq 4. Forward direction, R ~ ( N H 3 ) 4 ( b p y ) ~ +
+ Ru(NH3)4(phen)?+.
Reverse direction, R ~ ( N H ~ ) ~ ( p h e+n ) ~ +
Ru(Nki3Mb~~)~'. Electrochemical Measurements. A PAR Model 176 and 175 system with a Hewlett-Packard Model 7000A x-y recorder was used for potential measurements. The potentials of the R ~ ( e n ) 3 ) + / ~and + Ru(NH3)h3+I2+redox couples were measured v5. an internal standard reference reaction, the R ~ ( N H 3 ) 4 ( b p y ) ~ +couple. / ~ + Formal potentials were measured by cyclic voltammetry at a pyrolytic graphite electrode,21taking the midpoint potential of reversible voltammograms to be Ell2. Potentials were uncorrected for errors caused by differences in diffusion coefficients between the Ru(l1) and Ru(II1) complexes. It was assumed that this correction would be the same for the two redox couples and that it would cancel in determining AE for the reaction
Ru(en)j3+
+ R u ( N H ~ ) =~ ~R +~ ( e n ) 3 ~++R u ( N H ~ ) ~ ~ +
0.00
+
k5
R ~ ( N H 3 ) 4 ( b p y ) ~ +R ~ ( N H 3 ) 4 ( p h e n ) ~ + ; = r k-5
+
R ~ ( N H 3 ) 4 ( b p y ) ~ +R ~ ( N H 3 ) 4 ( p h e n ) ~ +(5) was measured as a function of ionic strength and temperature in C104- and CF3S03- media. The equilibrium constant from potential measurements a t 25 "C for reaction 5 is essentially unity (AE < 0.005 V in 0.1 M CF3S03-) which requires that ks = k-5 = kex. Sample data for the rate of approach to equilibrium in 0.1 M HC104 a t 25 "C a r e given in Table I. Integrated first-order plots for these runs were generally linear t o greater than 90% of the reaction. T h e rate of approach to equilibrium is well described by eq 4.A more important observation is that the exchange rate constant is independent of the direction from which the equilibrium is approached. A complete listing of the experimental data for this reaction and the other reactions studied in this work a r e given in supplemental tables. Values of AH*, AS*,and least-squares best fit rate constants a t 25 "C a r e given in Table 11 for the [R u ( NH3)4( bpy) /Ru(NH3)4( phen)] 3+/2+ exchange reaction in both C104- and CF3S03- media. T h e electron transfer reaction given in eq 5 is expected to be a n excellent approximation to the true tetraamminebipyridineruthenium(II)/-(111) exchange reaction. Within error there is no free-energy difference between the reactants and products in reaction 5 and the two complexes are virtually the same size. Moreover, the kinetic data for the Ru(NH3)d( b ~ y ) ~ + / *exchange + reaction are well fit by the rate expression (eq 4)a t all the ionic strengths and temperatures used in this work. This implies that not only is AGO = 0 for reaction 5 but also that AH" = 0 and AS" = 0. From electrode potentials a t 25 and 0 "C, AH" and AS" for reaction 5 a r e estimated to be -0.1 kcal mol-' and -0.8 cal deg-] mol-', respectively.
0.20
0.30
0.40
0.50
Ji; I+fi
Figure 1. Plot suggested by the Guggenhcim equation showing thc ionic strength dependence or the rate constants for the R~(NH3)4(bpy)~+/~+ exchangc reaction at 25 "C: circles, HC104 medium; triangles. CF3SO3H
medium. The linc has the Debye-Huckcl limiting slope of 6.12. Table 11. Rate Constants and Activation Parameters of the
R ~ ( b p y ) ( N H 3 ) 4 ~ +Electron /~+ Exchange Reaction medium, M
Temperature control was provided by immersing the electrochemica cell in a water bath of the desired temperature. Differences in poten~+-RUtials at 25 "C were measured for the R U ( ~ ~ ~ ) ~ ( N F I ~ ) ~ ~ + /0.002d 0.01 d (phen)z( N H3)23+/2+ and Ru( N H3)4( b ~ y ) ~ + / ~ + - N R H3)4u( hen)^+/^+ reaction systems by a similar internal reference tech0.04d 0.10d nique.
Results [R~(NH3)4(bpy)/Ru(NH3)4(phen)]~+/~+ Exchange Reaction.22 T h e rate of the electron transfer reaction
0.10
I .OOd
0.002e 0.01 e
0.03" 0.10e 1 .00'
k2S°C,' M-1 s - l
6.62 X IO4
1.40 x 105 3.77 x 105 7.12 X lo5 3.25 X lo6 8.73 x 104 2.76 X IO5 7.3 x 105 2.2 x 106 1.2 x 107
AH*,b
AS*,
kcal mo1-I
cal deg-' mol-1
4.1 4.0
-23 -22
3.1 2.8
-21
4.3
-22 -24 -25 -23 -22
2.9 2.1 I .9 1.2
-19
Least-squares best fit value at 25 "C. The error in AH* is f 0 . 5 kcal mo1-l. The error in AS* is f 3 cal deg-I mol-'. Medium is HTFMS. Medium is HC104. Therefore the activation parameters measured for reaction 5 should be a n excellent approximation to those for the desired exchange reaction. A similar ligand substitution technique has previously been used by Wilkins and YelinZ3and by Young et al.24 to estimate the rate constants for the FeEDTA2-/- and the R u ( b ~ y ) 3 ~ + exchange /~+ reactions, respectively. T h e rate constants a t 25 "C were fit to the Debye-Huckel equation
and to Guggenheim's modification of the Debye-Huckel equation which sets p7= 1. In eq 6, z~ and 2 2 a r e the charges of the reactants, a and a r e the Debye-Huckel constants, equal to 0.51 and 0.329, respectively, at 25 "C, p is t h e ionic strength, and 7 is the distance of approach of the centers of the reactants, which will be discussed in a later section. A plot of log k vs. 4 / ( 1 (Guggenheim equation) is shown in Figure 1. Significant deviation from linearity is seen a t high ionic strength. This is not surprising in view of the failure of Debye-Huckel theory to fit activity coefficients a t high ionic strength.2s T h e data in CF3S03- media, however, do have the correct Debye-Huckel limiting slope of 6.12. This is shown by the solid line in Figure 1. These results suggest that the Guggenheim equation adequately accounts for the ionic strength dependence of the rate constants as the CF3S03medium approaches infinite dilution. The data in ClO4- me-
+ 4)
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which the equilibrium is approached. The exchange rate constant is (8.4 f 1.1) X lo7 M-' s-' a t 25.0 O C in 0.1 M HC104. T h e standard deviation of the rate constant is large because the range and absolute values of the concentrations of reactants for which the rate could be measured were small (1 -2.5 X M ) , and the observed first-order rate constants were near the limit of the stopped-flow method (260-410 s-l). R ~ ( e n ) 3 ~ +RU(NH&~+Reaction. T h e rate of the title reaction was measured in order to confirm the exchange rate constant reported for the R u ( N H ~ ) ~ ~ couple + / ~ + a t p = 0.1 M.28 The R u ( N H ~ ) ~ ~ exchange + / ~ + rate constant was first reported by Meyer and Taube in a n elegant experiment inT h e most precise volving the substitution of ND3 for "3. value for the exchange rate constant in their study was obtained a t p = 0.013 M . The exchange rate constants for the Ru( e r 1 ) 3 ~ + / ~and + R u ( N H ~ ) ~ ~ couples + / ~ + a r e expected tb be similar since the complexes a r e virtually the same size and the ethylene-diamine ligand is not expected to cause steric restraints a s the reactants approach one another. In CF3S03- media, the rate constant for the net reaction
+
4.0
r
0.00
1
I
I
0.10
0.20 ~
-
O
.
l
l
0.30 r
I +1.41Jp
Figure 2. Nonlinear least-squares best fit of the rate constants at 25 " C for the R ~ ( N H 3 ) 4 ( b p y ) ~ + exchange /~+ reaction in CF3SO3H media to eq I .
dium, by contrast, are less well behaved. In this case the limiting slope has a value of 9-10 rather than the theoretical value of 6.12. A plot of the difference in rate constants in C104- and CF3S03- media vs. the concentration of ClO4- is linear in the range [C104-] = 0.002-0.10 M . This indicates that the data in HC104 can be fit by a two-term rate law of the form rate = k,,[Ru(II)] [ R u ( I I I ) ]
+ k'[Ru(II)] [Ru(III)] [C104-]
The k' term represents catalysis of the exchange reaction, probably by ion-pair formation of C104- with the highly charged ruthenium(II1) complex. N o spectroscopic evidence for ion-pair formation between R ~ ( N H 3 ) 4 ( b p y ) ~and + C104was found. T h e correlation of the data with the exact Debye-Huckel equation (eq 6) is less satisfactory. T h e deviations from the calculated line in CF3C03- media a r e in the same direction as the deviations in C104- media for which a n argument for ion-pair formation has been presented. By contrast, the extended equation
(7) with ko = 4.14 X lo4 M-' s-I, b = 1.41 M-1/2, and c = -0.65 M-I, does fit the CF3S03- d a t a well over the entire ionic strength range studied.26 This is shown in Figure 2. The fitted value of 07 = b = 1.41 corresponds to a value of 7 which is roughly a factor of 2 smaller than the value calculated from the mean "hard sphere" radii (see below) of the reactants. Newton2' has found similar effects in treating the influence of ionic strength on the rates of oxidation-reduction reactions of actinide ions. [Ru(bpy)2(NH&/R~(phen)z(NH3)21~+/~+ Exchange Reaction. The rate of approach to equilibrium of the electron transfer reaction
+
ka
Ru(bpy)~(NH3)2~+ Ru(~hen)2(NH3)2~+
k-a
+
R u ( ~ P Y ) ~ ( N H ~ Ru(~hen)2("3)2~+ )~~+
(8)
was measured at 25.0 O C in 0.10 M HC104. Potential measurements show that within experimental error the equilibrium constant for reaction 8 is unity ( A E S 0.004 V ) . T h e d a t a are well fit by the rate expression given in eq 4 and the calculated second-order rate constant is independent of the direction from
-
+
Ru(en)13+ t R u ( N H ~ ) ~ ~ R+ ~ ( e n ) 3 ~ +R u ( N H ~ ) ~ ~ + (9) is 2.70 X l o 4 M-' S-I a t 25 OC and p = 0.10 M . In order to calculate a n exchange rate constant, the rate constant for t h e cross reaction was corrected for the free-energy change by means of the Marcus equation k12 = ( k i i k 2 2 K 1 2 f i d ] / ~ Iogfi2 = (log K i d 2 / 4 log ( k i 1k22/Z2)
(10) where k12 is the rate constant for the cross reaction, k l l and k22 are the exchange rate constants of the reactants, K12 is the equilibrium constant for the cross reaction, and Z = 10" M-l s-I. In the case in question, k l l and k22 a r e expected to be virtually the same and consequently k,, = k 1 2 / ( K 1 f 1 2 ) ~ / ~ . From measurements of the difference in formal potentials of the R u ( I I I ) / R u ( I I ) complexes, K12 is 73 and therefore k,, is calculated to be 3.2 X lo3 M-I s-l (25 O C , p = 0.10 M ) . This is in excellent agreement with the value of 4 X lo3 M-I s-l reported by Meyer and Taube. T h e enthalpy and entropy of activation for the Ru(NH3)63+/2+exchange reaction are also of interest. The values reported by Meyer and Taube28 for AH* and AS* a t p = 0.01 3 M a r e 10 kcal mol-' and - 1 1 cal deg-' mol-', respectively. As will be noted in the Discussion section, the value of AS* appears to be too positive by a factor of more than 2. For this reason, the activation parameters for reaction 8 were measured (AH* = 2.4 f 0.5 kcal mol-' and AS* = -30 f 3 cal deg-I mol-', y = 0.10 M CF3SO3-). The activation parameters for the desired exchange reaction can be estimated using the equations derived by Marcus and S ~ t i n . ~ ~
AG12O 4(AGl1* AG22*) where AG* = - R T In (k/Z), AG* = -RT In (kh/kBT), AGi = AG* - R T In (hZ/kBT), A H + = AH* - RT/2, and A S * = AS* - R/2. As in eq 10, the subscript 12 refers to the cross reaction and 11 (and 22) refers to the exchange reaction. A H l 2 O and A S 1 2 O for reaction 9 were measured from electrode potential data. The measured values of AE' a r e 0.102 and 0.109 V a t 25 and 0 OC, respectively, in 0.10 M CF3SO3-. Thus A H o and ASoare -4.3 kcal mol-] and -6.4 cal deg-I mol-', respectively. These values are in reasonable agreement
a=
+
Brown, Sutin
/ Electron Exchange Reactions of Ammine Complexes of R u ( l I ) and - ( I n )
887
Table 111. Electron Exchange Rate Constants of Ruthenium Ammine Complexes at 25 OC
medium
reaction ~~
~
Ru(N H 3)63+/2+
4.3 x 103 3.2 x 103
0.1 M HC104 0.1 M CF3SO3H 0.1 M CF3S03H 0.1 M CF3SO3H 0.1 M HC104 0.1 M HC104 0.1 M HC104
R~(NH3)5py~+/~+ R~(NH3)4(bpy)~+/'+ R~(NH3)2(bpy)2~+/~+ Ru(bpy) 33+/2+
1.1
x
7.7 x 2.2 x 8.4 x 4.2 X
3.3
105
3.8
105
4.4
b this work 32c this work this work this work 24
106
107
5.6
IO8
6.8
The exchange 0 Mean radius, i = '/2(d1d*d3)'/~. T. J. Meyer and H. Taube, quoted in H . Taube, Ado. Chem. Ser., No. 162, 127 (1977). rate constant at 25 "C and 1 .O M CF3SO3H is 4.75 X IO5 M-'s-I; it was empirically corrected tow = 0.1 hl by multiplying the rate constant at p = 1.0 M by 0.23.
with AHo= -1.1 kcal mol-] and ASo= +3.9 cal deg-' mol-] calculated from the data of Lavallee e t al.30,3' a t p = 1 .O M CF3SO3-. T h e values of AH* = 4.5 kcal mol-] and AS* = -27 cal deg-l mol-] a r e then estimated for the R u ("3)63+/2+ exchange reaction, using the values of A H o and ASo measured in this work. Dependence of Exchange Rates on the Size of the Reactants. T h e rate constants a t 25 OC and 0.1 M ionic strength for the R u ( N H ~ ) ~ ~ + R / ~u +( ,N~ H~ ~ ) , ~ ~ ~ +Ru(NH3)4/~+,~~ ( b ~ y ) ~ + / ~R +~ (, N H 3 ) 2 ( b p y ) 2 ~ + / ~and + , R ~ ( b p y ) 3 ~ + 24 /~+ exchange reactions are summarized in Table 111. The general trend in the electron exchange reactions of these complexes is an increase in rate with a n increase in the size of the complex. Although the complexes R u ( N H ~ ) ~and ~ +R ~ ( b p y ) 3 ~a +r e spherically symmetrical, the other reactants considered here a r e not. For purposes of comparison of the rates and also for theoretical purposes (the theory which has been developed for outer-sphere electron exchange reactions is for spherical reactants) we have calculated the radii equivalent to the sphere of equal volume using the relation
a = '/2(d1d2d3)'/~ where the d, are the "diameters" along the three L-Ru-L axes. These radii a r e included in Table 111. Values of d, were estimated from C P K molecular models and corrected to agree with known crystallographic results. For NH3-Ru-NH3, "3Ru-pyridine, and pyridine-Ru-pyridine diameters, the values used a r e 6.6, 10.2, and 13.6 A, respectively. A plot of log k vs. 1/F, where k is the rate constant for electron exchange and i' is the mean distance of separation of the ruthenium centers, taken to be 2a, is presented in Figure 3. The plot shows good linearity. Figure 3 can be used to predict the exchange rate constants of other ruthenium amminepyridine complexes. Accordingly we estimate exchange rate constants of 8 X 1 O6 and 2 X lo8 M-I s-l for the couples Ru( t e r ~ y ) ( N H 3 ) 3 ~ + / (F ~ + = 9.7 A) and Ru(terpy)(bpy)(NH3)3+/2+(i' = 12.3 A), respectively, a t 25 OC and p = 0.1
I\ I
0.06
k = Z exp[-(w,
+ AG,,* + AGout*)/RT]
(1 1)
0.08
1
1
0.10
0.12
I
1
0.14
0.16
I / T , %-I
Figure 3. Plot of the logarithm of the observed exchange rate constant vs. the reciprocal of the mean distance of closest approach of the ruthenium 2, R ~ ( N H 3 ) 5 p y ~ + / ~3 ,+ ;Ru(NH3)dcenters: 1, Ru(NH&?/*+; ( b p ~ ) ~ + 4, / ~R~(bpy)z(NH3)2~+/~+; +; 5, R ~ ( b p y ) 3 ~ + / ~ + .
In the above expressions, f l and f2 are t h e breathing force constants of the two reactants, Aao is the difference between the equilibrium metal-ligand bond distances of the two reactants, al and a2 a r e the radii of the two reactants, r is the separation of the metal centers in the activated complex (assumed equal to a ] 4,and n and D,a r e the refractive index and static dielectric constant of the solvent, respectively. 2 is the collision frequency of neutral molecules in solution and w , is the work required to bring the two reactants together. Z is usually taken to be 10" M-' s-l and is calculated from the equation
+
M. Discussion T h e results will be compared with t h e predictions of two adiabatic electron transfer models. T h e two models that will be discussed are the Marcus reactive-collision description and the ion-pair preequilibrium scheme outlined in the Introduction. We start first with the equations of the Marcus theory (eq 1 1- 13).3-6
I
Z=
+
N [ 8 r k ~ T ( m l m2)/m1m2]'/~r~
(14) 1000 which has been derived for gas-phase collisions ( mI and m2 are the masses of the two reactants and N is Avogadro's number). In terms of the transition state theory expression kBT k =h exp[-AG*/RT] the free energy of activation for a n exchange reaction according to the Marcus model is hZ AG* = -RT In - W, AGin* AGout* (1 5) kBT The term R T In (hZ/keT) in this formulation arises from the loss in rotational and translational degrees of freedom in
+ +
+
888
J o u r n a l of the American Chemical Society
forming the activated complex from the separated reactants and is given the symbol AG,,,ns. W e next consider the formulation of the electron exchange process in terms of an ion-pair preequilibrium (eq 1-3). In this description the exchange rate constant is given by eq 1619.2 k = Kok,, k
''
(16)
= -k B T exp[-ACx*/RT]
h
ACx* = AG,,*
(17)
+ AGO,,*
(18)
The above expression for KO,the ion-pair equilibrium constant, has been derived from both diffusional33aand free volume33b considerations and has been applied with some success to the rates of substitution reactions which a r e believed to go by an interchange mechanism.34 In terms of transition state theory the activation free energy according to the ion-pair preequilibrium model is 4aNr3 AG* = -RT In - w, AG;,* AGO,,* 3000 T h e Marcus and ion-pair formulations of the rate constant can be put on a common basis by writing eq 1 1 in the form
+ +
+
Zh ksT (21) k = -exp[-w,/RT] -exp[-ACx*/RT] kBT h Comparison of eq 21 with eq 16 and 17 shows that the rate constant for electron transfer in the Marcus formulation can also be formally expressed as the product of an equilibrium constant for precursor complex formation, given by eq 22, and a rate constant for electron transfer within the precursor complex, given by eq 17. Zh KO = -exp[-w,/RT] ksT T h e preequilibrium assumption for precursor complex formation and the use of eq 19 and 22 for K Omerit additional comment. The preequilibrium assumption requires that the dissociation of the precursor complex be rapid compared to the rate of electron transfer within the precursor complex, that is, that the electron transfer not be diffusion controlled. If the electron transfer is diffusion controlled then it is necessary to make a steady-state assumption for the concentration of the precursor complex. So far as the expressions for K Oa r e concerned, eq 19 has been derived for ion-pair formation between oppositely charged reactants. For such systems the potential energy of interaction is a minimum when the two reactants are in contact. The same is not true for similarly charged reactants. For the latter systems eq 19 (and other analogous equations) can still be used with r = ( a , a2). However, although t h e equilibrium constant in this case still gives the statistical distribution of reactants that a r e in contact, r = (a1 a2) no longer corresponds to a minimum in the interaction free energ^.^^ With this reservation in mind, we will continue to use eq 19 for similarly charged reactants. Equation 22, which has been derived from the kinetic theory of gases, glosses over the details of the diffusional process in liquids. Nevertheless, the use of 2 is justified by the fact that it provides a reasonable estimate of the total number of collisions per unit time between a pair of molecules in solution. The ratio of the equilibrium constants for precursor complex formation given by eq 19 and 22 is
+
+
/
101.4
/
February 14, 1979
where ml = m2 = m, M = Nm, and r is in Angstroms. T h e difference between the two methods of calculating the rate constants is small for small reactants but, a s will be pointed out in the next section, is significant for the reactions discussed here. An important term in the expressions for the free energy of activation is the work required to bring the two reactants together. Since the Debye-Huckel theory fits the ionic strength dependence reasonably well to p = 0.1 M (for the R u ( N H 3 ) 4 ( b ~ y ) ~ + /exchange ~+ reaction the error in the rate constant a t p = 0.10 M from Debye-Huckel theory is only a factor of 2 based on the rate constant extrapolated to p = 0) we will use the expression for the work term appropriate to the Debye-Huckel theory.
where the symbols have been previously defined. I n the limit of infinite dilution the above expressions are simply a statement of Coulomb's law which gives the energy required to bring two charged spheres from infinity to a separation distance T in a medium of dielectric constant D,. Comparisonof Observed and Calculated Rate Constants. As noted in the Introduction, the contribution to the electron exchange activation energy from the reorganization of the inner-coordination spheres in ruthenium ammine complexes is small. For the R u ( N H ~ ) ~ ~ exchange + / ~ + reaction, Auo is known from X-ray crystallographic determination to be 0.04 T h e symmetrical R u - N stretching frequency of R u ( N H ~ ) ~is ~reported + to be 500 cm-' 37 and assuming that the force constants of Ru(l1) and Ru(II1) are not appreciably differentfi = f 2 = 2.5 X l o 5 dyn cm-' can be calculated. Thus + / ~ + reaction using eq 12, AC,,* for the R u ( N H ~ ) ~ ~ exchange is 0.9 kcal mol-l. Crystal structures have also been determined for pentaamminepyrazineruthenium(I1) and -(111)38and for cis-tetraamminebis(isonicotinamide)ruthenium(II) and -(111),39 which a r e good analogues for estimating AG,,* for / ~ +Ru( N H 3)4( b ~ y )/2+~ exchange the R u ( N H3) ~ p y ~ + and reactions, respectively. For both of these exchange reactions AG,,* is estimated to be 1 .O kcal mol-'. Within the error of the measurements there is no difference in metal-nitrogen bond lengths between tris(phenanthroline)iron(lI) and /~+ This result suggests that AG,,* for the R ~ ( b p y ) 3 ~ + exchange reaction is negligible. Although there are no structural results available for the R ~ ( b p y ) 2 ( N H 3 ) 2 ~ + /system, ~+ AG,n* for this exchange reaction is also expected to be very The observed rate constants for the electron exchange reactions of the ruthenium complexes can now be compared with the theoretical predictions using the equation kcalcd = Q exp[-(wr
+ AGout* + AGin*)/RTl
(26)
The reactive-collision and ion-pair preequilibrium formulations differ only in the expressions used for the preexponential term Q: in the former case Q is simply equal to 2 while in the latter case it is equal to ( k ~ T / h ) ( 4 7 r M ~ / 3 0 0 0 )The . expressions for wr, AGout*, and AG,,* have been previously given (eq 24, 13, and 12, respectively). T h e formulas for wr and AGOut*with constants a t 25 OC and a t p = 0.1 M a r e
in kcal mol-' for i; (= 2 4 in Angstroms. T h e observed rate constants are compared with the predictions of eq 26 in Figure
889
Brown, Sutin / Electron Exchange Reactions of Ammine Complexes of R u ( l 1 ) and - ( I l l )
Table IV. Comparison of Terms Contributing to Calculated Rate Constants for the Electron Exchange Reactions of Ruthenium(ll)/-(Ill) Couples at 25 O C and 1 = 0.1 M
exchange reaction
Ru(N H3)63+/2+
F. A
6.6 2.1 x IO" 4.5 x 10'2 2.28 6.82 0.9 4.7 x 103 9.6 x 10' 2.1 x 10' 4 x IO'! 3.2 x 103 8
Z , M-I s-I Q , M-' s-l w,,kcal mol-' AGou,*, kcal mol-'
lC,,*, kcal mol-' k c a l c d , M-' S - ' kcillcd, M - ' S-' kc;llccJ, M-' S - I f kobsd, M-' S - I a
Ru(N H3)~py'+/~+ Ru(N H3)4( b ~ y ) ~ + / ~ Ru(bpy)2( + N H3)23+/2+
1.51
5.1 1 1 .0
1 .0
2.6 x 7.5 x 2.8 x 7.7 x
3.7 x 104 8.6 X I O 4 2.5 X I O h 1.1
x
11.2 4.0 X I O " 2.2 x 1013 1.05 4.02
8.8 2.9 X IO" 1 . 1 x 10'3
7.6 2.4 X 10" 6.9 x 10'2 I .87 5.92
1051
R~(bpy)3~+/~+ 13.6 5.2 X 10" 3.9 x 1013 0.77 3.31 -0C
-0C
1.9 x 107 7.7 x 107 4.3 x 109 8.4 x 107 g
IO' 105 107 10s 8
1.0 x 108 5.3 x 108 4.0 X 1 O ' O 4.2 X IO8
*
Z calculatcd from cq 14. Q iscqual to (k~T/h)(4nM3/3000). Assurned to bc 7cro. Equation 1 1 with Z = 10Il M-I s-l.
I 1 with Z calculated from cq 14. f Equations 16-19,
X
4 and in Table IV for both the reactive collision formulation (eq 1 1 ) and the ion-pair preequilibrium formulation (eq 16). T h e agreement between the observed and calculated rate constants is much better using eq 1 1. The agreement using a fixed value of Z is acceptable but the agreement with the observed rate constants improves when Z is calculated from eq 14. The latter equation allows for differences in the sizes and masses of the reactants. Calculations based on eq 16 show the expected slope but the absolute rate constants are about a factor of 40 too high. The agreement between the experimental results and eq 16 can be improved if a value of 7 equal to approximately 70% of 25 (Table I l l ) is used. That a smaller value of F may be appropriate was also suggested by the fit of the ionic strength dependence of the rate constants to eq 7 . Note, however, that this would require that the ligands of one reactant penetrate the other reactant's inner-coordination sphere.42 Enthalpy and Entropy of Activation. T h e entropy of activation for an electron exchange reaction can be calculated by differentiating the equation for the frec energy of activation with respect to tempcrature (Gibbs-Helmholtz equation), Sf = -d(AG*)/bT
As* = AS,,,,,
-awr t ASout* + ASin* dT
(29)
(30) where the Debye-Huckel expression (eq 24) for the electrostatic work has been used. At infinite dilution this cquation simplifies to
bWro - w,"b In D, --
(31) bT Tbln T where b In D,/b In T = - 1.368 for water a t 25 "C. The two formalisms for the free energy of activation differ in the equation for AG,,,,, and thus will also differ in AS,,,,,. The expressions for AS,,,,, derived for the reactive collision and the ion pair preequilibrium formulations are given by eq 32 and 33, respectively. liZ R Astr,,, = R In -- kBT 2
KIG3)
AS,,,,, = R In -
e
Equation
This work. Refcrcncc 24. I Rcfercncc 28. Reference 32.
(33)
There is good evidence that ASo,,* and S i n * can be ignored. The energy required to rearrangc the inner coordination spheres of the ruthenium complexes is very small and thus
9'0
t
/ 9'
I
l o g 'ob,
Figure 4. Plot of the logarithm of the calculated rate constant vs. the log-
arithm of the observed rate constant for the series of ruthenium complcxes: triangles, calculated from eq 16-19; circles, calculated from eq 1 1 with Z calculated from eq 14; squares, calculatcd from eq I I with Z fixed at 10'' M-I S-I. 1, R U ( N H ~ ) ~ ' + /2,~ + R;U ( N H ~ ) ~ P Y ~3, +Ru(NH~)I/~+; ( b p ~ ) ~ + / ' 4, + ;R~(bpy)z(NH3)2~+/~+; 5 , Ru(bpy)3'+I2+.
As,,* will also be very small. hso,,* is also expected to be very small from theoretical considerations. In the studies of Fischer et al.43 and of Rieder et al.,44 the entropy of activation for intramolecular electron transfer within binuclear Co(II1)Ru(l1) complexes was found to be near zero. Based on these considerations, we will neglect any contribution to the entropy of activation from these terms and assume that AGO,,* = AHo,,* and ACi,* = AHi,*. T h e enthalpy of activation can be calculated from an alternative formulation of the Gibbs-Helmholtz equation, AH* = ~ ( A G * I T )1IT). ~(
For the reactive-collision model the equation is
AHtrans =
- RT/2
(35)
while for the ion-pair preequilibrium model AH,,,,, is equal to zero. T h e values of AH* for the two formulations will therefore differ by only RT/2 or 0.3 kcal mol-'. The difference between the entropies of activation calculated from the two
890
Journal of the American Chemical Society
-
6.0
/
101:4
/
February 14, 1979
tt
1 I
I 0 00
1
0.20
0.40
0.60
0.80
1.00
JT;. MI'' Figure 5. Plot showing the entropy of activation for the Ru(NH3)d(bpy)3+/2+ exchange reaction as a function of ionic strength: squares,
CF3SO3H medium; circles, HC104 medium. The lines were calculated from eq 29 and 32 with the follow>ingvalues of E a, 7.0 A; b, 9.0 A; c, 14.0
A.
w , = wro - wrob* I S b G
Table V. Comparison of Observed and Calculated Entropies and Enthalpies of Activation at Zero Ionic Strength for the Ru(NH3)d(bpvl3+/*+Exchange Reaction
ASo*(obsd), cal deg-' mol-' AHo* (obsd), kcal mol-' F,
medium. The expression in eq 36 is the equivalent of expressing the ionic strength dependence of the rate constant by eq 7 .
A
ASo* (calcd, eq 37), cal deg-' mol-' ASo* (calcd, eq 40),cal deg-l mol-' 4Ho* (calcd, eq 38), kcal mol-' AHo* (calcd, eq 39), kcal mol-'
-24& 3 4.0 i 0.5
9.0 -22.1 - 1 1.7 4.1 5.0
4.5
-22.6 8.9
models depends upon the size of the reactants and will typically be some 5-15 cal deg-l mol-' for the complexes considered in this study. The ionic strength dependence of the entropy and enthalpy of activation for the R ~ ( N H 3 ) 4 ( b p y ) ~ + / *exchange + reaction is shown in Figures 5 and 6 , respectively. T h e solid line in each figure has been calculated from eq 29 and 34 using 2 = 1 01' M-I s-l and F = 9 A. It will be seen (Figure 5 ) that the observed entropy of activation does not show the predicted increase with increasing ionic strength; instead the entropy is essentially independent of ionic strength. The increase in rate constant wi.th increasing ionic strength is reflected almost entirely in a decrease in t h e enthalpy of activation. This is contrary to the expectation from eq 34 in which a slight increase in enthalpy with increasing ionic strength is predicted (Figure 6 ) . This behavior is not unique to this ruthenium system but has also been observed for the electron transfer reactions of some aquo metal ions45 A smaller ionic strength dependence of the entropy of activation is predicted by the Guggenheim modification of the Debye-Hiickel equation and by t h e extended Debye-Huckel equation derived by Waisman et al.46 However, the predicted ionic strength dependence is still larger than observed for the R ~ ( N H 3 ) 4 ( b p y ) ~ + /exchange ~+ reaction and for the aquo metal ions. T h e observed trend in AH* and AS* with increasing ionic strength in C104- media vs. CF3S03- media suggests that ion pairing or other specific anion effects a r e responsible for the deviations from the predicted behavior. As discussed above, there is good evidence for ion pairing between the Ru(I11) complex and C104- relative to CF3S03- media. There is, however, a n alternative explanation for the dependence of the activation parameters on the ionic strength of the
+ 2.303RTcp
(36)
Here wro = zlzze2/D,T. and b and c a r e empirical constants taken from the nonlinear least-squares fit of the data to eq 7 . Utilizing this expression a n entropy of activation which is independent of ionic strength can be obtained if the dielectric constant or its temperature derivative is assumed to be a function of ionic strength. Although the ionic strength data can be rationalized in this manner, a more fundamental difficulty lies in the use of a dielectric continuum model for highly charged ions such as those employed in this study. Because of the difficulty in interpreting the ionic strength dependence of the activation entropy and enthalpy, activation parameters for the R ~ ( N H 3 ) 4 ( b p y ) ~ + /exchange ~+ reaction a t infinite dilution were obtained by extrapolating the rate constants t o p = 0 using eq 7 . This was done a t each temperature. The entropy and enthalpy of activation a t infinite dilution within the reactive-collision formulation are given by eq 37 and 38, respectively.
+
w,' b In D , hZ R Aso* = -R In-T b1nT) kBT 2 b In D , AHo* = wr0 (1 - IiT AGO,,* AGi,* bInT 2
( -)
+
+
(37) (38)
The value of AHo* calculated from the ion-pair preequilibrium formulation
AHo* = w,'
( )--: ,a 1
+ AGout* + AGi,*
(39)
differs only slightly from the reactive-collision formulation. T h e entropy of activation calculated from the ion-pair preequilibrium formulation is given by w O b In D , Aso* = 2- - R l n ( g ) (40) T blnT T h e experimental activation parameters a r e compared with the calculated values in Table V. T h e values of AS,* and AHo*, calculated from eq 37 and 38, respectively, a r e in excellent agreement with the observed values. By contrast, the entropy of activation calculated from the ion-pair preequilibrium formulation is much too positive. If a smaller value of F is used, the agreement between the observed entropy and that calculated from eq 40 is improved. However, using a value of F derived from the ionic strength dependence of the rate constant a t 25 O C increases the value of AHo* calculated from eq
(
)+
Brown, Sutin / Electron Exchange Reactions of Ammine Complexes of Ru(I1) and - (111)
89 1
AGout* (Table IV). T h e above comparisons thus provide no 39 to such a n extent that it is in poor agreement with the obevidence that t h e expression for AGO,,,* is in error. served value. Other factors which have been neglected in the above disO n e further point with regard to the activation parameters cussion are steric effects, nonadiabaticity, and alternative deserves mention. T h e entropy and enthalpy of activation for forms of the frequency factor. T h e absolute rate theory the R u ( N H ~ ) ~ ~ exchange + / ~ + reaction were calculated from preexponential term kT/h has been used in this discussion. the net reaction between R ~ ( e n ) 3 ~and + R u ( N H ~ ) ~ If~ the +. Other expressions for the frequency factor have been proentropy of activation is not a strong function of ionic strength, posed.2 Including these effects may improve the agreement then the observed value a t p = 0.10 M , -27 f 3 cal deg-' between the kinetic parameters calculated for the ion-pair mol-', is reasonably close to the expected value for a n F of 7 A. T h e reported entropy of activation for the R ~ ( b p y ) 3 ~ + / ~ + model and the observed values.51A calculation of the electronic interaction energy of the Ru(1I)-Ru(II1) system will evidently is exchange reaction a t p = 0.1 M , -6.6 cal deg-' be of considerable interest. In the absence of this information more positive than expected on the basis of the present treatwe may conclude that the Marcus equations provide a better ment. rationalization of the kinetic data. Conclusions and Implications for Other Exchange Reactions. Finally, if the ionic strength dependence of the entropy of T h e ionic strength dependence of the rate constants and actiactivation for the R u ( I I ) / R u ( I I I ) exchange reaction can be vation parameters determined in this work cannot readily be generalized to other reactions, then the measured entropy of interpreted in terms of the models used. Consequently actiactivations for aquo metal ions of ca. -25 cal deg-' mol-' a t vation parameters were computed a t zero ionic strength and 0.1-1.0 M ionic strength cannot be taken a s evidence for compared with the experimental values. At zero ionic strength nonadiabaticity when observed and calculated values a r e t h e semiclassical model derived on the basis of the reactive compared (as has been done, for example, in ref 46). Thus, collision formulation of an activated complex (Marcus theory) when extrapolations a r e made to infinite dilution, the calcugives excellent agreement with the rates and activation palated entropy of activation for the Fe(H20)63+/2+exchange rameters for the exchange reactions of the ruthenium ammine is in good agreement with the experimental value.I0 The calcomplexes. This model also accounts satisfactorily for the culated activation enthalpy is, however, several kilocalories linear dependence of log k on 1 /F. per mole too high. It has been proposedl3l0 that nuclear tunAs shown above, the Marcus equations can be recast in neling is occurring in this exchange reaction and recent calterms of the preequilibrium formation of a precursor complex culations indeed show that such effects are appreciable in this followed by rate-limiting electron transfer within the complex. system.50However, nuclear tunneling effects are not important The expression for the equilibrium constant for the formation for systems where the inner-shell reorganization energies a r e of the precursor derived in this manner differs from the consmall. This is the case for the ruthenium ammine systems ventional expression for ion pair formation. From the better discussed here. agreement of the rate constants calculated from the reactive collision model with the experimental d a t a it might be conAcknowledgment. This work was performed a t Brookhaven cluded that the preexponential term given by the reactive National Laboratory under contract with the U S . Department collision model is the appropriate one. However, this conclusion of Energy and supported by its Office of Basic Energy Sciis not necessarily correct. T h e data in Table IV show that ences. T h e authors wish to thank Dr. B. S. Brunschwig for AC,,* is small and that the largest contribution to AC* for assistance with the calculations and for helpful discussion. The each exchange is from AGO,,*. Thus it could still be that the conventional ion-pair expression is the appropriate one to use, authors also wish to thank Dr. C . Creutz for her interest and encouragement during the course of this work. but that the expression for AGO,,* is in error. For this explanation to be correct the "real" value of AGO,,* would have t o Supplementary Material Available: Tables containing the raw kibe larger than the value given by eq 13. netic data ( 3 pages). Ordering information is given on any current Additional information on this point can be obtained from masthead page. a consideration of the barrier to electron transfer within binuclear complexes. In such systems the question of the stability References and Notes constant of the precursor complex (and ionic strength effects) N. Sutin, Annu. Rev. Nucl. Sci., 12, 285 (1962). is circumvented. Theoretical considerations show that provided N. Sutin, "Bioinorganic Chemistry", Vol. 2, G. L. Eichhorn, Ed., American that the distortions are harmonic and the electronic interaction Elsevier, New York, N.Y., 1973, Chapter 19, p 611. between the two metal centers is not too large, the barrier for R. A. Marcus, J. Cbem. Pbys., 24, 966 (1956). R. A. Marcus, Discuss. Faraday Soc., 29, 21 (1960). light-induced electron transfer within the binuclear complex R. A. Marcus, J. Chem. Pbys., 43, 679 (1965). should be equal to four times t h e thermal activation barrier, R. A. Marcus, Annu. Rev. Pbys. Cbem., 15, 155 (1966). N. S. Hush, Trans. FaradaySoc., 57, 557(1961). in other words,47 Eo, = 4Eth = 4(AG,,*
+
AGO,,*)
+
T h u s (AG,,* G o u t * ) for the thermal electron transfer in a binuclear complex can be estimated from the position of the intervalence absorption band in the complex. For
,,,A
is 1050 nm in D 2 0 corresponding to E , = 27.2 kcal mol-' and (ACi,* AGO,,*) = 6.8 kcal mol-P.48 If we now assume that the thermal electron transfer within the binuclear complex provides a good model for the electron transfer within t h e precursor complex for the R ~ ( N H 3 ) 5 p y ~ + / ex~+ ~ h a n g e , then ~ ~ ,the ~ ~barrier (AGin* AGout*)for the latter exchange is calculated to be -6.8 kcal mol-'. This value is in excellent agreement with the reorganization barrier calculated for the R u ( N H 3 ) ~ p y ~ + /exchange ~+ reaction using eq 13 for
+
+
N. Sutin, Acc. Cbem. Res., 1, 225 (1968). N. Sutin, Adv. Cbem. Ser., No. 162, 156 (1977). N. Sutin, "Tunneling in Biological Systems", B. Chance, Ed., Academic Press, New York, N.Y., in press. Abbreviations used for ligands in this paper are as follows: py. pyridine: bpy, 2,2'-bipyridine; phen, 1,lO-phenanthroline; en, ethylenediamine;terpy, 2,2',2"-terpyridine. (a) J. L. Cramer, Ph.D. Dissertation, University of North Carolina at Chapel Hill, 1975; (b) V. E. Aivarez, R. J. Allen, T. Matsubara, and P. C. Ford, J. Am. Chem. Soc., 96, 7686 (1974). S. E. Diamond and H. Taube, J. Am. Cbem. SOC.,97, 5921 (1975); S. E. Diamond, Ph.D. Dissertation, Stanford University, 1975. R. W. Callahan, G. M. Brown, and T. J. Meyer, Inorg. Chem., 14, 1443 (1975). G. Sprintschnik,H. W. Sprintschnik, P. P. Kirsch, and D. G. Whitten, J. Am. Cbem. Soc., 99, 4947 (1977). G.E. Bryant, J. E. Fergusson, and H. K. J. Powell, Aust. J. Cbem., 24,257 (1971). T. J. Meyer. Ph.D. Dissertation, Stanford University, 1966. J. R. Pladziewicz. T. J. Meyer, J. A. Broomhead, and H. Taube, Inorg. Cbem., 12, 639 (1973). B. S. Brunschwig and N. Sutin, Inorg. Cbern., 15, 631 (1976). R. W. Callahan, F. R . Keene, T. J. Meyer, and D. J. Salmon, J. Am. Cbem. Soc., 99, 1064 (1977).
892
Journal of the American Chemical Society
(21)G. M. Brown and W. D. K. Clark, un ublished work. (22)The [ R ~ ( N H ~ ) ~ ( b p y ) l R u ( N H ~ ) ~ ( p h eelectron n ) ~ ~ + /transfer ~+ reaction has previously been studied in 1 M HC104.12a We have been unable to reproduce the rate constants reported in ref 12a. (23)R. G. Wiikins and R. E. Yelin, Inorg. Chem., 7, 2667 (1968). (24)R. C. Young, F. R. Keene, and T. J. Meyer, J. Am. Chem. Soc., 99,2468 (1977). (25)k . A. Robinsonand R. H. Stokes, "Electrolyte Solutions", 2nd ed.,Academic Press, New York, N.Y., 1959,p 227. (26)The computer program used to obtain the values of the constants was based on R. H. Moore and R. K. Zeigler, Los Alamos Scientific Laboratory Reports LA-2367,1959,and P. McWilliams, LA-2367Addenda, 1962.This program was generously supplied by Dr. T. W. Newton. Each rate constant was weighted according to its reciprocal.
(27)T. W. Newton, "The Kinetics of the Oxidation-Reduction Reactions of Uranium, Neptunium, Plutonium, and Americium in Aqueous Solutions", ERDA Critical Review Series, TID-26506,1975. (28)T. J. Meyer and H. Taube, lnorg. Chem., 7, 2369 (1968). (29)R. A. Marcus and N. Sutin, Inorg. Chem., 14,213 (1975). (30)D. K. Lavallee, C. Lavallee, J. C. Sullivan, and E. Deutsch, Inorg. Chem.,
12, 570 (1973). (31)C.Lavallee and D. K. Lavallee, Inorg. Chem., 16,2601 (1977). (32)M. Abe, G.M. Brown, H. J. Krentzien, and H. Taube, to be published. (33)(a) M. Eigen, 2. Phys. Chem. (FranankfurtamMain),1, 176(1954);(b)R. M. Fuoss, J. Am. Chem. SOC.,80,5059(1958). (34)R. G. Wilkins, Acc. Chem. Res., 3 , 408 (1970). (35)The close-contact distance does, however, correspond to the maximum
-
rata -. constant - - - .- .
(36)H. C. Stynes and J. A. Ibers, Inorg. Chem., IO, 2304 (1971). (37)W. P. Griffith, J. Chem. SOC.A, 899 (1966). (381 M. E. Gress. C. Creutz. and C. 0. Ouicksali. unDublished work (39)D E. Richardson, D. D. Walker, J. E. Sutton, and H. Taube, unpublished
/ 101.4 / February 14, 1979
work.
(40)A. Zalkin, D. H. Templeton, and T. Ueki, Inorg. Chem., 12, 1641 (1973); J. Baker, L. M. Engeihardt, B. N. Figgis, and A. H. White, J. Chem. Soc., Dalton Trans., 530 (1975). (41)The calculations of AG int are basea on a harmonic potentialenergy surface and have not been corrected for the zero-point energy of the reactants. For the Ru(NH~)~~+/'+ system, the contribution from the zero-point energy is -0.6 kcal mol-'. (42)Using the "hard sphere" radii of the reactants, 7 is 6.9 A for the Fe( H z D ) ~ ~ + ' exchange ~+ reaction. The Fe-Fe distance can be decreased to 5.5 A without creating a H-H contact shorter than twice the van der Waals radius of an H atom (M. D. Newton, personal communication). (43)H. Fischer, G. M. Tom, and H. Taube. J. Am. Chem. Soc., 98, 5513
(1976). (44)K. Rieder and H. Taube, J. Am. Chem. Soc., 99, 7891 (1977). (45)A. Ekstrom, A. B. McLaren, and L. E. Smythe, Inorg. Chem., 15, 2853 (1976). (46)E. Waisman, G. Worry, and R . A. Marcus, J. ElectroanaL Chem., 82, 9 (1977). (47)N. S.Hush, Prog. Inorg. Chem., 8,391 (1967). (48)G. M. Tom, C. Creutz. and H. Taube, J. Am. Chem. SOC., 96, 7827 (1974). (49)C. Creutz, Inorg. Chem., 17, 3723 (1978). (50) M. D. Newton, personal communication. (51)Better agreement between the observed kinetic parameters and the values calculated from the ion-pair model is obtained if a frequency factor appropriate to the orientation vibrations of the solvent molecules (-10'' s-' if frequency dispersion is neglected) is used. The use of a solvent libration frequency rather than kTlh for the preexponential factor appears justified for the ruthenium systems considered here because the inner-sphere barriers are very small, and consequently almost all of the activation energy arises from the solvent reorganization.
Crystal and Molecular Structures of Decamethylmanganocene and Decamethylferrocene. Static .Tahn-Teller Distortion in a Metallocene Derek P. Freyberg, John L. Robbins, Kenneth N. Raymond,* and James C. Smart Contribution f r o m the Department of Chemistry, Unicersity of California, Berkeley, California 94720. Receiced June 28, I978
Abstract: The crystal and molecular structures of bis(pentamethylcyclopentadienyl)manganese(ll) and -iron(ll) have been determined by single-crystal X-ray diffraction. The crystal packing of the two compounds is closely related and highly ordered, allowing a detailed comparison of structural parameters. Both metallocenes contain planar, staggered MesCp rings. The ferrocene corresponds to a molecular symmetry of D5d with average Fe-C and C-C distances of 2.050 (2) and 1.419 (2) A, respectively. The low-spin manganocene has an orbitally degenerate 2E2Eground state in D5,j symmetry. This degeneracy is relieved in the solid state by ( 1 ) a distortion of the Cp rings in which C-C ring distances range from 1.409 (2) to 1.434 (2) A and (2) a small slippage of the top and bottom halves of the metallocene "sandwich" to give Mn-C bond lengths which range from 2.105 (2) to 2.1 18 ( 2 ) A. In both structures the methyl groups bend away from the metal atom 0.06 8, from the Cp rings. Orange crystals of (Cj(CH3)5)2Mn conform to the space group C2/c with a = 15.143 (4) A, b = 12.248 (3) & c = 9.910 ( 3 ) & and p = 93.56 (3)'. For 2581 independent reflections with F,12 > 3a(FO2),R = 3.6%, R, = 5.0%. Orange crystals of (C5(CH3)&Fe conform to the space group Cmca with a = 15.210 (3), b = 1 1.887 (2), and c = 9.968 ( 2 ) A. For 1217 independent reflections with F,? > 3o(Fo2),R = 3.9% and R,, = 5.5%. Both structures have four molecules per unit cell with Ci (Mn) and CZh (Fe) crystallographic site symmetry, respectively.
Introduction Previous structural investigations of metallocenes have demonstrated the dependence of the metal-to-(ring carbon) distance [ R ( M - C ) ] on the spin state of the molecule. M a n ganocene [(v-C5H&Mn or Cp2MnI possesses a high-spin 6 A l p ( [ e 2 g 2 a ~ g l e l g 2electronic ]) configuration in benzene solution and in the vapor phase.2 Bunder and Weiss3 have determined t h e structure of solid CpzMn, which is polymeric, while a gas-phase electron diffraction4 study yielded an R ( Mn-C) of 2.383 (3) 8,. This is a n exceptionally long metal to ring bond when compared to other metallocenes of the first transition series, where R ( M - C ) ranges from 2.064 (3) 8, for CpzFe to 2.280 ( 5 ) 8, for C p ~ vMagnetic .~ susceptibility, EPR,6 and UV photoelectron2 studies of 1 ,l'-dimethylmanganocene 0002-7863/79/1501-0892$01.00/0
[(MeCp)2Mn] have demonstrated a thermal equilibrium be) low-spin (2E2g, [e2g3a1g2])electween high-spin ( 6 A ~ gand tronic configurations, with the high-spin form predominating a t elevated temperatures. A gas-phase electron diffraction investigation similarly revealed the presence of two isostructural species in the vapor a t 100 OC, with average R(M-C)s Comparison of these bond of 2.433 (8) and 2.144 (12) lengths with the bond length observed in the high-spin CpzMn led to the conclusion that the former distance represents high-spin and the latter low-spin (MeCp)zMn. An unusually large Mn-C vibrational amplitude (0.160 A) was noted for low-spin (MeCp)zMn, and it was concluded that this was a manifestation of a dynamic Jahn-Teller distortion involving ring-tilting modes. The 2EzEconfiguration is orbitally degenerate; thus in theory the low-spin manganocene is subject to 6 1979 American Chemical Society
