J . A m . Chem. S o t . 1980, 102, 5519-5526
5519
Oxidation-Reduction Reactions of Complexes with Macrocyclic Ligands. Energetics and Dynamics of Methyl Exchange’ John F. Endicott,* K. P. Balakrishnan, and Chung-Lai Wong Contribution from the Department of Chemistry, Wayne State University, Detroit, Michigan 48202. Received November 7 , 1979
Abstract: Intrinsic and thermodynamic components of reactivity have been obtained from rate and equilibrium measurements (N4a tetraaza macrocyclic for the methyl-bridged electron transfer reactions of several CO(N~)(OH~)CH~~+/CO(N~)(OH~)?+ ligand) couples, for the C0(dmgH)~(0H~)CH,/Co**(dmgH), couple, and for the methylcobalamin/cob(II)alamin couple. The intrinsic (free energy independent) barriers to methyl-bridged electron transfer are smallest in the cobalamin couple and largest for complexes of the most sterically hindered of the neutral macrocyclic ligands. It is proposed that the intrinsic kinetic barrier to these reactions can be represented in terms of a three-center-three-electron (Co-CH,Co) bonding description of the transition state. Factors which contribute to the intrinsic barrier are those which contribute to bond strength (electron affinity, separation of donor and acceptor centers, etc.); Franck-Condon factors do not appear to play a dominant role in these reactions. Thermodynamic parameters for the various Co-CH3/Co(II) couples can be related by means of simple thermochemical cycles to differences in reactant and product C e C H , bond energies, entropy differences of outer-sphere redox couples, and a collection of relatively small solvation terms. Data from other studies on photohomolysis threshold energies and the temperature dependence of electrode potentials permit the estimation of Co-CH, bond energies for several complexes. The Co-CH3 bond energies vary from -48 to -33 kcal mol-’. The Co-CH, bond tends to be stabilized by unsaturation of the equatorial ligand and to be very sensitive to stereochemical perturbations.
Introduction T h e effectiveness of reagents in group transfer reactions is frequently discussed in thermodynamic rather than mechanistic terms. Thus, the observation of oxidation-reduction or electrophilic displacement accompanying the methylation reactions of methylcorrinoid complexes has been rationalized in terms of the redox potential of the a c ~ e p t o r . ~Similar ,~ concerns arise, perhaps in a more subtle way, in the frequent postulation that cobaltcarbon homolysis is the key step in much of the metabolic functioning of coenzyme B12.4-6 It remains to be demonstrated that the reactivity in even the simplest of these systems is due to thermodynamic rather than intrinsic kinetic factors. Of course this ambiguity is not unique to reactions of enzymic or of organocobalt complexes since the separation of the thermodynamic and “intrinsic” components of reactivity patterns is rarely a simple matter. However, the intrinsic kinetic barriers to many reactions of cobalt complexes are especially large,“I0 so there is considerable ( I ) (a) Partial support of this research by the National Institutes of Health (AM 14341) is gratefully acknowledged. (b) Presented in part at the 178th National Meeting of the American Chemical Society, Washington, D.C., Sept 1979, INOR 054. (2) Ridley, W. P.; Dizikes, L . J.; Wood, J. M. Science 1977, 197, 329. (3) (a) Fauchiang, Y.-T.; Ridley, W. P.; Wood, J. M. In “Organometals and Organometalloids”, Brinckman, F. E., Bellama, J. M., Eds.; ACS Symposium Series, No. 82; American Chemical Society: Washington, D.C.. 1978; Chapter 4, p 54. (b) Thayer, J. S. In ref 3a, Chapter 12, p 188. (c) Kochi, J . K . In ref 3a, Chapter 13, p 205. (4) (a) Ables, R. H.; Dolphin, D. Acc. Chem. Res. 1976, 9, 114. (b) Ables, R. H. In “Biological Aspects of Inorganic Chemistry”, Addison A. W.. Cullen, W. R., Dolphin, D., James, B. R., Eds.; Wiley-Interscience: New York, 1977. (5) Babior, B. M. Arc. Chem. Res. 1975, 8, 376. (b) Krouwer. J. S.; Babior, B. M. Mol. Cell. Biochem. 1977, 15, 89. (6) Golding, B. T. In “Comprehensive Organic Chemistry”. Haslam, E., Ed.; Pergamon Press: New York, 1978; Vol. 5. (7) (a) Linck, R. G. M T P Ini. Rec. Sei.: Ser. One 1972, 9, 303. (b) MTP Inr. Rev. Sci.: Ser. Two 1974, 9, 173. Surc. Prog. Chem. 1976, 7, 89. (8) Sutin, N. In “Inorganic Biochemistry”, Eichhorn, G. L., Ed.; American Elsevier: New York, 1973; Chapter 19, p 161. (9) (a) Endicott, J . F.; Durham, B. In “Coordination Chemistry of Macrocyclic Compounds”, Melson, G . B.. Ed.; Plenum Press: New York, 1979; Chapter 6. (b) Glick, M. D.; Kuszaj, J. M.; Endicott, J. F. J . Am. Chem. SOC. 1973, 95, 5097. (c) Glick, M. D.; Schmonsees, W . G.; Endicott, J. F. Ibid. 1974, 96, 5661. (d) Durham, B.; Endicott, J. F.; Wong, C. L.; Rillema, D. P. Ibid. 1979, 101, 847. (e) Wong, C. L.; Endicott, J. F., work in progress. (IO) Durham, B. Ph.D. Dissertation, Wayne State University, 1977.
0002-7863/80/ 1502-55 19$01. O O / O
cause to suspect that “purely kinetic” factors may be of great importance in determining reactivity patterns even in cobaltmediated alkylations. The complexity and variety of these reactions are illustrated by the oxidation of organocobalt complexes by powerful oxidants such as Ce’V,391’formally CH3- transfer (“electrophilic displacements”) to mild oxidants such as Hg2+,233 and formally CH, transfer to a strong reductant such as Cr2+.3a,3cJ2 In some sense each of these is an oxidation-reduction reaction, subject to the kinetic constraints typical of electron-transfer processes. The methylation of Cr2+ has been described as a “reductive homolytic cleavage”, but is formally analogous to the well-known halide-bridged inner-sphere electron-transfer reactions so common in the oxidation-reduction chemistry of cobalt and chromium.7-10,13314In fact a common mechanistic description of the halide and methyl-bridged reactions has been proposed15 which involves three-center-three-electron bonding descriptions of the transition states. The methyl-bridged electron-transfer reactions have tended to have much smaller rate^^^,'^ than the analagous halide-bridged This is consistent with the small electron affinity of C H 3 and the consequent relatively “weakly bound” transition state for the methyl-bridged reactions. Nevertheless, an appreciable range of reactivities has been observed in the Cr2+ reductions of methylcobalt complexesI2 and in methyl transfer between different cobalt Unfortunately, these previous studies have not been able to distinguish the intrinsic kinetic components of observed reactivity differences from those variations in reactivity which arise only from differences of the driving force of the reactions. ( 1 1) (a) Halpern, J.; Chan, M. S.; Hanson, J.; Roche, T. S.; Topich, J. A. J . A m . Chem. Soc. 1975, 97, 1606. (b) Halpern. J. A,; Chan, J. S.; Roche, T. S.; Tom, G . M. Acta Chem. Srand., Ser. A 1979, 33, 141. (12) (a) Espenson, J. H.; Shveima, J. S. J . Am. Chem. Soc. 1973,95,4468. (b) Espenson, J. H.; Sellers, Jr., T. D. Ibid. 1974, 96, 94. (13) Haim, A. Acc. Chem. Res. 1975, 8, 264. (14) (a) Taube, H. “Electron Transfer of Complex Ions in Solutions”; Academic Press: New York, 1970. (b) Taube, H. Can. J . Chem. 1959. 37, 129. ( 1 5 ) Endicott, J. F.; Wong, C. L.; Ciskowski, J. M.; Balakrishnan, K. P. J . Am. Chem. Soc., in press. (16) (a) Van Den Bergen, A,; West, B. 0 .Chem. Commun. 1971, 52. (a) J . Organomer. Chem. 1974, 64, 1125. (17) Dodd, D.: Johnson, M. D. Chem. Commun. 1971, 1 3 7 1 .
1980 American Chemical Society
5520 J. Am. Chem. Soc., Vol. 102, No. 17, 1980 Recent work in this laboratorygd has shown t h a t intrinsic and thermodynamic components of reactivity patterns can be separated even f o r inner-sphere e l e c t r o n - t r a n s f e r reactions. The p r e s e n t report describes our studies of t h e methyl-bridged electron-transfer reactions of a series of macrocyclic cobalt complexes. The intrinsic kinetic barriers which we h a v e found for t h e m e t h y l - b r i d g e d electron-transfer reactions span a far greater range than previously found for halide-bridged reaction^.^^^'^^^^ Since this w o r k nec e s s i t a t e d the determination of equilibrium c o n s t a n t s for m e t h yl-bridged reactions, t h e combination of d a t a from the p r e s e n t s t u d y w i t h photochemically d e t e r m i n e d Co-CHI bond energiesi9 has p e r m i t t e d us t o establish Co-CH3 bond energies for met h y l c o b a l a m i n and several c o m p l e x e s w i t h s y n t h e t i c e q u a t o r i a l ligands.
Endicott et ai. Spectrophotometric Determinations of Equilibrium Constants. Owing to the large differences in absorptivity between methylcobalamin and ~ o b ( I I ) a l a m i n these , ~ ~ ~reagents ~~ were used in most of the equilibrium determinations. To maximize sensitivity, reactants were chosen so that the extent of reactions would be small. Reaction solutions were deaerated and thermostated a t 25 “ C . Absorbance readings were made over a period of 1 day or more, until a constant reading was obtained. The transfer of the methyl group in several of the macrocyclic systems was demonstrated from ‘ H N M R spectra, using a Varian T-60 spectrometer. The chemical shifts of methyl groups on the equatorial ligands and the Co-CH! group were sufficiently different from complex to complex to permit identification of the methylcobalt complexes present in the equilibrated mixtures. Quantitative N M R measurements were precluded by the limited solubility of most of the complexes.
Experimental Section Preparation of the Complexes. Methylated cobalt complexes containing synthetic equatorial ligands were prepared by means of procedures described in the l i t e r a t ~ r e . ’ ~ Methylcobalamin -~~ was obtained from Sigma Chemical Corp. Spectrophotometric data for all complexes and microanalytical data for the synthetic complexes were in excellent agreement with literature reports. Most of the cobalt(I1) complexes containing macrocyclic ligands were prepared by standard literature technique^."^^^ Owing to the extreme oxygen sensitivity of C 0 ( d m g H ) , ( 0 H ~ ) ~Co([ , 14]aneN4)(OH2),2+,24 Co(Me2[14]4,1 1-dieneN4)(OH2)22+,24 and cob(II)alamin, these complexes were prepared in solution immediately before use. To prepare C ~ ( d m g H ) ~ ( o H , )we , mixed stoichiometric amounts of Co(0,CCHJ2-6H2O and dimethylglyoxime (dmgH2), each dilute in deaerated 0.1 M N a 0 2 C C H , . To prepare solutions containing Co([14]aneN4)(OH2)22+,we mixed carefully deaerated 0.1 M NaCIO, solutions of Co(C104),.6H20 and [ 14]aneN4 (in slight stoichiometric excess). Solutions of Co(Me2[14]4,1 l-dieneN,)(OH2)22+and cob(I1)alamin were prepared by reduction of solutions of Co(Me2[ 1414,Il-dieneN4)(OH2)23C 25.26 and Sigma Chemical Corp. hydroxycobalamin 0.1 M in N a C F 3 S 0 3 with R U ( N H , ) , ~ + ,amalgamated zinc, or Cr2+. Solutions of Ru(NH3)? in 0.1 M NaCIO, or 0.1 M NaCF3S0, were prepared by reduction of argon-purged solutions of R U ( N H , ) , ) ~with amalgamated zinc. The Ru(NH,),CI, was obtained from the MattheyBishop Co. All solutions were prepared with redistilled, deionized water. Reagent-grade chemicals were used throughout. Kinetic Procedures. Rapid reactions were followed by using an Aminco stopped-flow apparatus9 with either oscilloscopic or recorder readout. The rates of the slower reactions were monitored by using a Gilford 250 spectrophotometer with a thermostated cell compartment and a programmed sampling attachment. All reactions were run under pseudo-first-order conditions. In most cases the methyl complexes Here in more than fivefold excess of the cobalt(I1) complexes. Reagent solutions were separately purged with Cr2+-scrubbed N 2 and transferred through serum caps by means of syringes equipped with platinum needles. For the slower reactions, the reaction cell was usually a I-cm spectrophotometer cell equipped with a serum cap and purged with N 2 prior to transfer of the reactant solutions. (18) Endicott, J . F.; Wong, C. L.. work in progress. (19) (a) Mok, C. Y.; Endicott. J. F. J. Am. Chem. SOC.1977, 99. 1276. (b) Ibid. 1978, 100, 123. (c) Ciskowski, J. M.: Endicott, J. F., work in progress. (20) (a) Roche. T. S.; Endicott. J . F. J. A m . Chem. SOC.1972, 94, 8622. (b) Inorg. Chem. 1974, 13, 1575. (21) (a) Jackels, S. C.; Framery, K.; Barefield, E. K.; Rose, S . J.; Busch, D. H. Inorg. Chem. 1972,II. 2893. (b) Farmery. K.; Busch, D. H. Ibid. 1972, 11, 2901. (22) Schrauzer, G . N . Inorg. Sj,nih. 1968, 1 1 , 61. (23) Endicott, J . F.; Lilie. J.; Kuszak, J . M.; Ramaswany, B. S.; Schmonsees, W. G.; Click, M. D.; Rillema, D. P. J. A m . Chem. SOC.1977, 99, 429. (24) Ligand abbreviations: Me4[14]tetraeneN4= 2,3,9,10-tetramethyl1,4,8,1I-tetraazacyclotetradeca-1.3.8.10-tetraene;Me,[ 14]4,11 -dieneN, = 5,7,7,12,14,14-hexamethy1-1,4,8.1 I -tetraazacyclotetradeca-4,1I-diene; [ 141aneN4 = 1,4,8,1 I-tetraazacyclotetradecane;Me2[14]4,1 I-dieneN4 = 5.1 2dimethyl-I ,4,8,1I -tetraazacyclotetradeca-4,1I-diene; Me2pyo[141trieneN, = 2,12-dimethyl-3,7,1 I,l7-tetraazdbicyclo[ 11.3.l]septadec-l(17),2,11 - I 3.1 5 pentaene; bpy = 2,2’-bipyridine; dmgH = 3,4-dimethylglyoximate ( I - ) : sepulchrate = (S)-1,3,6,8,10,13,16,19-octaazabicyclo[6.6.6]eicosane. (25) (a) Hay, R. W.; Jeragh, B. J . Chem. SOC.,Dalton Trans. 1977, 1261. (b) Hay, R.W.; Lawrence, G . A . Ibid. 1975, 1466. (26) Wong, C. L.; Switzer, J . A.: Balakrishnan, K. P.; Endicott, J . F. J . Am. Chem. SOC.,in press.
[ 14]aneN,
rN‘1 Me,[14]4,11dieneN4
Me4[14]tetraeneN,
m H , rN’1 Me, [ 1 4 ] 4 , 1 I d i e n e N ,
Me,pyo[ 14]trieneN,
Results
The results of our k i n e t i c d e t e r m i n a t i o n s are summarized in Table I and presented in greater d e t a i l in Table S-I .29 T h a t t h e reactions observed involve m e t h y l t r a n s f e r between c o b a l t complexes h a s been qualitatively d e m o n s t r a t e d by ‘ H N M R spectroscopy and by the observation of the expected c o m p l e m e n t a r y changes in cobalt(I1) and m e t h y l c o b a l t complex absorbancies. Since t h e alkylcobalt complexes tend to be reduced a t --I V vs. NHE,I9 outer-sphere reduction.of the organocobalt complexes by C o 1 * ( N 4 ) complexes is u n f a v o r a b l e by 1-1.5 V. M o s t of t h e reasons for excluding a l t e r n a t i v e reaction p a t h w a y s have been discussed in t h e earlier l i t e r a t u r e . “ , i s We have q u o t e d a few kinetic p a r a m e t e r s f o r r e a c t i o n s w i t h q u i t e unfavorable equilibrium constants. Such r a t e c o n s t a n t s are nearly always complicated by t h e approach of t h e reacting mixture to e q u i l i b r i u m ; however, t h e s e approximate numbers are useful as o r d e r of magnitude checks on some of the analyses developed below.
Equilibrium c o n s t a n t s are s u m m a r i z e d in Table 11. G r e a t e r d e t a i l of the experimental d e t e r m i n a t i o n s c a n be found in T a b l e s-11.29
Discussion W h i l e t h e m e t h y l - b r i d g e d electron-transfer r e a c t i o n s investig a t e d here are g e n e r a l l y much slower in r a t e t h a n t h e corresponding halide-bridged reaction^,^^,^ t h e r a n g e of reactivity is far g r e a t e r than previously found for a n y o t h e r single c l a s s of electron-transfer reactions of related macrocyclic c o m p l e ~ e s T. ~h u~s ~, ~ rates vary over a 106-fold range even for methyl-bridged reactions w i t h AGO < 0. When c o r r e c t i o n s are made for t h e free-energy contributions, t h e r a n g e of reactivity is found t o s p a n s o m e eight o r d e r s o f m a g n i t u d e (see below). In an electron-transfer context this l a r g e r a t e variation would be associated w i t h s o m e s o r t of Franck-Condon reorganizational barrier. However, the large trans influence of t h e Ce-CH3bond weakens t h e X-(Co-CHJ bond30331 ( 2 7 ) Hogenkamp. H. P. C. I n “Cobalamin”. Baboir, B. M.. Ed.; WileyIntcrscience: Ne& York, 1975; Chapter I . p 21. ( 2 s ) Dunne. C. P. Ph.D. Dissertation, Brandeis Cniversity. 1971. (29) See paragraph at end of paper regarding supplementary material. (30) Lenhert, P.J. Chem. Commun. 1967. 980.
J . A m . Chem. SOC.,Vol. 102, No. 17, 1980 5521
Oxidation-Reduction of Complexes with Macrocyclic Ligands Table I. Summary of Rate Constants for Methyl-Bridged Electron-Transfer Reactions'
CoRJ,)(OH,)CH,
+ Co"(N,')(OH,),
N, '
N,
kab
F== kba
Co"(N,)(OH,),
mediumb
+ Co(N,')(OH,)CH,
temp, "C
kab, M-' s-' 0.51 i 0.01 (2) 1.07 i 0.06 (11) 5.03 i 0.06 (2) 10.9 i 0.3 (2)
kba, M-'
S-'
19.8 0.25 i 0.02 (6) 25 1.02 i 0.02 (2) 33.4 1.82 * 0.07 (2) 38.5 0.46 f 0.02 (2) 19.8 0.1 M HClO, 0.28 i 0.02 (3) 1.01 i 0.02 (6) 25 0.1 M HC10, 602 * 30 (4) 25 Me,pyo[ 14]trieneN, corrine 1.55 i 0.08 25 corrine Me, [ 14]4,11dieneN, -760 i 55 (3)f 25 corrine (dmgH), 3.96 * 0.14 (7) Me,[ 141tetraeneN, 25 (dmgH), 9.39 i 0.13 (9) 0.1 M HClO, 25 10.4 i 0.6 (2) 0.1 M NaO,CCH, 25 0.1 M NaO,CCH, 25 Me,pyo[ 14]trieneN, 4.6 i 0.5 (3) (dmgH), 2.95 i 0.06 (2) 25 0.1 M NaO,CCH, [ 14]aneN, (dmgH), 25 0.059 0.1 M NaO,CCH, Me, [ 14]4,1 ldieneN, (dmgH), -0.14 i 0.01 (5)f 27.3 (5) 25 Me,pyo[ 14]trieneN, Me, [ 14 ] tetraeneN, 0.13 i 0.02 (4) 25 Me, [ 14 ] tetraeneN, [ 14]aneN, 0.32 i 0.01 (4) 25 Me,pyo[ 14]trieneN, [14]aneN, 28.6 0.1 M HCF3S03 0.010 Me6[14]4,11dieneN, Me, [ 14]tetraeneN, 35.2 0.1 M HCF,SO, 0.022 0.032 42.8 0.1 M HCF3S03 -3 x io-, f 28.6 0.1 M HCF3S03 Me, [ 14]4,11dieneN, Me,pyo[ 14]trieneN, 0.017 -4 x 10-4 f 35.2 0.027 -5.6 X 42.8 0.047 4.4 x lo-, Me6[14]4,11-dieneN, 28.6 Me,[14] l,ll-dieneN4-13-one 0.1 M HCF3S03 6.8 X 35.2 42.8 1.4 x 10-3 Me,pyo[ 141trieneN, Me,[l4]1,11-dieneN,-13-one 0.1 M HCF3S03 1.8 x 10-3 28.6 3.1 x 10-3 35.2 5.3 x 10-3 42.8 'Details of concentrations, etc., may be found in Table S-I. 0.1 M NaClO, except as indicated. Number of determinations in parentheses. Methylcobalamin. In neutral solution the benzimidazole base is coordinated to the trans axial position rather than H,O. e Cob(I1)alamin. Estimated rate constant for a reaction which did not go to completion. Me, [ 141tetraeneN,
corrind
Table 11. Kinetic and Thermodynamic Parameters for Methyl-Bridged Electron-Transfer Reactionsa
N,-a
N, -b
AG*
aH'ab,
Kab(25"C) kcal mi?' kcal mol-' AS*,b, eU corrin Me. I14 .1tetraeneN, 4.3 i 0.6C)d 15.2 7.5 i 0.8 -22 i 4 3.6 i 0.4d*e 15.2e 44 -t 17f 11.4 Me, pyo [ 141trieneN, corrin (1.7 -t 0.3)103 corrin 14.9 Me,[ 14]4,lldieneN, corrin Me, [ 14]4,11dieneN, 0.25 i 0.04f corrin 59 i 10f 8.6 (dmgH), [ 14]aneN, 8ilf corrin 14.4 Me, [ 14]tetraeneN, 0.38 i 0.04d (dmgH), 14.3 (2.9 t 1.4)lOP Me,pyo[ 14]trieneN, (dmgH), (5.0 i 1.5)102g 14.5 [ 14]aneN, (dmgH), Me, [ 14]4,1ldieneN, (1.0 * O.3)1O5p 16.9 (dmgH), (1.1 i O.4)lOz Me,pyo[ 141trieneN, Me, [ 14 JtetraeneN, 13.2 Me, 114ltetraeneN, 34 i lop I14 laneN, 16.4 Me,p yo [ f 4 ] trieneN,, [liianek, 6 i 2g 15.9 Me6[14]4,11-dieneN, Me, [ 14]tetraeneN, (7 i 21103 R 18.1 112 -33 i 4 Me6[14]4,11dieneN, Me,pyo[ 14]trieneN, 40 i 5g 17.9 312 -23 i 4 ' The "sense" of the reagents is the same as in Table I. See Tables I and S-I for conditions and details. Based on kab = Ze-AG*ab/RT; Z = 10'' M-' s-'. &Tab = 1.6 i 0.5 kcal mol-' ; = 2.9 -t 2 eu; benzimidazole coordinated. d K a b = kab/kba. e Benzimadazole replaced by H,O;0.1 M HClO,. f Spectrophotometric determination. p Calculated, K,b = KacKcb or K,b = K,,/K,d, from combinations of equilibrium constants in this table. .,L
(in our cases X = H 2 0 or benzimidazole), so that contributions associated with bond-length changes trans to the briding group must be even smaller than those found for halide-bridged electron t r a n ~ f e r . ~These ~ . ~ several different kinds of variation in the activation free energy with the changes in Co-OH, bond length are illustrated in Figure 1 for self-exchange electron-transfer reactions. In order to gain insight into the origin and variations of the barriers to methyl-transfer reactions, it is necessary to (31) Endicott, J. F.; Halko, D. J.; Butler, W. M.;Glick, M. D. Proceedings of the XVII International Conference on Coordination Chemistry. Dublin, Ireland, Aug 1974; Paper 3.43.
separate the intrinsic kinetic factors from the contributions of the overall free-energy changes. These components of the free energy of activation are considered in separate sections below. A. Thermodynamics of Methyl-Bridged Electron Transfer. Co-CH, Bond Energies. W e have been able to measure equilibrium constants, Knb,for several of the methyl-transfer reactions. Analogous equilibrium constants for outer-sphere electron-transfer reactions can be analyzed in terms of the separate contributions of the redox couples of each of the reactant partners (e.g., in terms of differences in the standard electrode potentials for the two redox couples). Such a linear analysis permits one to calculate equilibrium constants which are especially difficult to measure and
5522 J . Am. Chem. SOC.,Vol. 102, No. 17, 1980
Endicott et al.
Table 111. Intrinsic Thermodynamic and Kinetic Parameters for Cobalt-Methyl Complexes
s,,~T comulex
eu
re1 redox couple free energy GGj,b kcal mol-'
re1 CoCH, bond energy mj,CH, C H,
kcal mol-'
CoCH, bond energy mj,CH3$ kcal mol-'
intrinsic reorganiza tional f r e e energy AG*i;, kcal mol-' e
methylcobalamin (MeB,,) -10f 0 0 46 11.7 * 1.2 (3) aquomethylcobalamin -10f -0 --1.5 -44 -12 Co(dmgH)(OH,)CH, -10f 1.0 +1 47 * 2 -11a Co(Me,pyo[ 14]t1ieneN,)(OH,)CH,~+ 29 -2.3 -4.5 (-7) 41 (38) 12.7 * 1.5 (3) Co(Me, [ 14]tetraeneN,)(OH,)CH,2+ 23 0.9 +0.5 (-2) 46 ? 2 (44) 17.6 * 1.5 (3) Co([ 14 ]aneN,)(OH,)CH, '+ 36 -1.3 -6 (-8) 40 (37) 17.8 (1) 45 -4.5 Co(Me, [ 14]4,lldieneN,)(OH,)CH,1' -12 (-14) 33 (31) 22.7 * 1.5 (3) Co(Me, [ 14]4,11dieneN4)(OH,)CH," 36 0.8 -3.5 (-6) 42 (40) a Reference 32 except as indicated. Freeenergy change for the reaction CO(N,)(OH,)CH,~+ + B,,, +Co"(N,) + MeB,,, except as indicated. Relative to MeB,,: AH~,cH,- AH, CH, = AGj, + T(Sr4j - Srcqa)+ 6 AG,j, with 6 A G d = 3.5 kcal mol-' (values in parentheses based on 6 AG,j = 1 kcal mol-' ;see discussion in text). No corrections for solvation are included. Based on photohomolysis threshold values energies (corrected by 2 kcal mol-' for AI+,") as indicated for Co(dmgH),(OH,(OH,)CH,'+ and Co(Me, [ 14]tetraeneN4)(OHz)CH,2+; in parentheses based on 6 AC,j = 1 kcal mol-' (see footnote c ) ; uncertainties are estimated at *3 kcal mol-' except as indicated. Bond energies are with respect to the aqueous medium; there may be a solvation contribution. e Mean apparent reorganizational barriers for selfexchange reactions of indicated complexes; values are determined by combinations of three independent rate constants k , , k ' b , k a b ) ; numbers in parentheses are the number of different combinations of rate constant used in computing the mean values of AG jj. ' r JEstimates based on trends in ref 32. Based on Figure 3.
i
it permits some convenient checks on the reliability and consistency of measured equilibrium constants. A linear analysis of equilibria in inner-sphere electron-transfer reactions is also possible. This is shown by consideration of Scheme I. Since -RT In Kob = AGo,b(Is) = AHoab- TASoab,the components of the free-energy change may be analyzed in terms of the different entropy and enthalpy cycles. Thus
The only "cross term" in eq 1 is the entropy change associated with outer-sphere electron transfer, A s o , b ( o s ) . This term is simply the difference in the entropy change associated with the outer-sphere redox couples of the respective diaquo complexes: A s o , b ( o s ) = Src,b - SI,,. Values of Srcj have been determined by Weaver and c o - w o r k e r ~for ~ ~most , ~ ~ of the macrocyclic complexes used in this study. Obviously it is possible to group the terms of eq 1 in such a way that AGoab(1S)= AGO- Acb, separating the contributions of reactants a and b. As a consequence it is valid to assume that the reactants contribute linearly to AGab(IS), and equilibrium constants may be estimated for all the reactions we have investigated in this study. Such quantities are included in Table I1 and used below. Several of the terms in eq 1 merit further comment. For reactions symmetrical with respect to charge ( e g , for the synthetic tetraazamacrocyclic ligands which we have used), the last term is expected to be very small since the entropies of solvolysis of similarly charged cobalt(II1) complexes are expected to be similar (ASa,x,sE ASb,x,s);consequently the last term should be the smallest in eq 1, The values of AHa,sand AHb,s(the second term in eq I ; enthalpy changes associated with formation of five-coordinate cobalt(I1) species) could in principle be estimated from values of enthalpies of activation for axial substitution into the very labile, low-spin cobalt(I1) complexes. Unfortunately, little such information is available. However, these cobalt(I1) complexes that the activation parameters are all likely are so labile20,23~34~3s to be small. Assuming that substitutions on the low-spin cobalt(I1) species are largely determined by enthalpies of activation, we would (32) (a) Yee, E. L.; Cave, R. J.: Guyer, K. L.; Tyma, P. D.; Weaver, M . J. J . Am. Chem. SOC.1979, 101, I 131. (b) Weaver, M . J., private communication. (33) We are very grateful to Professor Weaver for his cooperation in
making these determinations. (34) Tait, A . M.; Hoffman, M. Z.: Hayon, E. J . A m . Chem. Sot. 1976, 98, 86. (35) Endicott, J. F.; Ferraudi. G . J . J . Am. Cheni. SOC.1977, 99. 243.
20
/
lot
I
0
I
0.2 dCQ"-OH2
-
I
I
0.4
06
dKcQtl$
Figure 1. Correlation of free energy independent activation free energy in kcal mol-') with bond-length changes (A)for different classes of electron-transfer reactions. Middle curve (closed circles) is for Co-
(N4)(OH2)23t.2+ outer-sphere self-exchange reactions; kinetic data based on ref 10; X-ray structural parameters based on ref 9b,c, 23, and Durham, B.; Anderson, T. J.; Switzer, J. A,; Endicott, J . F.; Glick, M. D. Inorg. Chem. 1977, 16, 271. Lower curve (open circles) is for Co-
(N4)(OH,)C12+/Co(N4)(OH2)22+ chloride-mediated inner-sphere selfexchange reaction: kinetic data based on ref 9d,e; structural data as for outer-sphere reactions, assuming "normal cobalt(II1)" bond lengths in the trans aquochloro complexes. The open circles at the top of the figure are for methyl-mediated inner-sphere self-exchange reactions: kinetic data from Table 111; X-ray structural data for N4 = Me4[14] tetraeneN4 from ref 23 and 31, C 0 ( [ 1 4 ] a n e N ~ ) ( O H ~from ) , ~ ~ref 23. A Co-OH2 bond length of 2.4 A has been assumed for Co([ 14]aneN4)(OH2)22+ outer-sphere self-exchange and based on the Co( [ 14]aneN4)(OH2)23+~2+ the correlation noted. A Co-OH, bond length of -2.1 8, has been assumed for Co(Me6[14]4,1l-dieneN,)(OH,)CH?+ based on the lability of the water molecule in this complex. Note that the only bond-length change occurs for the axial coordination positions in these reactions. Reactions represented for N4 = Me4[14]tetraeneN4( I ) , Me2[14]1,11dieneN4-13-one(2), Me6[14]4,1I-dieneN4 (3), and [14]aneN4(4).
-
- -
estimate AHi,s N 5 kcal mol-' for the complexes with N4 = neutral synthetic macrocycle ( k H P lo9 s - ' ) ~ .and ~ ~ Mj,s4 kcal mol-' for cob(I1)alamin and C ~ " ( d m g H )(kH20 ~ IO" s - ' ) . ~ ~ The first and third terms clearly make the largest contributions to eq 1. With values of the smaller contributions as noted above, and the measured values of Kab and SrcJ,we could readily obtain a relatice series of cobalt-methyl homolysis bond energies ( AHj,CH3
Oxidation-Reduction of Complexes with Macrocyclic Ligands
J . Am. Chem. Soc., Vol. 102, No. 17, 1980 5 5 2 3
Scheme I
quantities in parentheses in Table 111). Alternatively, we have used a n empirical approach for obtaining values of AH,,cH, in Table 111. The two approaches agree to within 3 kcal mol-]. Studies of photoinduced homolyses have indicated that the minimum excitation energy required to induce homolysis (Eth, obtained by extrapolation to zero of the quantum yield for homolysis) is a good measure of the homolysis bond en erg^.^^-^^ Values of the photohomolysis threshold energy for Co(Me4[ 14]tetraeneN4)(0H2)CH32+ and C ~ ( d m g H ) ~ ( o H ~ are )cH Eth~ = 48 f 2 and 49 2 kcal mol-',44 respectively. For the reaction {Co(Me4[14]tetraeneN4)(0H2)CH32t + C ~ " ( d m g H ) ~wel estimate AGOab = -0.6 kcal mol-'. If we put eq 1 in the form AGo,b = (AHa,x- AHb,x)- TASoab(OS) bACab ( 2 )
*
+
(36) (a) Endicott, J. F. In "Concepts in Inorganic Photochemistry", Adamson, A. W., Fleischauer, P. W., Eds.; Wile): New York, 1975; Chapter 3, p 83. (b) Endicott, J. F.; Ferraudi, G. J.; Barber, J. R. J . Phys. Chem. 1975, 79, 630. (c) Ferraudi, G. J.; Endicott, J. F.; Barber, J. R. J . Am. Chem. Sor. 1975, 97, 640. (d) Endicott, J. F.; Ferraudi, G. J. Inorg. Chem. 1975, 14, 3133. (e) Endicott, J . F. Ibid. 1977, 16, 494. (37) Values of Eth are in reasonable agreement with thermochemical estimates of the homolysis bond energy for Co-CI homolysis (ref 36c) and supplementary material. Since alk 1 radical cob(I1)alamin cage recombination reactions occur with k , 2 X 10ys-'.'8 the recombination apparently has an activation barrier of AQr 5 kcal mol-' (from k , = ( k B T / h )exp[-[AG'/ RT]]).Much of this barrier is probably associated with the change in geometry from the planar carbon in the alkyl radical to a nearly tetrahedral geometry around carbon in the cobalt-alkyl complex. Classically, the resulting reorganizational energy would be largely e n t h a l p i ~ . ' ~However, .~~ for the vibrational quanta > k T , the barrier is only weakly temperature d e ~ e n d e n t . ~ ' The threshold energies should be corrected for ~r (the enthalpic com onent of AG',) to obtain a bond dissociation energy42 Since uCHl 2kT$ A P r must be small. We have set A#, 2 kcal mol-]. (38) Endicott, J. F.; Netzel, T. L. J . Am. Chem. Soc. 1979, 101, 4000. (39) (a) Hush, N. S. Trans. Faraday SOC.1961,57, 557. (b) Prog. Inorg. Chem. 1967, 8, 391. ( c ) Electrochim. Acra 1968, 13, 1005. (40) (a) Marcus, R. A. Annu. Rec. Phys. Chem. 1964, 15, 155. (b) J . Phys. Chem. 1963, 67, 853. (c) Discuss. Faraday SOC.1960, 29, 21. (41) (a) Jortner, J.; Ulstrup, J. J . Am. Chem. Soc. 1979, 101. 3744. (b) Ulstrup, J.; Jortner, J . J . Chem. Phys. 1975, 63, 4358. (c) Kestner, N. R.; Logan, J.; Jortner, J. J . Phys. Chem. 1974, 78, 2148. (42) For example, see: Brenton. A. G.: Morgan, R. P.; Beynon, J . H. Annu. Reu. Phys. Chem. 1979, 30, 51. (43) Ellison, G. B.; Engelking, P. C.; Lineberger, W. C. J . Am. Chem. Soc. 1978, 100, 2556. (44) Ciskowski, J. C.; Endicott. J . F., work in progress.
--
-
-
then the experimental values of AGOab. AH,,cH~ = E,hJ, and Srcj lead to bAGd = -3.5 kcal mol-' for this reaction. As noted above, there is reason to believe that the terms contributing to 6AGa6are similar for the BI2 and dimethylglyoxime complexes; larger contributions, similar to one another, are expected for the macrocycle complexes. Thus, for the MeB12/Co11(dmgH)2reaction we have set bAG,b = 0 and for the MeB12/(Co11[macrocycle]) reactions we have set dACab= +3.5 kcal mol-' in order to obtain the relative bond energies in Table 111. W e have noted below that there does seem to be some small but systematic inconsistency in our kinetic and/or equilibrium data for reactions of dimethylglyoxime complexes. Thus, there is likely to be some small (12 kcal mol-l) error involved in our determination of bond energies referenced to the C ~ ( d m g H ) ~ / Co(Me[ 141tetraeneN4) system. We have nevertheless used this difference in 6AGabin order to have an experimental means for estimating each component of eq 1. Since the error introduced appears to be small, systematic, and consistent, it does not affect major features of the bond-energy differences. Substitution of the homolysis threshold energies for AH,,cH, for C O ( ~ ~ ~ H ) ~ ( O H and ~ ) CCo(Me4[ H, 14]tetraeneN4)(OH2)CH3" results in the set of Co-CH3 bond energies in Table 111. The temperature dependence of the MeB12/Co(Me4[14Itetrae n e N 4 ) ( 0 H 2 ) 2 +reaction gives AHoab= 1.6 0.5 kcal mol-', consistent with the inferred similarities in Co-CH3 bond energies for the corrin and Me4[14]tetraeneN4complexes. The nearly 15 kcal mol-' range of Co-CH3 bond energies is discussed further below. B. Intrinsic Kinetic Barriers. At the present time there is relatively little in the way of precedent to utilize in the separation of the contributions of the free-energy and intrinsic contributions to the rates of inner-sphere electron-transfer reactions. In the limit of weak interaction between donor and acceptor, one would expect the dependence of rate on driving force to be similar in inner-sphere and outer-sphere reactions.3w1 Halide-bridged electron-transfer reactions have been found to exhibit approximately the expected dependence on AGoabW,eIn reactions of closely related molecules, such as those employed in this study, it is reasonable to assume that kab and kbahave similar dependence on AGOa6. For AGOab small, kab will be proportional to 45-47 Under such cir-
*
5524 J . Am. Chem. SOC.,Vol. 102, No. 17, 1980
Endicott et al.
-Mlw\a+wbl
0
AG* lobs1
- 81b.kcdl mol-'
cumstances we may "correct" for the free-energy dependence of the inner-sphere electron-transfer rate either by considering the products, k,bkbo = (koob)2,or the differences hG*,b - 0.5AGo,b. In the present study, these approaches give identical results. Either approach results in a set of AGO-independent activation parameters: AGlab(IS;AGOab 0 ) . In principle these parameters could depend in a very complex manner on the contributions of the individual reactants. Since the individual reactants contribute linearly to the similar AGO-independent activation parameters for outer-sphere reactions, a simple means for examining the dependence of kabon the reorganizational contributions of individual reactants is to compare (1) AG*,b(IS; AGo,b 0) to Ac*,b(os; AGOab 0); ( 2 ) AG*,(IS; AGo, 0 ) to the outer-sphere self-exchange activation parameters AC*JJ(OS)for different reactants j . The last comparison has been discussed elsewhere.9d Either experimental comparison indicates that AG*Ob(IS/CH,; '/2AG*d(OS). We conclude that Ac*ab(Is;AGo,b 0) 0 ) may be represented bq the average of the separate contributions of some intrinsic parameter^.^^ y,,, for the respective reactant self-exchange reactions. Thus
-
-
6
4
I.iAG*~,ilS.CH,l
Figure 2. Graphical analysis demonstrating the self-consistency of a linear combination of intrinsic components (Y,,)to the activation free energy in methyl-mediated electron-transfer reactions (eq 3). The line is drawn through zero, with unit slope. Numbers designate combinations of equatorial ligands on the organocobalt and cobalt(I1) complexes: N, = Me4[14]tetraeneN4 ( I ) , Me6[14]4,11-dieneN, (3), [14]aneN4 (4), Me2pyo[14]trieneN4 (9,corrin (6; Le., methylcobalamin or BIzr). 8,, is a combination of work terms as discussed in the text.
- -
-
2
-+
analogous to the behavior found in outer-sphere electron-transfer reactions. Similar relationships have been found previously for the halide-bridged electron-transfer r e a c t i o n ~ . ~ The ~ , ~ work ,~~ term appropriate to inner-sphere reactions, WR4b(Is),has been discussed p r e v i o ~ s l y . ~ ~ (45) Generalized treatment^^^,^^ of group transfer reactions have shown that ActQb = aAGoab AG*,,,,M(cY,),where a is the BrBnsted slope, AG*,,ob is the intrinsic component of reactivity (AG',, evaluated at AG',, = O ) , and M ( a ) is a function of a. The simple function a-'= ( I exp[AGoob/AG',,.,]) proposed in ref 46 and 47 reduces to the well-known equations of Marcus40 for [AGn,b/AG',,ob]
