Proton Transfer Reactions in Macrocyclic Complexes and in Metal-peptide Complexes BY CHARLESE. BANNISTER,DALEW. MARGERUM* AND JOHN M. T. RAYCHEBA LOUISF. WONG Department of Chemistry Purdue University West Lafayette Indiana 47907 Received 12th May 1975 The rates of proton transfer reactions at the ycarbon atom in macrocyclic tetraazadiene complexes and at the nitrogen atom in metal peptide complexes are several orders of magnitude slower than the reaction rates of typical oxygen and nitrogen acids with similar pKa values. The Bronsted plots for the macrocyclic complexes deviate little from a slope of 0.5 over a wide range of APKa values while the metal peptides undergo a relatively fast transition from 01 values of unity to zero without reaching the diffusion limiting rates.In order to fit the data to the Marcus theory it is necessary to include in addition to the reorganizational barrier (A/4) a term Wi which represents the solvent reorgan- ization necessary to initiate hydrogen bonding after the encounter acid-base species are formed. The Wi term is in addition to the work necessary to form the encounter species but it is independent of ApK,. The metal-macrocyclic complexes have large h/4 values and small Wi values while the metal-peptide complexes have small h/4 values and large Wi values. The proton transfer kinetics of two types of coordinated ligands are examined in this work. The 14-membered macrocyclic-tetraazadiene complexes have proton addition or loss at a carbon atom (eqn (I)) while the metal-peptide complexes have H H HB MLf MLH2+ proton addition or loss at the peptide nitrogen accompanied eventually by changes in metal-peptide bonding (eqn (2)).The two types of complexes share some common M' M features. In both cases their bases lack readily available electron pairs for hydrogen bonding. The copper(I1) and nickel(I1) complexes of both types have pKa values in the range of 6-9 but their proton transfer rates (table 1 and table 2) are several orders of magnitude slower than is the case for "normal " acids and bases. Normal 78 C. BANNISTER D. MARGERUM J. RAYCHEBA AND L. WONG acids and bases according to Eigen's cla~sification,~ would have H,O+ and OH-rate constants in the vicinity of 1O'O M-I s-l. On the other hand the behaviour of the macrocyclic complexes and the peptide complexes with general acids and bases are not at all similar.Fig. 1 presents the data for the macrocyclic diene carbon acids of Nirr and Cul*,where the Bronsted a and p values are 0.50 over almost the entire ApK range of 20 units. By contrast the (log k log KH) plots for the triglycine complexes Cu(H_,glyglygly)- and Ni(H-,glyglygly)-have an S-shape as seen in fig. 2 with a values which appear to change rapidly from 0 to 1 to 0. APKa FIG.1.-Bronsted plots for the reactions of metal macrocyclic complexes (eqn (1)) with OH- H20 nitrogen bases and their conjugate acids. 0 NiLH2+ (pK 6.21) and NiL+ A CuLHZ+ (pKa 9.35) and CuL+ ApK = PKa(MLH)-PKa(HB). The bases from left to right are OH- OH- glycinamide Tris Et3N Hen+ Tris H2dienz+ Hen+ 2,6-lutidine H20 H20.r -4 16 14 12 10 8 6 4 2 0 -2 PKHB FIG.2.-Kate constants for the protonation reaction of the triglycine complexes (298 K) A Cu-(H-,glyglygly)-with the acids HzO H3B03 HzEDTA2- HOAc Hoxalate- and H30+; 0 Ni(H-2glyglygly)- with the acids HzO H3B03 H2EDTA2- Hmaleate- Hsuccinate- HOAc Hfumarate- Hoxalate- H2gly+,H30+. The detailed nature of proton transfer reactions which occur in the vicinity of metal ions has had relatively little study. With the peptide complexes the weakening or cleavage of the metal-N(peptide) bond during the protonation and the possibility of initial protonation of the peptide oxygen must be considered. These complicating factors do not occur with the macrocyclic carbon acid complexes where the metal- nitrogen bonding remains intact and there is only one atom which can lose or gain PROTON TRANSFER REACTIONS IN METAL COMPLEXES the proton.Since the acid-base rate constants of both types of complexes are large it is useful to consider a general mechanism which includes the diffusion limiting situations. GENERAL MECHANISM A mechanism for proton transfer reactions is given in eqn (3) where k and k-3 are defined as diflusion-controlled rate constants for the k2 k2 k3 A-H+B + (A-H)(B) + (A)(H-B) + A+HB (3) k-I k-2 k-3 eiicounter of the acids and bases and k- and k3 are for the diffusion-controlled separation of the encounter pairs. The k and k- rate constants in this mechanism include all the reorganizational energies needed (1) to establish hydrogen bonding after the (AH)(B) encounter complex is formed (2) to transfer the proton from A to B and (3) to break the hydrogen bonding in the encounter complex (A)(HB).If the mechanism is divided into these steps with encounter complexes as intermediates then a steady-state approximation can be used to give the forward rate constant k in eqn (4). This equation can be rearranged k-kIk2k3 -k2k3+ k- ik3 +k- 1k-2 (4) using the definition of the overall equilibrium constant K = (klk2k3)/(k-lk-2k-3) to give eqn (5) kl k-l+(k- 1/k2)+(k1/k-3)(1/K) (5) * When there is very little reorganizational energy needed for proton transfer the rate constant k2is very large and the middle term in the denominator of eqn (5)drops out giving eqn (6).This is typical of the k-kl (6) -1+(W-3)(1W) behaviour of " normal " acids and bases where kf equals k-,K = (klk2k3/k-lk-2) for small values of K and k equals k for large values of K.3 When the reorganizational energy (due to solvation changes hydrogen bonding and internal reorganization) becomes appreciable then the middle term in eqn (5) must be considered. The value of k2equals kiK; where k,"is the rate constant for proton transfer in the encounter complex when AG," is zero and x depends in part on K2. It is convenient to define k,"as the observed rate constant when K = 1. Then the observed rate constant for any value of K is given by eqn (7) provided that the k2 step is helping to limit the rate The value for x is derived from the activation energy for kf[k,= (kT/h)exp( -AG*/ RT)]according to the Marcus theory 4* as modified by Kreevoy,6 AG* = WR+(;1/4)(l+AGi/;1)' I AG; I < A (8) where AG; is the standard free energy of reaction within the reaction complex and W' is the work required to form the reaction complex.In our case the work required to convert the encounter complex to the reaction complex is Wd = (WR-AGY) and C. BANNISTER D. MARGERUM J. RAYCHEBA AND L. WONG similarly for the products Wi = (W,+AG;). Then it can be shown that x is given by eqn (9) and x, the value of x when K = 1 is given by eqn (10) 1 W'-W' RT x = -+ -[In K-111 KlK3] 2 21 411 x-xo = -RT In K. 41 When k," is small as with carbon acids eqn (11) holds and if A is large x is approximately equal to 1/2 while (x-x,) approaches zero k = /c;K~/(K -xo 1~3)~ (11) so that k = k;KO.' the frequently observed Bronsted relati~nship.~ The proton transfer reactions of the macrocyclic complexes where k," is 102-7M-' s-' for amine bases appears to fit this relation over a wide range of K values (log K = ApK in fig.1). Several interesting possibilities arise using eqn (7) when k,"has intermediate values (i.e. lo4to lo8 M-I s-' ). If a sufficiently large ApK range were possible the values of dlnk,/dlnK (c&. or P0bs.j would change gradually from 1 at very low K values to approximately 0.5 at K = I and gradually approach zero at very high K values. However the equations also predict that it would be possible to have c&.values which vary from 1 to 0 over a relatively narrow ApK range without k approaching the diffusion-limiting value of k,. Thus when 3 is small the value of x can change rapidly from 0 to 1 as K changes and yet the middle term in the denominator of eqn (7) can still predominate if WF; is large. The predicted &bs. value in eqn (12) is obtained by taking dlnk,/dlnK from eqn (1 1). It can be seen that a small value of A will cause a,bs. to change rapidly with InK. Naturally when 1-is small the Wd values must be relatively large to keep the k values below the diffusion limit. Kreevoy and Oh have reported this type of rapid change in c(obs. for the reactions of diazoacetate ion with R3NH+ acids. We appear to see the same effect for ctobs.in the reaction of acids with the metal peptide complexes. PROTON TRANSFER REACTIONS OF THE MACROCYCLIC COMPLEXES The NiLH2+(pK 6.21) and CuLH2-+(pK 9.35) complexes undergo large changes in their molar absorptivities (at 330-360 nm) when they react with base to form NIL+ and CuL+ (eqn (1)). The reactions can be observed by stopped-flow methods without the need to resort to coupled indicators and as a result relatively accurate rate constants are obtained. As seen in table 1 the H30+ rate constants and the OH- rate constants are lo3 to lo5 times smaller than is the case for " normal " proton transfer rate constants from oxygen or nitrogen acids and bases. In this respect the reactions are not unlike those involving the keto and enolate anion of acetylacetone (eqn (13)).H I HH PROTON TRANSFER REACTIONS IN METAL COMPLEXES However the macrocyclic diene ligand complexes offer some advantages for the study of carbon acids. (1) They do not have the second proton-transfer cycle involving the enolate acid (proton transfer to the oxygens) which complicates the acetylacetone TABLE 1 .-SECOND-ORDER RATE CONSTANTS FOR THE REACTIONS METAL MACROCYCLIC ACIDS AND BASES (EQN (I)) 298 K 0.1 M NaC104 complex a I.eactant b k/M-1 s-1 NiLH2+ OH-4.0~ lo6 105 CuLH2-OH-4.9~ NiLH2+ H20 2.6~ CuLH2f H2O 4.5 x 10-4 NiL+ H30f 2.3~ lo6 CuL+ H30+ 5.5~ 107 NiL+ H20 2.0~ 10-3 CuL+ H2O 3.3x lo-' * The acid dissociation constants for NiLH2+ and CuLHZ+ are 6.21 and 9.35 respectively in 0.1 M NaCIO at 298 K.b The acid dissociation constants for H30+ and H20are -1.74 and 15.52 respectively in 0.10 M NaC104 at 298 K. reactions.8 (2) The pK value of the acids can be changed by varying the metal ion without affecting the nature or geometry of the groups adjacent to the reaction site. (3) The large absorbance changes permit the reactions to be monitored directly. Table 3 gives the resolved rate constants for the rezctions of a number of acids and bases TABLE2.-RATE CONSTANTS 298 K a FOR REACTIONS OF M(H-2glyglygly)-WITH ACIDS WHERE M = Ni2+OR Cu2+ AND GLYGLYGLY = TRIGLYCINE complex b HB pKa(KB) kiiB/M-lS-Ni(H-2L)-H3B03 9.00 1 .ox lo-' 10' H2EDTA2-6.00 1.8~ Hmaleate-5.70 1.ox lo2 Hsuccinate-5.28 3.1 x lo2 HOAc 4.64 6.7~ lo2 Hfumarate-4.39 4.7x lo2 Hoxalate-3.51 2.5~ 104 H2!3lY+ 2.36 5.5~ 103 H30+ -1.74 7.3 x 104 Cu(H-2L)-H3B03 9.00 2.2 103 H2EDTA2-6.00 2.6~ HOAc 4.64 3.4~ 104 105 Hoxalate-3.51 3.9~ H30+ -1.74 1.3 x 107 For Ni(H-,L)- in 0.30 M NaC104 and for CU(H-~L)- in 0.10 M NaC104 solutions.b The acid dissociation constant for Ni(H-'L)- and Cu(HdIL)-are 7.7 and 6.7 respectively. with the nickel and copper macrocyclic complexes. All the points in the Bronsted plots in fig. 1 are for amine bases H,O and OH-reacting with MLH2+. The fact that the data for the NiI1and Cull complexes can be superimposed suggests that the reorganizational energies necessary for the proton transfer are the same for both complexes and that the pK differences adequately reflect the effect which the change of metal ions has on the rate constants.The k; value for the acetylacetone (acac) reaction in eqn (13) is lo3*'M-' s-' at C. BANNISTER D. MARGERUM J. RAYCHEBA AND L. WONG TABLE 3.-sECOND-ORDER RATE CONSTANTS FOR THE REACTION OF ACIDS AND BASES WITH THE METAL MACROCYCLIC COMPLEXES 298 K 0.10 M NaC104 acid base PaKWB) kBIM-1 s-~ kan/M-l S1 CuLH2+ 2,g-lutidine Hen+ 6.84 7.09 2.5~10' 8.1 x 10' 8.o~103 1.5 x 104 Tris 8.OO 1.6~lo2 3.6~103 EtSN 10.77 1.6~103 6.0~lo1 OAc- 4.64 2.3 x 10' 1.2x lo6 NiLH2+ gly-H2dien2+ 9.62 4.22 3.4x 10' 4.2~103 2.3 x 103 3.3 x103 Hen+ 7.09 2.3 x103 3.1 x lo2 Tris 8.OO 3.4~103 5.6~lo1 gl ycinamide gb-HPOZ- 8.04 9.62 6.70 8.4~103 1.1x105 6.4~104 1.3 x lo2 4.3x lo1 1.4~104 malonate2- 5.27 4.1 x 103 3.5~104 citrate3- 5.65 1.3 x104 4.6~104 aThe acid dissociation constants for NiLH and CuLH are 6.21 and 9.35 respectively.TABLE 4.-DEVIATIONS OF THE SECOND-ORDER RATE CONSTANTS FOR THE REACTION OF CHARGED BASES REACTING WITH MLH2+ acid base z Alog ka CuLH2+ Hen+ +1 +0.3 OAc-1 +1.0 glycinate -1 +0.8 NiLH2+ H2dien2+ +2 -0.2 Hen+ +1 +0.2 glycinate -1 +0.6 malona te -2 +1.4 HPOZ-2 +1.7 citrate -3 +1.7 aAlog k~ is the difference in log kB between the charged base and the Bronsted line given in fig. 1. The linear least square line using OH- H20and nzutral bases gives log k~ = 2.7-0.5 ApK where APKa = pKa(MLH)-pKa(HB). ApKa FIG.3.-Bronsted plot for the proton transfer rate constants of the metal macrocyclic complexes with OH- carboxylate bases and H20.0 NiLH2+,A CuLH2+ with the bases (left to right) OH- OH- gly- gly- OAC- HzO H20.PROTON TRANSFER REACTIONS IN METAL COMPLEXES 300.5 K which is very similar to the k,"value of lo2.' M-' s-' at 298 K; for the metal macrocyclic complexes with amine bases (eqn (I)). However the Bronsted plots for acac have significantly more curvature. In fact there is so little curvature in fig. 1 that in order for the data (with or without the OH-points) to fit eqn (8) (where AGi = AGO+ W,-W,) very large ;1/4 values are needed and the best fits give negative valuse for W and W,. Electrostatic attraction and repulsion have some influence as shown by table 4 where Alog k is the difference in log k for bases of charge 2 and the values expected (using the 0.5 Bronsted slope) for neutral bases of the same basicity.The anionic bases show much larger deviations than the cationic bases which is reasonable since the reaction site is not at the charge centres. The positive and negative bases should have different orientations relative to the metal ion with a greater distance between the metal centre and positive charged bases. TABLE5.-PARAMETERS (kJ mOl-') OF MARCUS THEORY acid base WR W'r 114 MLH2+ OH- RCO,' HzO 25 19 31 MLH2+ acac b OH- amines HzO OH- amines H20 -29(8) 39 -33(8) a 22 88(50) 26 acac b OH- RCO, H20 36 25 23 acac OH- RCO, H2O 44 38 14 RCO; amines C~(H-~glyglyhis)- 33 c= -1ld 5.9 The values in parenthesis are arbitrarily chosen to force WR and Wp to be slightly positive.The resulting fit has more curvature than the experimental data. b The Marcus parameters were calculated from the data of M. L. Ahrens M. Eigen W. Kruse and G. Maass Ber. Brmsenges. Phys. Chein. 1970 74 380. C M. M. Kreevoy and S. W. Oh J. Amer. Chem. SOC.,1973 95 4805. d C = (Wp-WR-AG&,). Fig. 3 gives the Bronsted plot for MLH2-'-reacting with OH- RCOO- and H20. This curvature can be fitted with the R/4 and WR values given in table 5. The 3,/4 values for the MLH2+ complexes are larger than for acac and the WR values are smaller. Several reasons can be suggested for larger A values including (1) the necessity of reorganizing more bonds when the metal is present (2) the need for greater electronic redistribution and (3) additional effects due to changes in the degree of axial solvation of the metal ion.Similarly several reasons can be suggested for lower W values including (1) the fact that MLH2+is already planar and needs less geometrical rearrangement than acac in order to initiate hydrogen bonding (2) the metal ion will tend to disrupt the solvent structure which might lead to less solvent reorganization as the hydrogen bonding is initiated. The relatively large rate constants for OH-with MLH2+ suggests the possibility that a metal hydroxide species could form prior to the proton transfer. We could find no evidence for a M(OH)LH+ species but the high OH-concentrations necessary to form it would cause rapid formation of MLf. However the trans diene complexes of Nil1 where proton loss from carbon atoms does not occur fail to form OH-comple~es.~A coordinated hydroxide ion would have reduced basicity and would require an intervening water molecule in order to accept a proton from the carbon atom.Hence the effectiveness of an M(OH)LH+ pathway is uncertain. Some acids and bases could have axial coordination to the metal ion with one atom and could transfer the proton with another atom. This may explain the particular effectiveness of HPOi-as a base and of H,PO as an acid. C. BANNISTER D. MARGERUM J. RAYCHEBA AND L. WONG PROTON TRANSFER REACTIONS OF METAL PEPTIDE COMPLEXES The lower part of the S-shaped Bronsted curves for Cu(H-,glyglygly)- and for Ni(H-,glyglygly)-is an anomaly which arises from considering H20 as a Bronsted acid when a second more favourable path is available if it acts as a Lewis base.Thus the solvent dissociation pathway for these species involves H,O replacement of the deprotonated nitrogen group from the metal followed by rapid solvent proton- ation of the -CON-'-) group. This pathway is observed for other metal-peptide complexes 2* lo and the general equation for the rate constant is given by eqn (14). kobs. = kd +kHBIHBl (14) Hence in the Bronsted plots we need to consider only why the slope changes from 1 to 0 before the rate reaches the diffusion limit. However a second difficulty arises as seen in the mechanism given in eqn (15) and (16) where M(Hm1G3)* is a reactive intermediate in which the peptide N has not yet moved away from the metal ion.This intermediate can react in ka MH-,G3 +HB + (MH-iGj)* +B k-s kb rapid (MH-1G3)*+B + MH-lG3B + products two ways with B as a Bronsted base (k-a)and with B as a Lewis base (kb). The resulting value of kHB is given in eqn (17) and we see that kHBis the actual proton-transfer rate constant only when k % kFa. In fig. 2 a11 the conjugate bases of HB can act as Lewis bases. When acids of non-complexing conjugate bases were tested they failed to give general acid behaviour with the triglycine complexes. This H FIG.4.-The copper(I1) complex of glycylclycyl-L-histidine,Cu(H-2glyglyliis)-. was the case for the Good buffers MES and PIPES as well as for 2,6-lutidine and 2-picoline with both Ni(H-,glyglygly)- and Cu( H-,glyglygly)-.With these bases k should be very small due to steric effects and an alternate mechanism is needed with H20 reacting as the displacing ligand so that only the H30+ rate constants are observed. All these buffers have pK values greater than 6. It is possible that more acidic HB species could give general acid behaviour. We cannot be certain from the trigiycine data alone if any of the rate constants in fig. 2 are actually due to proton- transfer steps although the HB species with pK < 6 might react in this manner. PROTON TRANSFER REACTIONS IN METAL COMPLEXES In order to avoid the above problem we examined the reactions of another peptide complex Cu(H-,glygly-L-his)- whose structure is given in fig. 4. Recent studies in this laboratory have shown that proton-transfer reactions can be made to be the rate- determining step when this complex is reacted in the presence of a high concentration of triethylenetetramine (trien).O Parallel conditions cannot be used for the triglycine 123456 lo2x [trien]~ FIG.5.-Observed first-order rate constants for the reaction of Cu(H-,glyglyhis)-with excess trien showing the approach to the limiting rates at high trien. Curve 1 no added general acid pH 7.5 calculated from resolved data. Curve 2 same conditions as curve 1 with 4.8 x loe3M H(HEPES)* added as HB pH 7.5. 7 6 5 m 24 M 23 2 I ' ' 11 8 7 6 I 5 I 4 I 3 I 2 I I I 0 I -I -2 P&(HB) FIG.6.-Bronsted plot for the proton-transfer dependent rate constants of Cu(H-,glyglyhis)-reacting with acids in the presence of excess trien.HB from left to right are Htris+ H(HEPES)* H(MES)* HOAc and H30+(p = 1.0 M 298 K). complexes because direct attack by trien as a nucleophile is too fast. However with Cu(H-,glyglyhis)- the nucleophilic reaction by trien is important only after a proton adds to the peptide group. Fig. 5 shows how the observed rate constants tend to level off as the trien concentration is increased. The effect of general acids is marked as seen by the higher plateau in the curve 2 run in the presence of 4.8 x lo3M H(HEPES)*. When reactions are run at high trien concentrations HEPES MES and Tris all accelerate the reaction as well as acetic acid and H30+. C. BANNISTER D. MARGERUM J. RAYCHEBA AND L.WONG Fig. 6 shows the variation of log kHB with the pKa(HB) value for these reactants. The mechanism where CuH-,L- is the glyglyhis complex is given in eqn (18)-(21) and (CuH-lL)* is a reactive intermediate with a proton present on one of the peptide nitrogens. (k,[H '1 +k;[H,]) k2[H2 trien '1 [CuH-,L-] rate = k- +k'_,[B-]+k2[Hztrien2+] At very high trien concentrations eqn (22) holds kobs. = kl[H+] +k',[HB]. Thus the presence of a large excess of a nucleophile removes the uncertainty about HB reacting in the proton-transfer step (H2trien2+ has a pK of 9.3 and does not contribute significantly as an acid). The H,O+ rate constant is 1.1 x lo7 M-l s-' f or Cu(H-,glyglyhis)- which agrees well with the value of 1.3 x lo7 M-l s-l for Cu(H-,glyglygly)- and the values close 1 to 107 ~-s-1 f or many other Cu(H-,tripeptide)- complexes.2 Therefore we conclude that all these reactions with H30+ are actually limited by the proton-transfer step.We propose that the curvature seen in fig. 6 is due to the situation described earlier where 2 has a small value and WR is relatively large. The small 2 causes gobs. to change rapidly as K becomes greater than unity and the kf value (kHB)levels off with large values of K(i.e. pKa(HB) = -1.74). The constants used to fit the curve in fig. 6 are given in table 5 A/4 = 5.9 kJ mol-l and W = 32.6 kJ mol-I. The reasons why the A/4 values are much smaller than the WRvalues are not clear but the degree of solvation of the reaction site may be involved. The behaviour of the deprotonated metal-peptides in intermediate between that of "normal " bases and the bases of carbon acids.CONCLUSION The rates of proton transfer reactions at the carbon atom of metal macrocyclic complexes and at the nitrogen atom in metal-peptide complexes are very different in their dependence on the ApK values of the reactants. In order to fit the data for either system the activation energy of the encounter species must have a term (Wi) which is independent of ApK as well as a term [1+ (AGi/A)I22/4 which depends on ApK,. The Wi term can be attributed to the solvent reorganization necessary to initiate hydrogen bonding after the work has been done to bring the reactants together in the encounter species. In the metal-peptide complexes this term is larger than the reorganizational barrier (A/4) and accounts for the limiting rates which are less than diffusion controlled.In the metal macrocyclic complexes A/4 is larger than W = (W{+AGY) but both terms change drastically with the type of base used. With the amine bases the MLH2+ Bronsted plots appear to be too linear. (The lack of curvature requires very large A/4 values which in turn means WRmust be negative to give the correct AG* values). The compensating nature of the 2/4 and Witerms makes predictions difficult. PROTON TRANSFER REACTIONS IN METAL COMPLEXES The work was supported by a National Science Foundation Grant and by Public Health Service Grant from the National Institute of General Medical Sciences. S. C. Cummings and J.G. Martin Inorg. Chem. 1973,95 1477. A review of the kinetics and mechanisms of metal peptide complexes is given by D. W. Margerum and G. R. Dukes in Metal Ions in Biological Systems vol. 7. ed. H. Sigel (Marcel Dekker New York N.Y. 1974) p. 157. M. Eigen Angew. Chem. Int. Ed. 1973,3 1. A. 0.Cohen and R. A. Marcus J. Phys. Chem. 1968,72,4249. R. A. Marcus J.Phys. Chem. 1968,72,891. M. M. Kreevoy and S. W. Oh J. Amer. Chem. Suc. 1973,95,4805. 'R. P. Bell The Proton in Chemistry (Cornell University Press Ithaca N.Y. 2nd edn. 1973 chap. 10 p. 195. * M. L. Ahrens M. Eigen W. Kruse and G. Maass Ber. Bunsenges.phys. Chem.,1970,74,380. F. P. Hinz Ph.D. Thesis 1973 (Purdue University). lo J. C. Cooper L. F. Wong D. L. Venezky and D. W. Margerum J. Amer. Chem. SOC.,1974 96,7560. N. E. Good G. D. Winget W. Winter T. N. Connolly S. Izawa and R. M. M. Singh Biochem. 1966 5 467.