iron  sulfur 
 ( [ fe  s ] ) clusters are ubiquitous electron - transfer ( et ) cofactors 
 that play a prominent role in many enzymes that mediate multi - e / h redox 
 transformations . in some instances , proton 
 transfer ( pt ) accompanies et , and the cluster undergoes proton - coupled 
 electron transfer ( pcet ) . as this type 
 of reactivity is increasingly being recognized to prevail in biological 
 [ fe  s ] clusters , it is important to establish factors that 
 affect the occurrence and the mechanisms of pcet ( stepwise et - pt or 
 pt - et , or concerted proton  electron transfer , termed cpet ) . perhaps the most - studied biological [ fe  s ] cluster known 
 to mediate pcet is the [ 2fe2s ] rieske cluster , in which one 
 fe is ligated by two cys residues , and the other by two his residues . the pcet reactivity enables the rieske cluster of oxygenase enzymes 
 to serve as both an et cofactor , delivering electrons to the active 
 site , and a structural gate , with reduction / protonation of the cluster 
 inducing structural changes that affect the active site . pcet is also the primary function of the rieske 
 cluster in the q - cycle of the mitochondrial and photosynthetic electron 
 transport chains . in this latter role , the diferric 
 cluster accepts a net h - atom ( e + h ) from a hydroquinone at the b - site . this reduces 
 the cluster to the mixed - valence state and protonates the imidazolate 
 ( his ) ligand ( the resulting semiquinone reduces cytochrome b ) . the 
 cluster then migrates to the c - site , donating an electron to cytochrome 
 c and the proton to a nearby base . the mechanism of the initial pcet 
 event is debated , with arguments for both stepwise pt - et and cpet being advanced . even less is known about both the mechanism and 
 base for the second pcet event . as et within the q - cycle is tightly 
 regulated to avoid formation of reactive oxygen species and energetically 
 wasteful short - circuits , it is of interest to 
 understand the mechanism(s ) of pcet of rieske clusters . in addition 
 to the rieske cluster , the recently discovered 3-cys 1-his mitoneet 
 [ 2fe2s ] cluster has also been shown to mediate pcet . clusters of this type are found in the outer 
 mitochondrial membrane and are promising 
 targets for cancer and diabetes therapeutics . the exact role of mitoneet clusters remains 
 unknown , and it has been suggested that they serve as a cluster transfer 
 protein and/or play a role in redox reactions , bioenergetics , and redox - sensing . the lone his - residue is crucial in controlling 
 the reduction potential , cluster stability , and pcet . the potential 
 to develop therapeutics , coupled with the uncertainty in its native 
 function , lends further motivation for studies that establish the 
 thermochemical , reactivity , and/or intrinsic properties of his - ligated 
 [ fe  s ] clusters . herein , we describe detailed thermochemical 
 and kinetic studies of a set of bis - benzimidazolate - ligated [ 2fe2s ] 
 clusters , which serve as a model for rieske and mitoneet clusters . our initial report described the synthesis and properties of the clusters 
 and preliminary kinetic studies . we now 
 show that three distinct protonation states can be accessed in the 
 mixed - valence state and hence that pcet can occur from two distinct 
 cluster congeners that differ by a proton . kinetic analysis and h / d 
 kinetic isotope effects ( kies ) for the pcet reactions with tempo additionally , 
 we examine the self - exchange rate constants for et , pt , and pcet . these results indicate that the mechanism of pcet at his - ligated [ 2fe2s ] 
 clusters should depend primarily on the thermodynamic coupling of 
 the redox partner , and the findings also suggest that the rate of 
 et at [ fe  s ] clusters is influenced by cluster size . the synthesis and characterization 
 of diferric [ fe2s2(bbim)2 ] ( 1 ) , mixed - valence [ fe2s2(bbim)2 ] ( 2 ) , diferric and protonated [ fe2s2(bbim)(bbimh ) ] ( 3 ) , and mixed - valence and protonated [ fe2s2(bbim)(bbimh ) ] ( 4 ) are reported elsewhere ( bbimh2 = 4,4-bis-(benzimidazol-2-yl)heptane ) . the cluster shown in grey has not been observed , and the thermochemical 
 values in grey are only estimates from other values . the mixed - valence 
 and twice - protonated cluster , [ fe2s2(bbim)(bbimh2 ) ] ( 5 ) , has not been previously characterized , but it was invoked 
 as an electrochemically observed intermediate in cyclic voltammograms 
 ( cvs ) of 4 at 20 c ( generated in situ from 2 and 1 equiv of [ pyh]otf ; py = pyridine ) . such cv experiments show two quasi - reversible couples that 
 are anodically shifted relative to the 1/2 couple . these are assigned to the 3/4 couple 
 and to that of the twice - protonated cluster congeners . addition of 
 1 equiv of base regenerates the cyclic voltammogram of 2 , indicating that the doubly protonated mixed - valence 5 might have enough stability at reduced temperatures for generation 
 and characterization . indeed , access to 5 is achieved 
 by addition of 2 equiv of [ dmap - h]otf to mecn solutions of 2 at 24 c ( dmap - h = protonated 4-dimethylaminopyridine ) . 
 over the course of minutes , solutions of 5 ( 0.47 mm in 
 mecn ) darken and form solids at room temperature ( see figures s1s4 ) . despite this thermal instability , 
 solutions of 5 can be prepared at reduced temperatures 
 for characterization . as for 4 , the twice - protonated 
 congener 5 is nmr silent at 20 c ( 5.7 mm , d3-mecn ) . addition of 2 equiv of the strong base bunp ( pyrr)3 ( pyrr = pyrrolidine ) 
 results in the reappearance of nmr resonances ascribed to 2 , in 75% yield , indicating reversible protonation . the epr 
 spectrum of 5 was obtained at 127 k ( see figure s3 ) . the spectrum can be fit to a rhombic g tensor with g = [ 1.990 , 1.950 , 1.885 ] 
 and corresponding linewidths , w = [ 65 , 40 , 60 g ] . though the exact site of protonation 
 is not known ( n vs s ) , previous studies of monoprotonated 4 suggests protonation at n , and 
 the partial localization of the electron in related systems suggests that both protonations should occur at one iron in 5 . the reaction between 4 and the nitroxyl radical tempo to generate 1 and tempoh was previously reported ( eq 1 ; n n = bbim ) . more detailed 
 kinetic studies on this system have now been performed using double - mixing 
 stopped - flow kinetic measurements in mecn under pseudo - first - order 
 conditions of excess tempo . solutions of 4 ( 0.25 mm ) 
 were generated in situ from mixing solutions of 2 and 
 [ dmap - h]otf , each 0.50 mm . after a delay time of 10 s , these solutions 
 of 4 were mixed with solutions containing excess tempo 
 ( 2 to 11 mm ) at several temperatures ( 25 to 50 c).1 to determine the kie , solutions of 4 and d-4 were generated by mixing 2 with a solution of either [ dmap - h]otf and ch3oh , or [ dmap - d]otf 
 and cd3od . the methanol ( 95 mm ) was added to the acid solution 
 to ensure high isotopic enrichment . at 25 c , rate constants 
 of 2480  33 and 335  10 m s were obtained for reactions of 4 and d-4 with tempo , respectively , indicating a kie of 7.4 
  0.3 . the k1h is in agreement with 
 that previously measured in the absence of methanol and indicates 
 a cpet mechanism . this corresponds to 
 g1h = 12.8  
 0.3 kcal mol and g1d = 13.9  0.3 kcal mol . the temperature dependence of k1 gives 
 s1 = 36.4 
  1.4 ( h ) and 38.1  1.6 e.u . ( d ) , and h1 = 1.99  0.22 ( h ) 
 and 2.62  0.21 ( d ) kcal mol . to establish 
 whether ion - pairing is affecting the kinetics of reaction 1 , the room temperature measurements were repeated 
 in 0.1 m bu4npf6 solutions in mecn ( 4 was generated in the absence of 
 methanol ) . from these measurements , a second - order rate constant of 
 2750  36 m s is obtained 
 at 25 c . this 11% increase in rate upon going from 0.5 
 to 100 mm ionic strength is a small effect and hence ion - pairing is 
 likely not playing a significant role . mixed - valence and twice - protonated 5 likewise reacts with tempo ( eq 2 ) 
 to generate diferric and protonated 3 (  50% ) 
 and tempoh (  100% ) , as ascertained by nmr spectroscopy ( see figure s22 ) . the decreased yield of 3 relative to tempoh may be due to competing degradation of 5 ( which likely generates paramagnetic species and free ligand , 
 as for the degradation of 4 ) , the instability of mixtures of 3 and 5 in the presence of tempoh / tempo , and/or the known instability of 3 . to overcome these challenges , double - mixing stopped - flow 
 kinetic measurements were undertaken under pseudo - first - order conditions 
 of excess tempo ( 1.35.3 mm ) in mecn . similar to the reaction 
 described above , 5 was generated by mixing a 0.51 mm 
 solution of 2 with a 1.01 mm solution of [ dmap - h]otf - containing 
 95 mm meoh . however , plots of kobs versus [ tempo ] have a nonzero intercept , suggesting competing degradation 
 of 5 ( kobs obtained from 
 global fitting ) . the kinetics were fit to a model with competing decomposition 
 of 5 , d / dt = kdec + k2[tempo ] . the kdec values from this analysis are 0.22  0.12 s for 5 and 0.13  0.02 s for 5-d2 at 25 c . the rate constants 
 ( k2 ) obtained for the reactions of 5 and 5-d2 with tempo 
 were 112  30 and 30  6 m s , respectively . the activation 
 free energy for the reaction of 5 with tempo 
 is 15 kcal mol at 25 c.2 the 
 known thermochemical parameters that interconvert cluster congeners 14 are shown in the top portion of scheme 1 . the ability to generate 5 allows construction of an expanded square scheme , in which 5 and 3 are related by pcet ( scheme 1 , bottom ) . the bond dissociation free energy 
 ( bdfe ) of 5 was determined from the equilibrium constant 
 for the reaction of 3 with excess tempoh ( 1.35.4 
 mm ) to form 5 and tempo ( reverse of eq 2 ) . owing to the instability of both 3 and 5 , k2 ( k2 = 1/k2 ) was determined using double - mixing stopped flow . solutions 
 of 3 were generated in situ from 1 and 1 
 equiv of [ dmap - h]otf , and after a delay time of 1 s , then mixed with 
 solutions containing excess tempoh . upon mixing , a decrease in absorption 
 at 526 nm was noted , indicative of cluster reduction . the resulting 
 mixture of tempo , tempoh , 3 , and 5 is not 
 stable , as evident from a subsequent increase in the absorption at 
 620 nm and loss of the isosbestic point at 350 nm ( see section g of 
 the si ) . analysis of the spectra at the 
 inflection point of the a620 versus time 
 plot , with the assumption that the equilibrium is established and 
 degradation is limited , gives k2 = 0.012  0.004 . a similar value of k2 is obtained from spectra at later times , when degradation 
 is known to have commenced ( see section g of the si ) . h bdfe in 5 of 
 63.9  0.9 kcal mol , using bdfetempoh = 66.5 kcal mol . it is not possible to use the more typical approach to determine 
 the n h bdfe in 5 from the pka of 5 and the reduction potential of 4 ( bdfe = 23.06 e1/2 + 1.37 pka + cg ; cg = 54.9  1.0 kcal mol in mecn ) . the instability of 5 , coupled with 
 the lack of nmr resonances for both 4 and 5 , prevents direct measurement of the pka of 5 . this equation can be used , however , to calculate 
 the pka from the bdfe of 5 and the e(3/4 ) , giving 
 pka ( 5 )  23.1.3 dynamic nmr methods 
 were employed to determine the rate constant for intermolecular et 
 self - exchange between 1 and 2 ( eq 3 and figure 1 ) . h nmr spectra of mixtures of 1 and 2 ( 2.0 
 mm cluster , d3-mecn ) reveal broadening 
 of the ligand resonances of both 1 and 2 . the broadening with no change in chemical shift is indicative of 
 slow chemical exchange on the nmr time scale . ( left ) overlay of stacked 
 1h nmr spectra ( experimental : purple ; fit : gold ) for solutions of 1 and 2 , with   +   = 2.0 mm , in d3-mecn at 26 c . ( right ) plot of w ( hz ) 
 vs   ( m ) . the rate constant for intermolecular et can be calculated 
 from eq 4 , assuming simple two - site exchange 
 in the slow exchange limit.4 in eq 4 , w is the line - width at half - height for a given resonance , 
 and kself - exchange is the rate 
 constant for self - exchange between species a and b ( 1 and 2 for eq 3 ) . for this analysis , the resonance at 10.71 ppm of 1 was employed ( corresponding 
 to the 4-position of the benzimidazolate and marked with an asterisk 
 in eq 3 ) , as it is well - separated from the other 
 ligand resonances of both 1 and 2 . from 
 the slope of the plot of w1 versus , a value of ( 1.20  0.06 )  10 m s is obtained for k3 at 26 c . activation parameters from rate constants measured at 24 , 
 16 , 5 , and 26 c are h3 = 2.2  0.2 kcal mol and s3 = 28 
  1 e.u . in the presence of 6.0 mm bu4npf6 , the rate constant is ( 7.4  0.6 ) 
  10 m s at 
 26 c , a decrease of about 40% . the et self - exchange rate of 3 and 4 could not be measured , owing to the high 
 basicity of 4 ( see figure s8 ) . attempts to generate solutions of 3 and 4 instead results in mixtures of 1 and 5 ( see scheme 1).5 the et self - exchange rate constant for the related [ fe2s2(saro)2 ] cluster system ( saro = thiosalicylate ) was also 
 measured by nmr line broadening ( eq 5 ; see section 
 f.v of the si ) . for these measurements , 
 solutions containing mixtures of the diferric and mixed - valence clusters 
 were prepared in situ , owing to the limited stability of the mixed - valence 
 cluster . substoichiometric amounts of 
 cocp*2 were added to 2.5 mm solutions of [ fe2s2(saro)2 ] , and then d3-mecn was added to adjust the final total concentration 
 of clusters to the desired 1.9 mm . as for mixtures of 1 and 2 , et self - exchange is slow on the nmr time scale , 
 and eq 4 can be used to determine the rate constant . the slope of the plot of w versus [ fe2s2(saro)2 ] ( resonances for both the diferric and mixed - valence congeners were 
 analyzed , see section f.v of the si ) , indicates 
 the rate constant k5 = ( 1.9  0.9 ) 
  10 m s at 
 26 c . although the uncertainty is large , due to some scatter 
 in the line broadening values , this rate constant is essentially the 
 same as k3 . as previously reported , the h nmr spectra of both 1 and 3 have seven well - resolved ligand resonances . this indicates effective d2h symmetry on the nmr time scale in solution , 
 which requires for 3 that there be rapid proton migration 
 among the four equivalent benzimidazolate groups . the h nmr spectra of 1 and 3 each show a well - resolved 
 peak for the resonance for protons at the 4-position of the benzimidazolates 
 ( marked with an asterisk in eq 6 ) at 10.71 and 
 10.65 ppm , respectively ( d3-mecn , 25 c ) . the rate of intermolecular pt exchange for 1 and 3 ( eq 6 ) was also studied by nmr line 
 broadening analysis . nmr spectra of mixtures of 1 and 3 in d3-mecn ( 1.94 mm ; 1:3 , 1:1 , 
 and 3:1 ) were prepared by addition of < 1 equiv of [ pyh]otf to 1 . h nmr spectra of these mixtures show a single 
 set of ligand resonances , which shift according to the mole fraction 
 of 1 and 3 . this indicates rapid intermolecular 
 pt exchange between 1 and 3 on the nmr time 
 scale . because there is no significant broadening of the coalesced 1 + 3 signal versus the weighted average of the 
 individual line widths , an accurate determination of the pt self - exchange 
 rate was not possible ( see figure s5 ) . 
 from the peak separation , the rate constant to just achieve coalescence 
 of the peaks would be 10 m s. this is a lower bound 
 for k6 at 25 c . the mechanism(s ) 
 for proton exchange in this system , the 1/3 self - exchange and the proton scrambling in 3 , are not 
 established by these experiments . we have only succeeded in generating 3 in situ by acid addition to 1 , so the conjugate 
 base of the acid is always present as py in the reactions described 
 above . in addition , mixtures of 1 and 3 are 
 not stable to excess base . thus , we can not determine whether the base 
 catalyzes the proton exchanges or whether it is direct pt between 
 clusters.7 nmr line broadening analysis was also used 
 to measure the rate constant for net intermolecular pt between the 
 mixed - valence cluster congeners 2 and 4 ( eq 7 ) . owing to the thermal sensitivity of 4 , , the h nmr spectrum of 2 ( d3-mecn ) features seven well - defined ligand resonances . addition of < 1 equiv 
 of [ dmap - h]otf to solutions of 2 results in broadening 
 of the resonances of 2 with no changes in the chemical 
 shifts . this indicates that pt is slow on the nmr time scale . assuming 
 a simple two - site exchange , the rate of intermolecular pt can be calculated 
 from eq 4 . at 20 c , the 
 resonance ascribed to the protons of the 4-position in the ligand 
 benzimidazolates is centered at 12.42 ppm and has a corresponding w2 of 138 hz . upon addition of 0.2 equiv of [ dmap - h]otf 
 to a 5.7 mm d3-mecn solution of 2 , this resonance broadens to 472 hz . this gives the rate 
 constant k7 of 9  10 m s at 20 
 c . the peak broadens into the baseline upon addition of an additional 
 0.3 equiv of [ dmap - h]otf to the sample ( 0.5 equiv total ) . as for the 
 diferric clusters , the mechanism of pt ( direct or base - mediated ) is 
 unknown the rate constant for the reaction that interconverts 1 and 4 ( eq 8) was likewise obtained 
 from nmr line broadening ( eq 4 ) . for these measurements , 
 mixtures of 1 and 4 were either prepared 
 by adding the appropriate amount of [ dmap - h]otf to mixtures of 1 and 2 or by adding 1 equiv of [ dmap - h]otf to 
 a solution of 2 ( to generate 4 ) followed 
 by the appropriate amount of tempo ( see section f.vi of the si ) . the same rate constant , within error , was 
 found for both procedures ( figure 2 ) . peaks 
 corresponding to 1 broaden and do not shift in mixtures 
 of 1 and 4 , showing that exchange between 1 and 4 is slow on the nmr time scale at 30 
 c ( 4 is nmr silent ) . the rate constant was obtained 
 from the broadening of the peaks when both species were present . from 
 the slope of the plot of w1 versus   ( figure 2 ) , a value 
 of 3.8  0.7  10 m s is obtained for k8 at 
 30 c . blue circles correspond to data 
 collected when mixtures of 1 and 4 were 
 prepared from mixtures of 1 and 2 + [ dmap - h]otf . pink squares correspond to data collected when mixtures of 1 and 4 were prepared from 4 + tempo . the thermochemistry of interconversion between the [ fe2s2(bbim)x(bbimhy)2x ] cluster congeners 
 is shown in scheme 1 . the nh bdfe of 4 and 5 are 60.5  1.0 and 63.9  0.9 
 kcal mol , respectively . the twice - protonated 5 is less reducing 
 in a pcet sense than the singly protonated 4 . it 
 is instructive to compare the thermochemical parameters of the model 
 system to those of biological clusters ( table 1 ) . rsrp and ttrp are high - potential 
 rieske proteins that are associated with the bc1 complex of the q cycle . bphf is the low potential rieske 
 ferredoxin of biphenyl dioxygenase , and mn is the mitoneet cluster . the bdfes for these clusters are obtained from the ph dependence of 
 their aqueous reduction potentials following ref ( 19 ) ( table 1 ) . the biologically relevant bdfes interconvert the mono- 
 and twice - protonated clusters , but it is valuable to see the zero / monoprotonated 
 values as well . from this perspective , for the biologically relevant 
 mono - protonated state , the rieske clusters of the q cycle are more 
 oxidizing than either that of bphf or mn ( 6 kcal mol ) or the model cluster ( 10 kcal mol ) . this is consistent with their critical role of oxidizing the appropriate 
 hydroquinone as part of the q cycle . by 
 contrast , the bphf cluster serves as an et cofactor , reducing the 
 active - site fe for dioxygenase enzymes . mono-/twice - protonated 
 refers to the pcet event that interconverts the mixed - valence and 
 twice - protonated cluster with the diferric and monoprotonated cluster . zero-/monoprotonated refers to the pcet event that interconverts the 
 mixed - valence and monoprotonated cluster with the diferric and deprotonated 
 cluster . thermodynamic coupling refers to the shift in pka upon redox change ( and conversely the shift in e1/2 upon protonation ) . the bdfe and extent of thermodynamic coupling for 
 the enzymatic clusters are calculated here from the reported reduction 
 potentials and pka values ( bdfe = 23.06 e1/2 + 1.37 pka + cg ; cg = 57.6  1.0 kcal 
 mol in water ) . rsrp = high - potential 
 rieske cluster from the cytochrome bc1 complex of rhodobacter sphaeroides that oxidizes ubiquinol . ttrp = high - potential 
 rieske cluster from the cytochrome bc1 complex of t. thermophilus that oxidizes menaquinol . bphf = low - potential rieske protein 
 that is the soluble ferredoxin of the biphenyl dioxygenase of burkholderia sp . strain lb400 . the sum of pk1 and pk2 must be equal to the difference between ealk and eacid ( whcn corrected for different 
 units ) . from this , ealk is estimated to 
 be  0.281 v. pkred2 was reported as > 12.5 in ref ( 2b ) . though the mitoneet protein only has one his that 
 coordinates the [ 2fe2s ] cluster , there are two protonation 
 events reported in ref ( 2b ) ; the second protonation likely occurs at a residue near the his 
 or cluster . the difference 
 in bdfes between the mono- and twice - protonated congeners is larger 
 for the q - cycle rieske clusters ( 3.7 kcal mol ) than for the other biological clusters ( 1 kcal mol ) . this may have a role in regulating the flux of e / h in the q cycle . a similar difference in bdfes one 
 valuable parameter for a pcet active site is the extent of thermodynamic coupling between the electron and the proton . this is defined as the shift in pka upon redox change and the shift in e1/2 upon protonation , which are equal by hess 
 law : in kcal mol , 1.37 pka = 23.06 e1/2 . for the unprotonated - to - monoprotonated cluster , because neither 
 the reduction potential nor the pka of 
 the diferric and twice - protonated cluster is known , the extent of 
 thermochemical coupling is not known for the twice - protonated cluster . however , because the pka for the diferric 
 and twice - protonated cluster must be less than that of 3 , a lower limit for the thermodynamic coupling is estimated to be 
 3.4 kcal mol . the thermodynamic coupling 
 for the biological mono / diprotonated clusters is larger for the rieske 
 clusters of the q cycle ( 6.5 kcal mol ) 
 than for those of either bphf or mn ( 4.5 kcal mol ) . the thermodynamic coupling of the model cluster in the twice - protonated 
 state unfortunately could not be determined . the nonprotonated / monoprotonated 
 coupling is larger for the model system ( 5.6  0.5 kcal mol ) than for all of the biological clusters ( in this 
 protonated state ) . it should be noted , however , that these are all 
 relatively small values for the pcet coupling . this coupling is 60 
 kcal mol for tempoh and for toluene and can approach 
 zero when the redox and acid / base sites are well - separated . it has been suggested that the stronger 
 coupling in the q - cycle clusters ( relative to the oxygenase clusters ) 
 may implicate cpet , as opposed to stepwise processes . indeed , the monoprotonated model cluster 4 , which has a similar extent of thermodynamic coupling , is capable 
 of undergoing concerted proton  electron transfer , as exemplified 
 by the reaction with tempo , ( as does 5 , vide infra ) . 
 in these reactions , the preference for a cpet mechanism is largely 
 due to the very large thermodynamic coupling of tempoh ( 60 
 kcal mol ) . the ability to generate the clusters 
 that would be intermediates in the stepwise mechanism suggests that 
 the coupling may not be substantial enough to enforce a concerted 
 mechanism . hence the increased coupling observed in the high - potential 
 rieske clusters relative to the low - potential proteins may not be 
 sufficient to enforce a concerted mechanism . by comparison , other 
 biological pcet cofactors have larger thermodynamic couplings : 16.6 
 kcal mol for tyrosine and 15 kcal mol for hydroquinone . thus , 
 it seems that the possible mechanisms for pcet at the [ 2fe2s ] 
 clusters , concerted versus stepwise , may be determined by the extent 
 of thermodynamic coupling in the redox partner . the rapid h - atom transfer 
 from 4 and 5 to tempo is consistent with 
 the very low n we previously reported 
 the rate constant and activation parameters for the reaction of 4 with tempo ( eq 1 ) . comparison of g1 with the free energy changes associated with initial 
 et or pt transfer , get1 and 
 gpt1 , indicates that this 
 reaction must occur via a concerted proton reported here are kinetic measurements in the presence of ch3oh and cd3od to determine the kinetic isotope effect ( kie ) 
 and its temperature dependence . at 25 c , a kie of 7.4  
 0.3 the entropic contributions to the activation 
 free energy are the same ( within error ) , and thus the difference in 
 activation free energy is due primarily to hh these findings are interesting 
 in light of the unusual isotope effect observed by cape et al . this effect is reproduced in other studies on quinol oxidation by 
 a ruthenium model complex and in theoretical 
 calculations . that the model system described 
 here does not exhibit this unusual isotope effect is consistent with 
 the idea that this effect depends on the quinol being the substrate . the kinetic data for the reaction of 5 and tempo must 
 be interpreted with caution due to the competing degradation of 5 . however , it is clear that the reaction occurs by concerted 
 proton  electron transfer ( cpet ) . the activation free energy 
 of 15 kcal mol at 25 c is substantially 
 smaller than the ground state free energy changes for either initial 
 pt or et , gpt  38 
 kcal mol ; get >  22 kcal mol ) . we simply 
 note that the reaction is slower than that of 4 with 
 tempo , 112  20 m s for 5 versus 2480  33 this factor of 22 lower rate constant 
 is consistent with the lower driving force for the reaction of 5 . using the marcus cross - relation , the 3.4 kcal mol difference in bdfes between 5 and 4 predicts a factor of 17 difference in rate constants , well 
 within the uncertainties of this analysis . thus , the cpet intrinsic 
 barriers are not significantly different for 4 and 5 . to gain 
 further insight into the pcet reactivity of rieske clusters , rate 
 constants for several self - exchange processes have been measured . these rate constants are a direct measure of the intrinsic 
 barrier , the intrinsic facility of the reagent to do the reaction 
 of interest . measured at 299 k in d3-mecn . h2bim = 2,2-bi - imidazoline . measured in the presence of pyridine ( equimolar 
 with 3 ) . the rate constant for et self - exchange 
 between 1 and 2 ( eq 3 ) k3 is ( 1.20  0.06 )  10 m s. this rate constant 
 observed is roughly 1 order of magnitude slower than that measured 
 for related s - ligated [ 4fe4s ] and [ 4fe4se ] clusters , 
 measured analogously in d3-mecn at similar 
 concentrations . however , the enthalpic 
 barrier for 1/2 self - exchange is 1.4 
 kcal molsmaller than that for 
 [ fe4s4(s - p - c6h4me)4 ] . although the 
 differences are small , the slower et for the [ 2fe2s ] cluster 
 system 1/2 is apparently due to its larger 
 entropy of activation ( by 11 e.u . ) versus [ fe4s4(s - p - c6h4me)4 ] . the difference in et properties 
 could be attributed to either the ligand type ( n vs s ) and/or the 
 cluster size . to distinguish between these possibilities , the et self - exchange 
 rate for a second type of [ 2fe2s ] cluster the 
 instability of s - ligated mixed - valence [ 2fe2s ] clusters precluded 
 a direct comparison of all s - ligated clusters , so instead , the mixed s / o - ligated cluster , [ fe2s2(saro)2 ] was 
 examined . the et self - exchange rate constant k5 for this cluster ( eq 5 ) is ( 1.9  
 0.9 )  10 , which is within the uncertainty of the 
 value for 1/2 and again roughly an order of magnitude 
 slower than that of the related [ 4fe4s ] clusters . the 
 effect of cluster size on high - spin iron species can be further examined 
 by contrasting the et self - exchange rates of the [ 2fe2s ] clusters 
 to [ fe(h2bim)3 ] monomeric complexes . the et self - exchange rates for the [ 2fe2s ] clusters are 1 
 order of magnitude larger than in the monomeric systems . thus , our results suggest that cluster size , 
 not ligand composition , controls the et self - exchange kinetics for 
 high - spin iron species . the larger clusters have larger et self - exchange 
 rates and smaller intrinsic barriers . this may be attributed to more 
 electron delocalization as cluster size increases , which would decrease 
 both the inner- and outer - sphere reorganization energies . the self - exchange rate constants reflect the intrinsic 
 barriers and therefore the rate of all et reactions involving these 
 reagents , following marcus theory . the differences highlighted here 
 should correspond to a factor of 34 times in cross rate constants 
 ( [ 4fe4s ] vs [ 2fe2s ] , or [ 2fe2s ] vs [ fe ] ) , 
 for et reactions with different redox partners . these results clearly 
 indicate that the cluster size modulates the intrinsic barrier to 
 et . this contrasts with previous computational studies that predicted 
 no clear trend for the inner - sphere reorganization energy of [ fe  s ] 
 clusters with size ( in vacuum ) . these 
 studies do however suggest that the hydrogen - bonding of the protein 
 environment can substantially reduce the inner - sphere reorganization 
 energy . comparison of self - exchange rates of synthetic and biological 
 [ 4fe4s ] clusters indicate a much slower self - exchange rate 
 for biological clusters . combined , this underscores 
 the importance of hydrogen bonds , sterics , and 
 the local protein environment to reorganization energies . nonetheless , 
 for proteins with similar environments , the results presented here 
 suggest that the rate of et should vary with cluster size . the 
 control of et rates to / from enzyme active - sites is crucial for catalysis . nature employs a variety of [ fes ] clusters which differ in size , ligand , 
 and metal identity , and the choice of cluster type remains unknown . it has been proposed that the choice of cluster may be in part due 
 to stability and/or redox potential . computational studies suggest that [ 4fe4s ] 
 clusters are more robust than smaller analogues upon metal substitution , maintaining similar inner - sphere reorganization 
 energies and hence et rates . the results presented here indicate that 
 the cluster size also contributes the rate of et and hence may also 
 contribute to the choice of cluster in proteins . interpretation 
 of the pt rate constants must be done with caution , as the presence 
 of the conjugate base of the acid used to protonate the cluster is 
 present in solution . we simply note that in the presence of the conjugate 
 base , the pt self - exchange rate constants are faster than the et ones . the values obtained are similar to that of the related monomeric [ fe(h2bim)3 ] analogue ( obtained in the absence 
 of the conjugate base ) . recently showed that for a related bis - benzimidazolate ligated 
 [ 2fe2s ] cluster , electron localization 
 increases upon protonation in the mixed - valence state . this suggests 
 that the change in electron localization ( which would increase both 
 inner- and outer - sphere reorganization energies ) might affect pt . unfortunately , owing to the difficulties in obtaining accurate pt 
 rate constants for the system , no conclusions can be drawn from our 
 pt studies . the rate 
 constant for net pcet self - exchange between 1 and 4 is ( 3.8  0.7 )  10 m s at 30 c . this is slower than 
 the pt and et self - exchange rates , by 2 and 1 orders of magnitude , 
 respectively this self - exchange reaction could occur via concerted 
 transfer of e and h or by a stepwise et - pt or pt - et path . initial et and pt have different 
 transition states and barrier heights , but for the special case of 
 a self - exchange reaction , they yield the same intermediates ( eq 9 ) . additionally , for 
 a self - exchange process , the overall et - pt and pt - et paths are the 
 microscopic reverse of each other ( eqs 9 and 10 ) . they must therefore proceed at the same overall 
 rate for this g = 0 process . the 
 equilibrium constant k9 for eq 9 is 8  10 , based 
 on the difference in pka values of 3 and 4 ( equal to the difference in e1/2 of 1 and 3 ; this is equal 
 to the thermochemical coupling).910 the reverse of eq 9 , 2 + 3 ( eq 10 ) , can not occur faster than 
 the diffusion limit in mecn , k9  2  10 m s. as k9 = k9/k9 , k9 must be less than 10 m s. thus , the stepwise mechanism 
 of initial et or pt is potentially kinetically competent . the 
 rate constant for initial et can be estimated from the marcus cross - relation 
 ( eq 11).11 in eq 11 , kxy is the rate constant for 
 the et cross reaction of 1 with 4 , kxx and kyy are the self - exchange rate constants 
 for 1/2 and 3/4 , respectively , and kxy is the equilibrium constant for the cross reaction . fxy is a known function of kxy , kxx , kyy , and the individual 
 work terms associated with formation of the precursor / successor complexes 
 of the cross- and self - exchange reactions . assuming that k3/4 can be approximated as k1/2 ( 2  10 m s at 243 k ) , and that k1/4 has no temperature dependence , then k1/4 is predicted to 
 be 20 m s ( f  1 ) . this argues against a stepwise et - pt mechanism for the 
 pcet process , because this et barrier is 4 kcal mol larger than the measured activation free energy for the pcet self - exchange 
 of 1 and 4 . as the overall et - pt and pt - et 
 paths are the microscopic reverse of one another , this also argues 
 against the pt - et mechanism ( figure 3 ) . free energy 
 diagram for the pcet self - exchange reaction of 1 and 4 . the peak of the green ( lowest ) curve is the measured pcet 
 barrier . the blue and red curves represent the stepwise et - pt mechanism , 
 with the height of the et step ( blue ) derived from the marcus cross 
 relation ( eq 11 ) . the pt - et mechanism is the microscopic reverse ( red 
 then blue ) . to establish the feasibility 
 of a cpet mechanism we have shown that the marcus cross - relation ( eq 11 ) can be used to predict rate constants for cpet cross reactions 
 within 12 orders of magnitude . from the eyring equation , the rate constant for pcet self - exchange 
 between 1 and 4 at 25 c is estimated 
 to be 1.5  10 m s. the self - exchange rate constant for tempo / tempoh 
 in mecn is 4.7 m s , and the equilibrium constant for the reaction 
 of 4 with tempo is 2.5  10 . from these 
 values , the marcus cross - relation predicts the rate constant of 3.0 
  10 m s for 
 the reaction of 4 with tempo ( f  
 0.5 ) . the measured cross rate constant of 2480  33 m s is 2 orders of magnitude slower than 
 that predicted from the marcus cross - relation . thus , these results 
 are consistent with the measured pcet self - exchange rate constant 
 for 1/4 corresponding to a cpet pathway . additionally , these results suggest that the cross - relation can be 
 applied to cpet reactions that involve [ fe  s ] clusters and 
 hence can be more broadly applied to biological systems and related 
 clusters that do not have localized valences . thus , the mechanism 
 for pcet self - exchange between 1 and 4 likely 
 occurs via a cpet mechanism . the thermochemical 
 coupling of 5.6 kcal mol  is high 
 enough to preclude the stepwise mechanism , but not by much . this choice 
 of mechanisms is also likely important for biological rieske clusters , 
 which have a similar extent of thermodynamic coupling . this report describes the pcet reactivity 
 and thermochemistry of a set of bis - benzimidazolate - ligated [ 2fe2s ] 
 clusters . pcet can occur from two distinct protonation states , between 
 complexes 1 and 4 or between 3 and 5 . the measured et self - exchange rate constants 
 for 1/2 and for the related [ 2fe2s ] 
 cluster [ fe2s2(saro)2 ] are both an order of magnitude slower than that of the larger s - ligated 
 [ 4fe4s ] clusters . et self - exchange for the [ 2fe2s ] 
 clusters is an order of magnitude faster than that of a related high - spin 
 mononuclear iron complex , suggesting that the intrinsic barrier to 
 et is modulated by cluster size . the measured rate constant for pcet 
 self - exchange between 1 and 4 is consistent 
 with a cpet mechanism . combined , these findings suggest a small bias 
 for cpet mechanisms at imidazole - ligated [ 2fe2s ] clusters 
 such as the rieske and mitoneet clusters . however , the choice of mechanism  stepwise 
 versus concerted  is likely controlled by the thermodynamic 
 coupling of the redox partner .
this report describes the thermochemistry , 
 proton - coupled electron transfer ( pcet ) reactions and self - exchange 
 rate constants for a set of bis - benzimidazolate - ligated [ 2fe2s ] 
 clusters . 
 these clusters serve as a model for the chemistry of biological 
 rieske and mitoneet clusters . 
 pcet from [ fe2s2(prbbim)(prbbimh)]2 ( 4 ) and [ fe2s2(prbbim)(prbbimh2)]1 ( 5 ) 
 to tempo occurs via concerted proton  electron transfer ( cpet ) 
 mechanisms ( prbbimh2 = 4,4-bis-(benzimidazol-2-yl)heptane ) . 
 intermolecular electron transfer ( et ) self - exchange between [ fe2s2(prbbim)2]2 ( 1 ) and [ fe2s2(prbbim)2]3 ( 2 ) occurs with a rate 
 constant of ( 1.20  0.06 )  105 m1 s1 at 26 c . 
 a similar self - exchange rate 
 constant is found for the related [ 2fe2s ] cluster [ fe2s2(saro)2]2/3 , saro2 = thiosalicylate . 
 these are roughly an 
 order of magnitude slower than that reported for larger [ 4fe4s ] 
 clusters and 1 order of magnitude faster than that reported for n - ligated 
 high - spin iron complexes . 
 these results suggest that the rate of intermolecular 
 et to / from [ fe  s ] clusters is modulated by cluster size . 
 the 
 measured pcet self - exchange rate constant for 1 and 4 at 30 c is ( 3.8  0.7 )  104 m1 s1 . analysis of 
 rate constants using the marcus cross - relation suggests that this 
 process likely occurs via a concerted proton 
 electron transfer 
 ( cpet ) mechanism . 
 the implications of these findings to biological 
 systems are also discussed , including the conclusion that histidine - ligated 
 [ 2fe2s ] clusters should not have a strong bias to undergo 
 concerted e/h+ transfers .