the design of h2 oxidation and production electrocatalysts 
 is critical for the development of alternative renewable energy technologies . 

the [ fefe]-hydrogenase enzymes catalyze these reactions effectively 
 with binuclear fe metal centers , as depicted in figure 1 .
fourier transform infrared spectroscopy 
 ( ftir ) and electron paramagnetic resonance ( epr ) studies on the native 
 enzyme have identified a mixed - valence oxidized state , hox , and a diamagnetic reduced state , hred .
the hox state is well - characterized and features an obvious 
 site for binding the h2 substrate on the distal fe center , 
 denoted fed in figure 1 .
the structure 
 of the hred state is less clear because x - ray crystallography 
 of biological systems can not easily resolve hydrogen atoms .
although 
 hypothesized for more than a decade , an azadithiolate 
 bridgehead with an amine group pendant to the fe metal center has 
 only recently been confirmed experimentally .
relative to biophysical studies , an advantage of model systems is 
 that hydride and dihydrogen species are readily observed by h nmr and , in some cases , x - ray crystallography .
moreover , model systems are more computationally tractable , thereby 
 providing additional structural and mechanistic insights . oxidized 
 ( hox ) and reduced ( hred ) intermediates of the 
 [ fefe]-hydrogenase enzyme s active site with the azadithiolate 
 ( adt ) cofactor . a variety of h2-producing model systems inspired by [ fefe]-hydrogenases have been 
 synthesized .
many of these models suffer from high overpotentials ( i.e. , negative 
 reduction potentials ) for hydrogen production .
the recent h2-producing models fe2(xdt)(co)2(dppv)2 ( xdt = pdt , adt ) , depicted in figure 2 , rely 
 on an electrode in place of the [ fe4s4 ] clusters 
 that normally support electron transfer in the enzyme .
furthermore , 
 in these models the cn and one of the co ligands are replaced by diphosphine 
 ( dppv ) ligands .
the presence of sterically 
 crowded , electron - rich ligands on diiron carbonyl has been shown to 
 stabilize the desired terminal hydride species . through this approach ,
the most recent advance has revealed a key 
 intermediate wherein the hydride is dihydrogen bonded to the protonated 
 azadithiolate cofactor .
this paper 
 analyzes computationally the recent advances in the models and chemistry 
 of the [ fefe]-hydrogenases . this paper has two components : benchmarking 
 the computational methodology for these model systems and providing 
 insights into the mechanism of h2 production .
the benchmarking 
 provides the validation that is necessary to support the more hypothetical 
 mechanistic predictions . in the first part of this paper
, the computational 
 methods are benchmarked by comparing experimental and theoretical 
 structures , infrared ( ir ) vibrational frequencies of the co groups , 
 reduction potentials , and relative pka values .
in particular , we examine these model systems 
 in the various oxidation states and protonation states along proposed 
 mechanistic pathways for h2 production .
of particular interest , 
 we aim to clarify the nature of the doubly protonated ammonium - hydride 
 intermediate , which has been characterized crystallographically for 
 this bimetallic system .
such doubly protonated 
 intermediates have not been observed in bioinspired monometallic ni - based 
 catalysts , although a mono - fe catalyst in the doubly protonated state has very 
 recently been characterized by dubois and co - workers .
we also present additional experimental data to validate 
 the theoretical studies and to test predictions generated by the calculations .
ii , we introduce the nomenclature for the species studied 
 and describe the computational methods used to calculate the structures , 
 co vibrational frequencies , reduction potentials , and pka values for these species .
section iii presents the results and analysis , starting with the geometries 
 and vibrational frequencies , followed by the reduction potentials 
 and an analysis of the spin densities to determine the oxidation states 
 of the metal centers .
the second part of this section focuses on the 
 protonation states and relative pka values 
 and presents an analysis of possible h2 evolution mechanisms 
 in the context of the experimental and computational data . concluding 
 remarks are presented in section iv .
the diiron model systems can adopt 
 numerous isomeric and geometric forms . borrowing the nomenclature 
 generally employed in enzymatic studies , the fe center with the hydride 

is denoted distal ( fed ) and the opposite fe center is denoted 
 proximal ( fep ) . herein , we will abbreviate the ( fepfed)(xdt)(co)2(dppv)2 catalysts 
 as [ ( fefe)xdt ] for notational simplicity .
figure 2 depicts the electrocatalyst in the terminal hydride ( th ) form with xdt representing either a propanedithiolate 
 ( pdt ) , [ th-(fefe)pdt ] , or an azadithiolate ( adt ) , [ th-(fefe)adt ] . 
 in this notation ,
figure 3 depicts 
 all of the protonation states of the [ ( fefe)adt ] species studied in 
 this work .
a similar scheme for the [ ( fefe)pdt ] species is available 
 in the supporting information ( figure s17 ) .
model 
 of the hred state of the enzyme , where the role of the 
 [ fe4s4 ] cluster is replaced by 
 an electrode and the other ligands are replaced by 1,2-bis(diphenylphosphino)ethylene 
 ( dppv ) .
the x represents the heteroatom in the dithiolate bridge ( xdt 
 = pdt , adt ) .
schematic depiction of the various [ ( fefe)adt ] 
 species , where each row represents a different protonation state of 
 the catalyst . only the isomers with the lowest free energies
the dashed lines ( p1 , p2 , p3 , p4 , 
 and p5 ) correspond to pathways for which structural and electronic 
 changes can be monitored by co values ; they 
 do not necessarily correspond to reaction pathways . although the terminal hydride ( th ) species are thermodynamically less stable than their 
 associated bridging hydride ( h ) isomers in model 
 systems , experiments indicate that the terminal hydride species are 
 much more catalytically active : they generate h2 faster 
 and at less negative potentials than their bridging hydride counterparts .
the dependence of the reduction potential on the regiochemistry 
 of the hydride remains unexplained but appears to be catalytically 
 relevant .
whereas the [ ( fefe)pdt ] complex 
 requires strong acids to form the terminal hydride species , [ th-(fefe)pdt ] , the nearly isostructural [ ( fefe)adt ] 
 complex can be protonated with weak acids due to the proposed relay 
 activity of the azadithiolate .
specifically , 
 the presence of the azadithiolate bridge permits the formation of 
 the ammonium tautomer , [ ( fefe)adt - h ] , and subsequent intramolecular proton transfer to the 
 fed leads to the terminal hydride species , [ th-(fefe)adt ] ( figure 3 ) . both [ th-(fefe)adt ] and [ th-(fefe)pdt ] convert 
 to their respective bridging hydride isomers irreversibly at room 
 temperature .
upon equilibration , two bridging 
 hydride species form , sym-[h-(fefe)adt ] and unsym-[h-(fefe)adt ] , which differ in the orientation of the dppv ring on the 
 fed center relative to the dppv ring on the fep center ( figure 3 ) .
the adt - containing 
 hydride species can undergo a second protonation with stronger acids , 
 leading to the doubly protonated species , [ th-(fefe)adt - h ] ( figure 3 ) .
again , [ th-(fefe)adt - h ] isomerizes into two bridging hydrides , sym-[h-(fefe)adt - h ] and unsym-[h-(fefe)adt - h ] , albeit at a slower rate than the singly protonated analog .
although less thermodynamically stable than 
 the bridging hydride species , the terminal hydride species , [ th-(fefe)adt - h ] , is poised for h2 production due 
 to the close proximity of the ammonium and fe - hydride centers in the 
 doubly protonated species .
density functional theory ( dft ) calculations were performed to 
 characterize the structural and energetic properties of the pertinent 
 species in the catalytic scheme .
all calculations were performed using 
 the gaussian 09 electronic structure program . for geometry optimizations ,
the starting geometries were obtained 
 from the corresponding crystal structures , which are available for 
 the [ ( fefe)pdt ] , [ ( fefe)pdt],unsym-[h-(fefe)pdt ] , and unsym-[h-(fefe)pdt ] species , as well as the [ ( fefe)adt ] and [ th-(fefe)adt - h ] species .
the starting geometries for species without crystal structures 
 were obtained by manually altering the most closely related crystal 
 structure .
optimizations in the gas phase and solution phase resulted 
 in similar structures for several representative species , so gas phase 
 optimizations were used herein for computational efficiency .
a comparison 
 of the structures optimized in the gas phase and solution phase for 
 several representative species is available in the supporting information ( table s2 ) .
the dft calculations 
 were performed using the b3p86 density functional with the stuttgart pseudopotential and associated basis set of preuss 
 and co - workers ( sdd ) for the fe centers , the 6 - 31 g * * basis set for the active hydrogens , the 6 - 31+g * basis set for the bf4 counterions , and the 6 - 31 g * basis set 
 for all other atoms . to obtain the solvation free 
 energies
, we used the conductor - like polarizable continuum model ( c - pcm ) with the bondi atomic radii and included 
 nonelectrostatic interactions , namely , the dispersion , repulsion , and cavitation energies .
the solvation free energies were calculated 
 in dichloromethane ( ch2cl2 ) to coincide with 
 the experiments unless otherwise stated .
the co vibrational frequencies 
 were calculated within the harmonic model and were scaled by a factor 
 of 0.9850 , as indicated by previous studies .
the vibrational frequency shifts , co , were 
 calculated for the dashed pathways shown in figure 3 .
for the [ th-(fefe)adt ] and [ th-(fefe)adt - h ] species , the presence of the semibridging co ligand allows for the 
 assignment of two distinguishable co stretching frequencies : the higher 
 co corresponds to the terminal co attached to the 
 fep center , and the lower co corresponds 
 to the semibridging co. for all other species , both co ligands are 
 terminal , so their stretching frequencies are less separated . in general
, dft does not consistently provide reliable absolute pka s and reduction potentials because 
 of limitations in the functionals , basis sets , and solvation models , 
 as well as uncertainties in the free energies of the electron , proton , 
 and electrode . as discussed previously ,
the calculation of pka s and 
 reduction potentials relative to related reference systems with known 
 experimental values has been shown to be more reliable because many 
 of the systematic errors cancel .
for this reason , we discuss only 
 relative reduction potentials and pka s 
 in this paper .
the structures and energies of all complexes discussed 
 herein are provided in the supporting information . the reaction free energies associated with reduction and 
 deprotonation were calculated using the born  haber thermodynamic 
 cycle .
the reaction free energy for reduction , gr(e ) , was calculated using the expression1 in this expression , gs(red ) and gs(ox ) are the solvation free energies of 
 the reduced and oxidized species , respectively , and ggas is the gas phase reaction free energy calculated using the standard 
 relation ggas = hgas  tsgas. a similar expression was used 
 to calculate the reaction free energy for deprotonation , gr(h ) . for reasons mentioned above , the reduction 
 potentials were calculated relative to a related reference reaction 
 for which the experimental value is known
. this procedure accounts 
 for systematic errors associated with the selected theoretical method 
 and basis set and avoids the determination of the free energies of 
 the electron and the electrode because these terms cancel .
detailed 
 descriptions of this methodology can be found elsewhere . for our specific application , we used the following 
 expression to calculate the reduction potentials:2here , e is the reduction potential 
 of the [ ( fefe)adt ] species of interest , eref is the 
 experimentally measured reduction potential of the reference species , 
 which is the [ ( fefe)pdt ] species in this work , gr(e ) is the calculated difference in reaction free 
 energies ( eq 1 ) for reduction of the species 
 of interest and the reference , and f is the faraday 
 constant .
all calculated and experimental reduction potentials are 
 given in volts ( v ) relative to the ferrocene / ferrocenium ( fc / fc ) couple in ch2cl2 .
the irreversible 
 reduction potentials of the doubly protonated species are calculated 
 relative to the reduction potentials of the corresponding singly protonated 
 species and are labeled eprot. the cyclic voltammetry 
 ( cv ) experiments were performed at 273 k , and the reduction potentials 
 were also calculated at this temperature .
we used the standard relationship , pka = gr(h)/(rt ln 
 10 ) , to calculate the pka values . in this 
 expression , gr(h ) corresponds to the calculated 
 reaction free energy for deprotonation , r is the 
 gas constant , and t = 233.15 k to coincide with experimental 
 conditions . due to the limited experimental pka data for the [ ( fefe)pdt ] systems and its inherent inability 
 to doubly protonate , these complexes were not used as references . 

instead , we calculated pka , which 
 is defined to be the difference between the pka values for two specified states of the [ ( fefe)adt ] complex . 

the reported pka values were calculated 
 in ch2cl2 to coincide with experimental conditions 
 and in acetonitrile ( ch3cn ) to coincide with the reference 
 pka values used in the interpretation 
 of the experimental values because a pka scale is not well established for ch2cl2 .
we optimized the 
 geometries of the various species discussed above and compared the 
 structures and key vibrational frequencies to available experimental 
 data .
the optimized geometries are in reasonable agreement with the 
 x - ray crystal structures .
table 1 provides 
 a comparison of the most relevant bond lengths for the various species . 

structural and energetic information on all systems studied herein 
 are provided in the supporting information .
the relative free energies of the species depicted in figure 3 are provided in table 2 . 

moreover , the relative free energies of these species and other isomers 
 of higher free energy are provided in figures s15 and s16 , supporting information .
experimental data from ref ( 40 ) . experimental 
 data from ref ( 46 ) . experimental data from ref ( 35 ) . experimental data from ref ( 41 ) . experimental data from ref ( 38 ) . not applicable because the hydrogen is not present 
 for certain species or the distance is not relevant for the doubly 
 protonated species .
values 
 given in kcal / mol relative to the unprotonated species , [ ( fefe)adt ] , in ch2cl2 at 
 298.15 k. the free energy of a solvated proton should be included 
 to obtain free energies relevant to the protonation reactions . the optimized geometry for the doubly 
 protonated species , [ th-(fefe)adt - h ] , exhibited one key 
 difference from the crystal structure , namely , the dihydrogen distance 
 nhhfe .
this dihydrogen distance was dhh = 1.88  in the crystal structure 
 and dhh = 1.40  
 in the optimized geometry .
thus , dft leads to a significantly shorter 
 dihydrogen distance that corresponds to a stronger dihydrogen bond .
a previous dft study on a model of the [ fefe]-hydrogenase active 
 site also showed an underestimation of the dihydrogen distance for 
 a related doubly protonated species .
this 
 smaller dihydrogen distance in the [ th-(fefe)adt - h ] species was found for a wide range of density functionals , as shown 
 in table s3 , supporting information .
however , 
 dihydrogen bond distances have also been shown to be extremely sensitive 
 to weak intra- and intermolecular interactions , such as ion - pairing .
moreover , neutron diffraction experiments are 
 expected to provide more reliable positions for hydrogen atoms than 
 x - ray diffraction , which most likely overestimates this distance .
a recent neutron diffraction study on a monometallic 
 fe hydrogenase model using the noncoordinating counterion , bar4 , found the nhhfe 
 dihydrogen bond to be 1.49  . in 
 contrast , the doubly protonated structure , [ th-(fefe)adt - h ] , was determined with x - ray crystallography and included 
 bf4 ions that could exhibit significant 
 ion - pairing effects .
given the 
 difference in the crystallographic and calculated dihydrogen bond 
 length in [ th-(fefe)adt - h ] , we hypothesized that this 
 discrepancy was due to the omission of the bf4 ions in the geometry optimizations . to test this hypothesis , we 
 also optimized the structure including one or two of the bf4 ions closest to the azadithiolate bridge in the 
 crystal structure
. figure 4 illustrates that 
 the geometry optimizations including either one or two bf4 ions improved the agreement between dft and experiment 
 by shifting the amine bridgehead and elongating 
 the dihydrogen distance .
the bond lengths given in table 3 show that including the ion - pairing interactions 
 preserves the fefe and feh distances 
 while elongating the dihydrogen distance .
although the inclusion of 
 counterions improves the agreement with the doubly protonated crystal 
 structure , we omit the counterions in the calculations of other quantities , 
 such as reduction potentials and spin densities , to maintain consistency 
 among the various species studied under a range of experimental conditions .
this structure was optimized in solution ( ch2cl2 ) using c - pcm without any bf4 counterions . superimposed 
 structures of the doubly protonated species , [ th-(fefe)adt - h ] , illustrating the better agreement between the crystal structure 
 and the optimized geometries when bf4 ions are included in the calculations .
the phenyl groups have been 
 removed , and the fehhn interaction is circled for 
 clarity .
color scheme : crystal structure ( gray ) and optimized geometry 
 with no bf4 ( red ) , one bf4 ( blue ) , and two bf4 ( green ) counterions .
the strong , distinctive absorptions at 2000 cm associated with co stretching can be used to probe 
 changes in the electronic structure due to protonation , isomerization , 
 reduction , and oxidation .
we calculated the change in the 
 co frequencies , co , for the five protonation 
 reactions depicted by dashed lines in figure 3 .
as shown in table 4 , the calculated co values due to protonation are within 10 cm of the experimentally measured values .
this level of agreement provides 
 validation for the structures of species for which crystal structures 
 are not available .
typically dft calculations are more reliable for 
 changes in frequencies than for absolute frequencies ; a comparison 
 between the calculated and experimental absolute frequencies is provided 
 in table s4 , supporting information . for 
 the present study
, the previously reported spectroscopic studies were repeated using the acid [ h(oet2)2]bar4 to eliminate the possibility 
 of ion pairing arising from the coordination of bf4 when using hbf4et2o , which 
 has been shown to participate in hydrogen - bonding interactions , particularly in complexes with protonated adt 
 ligands .
the agreement between calculated 
 and experimental frequencies is better for the bar4 salts ; these spectra are provided in the supporting information ( figures s6 and s7 ) .
the p1 , p2 , p3 , p4 , and 
 p5 protonation reactions are defined in figure 3 .
the second co value is assigned to the semibridging co. the co values 
 reflect the protonation sites , as indicated by both experimental measurements 
 and theoretical calculations .
the co values 
 associated with n - protonation are typically characterized by co frequency 
 increases of 20 cm .
the experimental 
 and calculated co values associated with 
 n - protonation to form either the singly or doubly protonated species 
 ( p1 , p4 , and p5 protonations ) exhibit this shift . while n - protonation 
 is associated with a relatively small co shift , 
 formation of the terminal and bridging hydrides ( p2 and p3 protonations , 
 respectively ) is associated with much higher shifts of 70 
 cm . in both cases ,
two well - resolved bands are 
 observed in the spectra , but the bands are much more energetically 
 separated for the terminal hydride species than for the bridging hydride 
 species . the band at lower frequencies in the terminal hydride species 
 is assigned to the semibridging co , which exhibits a smaller co shift of 40 cm .
our calculated 
 co values for the protonations leading to 
 the terminal and bridging hydride species ( p2 and p3 protonations , 
 respectively ) demonstrate this trend and agree well with the experimental 
 values ( table 4 ) .
an analogous figure and table 
 for the [ ( fefe)pdt ] complexes is provided in the supporting information ( figure s17 and table s1 ) .
the calculated reduction potentials 
 for the species in ch2cl2 are presented in table 5 . because the [ ( fefe)pdt ] species are used as the 
 reference systems , these reduction potentials agree exactly with experiment 
 by construction , and all other reduction potentials are calculated 
 relative to these values .
the agreement between theory and experiment 
 for the [ ( fefe)adt ] species is reasonable for the singly protonated 
 species with errors of 0.05 v vs fc / fc in ch2cl2 .
additional calculated reduction 
 potentials are provided in the supporting information ( table s5 ) .
a detailed analysis of the metal oxidation states of 
 the reduced species in terms of the spin densities is provided in 
 the next subsection .
unless otherwise indicated . [ ( fefe)pdt ] reactions were used as the reference 
 reactions , so the calculated and experimental values agree by construction .
experimental data from ref ( 79 ) . quasi - reversible reaction , so ep is reported .
e = 1.82 v vs fc / fc in ch2cl2 if calculated using the symmetric 
 bridging form .
experimental 
 data from ref ( 38 ) . irreversible reaction , so ep is reported .
e = 1.83 v vs fc / fc in ch2cl2 if calculated using 
 the symmetric bridging form .
due to difficulties in determining a suitable reference system for 
 the doubly protonated species , we calculated the difference between 
 the reduction potentials for the doubly and singly protonated species 
 ( eprot ) . using this formulation , we calculated 
 eprot = 0.59 v vs fc / fc in ch2cl2 .
as expected from basic electrostatic 
 arguments , the doubly protonated species has a less negative reduction 
 potential than the singly protonated species .
the experimentally measured 
 difference in these reduction potentials was 0.39 v vs fc / fc in ch2cl2 .
as discussed above , this error could be due to the neglect 
 of bf4 in the calculations .
note that 
 bf4 ions were present in the electrochemical 
 measurements for the doubly protonated species but not for the singly 
 protonated species .
furthermore , the effects of ion pairing on reduction 
 potentials are known to be pronounced in solvents of low dielectric 
 constants , such as ch2cl2 .
thus , the difference in the counterions present for the electrochemical 
 experiments of the singly and doubly protonated species could lead 
 to discrepancies in the comparison between calculated and experimental 
 results .
note that the experimentally measured reduction potentials 
 for the terminal hydride species are for quasireversible couples , 
 which could introduce additional discrepancies . for species with an unpaired 
 electron
, we analyzed the spin densities to determine the localization 
 of the unpaired electron .
for the reduced terminal 
 hydride species , [ th-(fefe)adt ] , the unpaired spin density is localized 
 entirely on the fep center , suggesting that the fep center is reduced .
this localization on the fep center is similar for the reduced terminal hydride species , [ th-(fefe)pdt ] , which is produced at a similar potential as the [ th-(fefe)adt ] species , indicating that the dithiolate is not a major influence 
 on the redox behavior for the terminal hydride species .
the spin densities 
 pertaining to the [ ( fefe)pdt ] complexes are provided in the supporting information ( table s6 ) .
previous studies also 
 examined the metal oxidation states upon reduction of [ h-(fefe)pdt ] by analyzing 
 the spin density with the bp86 functional and epr spectra of the mixed - valence 
 species .
these studies showed that reduction 
 of sym-[h-(fefe)pdt ] resulted in a species with the unpaired 
 electron delocalized between the fep and fed centers , sym-[h-(fefe)pdt ] .
however , reduction of unsym-[h-(fefe)pdt ] resulted in a species with the unpaired electron 
 localized on the fep center , unsym-[h-(fefe)pdt ] .
our calculations 
 revealed a similar trend with the bridging hydride species of the 
 singly and doubly protonated [ ( fefe)adt ] ( table 6 ) , although several important differences were observed . in 
 the singly protonated symmetric and unsymmetric [ ( fefe)adt ] bridging 
 hydride species , sym-[h-(fefe)adt ] and unsym-[h-(fefe)adt ] , the orientations of the dppv ligands on the two fe centers 

furthermore , the hydride is located symmetrically 
 between the two fe centers in both isomers for the oxidized state . 

, the bridging hydride is perturbed from this symmetric position . 
 in the reduced unsymmetric bridging hydride species ,
the hydride is 
 more closely bound to fed ( dfeh = 1.58  ) than to fep ( dfeh = 2.05  ) and resembles a terminal hydride . in the reduced 
 symmetric bridging hydride species ,
the hydride is more symmetrically 
 bound to the two iron centers ( dfeh = 1.60  for fed and dfeh = 1.77  for fep ) .
the observation that the reduction 
 of sym-[h-(fefe)adt ] maintains a more symmetric bridging hydride 
 is consistent with the observation that the spin density is somewhat 
 delocalized between the two fe centers .
in contrast , reduction of unsym-[h-(fefe)adt ] leads to a much more asymmetric bridged hydride , 
 and the spin density is localized on fep , which does not 
 have a bound hydride .
thus , unsym-[h-(fefe)adt ] is similar to [ th-(fefe)adt ] in that reduction occurs at the fep site , but 
 reduction of unsym-[h-(fefe)adt ] also involves motion of 
 the bridged hydride toward the fed site to resemble a terminal 
 hydride .
these observations are consistent with the observation that 
 the terminal hydride species is reduced more easily ( i.e. , at a slightly 
 less negative potential ) than the unsymmetric bridging hydride species 
 ( table 5 ) .
the bond lengths given without parentheses 
 correspond to the oxidized species as drawn , while those given in 
 parentheses correspond to the reduced mixed - valence species ( not drawn ) . 

the spin densities of the reduced mixed - valence species are reported 
 in table 6 .
the presence of the amine group in the azadithiolate bridgehead 
 affects the degree of asymmetry observed upon reduction of the symmetric 
 bridging hydride species .
although the bridging hydride is more symmetric 
 in the sym-[h-(fefe)adt ] species than in the unsym-[h-(fefe)adt ] species , more asymmetry is exhibited in the sym-[h-(fefe)adt ] than in the analogous sym-[h-(fefe)pdt ] species . 
 in the previous study of [ ( fefe)pdt ] bridging hydride species ,
reduction 
 of sym-[h-(fefe)pdt ] preserves the symmetry of the hydride position 
 to a higher degree , with dfeh = 1.68  and dfeh = 1.70  for the fep and fed centers , 
 respectively .
we have confirmed these 
 observations using the level of theory described within the present 
 paper and various other basis sets .
moreover , 
 these nearly symmetric feh bond lengths are associated 
 with nearly equal spin densities on the two fe centers .
as shown in 
 figure 5 and table 6 , the reduced symmetric protonated [ ( fefe)adt ] system , sym-[h-(fefe)adt ] , exhibits more asymmetry in these feh bond 
 lengths and unequal delocalized spin densities on the two fe centers .
the reduction of the doubly protonated bridging hydride species , unsym-[h-(fefe)adt - h ] and sym-[h-(fefe)adt - h ] , follows a similar trend but displays a slightly smaller 
 degree of delocalization of the spin density , as shown in table 6 .
according to the distances given in figure 5 , the asymmetry of the bridging hydride is slightly 
 more pronounced in both the symmetric and unsymmetric forms for the 
 doubly protonated species .
thus , reduction is expected to occur primarily 
 at the nonhydride fep center , as supported by the unpaired 
 spin densities given in table 6 .
this pattern 
 for the electron localization is also seen in doubly protonated terminal 
 hydride species , which will be discussed below .
previous experiments on the [ ( fefe)adt ] system 
 estimated a small difference in the pka of the first and second protonation steps ( pka  2 ) ; however , 
 our calculated values indicated much larger differences , as seen from 
 pka(p4 
this discrepancy between experiment and theory 
 prompted a reinvestigation of the acid  base chemistry of the 
 [ ( fefe)adt ] species .
the pka values can 
 be estimated by nmr measurements because each protonated species displays 
 a unique p nmr spectrum .
the experimental details and 
 spectra are provided in the supporting information ( figures s12 and s13 ) . according to these experiments , the protonation 
 reactions leading to the formation of [ ( fefe)adt - h ] , [ th-(fefe)adt ] , and [ th-(fefe)adt - h ] , defined as p1 , p2 , and p4 in figure 3 ,
correspond to pka values of 
 > 14.2 , 15.5 , and 6 , respectively .
the protonation pathways p1 , p2 , p3 , and p4 are defined in figure 3 , and the pka is determined 
 for the protonated species in each case .
these experiments were performed in ch2cl2 solvent , but the reference pka values pertain to ch3cn solvent . for reasons discussed in the methods section
this procedure accounts for systematic 
 errors associated with the selected theoretical method and avoids 
 the determination of the free energy of the solvated proton because 
 this term cancels .
note that the experimentally measured values are 
 only qualitatively meaningful because the experiments were performed 
 in ch2cl2 , which does not have a well - defined 
 pka scale , and the reference pka values of the acids pertain to ch3cn . as a result , we calculated the relative pka values in both ch2cl2 and ch3cn
. additionally , the effects of homoconjugation in these experiments 
 may distort the apparent pka measured . 
 as discussed above in the context of comparing the crystal structure 
 and optimized geometries
furthermore , it has been shown 
 experimentally that ion pairing between the bf4 counterion and the ammonium center can shift the equilibrium of 
 the singly protonated species toward [ ( fefe)adt - h ] .
p1 ) value indicates that the fed site is more basic than 
 the amine by at least 1.3 pka units ; 
 however , the amine is more readily protonated than the stereochemically 
 crowded fe site .
the greater basicity of the fed site than 
 the amine is corroborated by our calculated pka(p2 
p2 ) value measured experimentally indicates that 
 n - protonation of [ th-(fefe)adt ] to form [ th-(fefe)adt - h ] requires much stronger acids , as supported by our calculated 
 large , negative pka(p4  

again , 
 it is worth noting that the presence of the bf4 ions in the experiments may contribute to the remaining discrepancy 
 between theory and experiment .
moreover , the theoretical calculation 
 of pka differences for species with different 
 charges ( i.e. , + 2 and + 1 for the doubly and singly protonated species ) 
 is more challenging . turning our attention to the bridging hydride 
 isomers , previous experiments have suggested that the conversion to 
 the bridging hydride isomers is irreversible , and the bridging hydride 
 is estimated to be at least 2 pka units less acidic than the terminal hydride .
this observation is supported by the large , positive calculated 
 pka ( p3p2 ) value and the 
 thermodynamic stability of the bridging hydride isomers .
these pka trends are reproducible using different functionals , 
 as indicated by additional data provided in the supporting information ( table s8 ) .
the proposed mechanisms 
 for hydrogen evolution catalyzed by the [ ( fefe)adt ] system for weak 
 and strong acids are depicted in figure 6 . 
 initially , the amine group on [ ( fefe)adt ] is protonated to form the ammonium tautomer , [ ( fefe)adt - h ] .
an intramolecular 
 proton transfer occurs from the n to the fed to form the 
 terminal hydride , [ th-(fefe)adt ] . for weak acids , the terminal hydride 
 species , [ th-(fefe)adt ] ,
this pathway is shown in dotted 
 lines in figure 6 . for stronger acids ,
the 
 intramolecular proton transfer is followed by another protonation 
 at the amine group to generate [ th-(fefe)adt - h ] .
a possible 
 mechanism for this process is indicated with solid lines on the right 
 side of figure 6 .
the values for the spin densities 
 and bond distances for the species associated with this pathway are 
 given in table 8 .
the steps indicated with solid lines along the perimeter represent 
 the proposed pathway discussed in the main text .
our calculations indicate that reduction of [ th-(fefe)adt - h ] leads to the mixed - valence complex , [ th-(fefe)adt - h ] .
the spin densities and bond distances of this 
 species are given in table 8 .
this mixed - valence 
 species is characterized by the unpaired electron localized on the 
 fep center , which is in agreement with the reduction scheme 
 exhibited by the [ th-(fefe)adt ] and [ th-(fefe)pdt ] species discussed 
 previously . the nhhfe distance is shorter in [ th-(fefe)adt - h ] ( dhh = 1.30  ) than in [ th-(fefe)adt - h ] ( dhh = 1.40  ) but is still 
 larger than the distance in molecular h2 ( dhh = 0.74  ) .
although we were 
 unable to locate a minimum - energy species with h2 weakly 
 bound to an fed(i ) center , we found another type of h2 adduct intermediate with the unpaired electron delocalized 
 between the fep and fed metal centers .
this 
 h2 adduct , [ h2-(fefe)adt ] , is higher in free energy 
 than the mixed - valence doubly protonated species , [ th-(fefe)adt - h ] , by 5.82 kcal / mol but has several features that are potentially 
 catalytically relevant , as will be discussed below .
note that previous 
 theoretical studies on small models of the [ fefe]-hydrogenase active 
 site found that reduction of a doubly protonated fep(ii)fed(ii ) species could lead to the formation of a stable mixed - valence 
 h2 adduct intermediate , fep(i)fed(ii ) , where the fep center is the site of reduction and 
 the h2 ligand is loosely bound to the fed(ii ) 
 center .
these mixed - valence intermediates are similar 
 to the [ th-(fefe)adt - h ] species found herein ; however , the 
 [ h2-(fefe)adt ] species was not found in these previous studies .
in contrast to the [ th-(fefe)adt - h ] species , the [ h2-(fefe)adt ] species features a much shorter nhhfe 
 distance ( dhh = 0.79 
  ) , suggesting an activated h2 molecule . in conjunction 
 with the activated h2 bond distance , the average distance 
 between each hydrogen and the fed center is elongated ( dfeh = 1.75  ) , suggesting 
 that the h2 ligand is weakly bound to the fed center and poised for release .
another important structural feature 
 is that unlike all terminal hydride species reported in the present 
 paper , the semibridging co ligand in this h2 adduct is 
 nearly symmetrically bridged between the fep and fed centers , where dfeco= 2.06 and 1.89  , respectively .
the fepfed distance contracts ( dfefe = 2.69  ) to accommodate this bridging interaction .
this structural 
 property is reminiscent of the enzyme s hox state , 
 which features a nearly symmetrically bridged co ligand ( figure 1 ) .
moreover , the spin density is now delocalized 
 between the fep and fed center , 0.43 and 0.45 , 
 respectively , warranting the [ h2-(fefe)adt ] assignment .
this 
 delocalization of the spin density suggests the possibility for intramolecular 
 electron transfer to occur between the fep and fed centers concomitant with formation of a shorter h2 bond . 

note that the proposed mechanism in figure 6 is similar to mechanisms proposed previously for [ fefe]-hydrogenases 
 in terms of the reduction and protonation steps .
our objective is to 
 characterize the proposed intermediates and to analyze aspects such 
 as dihydrogen bonding and electron delocalization or localization 
 with respect to the metal centers .
release of h2 from 
 [ h2-(fefe)adt ] would generate another mixed - valence state , the 
 [ ( fefe)adt ] species shown in 
 figure 6 .
this mixed - valence species is closely 
 related to the hox state of the enzyme shown in figure 1 .
interestingly , the spin densities for this species , 
 which are given in table 8 , indicate fe oxidation 
 states that are opposite to the various other mixed - valence species 
 discussed in this paper . whereas the spin density was localized on 
 the fep center for the other purely mixed - valence species , 
 such as [ th-(fefe)adt ] and [ th-(fefe)adt - h ] ,
this hox - like species has the spin density entirely localized on the fed center , suggesting that the fed center is now 
 more reduced than the fep center . upon formation of this 
 [ ( fefe)adt ] species , the bridging 
 co
this analysis of the mechanism points to the importance of the bridging 
 co ligand , which seemingly behaves as a lever and indicator for intramolecular 
 electron transfer between the fe centers .
moreover , there is 0.16 
 spin density localized on the symmetric bridging co ligand in the 
 [ h2-(fefe)adt ] species , suggesting that it may be even more involved 
 in the electron transfer process .
in this paper , we investigated a proton reduction 
 catalyst , [ ( fefe)adt ] , which is modeled after the [ fefe]-hydrogenase 
 enzyme .
this model is characterized by incorporation of the azadithiolate 
 bridge , which facilitates the formation of a doubly protonated species 
 through a proton relay .
the calculated results agree well with the 
 experimental data for the geometries , co vibrational stretching frequencies , 
 and reduction potentials for the systems studied .
the calculations illustrate 
 that the nhhfe dihydrogen bonding distance in the 
 doubly protonated species is highly sensitive to the effects of ion - pairing 
 between the ammonium and bf4 counterions , 
 which are present in the crystal structure .
specifically , the inclusion 
 of bf4 counterions leads to a significantly 
 longer dihydrogen bond .
comparable weak interactions with the protein 
 backbone might be expected to influence the hh bonding 
 in the enzyme .
analyses of spin densities provide insight into the 
 oxidation states of the metal centers for the reduced singly and doubly 
 protonated species .
the non - hydride fe center ( fep ) was 
 found to be the site of reduction for terminal hydride species and 
 for unsymmetric bridging hydride species .
in contrast , the reduced 
 symmetric bridging hydride species exhibited a significant degree 
 of spin delocalization between the fe centers , although these species 
 exhibited more asymmetry than the analogous [ ( fefe)pdt ] species .
these 
 differences in the degree of spin localization , as well as the movement 
 of the hydride upon reduction of the unsymmetric bridging species , 
 may be related to the experimental observation that the terminal hydride 
 species are reduced at less negative potentials than their bridging 
 hydride isomers .
this analysis suggests that the bridging hydrides may be considered 
 to be quasi - terminal hydrides for the unsymmetric species .
a 
 combined experimental and theoretical study of the relative pka values for the various species in the catalytic 
 cycle provides further insights .
the fed site was found 
 to be more basic than the amine , although the amine is more readily 
 protonated .
moreover , the bridging hydride species was found to be 
 more thermodynamically stable than the terminal hydride species .
these 
 observations are consistent with the initial protonation of the amine , 
 followed by intramolecular proton transfer to the fed site 
 to produce a terminal hydride species , followed by isomerization to 
 the bridging hydride species at room temperature but not at low temperatures . 
 in terms of forming the doubly protonated species ,
the amine site 
 is significantly less basic for the terminal hydride species than 
 for the unprotonated species .
both the experimental and theoretical 
 data indicate that a stronger acid is required for this second protonation .
in addition , these calculations implicate a possible pathway for 
 h2 evolution that involves an intermediate with h2 weakly bonded to one fe , a short h2 distance similar 
 to the molecular bond length , the spin density delocalized over the 
 two fe centers , and a nearly symmetrically bridged co ligand .
h2 bonding is relatively weak and that the product h2 is 
 poised for release . upon h2 release , the mixed - valence 
 species produced is closely related to the hox state of 
 the enzyme .
the key features of this proposed mechanism highlight 
 the roles of the ammonium - hydride interaction , flexibility of the 
 bridging co ligand , and intramolecular electron transfer between the 
 fe centers in the catalytic cycle . while these bioinspired models 
 are effective catalysts for h2 production , the challenge 
 of designing molecular electrocatalysts that can perform with weaker 
 acids and lower overpotentials remains .
further investigation of the effects of ligand substitution at the 
 fe centers will help guide the design of more effective h2-producing catalysts .
 the [ fefe]-hydrogenase enzymes catalyze 
 hydrogen oxidation and production efficiently with binuclear fe metal 
 centers . 
 recently the bioinspired h2-producing model system 
 fe2(adt)(co)2(dppv)2 ( adt = azadithiolate 
 and dppv = diphosphine ) was synthesized and studied experimentally . 
 in this system , 
 the azadithiolate bridge facilitates the formation 
 of a doubly protonated ammonium - hydride species through a proton relay . 
 
 herein computational methods are utilized to examine this system in 
 the various oxidation states and protonation states along proposed 
 mechanistic pathways for h2 production . 
 the calculated 
 results agree well with the experimental data for the geometries , 
 co vibrational stretching frequencies , and reduction potentials . 
 the 
 calculations illustrate that the nhhfe dihydrogen 
 bonding distance in the doubly protonated species is highly sensitive 
 to the effects of ion - pairing between the ammonium and bf4 counterions , which are present in the crystal 
 structure , in that the inclusion of bf4 counterions leads to a significantly longer dihydrogen bond . 
 the 
 non - hydride fe center was found to be the site of reduction for terminal 
 hydride species and unsymmetric bridging hydride species , whereas 
 the reduced symmetric bridging hydride species exhibited spin delocalization 
 between the fe centers . according to both experimental measurements 
 and theoretical calculations of the relative pka values , 
 the fed center of the neutral species 
 is more basic than the amine , and the bridging hydride species is 
 more thermodynamically stable than the terminal hydride species . 
 the 
 calculations implicate a possible pathway for h2 evolution 
 that involves an intermediate with h2 weakly bonded to 
 one fe , a short h2 distance similar to the molecular bond 
 length , the spin density delocalized over the two fe centers , and 
 a nearly symmetrically bridged co ligand . 
 overall , this study illustrates 
 the mechanistic roles of the ammonium - hydride interaction , flexibility 
 of the bridging co ligand , and intramolecular electron transfer between 
 the fe centers in the catalytic cycle . 
 such insights will assist in 
 the design of more effective bioinspired catalysts for h2 production . 