Computational Chemical Analysis of [FeFe] Hydrogenase H-Cluster Analogues To Discern Catalytically Relevant Features of the Natural Diatomic Ligand Configuration

Published: June 17, 2011

r 2011 American Chemical Society 8691 dx.doi.org/10.1021/jp112296d | J. Phys. Chem. A 2011, 115, 8691–8704

ARTICLE

pubs.acs.org/JPCA

Computational Chemical Analysis of [FeFe] Hydrogenase H-ClusterAnalogues To Discern Catalytically Relevant Features of the NaturalDiatomic Ligand ConfigurationChristopher H. Chang

Computational Science Center, National Renewable Energy Laboratory, 1617 Cole Boulevard, MS 1608, Golden,Colorado 80401, United States

bS Supporting Information

’ INTRODUCTION

In the context of the global search for carbon-neutral fuelregimes, the carbon-free dihydrogenmolecule ranks prominentlyas a renewable resource, able to be generated from plentiful waterby electrolytic reversal of the H2 oxidation reaction. Nature’ssolution to optimizing biocatalysts for the cathodic half-reaction(2H+ + 2 e� f H2) under cellular constraints are the hydro-genases, of which the diiron ([FeFe]) hydrogenase is commonlyfound associated with H2 evolution. Proton reduction occurs atthe active site “H” metallocluster, consisting of a [4Fe4S]cubane-type subcluster, and a unique [2Fe] cluster with a(η2,η2)-bridging dithiolate ligand and extensive carbonyl andcyanide ligation. The exact nature of the dithiolate ligand remainsa subject of debate,1�3 although recent spectroscopic evidencesupports a dithiomethylamine (DTMA) ligand,2 as does a recentstudy wherein theoretical approaches were coupled to crystal-lographic refinement.4 Uncertainty in the precise chemicalcomposition of the dithiolate bridge notwithstanding, the dia-tomic ligand identities and configuration in the [2Fe]H clusteroxidized resting state have been largely settled on the basis ofhydrogen bonding arguments from crystallographic structures5

and vibrational spectroscopy.6,7 The canonical structure is com-posed of two cyanide and three carbonyl ligands arrangedsuch that the terminal cyanide and carbonyl groups are each“trans” to one another across the Fe�Fe bond and within the

(N)C�Fe�Fe�C(N) plane, with the remaining carbonyl occu-pying a bridging position between the Fe ions through at least aportion of the catalytic cycle.7 A hydride equivalent occupieseither an axial position on the terminal Fe ion (i.e., the Fe ion thatis not directly bridged to the [4Fe4S]H cluster through cysteinateligation, and that is weakly if at all bound to an aquo ligand incrystallographic structures5,8), or through rearrangement a brid-ging position between Fe ions, with the CObr becomingterminal.7 With a secondary amine functionality in the bridgingdithiolate, a tempting mechanism is a concerted proton transferfrom a hydrogen-bonded cysteine (Cys-299 in the Clostridiumpasteurianum (C. pasteurianum) structure) to a terminal hydridethrough intermediacy of the dithiomethylamine ligand.9,10 Me-chanisms consistent with protonation of a terminal hydride havefound support in model and theoretical studies.11�15

Independently of the precise structures occupying the catalyticscheme, the question arises of whether the accepted diatomicligand configuration is functionally valuable to the mechanism forproton reduction or whether it is an evolutionary vestige ofbiosynthetic pathways. In vivo synthesis of [2Fe]H is known torequire the participation of two to three proteins, depending on

Received: December 27, 2010Revised: May 12, 2011

ABSTRACT: Density functional theoretical models of the electronic structure of severalconfigurational isomers and analogues of the [2Fe]H H-cluster in [FeFe] hydrogenasewere analyzed to identify distinguishing features of the canonical cofactor structurepotentially relevant to catalysis. Collective analysis of geometric changes over models ofoxidized and reduced [2Fe] clusters highlighted movement of the bridging carbonyl andanticorrelation of the proximal and distal Fe�Cterminal bonds as key explanatory factors forvariance over the considered models. Charge and bond order analysis suggest that as thebridging carbonyl favors the distal iron upon reduction, bonding simultaneously becomesmore ionic in nature, raising the possibility of simple electrostatic stabilization as a factor incharge accumulation prior to ultimate H2 creation and release. Frontier orbital energiesshow cis and trans arrangements of cyanide on the Fe�Fe core to have distinctive energiesfrom the other models, which may be important for redox poise. Altogether, few factorsqualitatively distinguish the cis- from the trans-cyano configurations, which may in fact enhance catalytic robustness underconditions leading to exchange of the bridging and terminal carbonyl ligands. However, the naturally occurring trans configurationpossesses two distinct donor�metal�acceptor S�Fe�C(O) interactions, which might play a role in enforcing a low-spin groundstate for the hydridic mechanism of H2 production.

8692 dx.doi.org/10.1021/jp112296d |J. Phys. Chem. A 2011, 115, 8691–8704

The Journal of Physical Chemistry A ARTICLE

the genetic arrangement of three separable functionalitiesdubbed HydE, HydF, and HydG.16�19 Cells expend a consider-able amount of energy in synthesizing these biosynthetic proteinsand manufacturing the [2Fe] center, and it is conceivable that anefficient synthetic pathway compatible with life is unique, or atleast far enough removed from equivalent evolutionary optimathat life has settled on only one pathway for H-cluster biosynthe-sis. However, it is difficult to imagine coevolution of four polypeptidesinvolved in a decoupled process (i.e., synthesis of the metallocluster,insertion of the metallocluster, and proton reduction catalysis)without specific selection on the functional outcome. If on theother hand the diatomic ligand configuration is mechanisti-cally significant, distinctive bonding or electronic propertiesover other conceivable ligand arrangements are expected.

A simple functional interpretation of CO/CN presence at ametal center catalyzing reduction is stabilization of low-valentstates through π-back-bonding. In the context of H2 formation,the transition metal ligand sphere is required to be electron-donating (with respect to themetal ions) enough to form anH2 σbond, but electron-withdrawing enough to prevent donation intothe H2 σ* orbitals, which would stabilize a dihydride state overboundmolecular H2.

20 However, the precise need for a particulararrangement of such ligands is unclear. The model compound(μ-pdt)Fe2(CO)6 reacts with cyanide regioselectively to form(μ-pdt)[Fe(CO)2(CN)]2

2-,21�23 suggesting at least a thermo-dynamic if not a biosynthetic rationalization for one cyanideoccupation per iron ion. Specific functional consequences of theindividual diatomic ligands have been proposed previously.Interaction between the aza nitrogen of the bridging dithiolateligand and the carbon atom of the resting-state bridging carbonylligand upon H-cluster pseudorotation was speculated on thebasis of inorganic model studies to serve as a monitor of changesin Fe electron density.24 A theoretical study found an ironhydride intermediate with Ncyano protonation approximatelyequienergetic with undissociated Fe-bound H2 but separatedby a thermally prohibitive barrier of 38 kcal/mol.25 An interestingfeature of the [2Fe]H center is a carbonyl ligand that symme-trically bridges the Fe ions in the Hox state,5,8,26 becomingasymmetrically bound or terminal in a more reduced state whileretaining its position between the iron ions.7

To determine if a rationalization for mechanistic significance isfeasible, the present work explores the electronic structural andbonding consequences of diatomic ligand perturbations from itspresumed configuration in oxidized and reduced [2Fe]H clustermodels. Results from density functional theory geometry opti-mizations, extended-basis single-point calculations, and bondinganalyses are reported, including the variations of geometry,charge, frontier orbital energies, and bond orders. Possiblefunctional significance of several interesting features discoveredamong the configurational isomers here are discussed.

’METHODOLOGY

All calculations were done with the Gaussian 03 package.27

Bonding analyses were carried out with a version built fromsource code with version 5.0 of theNatural BondOrbital Analysispackage.28 Twelve native or configurationally perturbed [2Fe]Hmodels representing hypothetical oxidized and reduced states,analogous to the Hox and Hred. states of the natural [2Fe]Hcluster, in six configurations each (Figure 1) were built from thecrystallographic structure of the natural H-cluster,5 with bridgingcysteinate and [4Fe4S]H replaced by a methylthiol, and the open

coordination site on Fedistal filled with either an aquo (oxidizedmodels) or a hydrogen (reduced models) ligand. Broadly, theperturbations considered were making all terminal ligands iden-tical, ligand exchange to create geminal cyano configurations andexchange to create a cis arrangement relative to a dividing planecontaining both Fe ions and the bridging carbonyl. Sinceincluding all-carbonyl and all-cyano terminal ligation involveschanging the overall complex charge, continuum solvation usingthe integral equation formalism of the polarizable continuummodel (IEF-PCM),29�32 including a dielectric constant corre-sponding to dimethyl sulfoxide (46.7) was chosen to balance theinterests of damping the secondarily interesting charge perturba-tion with mimicry of the natural H-cluster environment (i.e.,protein interior, which is widely assigned low effective dielectricconstants based on dry powder measurements of ovalbumin33

and theoretical arguments34,35). Geometries were optimized withthe Perdew�Burke�Ernzerhof (PBE) functional.36,37 PBE has beenfound to provide good agreement between experimental andcomputed bond lengths, with a mean absolute error in first-rowtransitionmetal hydrides of 0.013 Å, nitrides of 0.019 Å, oxides of0.008 Å, and iron�carbonyl bond length deviations in Fe(CO)5of 0.006 (axial) or 0.026 Å (equatorial).38 In addition, a broad

Figure 1. Optimized model complex structures for oxidized (top) andreduced (bottom) systems. The reference frame here is used throughout thepaper to establish perspective, such that “front” refers to atoms or groups onthe reader’s side of the plane containing both irons and the bridging carbonylcarbon, “rear” to entities behind this plane, “proximal” to entities on the rightside of the plane containing both DTMA sulfur atoms and the bridgingcarbonyl carbon (hence proximal to where the pendant [4Fe4S]Hwould be),and “distal” to entities on the left side of this plane.Thedescriptive names herecorrespond to complexes I�VI rowwise from left to right. Elements Fe, S, O,N, C, andH are colored green, yellow, red, blue, gray, and white, respectively.



survey of first-row metal diatomics found PBE to yield a meanaverage error (MAE) of 0.020 Å, slightly underestimating sulfides(�0.008 Å; across ligands, Fe�X bond lengths showed an MAEof 0.030 Å.39 Amodification of the basis set used by Cao andHallfor their study of the H-cluster25 was employed. This basiscomprises the Hay�Wadt pseudopotential40 with small changesto the basis on Fe incorporated earlier,25 LANL2DZdp onsulfur,41,42 and D95 V++(d,p)43�45 on CHNO. The lattersubstitutes for a mixture of D95 V* and 3-21G used originallyand is intended to increase the basis set uniformity and com-pleteness. For subsequent single-point calculations to generateKohn�Sham determinantal wave functions for bonding analysis,the basis set was expanded toWachters+f for iron46 and Dunningtriple-ζ correlation-consistent bases with diffuse functions(aug-cc-pVTZ) for all other elements.47�49 Although the latterbasis was constructed to systematize the capture of correlationenergy in explicitly correlated wave function methods, the correla-tion-consistent basis sets were found to converge systematically tothe complete basis set limit for density functional theory in mostcases, particularly for hybrid functionals.50 We therefore believe thebasis sets used for bonding analysis to be large enough that thedescription of molecular electronic structure of the H-cluster modelcomplexes in this study will not be limited by basis set incomplete-ness or systematic bias.Selection of Density Functionals. To sample the potential

variability with respect to the density functional formulationused, exchange-correlation functionals representing three differ-ent physical formulations were tested from among “ab initio”energy functionals, i.e., functionals formulated from first princi-ples electronic arguments as opposed to purely empirical fittingto chemical data sets.51 The naming conventions in the Gaussianprogram package are used herein for convenience. SVWN5represents a purely local potential, combining Slater’s averagedexchange potential energy from the exchange charge density andde Broglie wavelength associated with the maximummomentumin a free electron gas52 with the extension of prior random phaseapproximation estimates for εc(rs) to more chemically relevantdensities and an improved fitting of the effects of spin polariza-tion on εc(rs).

53 The “5” in the functional name refers to the spinpolarization correction reported in ref 53 together with theirrefitted expression for εc(rs), where rs refers to theWigner�Seitzradius (the radius of a sphere containing electron densityequivalent to one electron, thus an inverse-cube-root proxy forelectronic density). The Generalized Gradient Approximation(GGA) Perdew�Burke�Ernzerhof exchange-correlation func-tional “PBEPBE” adds gradient corrections to the uniformexchange and correlation potentials, satisyfing formal scalingproperties for spin (EX[Fv,FV] = 1/2(EX[2Fv] + EX[2FV]); slowlyvarying (Δcf second-order gradient expansion), rapidly varying(Δc vanishes), and high-density (Δcf constant,Δx scales as thecoordinate scaling factor) limits; recovery of LDA linear res-ponse; and the Lieb�Oxford bound EX[Fv,FV] g EXC[Fv,FV].

36,37

Empirically this functional has performed well.54,55 ThePBE1PBE hybrid functional55 was included to assess the impactof orbital-dependent exchange, which exhibits an almost magicalability to improve density functional theory (DFT) results bycapturing some self-interaction correction, balancing an overlylocalized exchange-correlation hole and associated exaggerationof effective static correlation in local and semilocal functionals inthe λ = 0 limit, and mimicking some higher order correlationeffects from correlated wave function methods.56�58 The meta-GGA functional from Tao, Perdew, Staroverov, and Scuseria

(TPSS)59,60 was also included to sample the third rung of“Jacob’s ladder” including kinetic energy density. This functionalhas been shown empirically to perform well for first-transition-rowmetal complex geometries61 and geometries, dissociation energies,vibrational frequencies, and dipole moments.38

Charge and Bonding Analysis. The Kohn�Sham densitymatrices were analyzed with version 5 of the Natural BondOrbital Program package28 to derive bond order metrics, NPAcharges,62 and the various natural “X” orbital types (X = atomic,NAO;62 hybrid, NHO;63 bond, NBO;63 or localized molecular,NLMO64). Bond order definitions are shown in Scheme 1.Coulson,65Wiberg/Mayer,66,67 atom�atom overlap-weighted,68

and natural localized molecular orbital/natural population anal-ysis (NLMONPA)69,70 were calculated from the one-particledensity matrix for each density functional and complex studiedwith NBO5. Bonding in terms of the base NXO types (within thespin-unrestricted formalism and associated separate NBO anal-yses ofR- and β-spin density matrices for NLMONPA) as shownin Scheme 1 was analyzed.Data Reduction. Bond lengths, angles, and dihedral angles

were calculated for the oxidized and reducedH-cluster models onthe basis of atomic Cartesian coordinates and a bond list. Foreach quantity, variables with variance across the complexes belowa threshold (0.001 Å for bond lengths, 1.0� for angles) werediscarded. The data matrix thus screened was decomposed usingprincipal components analysis,71 in order to identify the primarycontributing geometric variables to differences among the com-plexes within oxidized and reduced states separately. Bond orderdata were deposited into an HDF5-format file for ease in accessand query. Variances across each complex for each bond ordermetric and bond were calculated and sorted in order to find whichbonds’ order and which metric served as the best discriminant forthe complex configuration. Analysis routines were coded into thePython programming language andmade use of the NumPy, SciPy,and matplotlib modules outside of those in the standard library.

’RESULTS

Geometry Optimization and Analysis. Fate of the AquoLigand in Oxidized Complexes. Starting from identical atomiccoordinates, but with atomic identities changed to reflect thediatomic ligand configuration in question, the energy of eachcomplex was optimized with respect to nuclear displacements.The structures at convergence are shown in Figure 1. The iron atom

Scheme 1. Definitions of Bond Order Metricsa

aThe one-particle density matrix is denoted by F, the overlap matrix byS, and hybrid orbitals by h. The preorthogonalized natural atomic orbital(PNAO), NAO, or preorthogonalized natural hybrid orbital (PNHO)basis for each quantity is given in the subscript. cij in the NLMONPAdefinition are the expansion coefficients of NLMO i for the NAO basisfunctions centered on atom A or B.



distal to the methylthiol ligand models the natural enzymatic sitemost directly involved in H2 production, and that is believed tobind a terminal hydrogen or hydride ligand in the protonreduction mechanism. Since the originally published crystal-lographic structure8 showed an electron density maximumassigned to a terminal water ligand 2.55 Å from the distal ironatom, and this structure has been speculated to correspond to anoxidized form in the catalytic cycle,7 this ligand was retained inthe oxidized models. Upon energy minimization, the Fedist�aquo bond alternately shortened in the all-terminal-carbonyl(2.12 Å), gem-distal-cyano (2.33 Å), and gem-proximal-cyano(2.43 Å) structures, or broke altogether in the all-terminal-cyano(3.43 Å), cis-terminal-cyano (3.66 Å), and trans-terminal-cyano(3.47 Å) models, with the latter structures possessing a hydrogenbond between water and the bridging DTMA nitrogen atom atconvergence. The observed dichotomy of fates points to apotential functional discriminant among the tested structures,namely, the strength of aquo ligation in the resting oxidized state.A strong iron�aquo bond would potentially interfere with ironprotonation in the catalytic cycle through an additional reactionbarrier. The findings here are consistent with previous QM/MMstudies of the full [2Fe]H�[4Fe4S]H cluster where one-electronreduction of the Hox

inact FeIIFeII state to Hox led to an order-of-magnitude decrease in water binding energy.72 From these data,one can argue against the all-CO and geminal structures aspotentially binding water too tightly, although a full examinationof the binding energy outside of the present work’s scope wouldbe required for a definitive assessment.Bond Lengths of Fe�CObr. Another feature of the H-cluster

that has drawn attention is the carbonyl ligand bridging the twoiron ions. Although this ligand would be predicted to change to aterminal position in mechanisms involving bridging hydrideintermediates, in mechanisms involving terminal hydrogen/hydride intermediates the function of this bridging ligand is ofgreater interest in functionally distinguishing the two iron sites.Table 1 compiles the bond lengths between the proximal anddistal iron and CObr for oxidized and reduced model complexes.Several patterns emerge from Table 1. First, the Feprox�CObr

bond lengthens upon reduction of any of the models considered,with a less prominent shortening of the Fedist�CObr bondevident in all cases save complex I, where the latter bond isessentially unchanged upon reduction. This pattern reflects a“swing” of the bridging carbonyl ligand toward the distal ironupon reduction, as would be expected if electron density weredelocalized from Fedist through π-back-bonding to produce a netstabilization of the reduced complex. However, examination ofthe C�O bond distance shows that reduction in all cases leads toa strongerC�O bond in the bridging ligand. Taken together withthe more dramatic Feprox�CObr distance increase relative to

Fedist�CObr, this suggests an interplay between proximal anddistal iron electron density delocalization into the π* system ofthe bridging carbonyl in different cluster redox states. Thus, inthe resting oxidized state, the more symmetrically disposed CObr

ligand accepts proximal Fe density into its π* orbitals; uponreduction by two electrons, disproportionately less density iscontributed by Feprox than by Fedist, leading to a net decrease inC�O bond length, and a less symmetric position between thetwo iron ions favoring Fedist.A role for the bridging ligand in buffering electron density in

the highly reduced H-cluster is also supported by this ligand’sdisposition in the two geminal dicyano models. As seen forcomplexes IV and V in Table 1 for both oxidized and reducedstates, CObr strongly favors the iron atom to which both cyanoligands are bound. Given the charge and σ-donating ability ofcyanide, this pattern is consistent with an electron-densitybuffering role for the bridging carbonyl ligand. Notably, thelongest C�O distances are seen in the all-cyano complex I, and theshortest distances in the all-carbonyl complex II, also consistent withthe ability of this carbonyl to absorb charge into its π* system. Thenature of the iron�carbon bonding of CObr is discussed below.Geometry—PCA Analysis. Rather than examine individual

geometry changes upon single perturbations, which amountsto examining individual covariance matrix elements with a two-row datamatrix, the geometric analysis of these model complexeshere were analyzed together to attempt to pull out overallcorrelation patterns between diatomic ligand perturbation andcomplex geometry. To accomplish this, principal componentsanalysis of oxidized and reduced systems separately were donewith those geometric quantities (bonds, angles, or dihedrals)showing variance across each group greater than a chosenthreshold (0.001 Å for bonds, 1� for angles and dihedrals).The resulting data were either mapped onto schematic repre-sentations of the generic complex structure, as illustrated inFigures 2�5, or tabulated in Tables S1 and S2 (dihedrals) of theSupporting Information. From a chemistry perspective, thisparticular analysis can be understood in analogy with the decom-position of a complicated molecular motion in terms of normalmodes and their contributions to the motion. However, insteadof analyzing the variation of atomic position across a vibration,the variation considered here is across the set of diatomic ligandvariants. Just as the coefficients associated with a geometricparameter in a normal mode encode relative magnitudes anddirections of motion within the mode, the PCA eigenvectorcomponents encode relative magnitudes and signs of covariancethat capture the maximum amount of overall variance within thedata. From this analysis, it is hoped that general patterns emergerelating to ways in which the [2Fe]H core adapts to terminalligand bonding changes, and a hypothesis as to the functional

Table 1. Feprox�CObr and Fedist�CObr Distances for Complexes I�VI in Oxidized and Reduced States

rFeprox�CObrrFedist�CObr

rCbr�Obr

complex oxidized reduced Δred. oxidized reduced Δred. oxidized reduced Δred.

I 1.961 2.047 +0.086 1.847 1.849 +0.002 1.212 1.202 �0.010

II 1.992 2.283 +0.291 1.915 1.841 �0.074 1.188 1.173 �0.015

III 1.982 2.109 +0.127 1.866 1.856 �0.010 1.198 1.187 �0.011

IV 2.187 2.533 +0.346 1.770 1.764 �0.006 1.197 1.183 �0.014

V 1.769 1.797 +0.028 2.293 2.203 �0.090 1.189 1.187 �0.002

VI 2.006 2.128 +0.122 1.863 1.849 �0.014 1.197 1.187 �0.010



significance of the natural trans-terminal-cyano configurationbecomes apparent.

Bond Length Variation across Models in the Same RedoxState. The analysis of bond lengths for the oxidized models

Figure 2. First three principal components for bond length variations across oxidized model complexes. The cumulative variance captured is given as apercentage below each schematic structure. Numbers associated with bonds are the largest 10 component contributions for each PC; values withmagnitudes over 0.4 are shown in bold red with slightly enlarged font; magnitudes over 0.1 are in bold red. Atoms and bonds not involved in significantvariations are grayed out for clarity.

Figure 3. First three principal components for bond length variations across reduced model complexes. The cumulative variance captured is given as apercentage below each schematic structure. Notation and scheme are identical to those in Figure 2.

Figure 4. First three principal components for bond angle variations across oxidized model complexes. The cumulative variance captured is given as apercentage below each schematic structure. Atoms and bonds not involved in significant variations are grayed out for clarity.

Figure 5. First three principal components for bond angle variations across reduced model complexes. The cumulative variance captured is given as apercentage below each schematic structure. Atoms and bonds not involved in significant variations are grayed out for clarity.



shows that most of the variation across complexes resides in theFedist�Oaquo bond length, as expected on the basis of dissocia-tion of water from some but not all of the complexes. The secondPC shows that most of the remaining variance is explained bydifferences in the bond between the iron atoms and the bridgingcarbonyl carbon, with the opposite signs confirming that length-ening of one bond correlates with a shortening of the other andvice versa. A more subtle point of interest is the like-signcorrelation of proximal terminal Fe�C bonds with the Fedist�CObr bond (�0.17, �0.18, and �0.75 in Figure 2, center) anddistal terminal Fe�C bonds with the Feprox�CObr (0.16, 0.17,and 0.56), and opposite-sign correlation between the terminaland bridging bonds on the same iron. This pattern also supportsthe idea of the bridging carbonyl ligand as a sort of buffer againstchanges in charge density on iron. For the oxidized complexes,the remaining variance up to 99.2% (Figure 2, right) is mostlyexplained by a slight anticorrelation between the proximalterminal diatomic ligands (+0.76 and �0.62).Analysis of the bond lengths in the reduced model complexes

is similar to that of the oxidized complexes, without the varianceassociated with water dissociation since the reduced complexeswere modeled as terminal hydrides. The first PC (Figure 3, leftframe) shows the same pattern of correlation between terminaland bridging diatomic ligation as the second PC for the oxidizedmodels. Although magnitudes for the terminal ligand bonds arecomparable to those found for the oxidized complexes, themagnitudes for the Fe�CObr bonds are reversed in this case,with the Feprox�Cbr bond carrying a weight of 0.83 and theFedist�Cbr�0.48, implying that the range of bond lengths for theformer explains a greater fraction of the variance in the first PCthan the latter bond. PC2 shows a positive correlation betweenthe two bridging bonds, both of which are anticorrelated with theterminal Fe�C bonds. Thus, there is a correlation betweenshorter terminal bonds and longer bridging bonds, which was notpresent in the largest three PCs for the oxidized complexes.Finally, PC3 for the reduced complexes is dominated by ananticorrelation between the Fe�C bonds of the terminal prox-imal diatomic ligands, a pattern also seen for PC3 for the oxidizedcompounds. In both cases, a fairly small amount of overallvariance across the models (0.9% oxidized, 4.4% reduced) isexplained by this PC, however, so assignment of a functionalsignficance for this relationship in the operation of the [2Fe]Hcenter is of questionable validity.Notably, the bridging dithiolate ligand and the heteroatoms of

the carbonyl and cyanide ligands are absent from the dominantcontributors to the top three PCs for both oxidized and reducedcomplexes, as is the methylthiol ligand standing in for cysteinateand [4Fe4S]H. This suggests that insofar as bond lengths canoffer information on functionally important changes in structure,the perturbations of the diatomic ligand heteroatoms affectprimarily the Fe2C5 core of the [2Fe]H center.Angle Variation across Models in the Same Redox State.The

PCA of angle variance in the oxidized models is summarized inFigure 4. Variation in the water geometry with respect to thedistal Fe atom is an important component of all three top PCs,again reflecting the dissociation of water and rotational freedomof this species. The anticorrelation of the H�O�Fe angles inPC1 (+0.80 and �0.56) reflects rotation around the axis goingthrough water O and perpendicular to the water plane; the directcorrelations seen in PCs 2 and 3 likely reflect a rotationalcomponent around the perpendicular axis that would increaseor decrease both H�O�Fe angles in concert, rather than water

bending. Aside from this relatively uninteresting variation, PC1shows components attributable to distal C�X motions (cyano,in the natural trans-terminal configuration), likely reflectingbending adjustments upon changes in water binding to the distaliron atom. PC2 contains a substantial contribution from water aswell, such that the covariations seen in this PCmay be due simplyto water geometry differences among themodels as well as effectsfrom the diatomic ligand configuration changes. One clearpattern seen is a bend of the bridging CO ligand in the Fe�C�O�Fe plane, with closing of the O�C�Fedist angle correlat-ing directly with closing of the Cbr�Fedist�Feprox angle, whichcan plausibly be attributed to the bridging ligand angular motionupon changes in bond lengths to the iron atoms. The componentassociated with the Fe�Fe�C angle (�0.14, frame B) could beprimarily associated either with changes in water binding (boundwater will have its hydrogen atoms pointing away from the 2-Fecore more so than free water, thus maximizing the H�O�Feangles and correlating with a closing of the C�Fe�Fe angle) orwith changes in bridging carbonyl positions upon diatomic ligandperturbation (an opening of the Fedist�Cbr�Obr angle correlat-ing with a shorter Fedist�Cbr bond and a more open Cterm�Fe�Fe angle in PC2). For the case of oxidized complex angles, PC3explains a larger portion of variance (9.8%) than was seen forbond lengths. Here (Figure 4, right), the dominant contributorsare bridging ligand bending. A similar sign pattern is seen withthe Fe�Cbr�Obr components (+0.58, �0.53), the Fe�Fe�Cbr

angle (�0.26), and the front terminal distal carbon (�0.25).More interesting, changes in the methylthiol geometry are seen,with all three proximal diatomic ligands moving in a cuppingmotion with respect to Feprox. Together with the bridgingcarbonyl components, this appears to reflect changes as theCObr bond length changes. Lengthening of the Feprox�Cbr bondgoes along with linearization of the Fedist�Cbr�Obr angle; thislikewise correlates with opening of the cup around Feprox(negative signs of components around the proximal iron andof the Fedist�Cbr�Obr in PC3 corresponding to similar motion,thus opening in the case of a linearized Fedist�Cbr�Obr angle).The reduced complexes lack the variation due to changes in

water binding and so more cleanly reflect the effects of diatomicligand perturbation on the [2Fe]H model structures. In PC1(Figure 5, left frame) we see the identical subpattern of Feproxcupping and CObr variation as was seen for the oxidizedcomplexes, suggesting this pattern is independent of watermovements in the latter. Here is also seen symmetric covariationof the Crd�Fedist�Feprox, Cfd�Fedist�Feprox, H�Fedist�Feprox,and Cbr�Fedist�Feprox angles, corresponding to a tendency forthe terminal ligands to “push” and “pull” with respect to thecomplexes’ long axis (along the Fe�Fe bond) in concert. Takentogether, a concerted change can be seen wherein as the bridgingcarbonyl favors Fedist, the hydride and terminal diatomics moveaway from Feprox (a pulling motion) and the angles around theproximal iron open up. PC2 is dramatically different, and for thefirst time participation of the bridging dithiolate ligand indetermining variance across complexes is seen. The dominantcontributors here are positive correlation between H�Fedist�Feprox (0.68) and Fedist�Cbr�Feprox (0.41) angles, and mutualanticorrelation with O�Cbr�Feprox angle (�0.43).Dihedral Angle Variation across Models in the Same Redox

State. The variation of dihedral angles across oxidized andreduced models is more difficult to represent graphically, sothe most significant data are tabulated in Tables S1 and S2 forthe sake of completeness. Little insight can be gleaned from



inspecting the data, aside from the general observation that thedominant contributions to variance across the model complexes inboth valence states are simply displacement of the terminal het-eroatoms of the linear diatomic ligands with respect to the [2Fe]Hcore frame, whatmight be characterized as “wagging”motion.Giventhat the terminal atoms are expected to have the greatest degree oftorsional freedom and that the atomic identities of these are beingperturbed, this observation is consistent and not unexpected.Charges.Natural Population Analysis charges for the 12model

complexes considered showed relatively little variation with

density functional. The raw data (not shown) indicated thatcharges derived from the hybrid functional densities are moredistinctive than those from the local, GGA, and meta-GGAfunctionals, but not significantly so for interpretive purposes. Anumber of trends can be seen from the data reported in Table 2.For the oxidized models, water is essentially neutral whetherbound or not, consistent with a weak coordinate bond. In bothoxidized and reduced models, the methylthiol and dithiomethyla-mine bridge are seen to deviate substantially from their formalcharges of �1 and �2, with strong charge transfer into the [2Fe]

Table 2. NPA Charges on [2Fe]H Model Atoms or Atomic Groupings for the Complexes Considereda

group complex I complex II complex III complex IV complex V complex VI

Oxidized

Feproxb �0.316( 0.056 �0.349 ( 0.044 �0.344( 0.029 �0.336( 0.040 �0.288( 0.048 �0.354( 0.034

Fedist �0.074( 0.067 �0.159( 0.049 �0.050( 0.057 �0.059( 0.067 �0.115( 0.059 �0.050( 0.048

SMT 0.178( 0.008 0.174 ( 0.014 0.208( 0.019 0.137 ( 0.013 0.176( 0.011 0.226 ( 0.018

SfDTMA �0.128( 0.048 0.046( 0.048 �0.056( 0.045 �0.085( 0.045 �0.098( 0.046 �0.038 ( 0.039

SrDTMA �0.139( 0.045 0.036( 0.048 �0.058( 0.026 �0.090( 0.045 �0.110( 0.044 �0.073 ( 0.030

Cfp 0.159( 0.003 0.621( 0.025 0.097( 0.003 0.595( 0.028 0.124( 0.010 0.634( 0.032

Crp 0.156( 0.003 0.620( 0.025 0.627( 0.033 0.592( 0.027 0.123( 0.009 0.092( 0.004

Cbr 0.486( 0.014 0.453( 0.008 0.454( 0.009 0.525( 0.016 0.567( 0.021 0.460( 0.011

Cfd 0.072( 0.003 0.638( 0.024 0.036( 0.009 0.107( 0.005 0.559( 0.026 0.026( 0.007

Crd 0.121( 0.003 0.662( 0.023 0.597( 0.027 0.108( 0.005 0.562( 0.025 0.602( 0.028

Xfp �0.727( 0.008 �0.411( 0.012 �0.596( 0.010 �0.492( 0.012 �0.599 ( 0.041 �0.496( 0.011

Xrp �0.725( 0.007 �0.412( 0.012 �0.494( 0.010 �0.492( 0.012 �0.594 ( 0.041 �0.601( 0.006

Obr �0.645( 0.012 �0.480( 0.014 �0.548( 0.011 �0.571( 0.012 �0.531 ( 0.023 �0.548( 0.012

Xfd �0.686( 0.006 �0.399( 0.011 �0.563( 0.005 �0.608( 0.007 �0.498 ( 0.013 �0.558( 0.009

Xrd �0.709( 0.007 �0.399( 0.011 �0.496( 0.010 �0.609( 0.007 �0.498 ( 0.013 �0.493( 0.011

MT 0.290( 0.003 0.393( 0.019 0.370( 0.005 0.297( 0.016 0.344( 0.009 0.377( 0.005

DTMA �0.401( 0.092 0.128( 0.100 �0.104 ( 0.081 �0.183( 0.090 �0.238( 0.073 �0.108( 0.080

diatomics �2.499( 0.035 0.894( 0.049 �0.885( 0.025 �0.845( 0.027 �0.785( 0.076 �0.883( 0.026

water 0.001( 0.000 0.093( 0.011 0.013( 0.002 0.126( 0.008 0.082( 0.011 0.017( 0.002

Reduced

Feprox �0.324( 0.067 �0.346( 0.051 �0.331( 0.053 �0.332( 0.043 �0.318( 0.053 �0.327( 0.055

Fedist �0.425( 0.043 �0.527( 0.026 �0.469( 0.031 �0.438( 0.035 �0.489 ( 0.035 �0.467( 0.031

SMT 0.230( 0.009 0.274( 0.012 0.248( 0.010 0.222( 0.006 0.228( 0.011 0.253( 0.010

SfDTMA �0.059( 0.041 0.071( 0.044 �0.008( 0.042 0.026( 0.037 0.000( 0.040 0.008( 0.040

SrDTMA �0.068( 0.040 0.064( 0.044 0.014( 0.038 0.016( 0.037 �0.008( 0.040 �0.003( 0.041

Cfp 0.154( 0.003 0.604( 0.026 0.090( 0.005 0.582( 0.030 0.124( 0.005 0.628( 0.030

Crp 0.150( 0.004 0.600( 0.026 0.624( 0.030 0.577( 0.030 0.122( 0.005 0.084( 0.006

Cbr 0.521( 0.030 0.486( 0.024 0.499( 0.028 0.530( 0.024 0.544( 0.028 0.501( 0.027

Cfd 0.192( 0.004 0.651( 0.024 0.143( 0.002 0.164( 0.003 0.622( 0.029 0.140( 0.002

Crd 0.195( 0.004 0.652( 0.024 0.657( 0.028 0.165( 0.003 0.624( 0.029 0.656( 0.028

Xfp �0.719( 0.003 �0.401( 0.009 �0.594( 0.005 �0.472( 0.008 �0.598 ( 0.006 �0.492( 0.008

Xrp �0.715( 0.003 �0.402( 0.009 �0.489( 0.008 �0.471( 0.008 �0.595 ( 0.006 �0.593( 0.004

Obr �0.607( 0.010 �0.425( 0.012 �0.518( 0.010 �0.531( 0.016 �0.513 ( 0.010 �0.517( 0.011

Xfd �0.745( 0.009 �0.402( 0.016 �0.614( 0.011 �0.634( 0.013 �0.494 ( 0.012 �0.614( 0.011

Xrd �0.746( 0.009 �0.402( 0.016 �0.498( 0.013 �0.634( 0.013 �0.494 ( 0.011 �0.497( 0.014

MT 0.342( 0.005 0.497( 0.017 0.421( 0.010 0.390( 0.006 0.411( 0.014 0.418( 0.010

DTMA �0.259( 0.079 0.319( 0.090 0.017( 0.080 0.059( 0.075 0.007( 0.081 0.015( 0.081

diatomics �2.320( 0.017 0.961( 0.063 �0.700( 0.038 �0.726( 0.035 �0.658( 0.038 �0.705 ( 0.037

hydrogen �0.015 ( 0.025 0.097( 0.020 0.063 ( 0.021 0.047( 0.021 0.047 ( 0.022 0.066( 0.021aAverage values are reported with standard deviation over the four density functionals PBE, PBE1PBE, SVWN5, and TPSS. bAbbreviations: prox,proximal; dist, distal; fp, front proximal; rp, rear proximal; fd, front distal; rd, rear distal; br, bridging; MT, methylthiolate; DTMA, dithiomethylamine;fDTMA, front sulfur of DTMA; rDTMA, rear sulfur of DTMA. Complex orientation given in Figure 1.



core for all complexes considered. In addition, from charge con-sideration alone the terminal “hydride” ligand in the reducedmodelsmore closely resembles atomic hydrogen in the minimum-energyresting-state geometries here; whether approach of a protonfrom the DTMA bridge or elsewhere polarizes the electrondensity awaits more detailed consideration of model hydroge-nase reaction mechanisms. Total charge on the diatomic ligandsshows expected trends, with the all-cyanide model complexescarrying ∼1.7 extra negative charge units than those with thenative dicyano composition, and the all-carbonyl models show-ing a deficit of approximately the same amount in the oppositedirection. Both of these models differ by two charge units fromthe dicyano models; thus, changes in the diatomic charges of amagnitude of less than two units imply the remainder of the[2Fe] core has a charge buffering capacity: on the order of 0.3charge equivalents over the dicyano reference values are ab-sorbed in the case of the all-cyanide model, whereas∼0.3 chargeequivalent is retained in the core of the all-carbonyl modeldespite two charge units being effectively “removed” versus thedicyano reference. The dicyano diatomic ligands themselves allcarry a net charge on the order of�0.8( 0.1, thus like the sulfurligands transferring a charge equivalent into the metallic core.Another notable relationship may be seen between the DTMA

and diatomic ligand charges across models in both the oxidizedand reduced cases. Across the oxidized dicyano complexesIII�VI, the sum of these ligands’ charges is constant at approxi-mately �1 despite small variations in how the charge is sharedbetween them. Replacement of two terminal carbonyls by cyanogroups decreases the DTMA + diatomics charge by 2, whereasexchange of cyano groups for carbonyls in complex II increasesthe charge by approximately the same magnitude. In the reducedmodels, III�VI carry a constant charge of about�0.65 (geminaldicyano) to �0.7 (cis/trans), with addition or loss of cyanidechanging their summed charge by almost two full units as inthe oxidized forms. Thus, the DTMA and diatomic ligandgroups appear to absorb or disperse overall charge in syn-chrony and to compensate one another as the diatomic ligandconfiguration changes.Reduction in this study might be thought of as addition of an

electron and a terminally bound proton to the system, therebymaintaining charge equality with the oxidized complexes. Thisscheme is in line with the current understanding of the mecha-nistically relevant valence states in [FeFe] hydrogenases, wherethe active oxidized [2Fe]H core is in an FeIFeII state exhibiting arhombic electron paramagnetic resonance signal with a low-fieldpeak at g= 2.10 73 and is brought to diiron(I) as part of the protonreduction cycle. The second electron in the two-electron H2

production reaction presumably resides on the pendant [4Fe4S]Hcluster for at least a brief time, although a spectroscopic signature(rhombic g = 2.06) for this state has only been definitively observedduring precatalytic activation of the inactive-oxidized diferrous state,peaking in intensity at �110 mV versus SHE.73,74 Despitecharge neutrality, reduction leads to a slight but generaldecrease in negative charge across the methylthiol, dithiolate,and diatomic ligands. Across the models, reduction leads toincrease of electron density on the distal iron of ∼0.5 equiv.Thus, addition of a proton and an electron to the oxidizedsystem leads to a charge rearrangement wherein the proton isessentially neutralized, and the distal iron carries a greatershare of the transferred charge from the complex ligands thanit does in the oxidized forms, with a slightly greater transfer ofcharge from these ligands upon reduction.

The charges of the bridging diatomic ligand are of specialinterest with respect to a hypothesis of a charge buffering role forthis moiety. In most of the complexes including the native trans-terminal-dicyano model, the charge on CObr actually becomesmore positive upon reduction; the lone exception is the gem-proximal model with both cyanide species on the proximal iron,where the total ligand charge becomes more negative by 0.005units. This complex is also distinguished by having Fedist carry anextra 0.1 electron in the oxidized state as compared with the otherthree dicyanide models, and Feprox a 0.1 electron deficit, despiteboth formally negatively charged cyanides being bound to theproximal iron. The trend toward lengthening Feprox�Cbr andshortening Fedist�Cbr distances upon reduction clear fromTable 1, concomitant with the apparent withdrawal of electroniccharge from the bridging ligand, leads to a picture wherein protonand electron addition leads to the liberation of existing charge onthe Fe ligands and localization on the distal Fe atom (∼0.5 unit),with the bridging carbonyl ligand moving into a position thatdecreases bonding to Feprox and increases bonding to Fedist, withthe balance leading to a slightly more positive overall CO charge.The changes in bond order across functionals and metrics areexplored below in greater depth.Notably, the native model complex VI shows identical trends

to all of the other models; thus, behavior of this configurationwith respect to charge delocalization during oxidation/reductiondoes not distinguish it from these plausible alternatives.HOMO/LUMO Energies. Since the frontier orbital energies

allow comparison of the relative electron affinities (oxidizedcomplex LUMOs) and ionization potentials (reduced complexHOMOs) among the complexes, the grouping of these valuescan give some qualitative insight into the effect of diatomic ligandconfiguration on [2Fe]H reactivity. The HOMO and LUMOenergies for the six models considered in both redox states, for allfour density functionals included in the study, are shown inTable 3. For the oxidized complex, both R- and β-spin data areprovided, although the latter are more relevant for injection of anelectron to form a closed-shell singlet reduced state. Threerelevant patterns emerge independent of the density functionalconsidered. First, one can immediately see that the all-terminal-cyanide complex (I) has orbital energies shifted higher than theother complexes, as would be expected on the basis of simpleelectrostatics and the additional two negative charge units carriedby this complex. Analogously, the all-carbonyl model (II) showsfrontier orbital energies shifted downward by an amount similarto the upward shift of model (I). Thus, a simple argument againstthese configurations revolves around a need for a redox poiseconsistent with biological electron transfer and H2 production,using the calculated values for complex VI as a reference. Apattern also emerges from Table 3 whereby the geminal com-plexes IV andV group separately from the cis (III) and trans (VI)complexes with respect to β-spin LUMO energies, being shiftedto more negative energies by∼0.02Ha (12.5 kcal/mol). No suchsystematic pattern is seen in the reduced complex models,suggesting that insofar as frontier orbital energies correlate witha distinguishing factor in the natural diatomic ligand configura-tion (VI), reduction of the [2Fe]H cluster has greater functionalsignficance as a determinant of structure than does oxidation ofthe protonated FeIFeI system. The cis configuration of cyanidegroups (III) gives rise to frontier orbital energies very similar tothe trans configuration (VI), such that the simple energeticarguments employed above are not sufficient to distinguishfunctionally these two structural options on this basis alone.



Variance in and Analysis of Bond Orders. The bonding in the12 model complexes considered was quantitated by consideringfour bond order measures: Coulson, Wiberg/Mayer, atom�atom overlap-weighted with a Natural Atomic Orbital basis,and NLMO/NPA, as defined above. The variance in bond orderwas calculated to determine which bonds are most affected bydiatomic ligand perturbations, and how if in any way the trans-cyano configuration (VI) stands out, with functionals and bondingmetrics considered separately; i.e., no averaging was done overthese variables. The largest variances were found generally for theCoulson bond order metric. For the purpose of discussion andpresentation, an arbitrary threshold of 0.1 on variance is con-sidered for the data in Table 4, with the full data provided asSupporting Information. The bonds showing the greatest varietyover the set of complexes by this definition were between Feproxand Cfp, Cbr, and SrDTMA, and between Fedist and Cbr, Crd, andSfDTMA. For each bond of the six considered in Table 4, a cleanvariation is seen between the variance in Coulson bond order anddensity functional class in the order local, GGA, meta-GGA, andhybrid. For all but the Fedist�Cbr bond, variance increases in theorder specified, implying that the hybrid PBEh functional togetherwith the Coulsonmetric results in the greatest discriminatory powerover the series of model complexes for these bonds.Several physically relevant trends are apparent in the bond

orders for complex model VI, as illustrated in Figure 6. First,reduction decreases bonding between iron and the terminaldiatomic ligands generally, while three of four Fe�DTMA bondsshow increases in their Coulson index (the exception beingFedist�SrDTMA). Second, decreased bonding between the distaliron and the bridging carbonyl is clear, with a concomitant

increase in Feprox�Cbr bonding. So, in general reduction corre-lates with stronger Fe�thiolate bonding, weaker terminal diatomicbonding, and a change in bridging carbonyl bonding to favor theproximal iron at the expense of the distal iron. This is in directcontrast with the changes in bond length shown in Table 1, wherereduction leads to a movement of the bridging carbonyl toward thedistal iron and away from the proximal iron. Thus, an inverserelationship between bond length and bond order is implied for ironbonding to the bridging carbonyl, to be resolved below.Interesting is the fact that complex VI represents the extremes

in Coulson bond order between Fe and the bridging thiolates aswell as the bridging carbonyl (Table 4). In the oxidized state, theproximal iron of complex VI has the most antibonding characterwith Cbr and SrDTMA compared to all of the other perturbedcomplexes considered. The highest Coulson bond order betweenFedist and Cbr is found for VIo; as seen in Figure 6, this fallsprecipitously upon reduction in opposition of expectations fromthe change in bond distance. Since generalized Coulson bondorders are known to deviate from “common-sense” expectationsof bond order, the trends for the other three bonding metricswere examined for this bond in VIo and VIr. [The originalCoulson order was defined for aromatic π systems, where therelative phases of the minimal p-orbital basis established all over-laps as positive; thus, all distinction between bonding and anti-bonding was carried in the signs of the density matrix elements. Forgeneral bases, this assumption is invalid and neither sign normagnitude of density matrix elements is definitively indicative ofbond order without information on the corresponding overlap aswell. Nevertheless, its powers of discrimination within a relatedfamily of molecules remains to be determined.] For all functionals,

Table 3. HOMO/LUMO Energies (Atomic Units) for Oxidized and Reduced [2Fe]H Model Complexesa

functional

complex SVWN5 PBE PBEh TPSS

Oxidized R

I �0.120 57/-0.054 82 �0.113 83/-0.044 63 �0.167 87/-0.011 50 �0.115 07/-0.040 16

II �0.217 84/-0.150 95 �0.212 50/-0.142 02 �0.257 94/-0.102 18 �0.214 04/-0.138 89

III �0.176 81/-0.115 05 �0.171 26/-0.104 95 �0.224 74/-0.071 41 �0.173 81/-0.102 00

IV �0.156 22/-0.094 57 �0.151 00/-0.085 50 �0.202 12/-0.054 15 �0.152 52/-0.082 45

V �0.160 70/-0.095 52 �0.155 41/-0.086 45 �0.214 54/-0.057 93 �0.157 44/-0.083 36

VI �0.180 83/-0.112 24 �0.174 85/-0.102 28 �0.225 77/-0.068 97 �0.177 13/-0.099 37

Oxidized β

I �0.116 94/-0.098 31 �0.109 88/-0.082 05 �0.165 65/-0.020 65 �0.113 06/-0.074 33

II �0.254 35/-0.200 32 �0.248 18/-0.187 52 �0.293 95/-0.133 04 �0.251 53/-0.182 61

III �0.187 47/-0.154 71 �0.179 32/-0.139 85 �0.221 36/-0.077 36 �0.180 30/-0.134 33

IV �0.167 02/-0.133 42 �0.159 84/-0.118 69 �0.222 40/-0.057 49 �0.162 65/-0.112 48

V �0.167 14/-0.134 21 �0.159 90/-0.118 00 �0.220 26/-0.057 12 �0.162 88/-0.110 37

VI �0.184 06/-0.157 70 �0.177 14/-0.142 01 �0.222 40/-0.078 85 �0.180 38/-0.135 64

Reduced HOMO

I �0.126 15/-0.072 04 �0.118 81/-0.062 18 �0.177 13/-0.022 82 �0.121 46/-0.058 62

II �0.243 70/-0.190 71 �0.236 86/-0.181 80 �0.277 24/-0.143 52 �0.237 91/-0.179 99

III �0.187 41/-0.127 07 �0.180 36/-0.117 80 �0.232 79/-0.080 45 �0.183 44/-0.115 50

IV �0.180 54/-0.130 08 �0.173 15/-0.121 07 �0.232 17/-0.084 08 �0.176 26/-0.119 24

V �0.178 89/-0.124 79 �0.172 01/-0.115 43 �0.232 69/-0.079 60 �0.175 43/-0.113 12

VI �0.188 96/-0.126 87 �0.182 24/-0.117 55 �0.232 91/-0.079 53 �0.185 99/-0.115 15aR- and β-spin orbital energies are reported separately for the S = 1/2 oxidized complex.



the Fedist�Cbr Wiberg and NLMO/NPA bond orders decreaseupon reduction, while the AAOWNAO bond order increases.Averaged over functionals, bond order decreases from 0.65 to0.55 for Wiberg and 0.79 to 0.59 for NLMO/NPA indices, butincreases from 0.46 to 0.53 for the AAOWNAO metric. Taken intotal and considered with the metric definitions in Scheme 1, this isconsistent with reduction correlating with more negative NAOdensity matrix elements and more negative overlaps betweenpreorthogonalized NAOs, which together would appear as anincrease of the AAOWNAO metric but a decrease of the threeothers. Thus, reduction of complexVI results in a strong decrease incovalent character between the distal iron and the bridging carbonyl.

The apparent contradiction of shorter bond length and weakercovalent bonding upon reduction can be resolved by the chargedata in Table 2. Reduction leads to greater negative charge on thedistal iron atom but greater positive charge of the bridgingcarbonyl group. The picture thus suggested is that of Fedist�Cbr

bonding becoming more ionic upon complex VI reduction, andthat the reduction in Fe�C bond distance arises not fromstronger π-back-bonding or more covalency, but rather electro-static stabilization of the accumulated negative charge on thedistal iron. This trend upon reduction is true across the six systemsconsidered excepting complex V, where the overall charge onCObr remains almost the same upon reduction.

’DISCUSSION

General Section. The present work examined whether thediatomic ligand configuration observed in the H-cluster of[FeFe] hydrogenases could have a mechanistic rationale asopposed to a purely evolutionary justification. To pursue theanswer, geometries, atomic charges, frontier orbital energies, andbond orders were examined in six model complexes in theiroxidized and reduced states.Geometry. A feature of the [2Fe]H cluster that has received

significant attention is the bridging carbonyl ligand. Underexperimental conditions this ligand in model complexes is oftenobserved to dissociate upon reduction and take up a terminallybound position on the distal iron atom, leaving the bridgingposition to host a hydride ion. Under the simulated physicalconditions here (minimum energy configurations starting fromthe bridging geometry seen in the enzyme, high-polarity solvent,and the model chemistries considered), no such completedissociation was observed.More importantly, a strong preferenceof CObr for irons with more formally negative ligands wasobserved, visible in Figure 1 for complexes IV and V wheretwo cyanides are bound to a single iron. To the extent that thebridging carbonyl must change its disposition upon oxidation/reduction, having such a large skew due to the “base ligation” (i.e.,ligation which is present in all catalytic states) would arguablyweaken the ability of the bridging ligand to adapt by a coupledincrease of Feprox�Cbr and decrease of Fedist�Cbr. The data inTable 1 show the changes in these bonds’ lengths upon reduc-tion. Complex VI, together with the cis-cyano complex III, aredistinguished in their balanced increase of proximal bondingtogether with a limited change in distal bonding.The principal component analyses displayed in Figures 2�5

are a somewhat unusual approach to global structural compar-ison, and so warrant further discussion. The utility of this analysisis in establishing dominant structural “communication patterns”within the confines of carbonyl and cyanide terminal ligation andto reason therefrom what unique features the trans configurationmight impart. Since the primary interest in the current report wasthe distinguishing characteristics, if any, of theH-cluster diatomicligand configuration, models perturbing this feature were con-structed. Bond lengths and bonding angles were separatelytreated as elements of a vector, and multivariate analysis methodsdeployed to represent the structural variance over the data setproduced by changing metal ligands as linear combinations ofbonding features that individually explain as much change aspossible in decreasing order of importance. For conceptualpurposes only, the positive and negative correlations presentedin Figures 2�5 map qualitatively to molecular vibrations, withbonding features over the data set changing symmetrically or

Figure 6. Coulson bond orders of Fe bonds in oxidized and reducedmodels VI. Centers not involved in the reported bonds have beenomitted for clarity. The bar glyphs associated with each bond reportbond orders for the oxidized (blue) and reduced (red) valence states.

Table 4. Variation of Generalized Coulson BondOrders overtheOxidized and Reduced [2Fe]HModel Complexes Studieda

bond functional variance low high

Feprox�Cfp SVWN5 1.18 �0.118 (IIIo) 2.82 (Io)

PBE 1.23 �0.125 (IIIo) 2.87 (Io)

TPSS 1.30 �0.156 (IIIo) 2.91 (Io)

PBEh 1.49 �0.255 (IIIo) 2.94 (Io)

Feprox�Cbr SVWN5 0.101 �0.179 (VIo) 0.814 (IVo)

PBE 0.103 �0.191 (VIo) 0.819 (IVo)

TPSS 0.110 �0.217 (VIo) 0.820 (IVo)

PBEh 0.138 �0.340 (VIo) 0.789 (IIo)

Feprox�SrDTMA SVWN5 0.184 �1.101 (VIo) 0.272 (IIIo)

PBE 0.198 �1.125 (VIo) 0.295 (IIIo)

TPSS 0.219 �1.149 (VIo) 0.345 (IIIo)

PBEh 0.272 �1.187 (VIo) 0.424 (IIIo)

Fedist�Cbr SVWN5 0.246 �0.790 (IVr) 0.854 (VIo)

PBE 0.244 �0.798 (IVr) 0.837 (VIo)

TPSS 0.242 �0.805 (IVr) 0.820 (VIo)

PBEh 0.212 �0.773 (IVr) 0.661 (VIo)

Fedist�Crd SVWN5 1.458 �0.255 (IVr) 3.08 (IVo)

PBE 1.479 �0.256 (IVr) 3.08 (IVo)

TPSS 1.546 �0.276 (IVr) 3.15 (IVo)

PBEh 1.643 �0.368 (IVr) 3.16 (IVo)

Fedist�SfDTMA SVWN5 0.251 �1.189 (IIo) 0.170 (VIr)

PBE 0.263 �1.202 (IIo) 0.182 (VIr)

TPSS 0.273 �1.218 (IIo) 0.189 (VIr)

PBEh 0.320 �1.244 (IIo) 0.243 (VIr)aBonds are grouped and ordered within each group by functional class(LSDA, GGA, meta-GGA, and hybrid). Extreme values populated bymodel VI are shaded.



antisymmetrically as such features would over time in the contextof vibration. By thinking of the resulting principal components asa sort of “pseudovibration”, one can discern the main changesresulting over the set of perturbations considered.For the oxidized models, the selected variation of diatomic

ligands here primarily affected the Fedist�water bond length,easily seen by the dissociation or near-dissociation of this ligandin themodels, and the associated variance in interatomic distance.The largest effects of configurational changes (oxidized PC2 andreduced PC1) within the H-cluster core are negative covariancebetween the two bridging Fe- carbonyl bonds and between eachsuch bond and its matching terminal diatomic ligands, whichimplies an anticorrelation between the proximal and distal endsof the cluster. Thus, a trans configuration should balance thedisposition of the bridging carbonyl between the two iron ions,relative to a geminal cyanide configuration. A second but lessdominant variation is the anticorrelation specifically between theproximal diatomic ligands (PC3), created by the interaction ofmodels III and VI. That this variation presents in isolation of therest of the H-cluster suggests minimal impact of a cis versus atrans cyanide configuration on the cluster bond lengths, and thuspotentially on function. A more dominant pattern, seen only inthe reduced cluster models (reduced PC2), is a positive correla-tion between the two bridging Fe-carbonyl bonds, negativelycorrelated with the terminal bonds. This variance might best beexplained by the all-cyanide and all-carbonyl models (I and II),suggesting that thesemodelsmight increase or decrease the bridgingcarbonyl interaction with both irons relative to the trans configura-tion. One might thus speculate that the trans-cyano (or cis-cyano)configuration modulates the overall bridging carbonyl interaction.Angular covariations for the oxidized complex all contain a

significant component from water; since this ligand dissociates inseveral models, there is ambiguity as to whether the angularvariation of the water correlates with such variation in the rest ofthe complex, or with bond dissociation—to establish this, a PCAwould need to include both bonds and angles in the data vector,which was not done here. Nonetheless, one can observe struc-tural communication within the cluster separately from its cause.PC1 is dominated by water itself, as was true for the bond lengthanalysis. Both PC2 and PC3 show anticorrelation between thebridging carbonyl Fe�C�O angles, as expected for changes inbonding to each iron—as Feprox/dist�Cbr bonding gets stronger,the Fe�C�O angle should linearize at the expense of the angleinvolving the weakening Fedist/prox�Cbr bond. The other notablechanges in PCs 2 and 3 for the oxidized models are simplyopening and closing of the Fe-diatomic ligand geometry as thebridging carbonyl changes. In PC2, positive correlation amongCrd�Fedist�Feprox, Feprox�Fedist�Cbr, and Fedist�Cbr�Obr

angles show an increase in angles as the bridging carbonyl bonds toFedist and decreases as it favors Feprox. PC3 illustrates similarchanges involving Cfd, and a movement of the proximal diatomicligands away from CObr as it bonds to Feprox. For the reducedmodels, PC1 shows similar covariance between angles of thebridging carbonyl and the terminal diatomic ligands around iron.The remaining two PCs show much more distributed changes,including motion of hydrogens in the bridging DTMA ligand.Given the more delocalized changes, it is difficult to pick outsignificant features, but variation of theHFe�Fedist�Feprox anglewith CObr angles is clearly visible in PC2.The relationship of the angular changes to the trans config-

uration is not clear directly. However, the pattern that emerges isthe covariation of the bridging carbonyl disposition with

diatomic ligand changes, as was also the case for the bond lengthanalysis above. Analysis of the angular changes therefore reinforcesthe above conclusions regarding the potential import of thenatural trans-cyanide, or the cis-cyanide, configurations in mod-ulating interaction of the bridging H-cluster carbonyl ligand.Charges.The NPA atomic charges presented in Table 2 bring

several points to light. Charge estimates are largely invariant tothe choice of density functional; considering the range of physicalmodels for electron correlation sampled over LSDA, GGA, GGAhybrid, and meta-GGA, this provides us with some confidence inthe results of the charge analysis. Water does not donate oraccept significant charge in the oxidized complexes, consistentwith a relatively weak bond. One-electron reduction and additionof a proton lead to a terminally bound hydrogen atom; in otherwords, this proton does not pull out more charge than is addedin the reduction process. Although the charge is conceptuallyconsistent with a hydrogen atom, this should not be interpretedas endorsement of a one-electron mechanism in subsequent H2

formation steps; rather, with the pendant [4Fe4S] cluster in itsreduced state, an additional proton will cause a substantial chargerearrangement as the H�H bond is formed. The negativelycharged DTMA sulfur ligands transfer most of their formal chargeinto the iron core, and the cyanides in the dicyano complexestransfer slightly more than one charge equivalent into the core.TheDTMA and diatomic ligand groups also seem to compensateone another, in that changes to the diatomic ligand configurationthat decrease the charge carried by this group lead to a matchingincrease in charge on the DTMA ligand and vice versa. Thefunctional significance of maintaining constant charge elsewherein the H-cluster complex through this push�pull behavior isunclear from charge analysis alone. Nevertheless, an enticingspeculation is that polarizability that maintains a more or lesscontant charge on the iron core would stabilize the catalyticredox cycle against stochastic variations in the immediate proteinenvironment associated with thermal motion.Reduction, although not changing the overall complex charge,

leads to a counterintuitive charge flow into the cluster core fromthe methylthiol, DTMA, and diatomic ligands, together withgreater negative charge on the distal iron and greater positivecharge on the bridging carbonyl. All other things equal, there willthus be a greater ionic attraction between the bridging carbonyland the distal iron upon cluster reduction. Examination ofCoulson bond order changes upon reduction in the natural transconfiguration VI (discussed further below) highlight a decreasedinteraction between Fedist and CObr, in contrast with the short-ening of the Fedist�Cbr bond length. Taken together, thisselection of computational data implies a predominantly ionicinteraction between the distal iron and the bridging carbonyl, atleast in the reduced state, that simultaneously shortens the bondwhile decreasing the covalent interaction.HOMO and LUMO Energies. With respect to distinguishing

the functional significance of the natural trans-cyano configura-tion from other possible variants, the frontier orbital energies arethe most telling. Models I and II differ from the natural con-figuration not only in the nature of the diatomic ligand heteroa-toms but in two charge units as well. Even in a polar solventmodel, this change in overall charge leads to substantial changesin orbital energies, with additional negative charge pushingorbital energies up and a charge deficit pushing them down byabout 0.05 Ha (31.4 kcal/mol, 1.36 eV). A similar result waspreviously found for the all-carbonyl model in the context of thefull [2Fe]H�[4Fe4S]H cluster model, where the energy decrease



of orbitals localized on the [2Fe]H cluster led to localizationof the [2Fe]H�[4Fe4S]H HOMO on the cubane cluster.75

A clustering on the order of 0.02 Ha (12.5 kcal/mol, 0.5 eV) inmagnitude is also seen between model pairs IV/V and III/VI.Thus, poising the redox potential of the cluster at a value nearthat found for the trans-cyano configuration rules out ligandconfigurations with more or less overall charge, as well as animbalanced cyanide distribution on one or the other iron ion.However, the distinctions between models III and VI are muchsmaller, on the order of 0.003 Ha (2 kcal/mol, 0.08 ev), leavingthe relative arrangement of cyanide groups with respect to theH-cluster bisecting plane potentially dictated by interests otherthan first-order H2 oxidation/reduction chemistry. In fact, to theextent that the bridging carbonyl can dissociate from Feproxduring catalysis and a pseudorotation occur to exchange the twocarbonyl ligands, this symmetry betweenmodels III andVI couldbe a catalytic asset. Binding of 13CO to the open distal siteconcomitant with photodissociation leads to complete exchangeof the distal terminal and bridging carbonyl ligands with theisotopically labeled pool under turnover conditions.76 This processcould dynamically exchange cis- and trans-cyanide conformations,although thermodynamic stability in the active site may ultimatelydictate a higher statistical occupancy of the trans configuration.Bond Orders. The original intent of analyzing H-cluster bond

orders over the sampled set of models herein was to determine ifthere existed one or more bonds whose orders best distinguishedthe trans configuration from alternatives. To this end, theCoulson bond order provided the largest variance among thecomplexes, while showing systematic clustering with respect tobond, density functional, and complex. The definition of thisbonding metric is simply the sum of density matrix elementsbetween NAOs belonging to the two atoms in question and soreflects the contribution of the respective orbital coefficients to thebond, irrespective of the overlap between the orbital functionsthemselves. The values thus derived range over positive and negativevalues and can deviate from chemical intuition. Nevertheless, fordetermining qualitative bonding changes of comparable bondsacross molecules or redox states with very similar geometries, theirsimplicity of definition is an advantage, avoiding averaging processessuch as squaring or weighting by overlaps intrinsic to other metrics.The largest variances over the models are seen in the

Feprox�Cfp and Fedist�Crd bond orders, independent of thedensity functional used. As laid out in Table 4, the range of theformer bond is established by oxidized model III (cis-cyano) onthe antibonding extreme and oxidized model I (all-cyano) on thebonding end. Interestingly, the bond orders are clustered, withmodels I and VI having orders near 3; II and IV near 0.5; and IIIand V slightly negative. Although chemical interpretation of thismetric is unclear, the extreme values present for the Feprox�Cfp

and Fedist�Crd bonds and absent for the others implies a specificcorrelation in signs of density matrix elements for these twobonds. Whether this arises from an artifact of the phase relation-ships in the Gaussian or NAO basis or has some chemicalsignficance is not clear. However, analysis of the other metricsshows Fedist�Crd in model IVo to have the minimum value of thesix oxidized complexes, and Vo the maximum, suggesting thisbond is most affected by the geminal displacement of the cyanoligands (data not shown). In short, although the Coulson metricshows substantial variance for these two bonds, its ability todistinguish these complexes generally in a manner suggestive ofchemical signficance will require deeper analysis outside thescope of the present report.

With respect to specifically distinguishing the natural config-uration VI, it shows some extremes of bond order with respect tothe studied set of complexes. In VIo the interactions between theproximal iron and both the bridging carbonyl and the rearDTMA sulfur atom are the most antibonding of the 12 com-plexes studied, while interaction between the distal iron and thebridging carbonyl is maximally bonding. The observation thatthe Feprox�SrDTMA link is highly antibonding, which would seemto contradict the argument above that this bond contributes tocomplex stabilization, illustrates a shortcoming of the Coulsondefinition—if the signs of the preorthogonal overlap (the PNAOproduct) and the density matrix elements (the expansioncoefficients) of two NAOs have the same sign, the net resultwill be a bonding interaction, as the AAOWNAObonding metriccaptures (see Scheme 1). In fact, the Wiberg, AAOWNAO, andNLMONPA bond orders averaged over functional and valencestate for Feprox�SrDTMA are 0.4, 0.3, and 0.5, respectively,consistent with a net bonding interaction. Upon reduction,model VI yields the strongest bonding between the distal ironand the front DTMA sulfur. In sum, the bonding data distinguishtwo potential features of importance: the donor�acceptorDTMA S�Fe�C(O) interactions which might be distinctivelystrong in the trans model VI and the Fe�Cbr bonding thatappears to be most and least covalent in the oxidized state forFedist and Feprox, respectively.

’CONCLUSIONS

The diatomic carbonyl and cyanide terminal ligand configura-tion of the natural H-cluster exhibits several features potentiallyimportant for catalysis. First, a uniform composition of terminalligands would likely move the reactive frontier orbitals out of theenergy bracket useful for H2 oxidation/proton reduction cata-lysis. Second, a geminal disposition of cyanide ligands wouldresult in a strong favoring of bridging carbonyl binding to thecyanide-bound iron, thereby overwhelming any modulatingeffect the carbonyl ligand has on the reaction mechanism. Third,the similarity in frontier orbital energies of cis- and trans-cyanoconfigurations could potentially benefit enzymatic stability bypreserving catalytic function upon either adventitious or mecha-nism-based exchange of the bridging and terminal distal carbonylligands through pseudorotation. The nearly constant chargetransfer from the combined DTMA and terminal diatomic ligandcomplement across the configurations studied points to polariz-ability and charge buffering in the iron core as a potentialadvantage in the design of H2-producing catalysts. Aside fromenzymatic hydrogen bonding patterns, the trans-cyano config-uration is nonetheless distinguished from the cis configuration bytwo individual trans donor�metal�acceptor S�Fe�C(O) in-teractions, which could stabilize the diatomic ligand arrangementobserved over the alternative. Thiolate ligands are known toexhibit moderate trans effects through π-donation, whereascarbonyls are strong π-acceptors.77 Configuration VI thus offersopportunity for strong S�Fe�C orbital mixing, enforcing a low-spin state on Fe which has been rationalized to lower transition-state energies for H2 heterolysis in NiFe hydrogenases78 andsimilarly for H2 formation in [FeFe] hydrogenases by proton-ation of the reduced H-cluster. Finally, contrary to expectationsthat stronger carbonyl binding to iron is associated with chargedelocalization and π-back-bonding, bonding and charge analysesshow increased Fe�CObr bonding correlates with an increase inionicity and decreased covalency, suggesting that any stabilization of



charge accumulation on the terminal iron atom of the H-clusterduring the proton reduction reaction is primarily electrostatic inorigin. To the degree that further study validates this observa-tion, catalyst designs may benefit from including this chemicalstrategy.

’ASSOCIATED CONTENT

bS Supporting Information. Tables listing principal com-ponents for dihedral angles of both oxidized and reduced modelcomplexes and ranked variances over the 12 model complexes.This material is available free of charge via the Internet at http://pubs.acs.org.

’ACKNOWLEDGMENT

This work was supported by the Chemical Sciences, Geosciencesand Biosciences Division, Office of Basic Energy Sciences, Office ofScience, U.S. Department of Energy underContractNo. DE-AC36-08GO28308. This research used resources of the National EnergyResearch Scientific Computing Center, which is supported by theOffice of Science of the U.S. Department of Energy under ContractNo. DE-AC02-05CH11231.

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Computational Chemical Analysis of [FeFe] Hydrogenase H-Cluster Analogues To Discern Catalytically Relevant Features of the Natural Diatomic Ligand Configuration