Israel Journal of Chemistry Vol. 41 2001 pp. 173–186

*Authors to whom correspondence should be addressed. E-mail:rich@chem.columbia.edu, lippard@lippard.mit.edu

Theoretical Studies of Diiron(II) Complexes that Model Features of theDioxygen-Activating Centers in Non-Heme Diiron Enzymes

MU-HYUN BAIK,a DONGWHAN LEE,b RICHARD A. FRIESNER,*,a AND STEPHEN J. LIPPARD*,b

aDepartment of Chemistry and Center for Biomolecular Simulation, Columbia University, New York, New York 10027, USAbDepartment of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

(Received 11 February 2002)

Abstract. We have applied high-level Density Functional Theory to investigatethe properties of recently characterized carboxylate-bridged diiron(II) complexessupported by 2,6-di(p-tolyl)benzoate (ArTolCO

2–) ligands. These compounds, pre-

pared as synthetic models for the reduced non-heme diiron centers in the enzymesMMO, RNR-R2, and ∆9D, reproduce the composition of the first coordinationsphere ligands as well as the core geometry. The experimentally observed flexibilityof the diiron cores in the model compounds, a main design target, was confirmedcomputationally. Details of a possible interconversion mechanism that transformsquadruply and doubly carboxylate-bridged isomers of [Fe

2(ArTolCO

2)

4L

2],

L = pyridine or related ligand, were examined. The orientation of the pyridineligands plays a major role and promotes an initial carboxylate shift of the bridgingcarboxylate ligand that is orthogonal to the pyridine ring plane. Alternative mecha-nisms were explored and evaluated. Structural features of the strongly coupleddiiron centers could only be reproduced reliably by using the experimentally deter-mined antiferromagnetic spin-coupling properties of the high-spin d6 iron(II) cen-ters. Use of the ferromagnetic-coupling scheme gave rise to a poor correlation of thecomputed structure with the experiment. The broken-symmetry orbitals required todescribe the antiferromagnetic coupling are compared to the MOs as classicalsymmetry-adapted linear combinations of atomic orbitals that form the basis for themagnetic coupling scheme. The molecular orbitals responsible for the dependence ofthe structural results on spin coupling were identified and used to evolve an intuitiveexplanation for the structural differences observed.

1. INTRODUCTIONCarboxylate-bridged diiron centers occur in the activesites of selected enzymes that bind and activate dioxygen.1

The hydroxylase component of soluble methanemonooxygenase (MMOH),2 the R2 subunit of class Iribonucleotide reductase (RNR-R2),3 and stearoyl-acylcarrier protein (ACP) ∆9 desaturase (∆9D)4 commonlyutilize four carboxylate and two histidine groups to sup-port non-heme diiron units. In catalytic cycles of theseenzymes, sequential reduction of dioxygen-derivedligands bound to iron affords high-valent Fe(IV) speciesthat activate either C–H or O–H bonds.3b,5 Efforts involv-ing both direct studies of the enzymes themselves andinvestigations of small-molecule synthetic surrogateshave been undertaken to elucidate the molecular details ofbiological O2 and C–H/O–H activation.

Previously, we6 and others7 demonstrated that steri-

cally hindered, m-terphenyl-derived carboxylateligands can be used to reproduce the primary coordina-tion sphere composition of MMOH, RNR-R2, and ∆9Dwithin a non-peptidyl framework. Specifically, 2,6-di-(p-tolyl)benzoate (ArTolCO2

–) can support the quadru-ply-bridged paddlewheel diiron(II) complex [Fe2(µ-O2CArTol)4(4-tBuC5H4N)2] (1) (Scheme 1),6b which insolution can rearrange to a doubly-bridged windmillisomer having the structure of the pyridine analogue[Fe2(µ-O2CArTol)2(O2CArTol)2(C5H5N)2] (2).6a,8 Struc-tural characterization of 2 in the solid state revealed thearchitectural resemblance of its diiron core to that of thebiological counterparts.6a Dioxygen activation by both 1and 2 further substantiated the functional relevance ofthese biomimetic constructs.6a,b,9

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The geometric flexibility of the diiron core and itsability to form a structure with open coordination sitesfor dioxygen binding are crucial requirements for aninorganic model complex designed to mimic the cata-lytic activity of the metalloenzymes. In addition to syn-thetic modeling efforts, recent computational studiesmostly based on Density Functional Theory (DFT)10

have provided important clues about the mechanism ofdioxygen binding and activation in metalloenzymes.11

The starting point for most quantum mechanical studiesis geometry optimizations that provide valuable struc-tural and thermodynamic data, which are difficult toobtain experimentally. Inorganic chemists have for de-cades utilized molecular orbital theory to understandand predict the electronic structure, reactivity, and spec-troscopic properties of a molecule. The use of ligand-field and group theory12 to derive semiquantitative MOdiagrams of transition metal complexes is a standardtopic within the inorganic curriculum today. Thus, it isnot surprising that the community has embraced recentadvances in high-level computational methods, such asDFT, that afford a powerful quantitative basis for mo-lecular orbital analyses in addition to thermodynamicand structural information. From an inorganic chemist’sviewpoint, the most interesting molecular orbitals in atransition metal complex are those dominated by thefive d-orbitals of the metal center that usually form thenon-bonding or metal–ligand antibonding frontierorbitals.13 Although the basic orbital energy scheme, thenature of the frontier orbitals, and the manner in whichthey control reactivity for a given structure are well-characterized for many organometallic systems,13,14 sys-tematic studies of molecular orbitals in the carboxylate-bridged diiron assemblies commonly found in dioxygen-activating metalloenzymes are rare in the literature.15

Knowledge of the most important and characteristicmolecular orbitals in these systems is challenging toobtain because the metal centers often display antiferro-magnetic (AF) coupling,1 which requires non-standardcomputational techniques.16

In this paper, we present a state-of-the-art theoretical

characterization of the different structural motifs en-countered in the new class of paddlewheel (1) and wind-mill (2) iron(II) dimers illustrated in Scheme 1. We sys-tematically compare the traditional molecular orbitals assymmetry-adapted linear combinations (SALCs) ofatomic orbitals12 with the broken-symmetry (BS) orbitals16

that are required for a correct description of the AF cou-pling. Similar studies are being conducted in our laborato-ries on computational models of key intermediates in thecatalytic cycle of MMOH in its native peptidyl environ-ment.11a,b Taken together, this detailed computationalwork will form the basis for a novel approach to identifythe most important molecular orbitals dictating the reac-tivity of the complex. This information will in turn providelogical pathways for tuning the energies and compositionof these orbitals to enhance the desired properties in newtarget synthetic model complexes.

2. COMPUTATIONAL DETAILSAll calculations were carried out using DFT as imple-mented in the Jaguar 4.1 suite17 of ab initio quantumchemistry programs. Geometry optimizations were per-formed with the B3LYP18 functional and the 6-31G**basis set where iron is represented using the Los AlamosLACVP** basis19 that includes relativistic effectivecore potentials. The energies of the optimized structuresare reevaluated by additional single point calculationson each optimized geometry using Dunning’s20 correla-tion-consistent triple-ζ basis set cc-pVTZ(-f) that includesa double set of polarization functions. For iron we used amodified version of the LACVP**, designated asLACV3P**, where the exponents were decontracted tomatch the effective core potential with the triple-ζ qualitybasis. All calculations were carried out without invokingsymmetry to ensure a fully flexible optimization.

One of the characteristic properties of the diironcomplexes investigated previously is the AF coupling ofunpaired electrons on the metal centers, also establishedfor the corresponding metalloenzyme cores in RNR-R2and ∆9D. In principle, multi-reference methods such asCASSCF are required to describe rigorously an AF-coupled spin-state of the dimer, which is impracticablefor systems of this size because of computational de-mands. In practice, Noodleman’s broken-symmetry(BS) approach, which makes use of the Heisenberg spinoperator formalism to obtain a reasonable electronicstructure description of transition metal dimers, has pro-vided a working protocol for single reference methodssuch as DFT employing the unrestricted spinformalism.11a–i We closely followed the protocol de-scribed elsewhere11a to obtain the BS orbitals and usedthe unrestricted spin formalism in all calculations. Es-sentially, the valence bond descriptions of the molecules

Scheme 1. Fe(II)–Fe(II) dimers that have been preparedand structurally characterized by single-crystal X-raycrystallography.6a,b

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were used as initial guesses to generate a molecularwavefunction in terms of localized orbitals that undergothe SCF procedure. The large number of unpaired elec-trons at the iron core and the intrinsic electronic flexibil-ity of the transition metals give rise to a number ofenergetically similar electronic states. Therefore, weused spin densities derived from Mulliken populationanalysis that have also been employed in many previousstudies11 to confirm that the correct, or at least a reason-able, electronic state had been reproduced.

3. OVERVIEWA commonly used benchmark for the accuracy of com-putational results is the comparison of the optimizedmolecular structure with the experimental one. Figure 1depicts the experimentally determined solid-state struc-ture of the paddlewheel isomer 1.6b Ideally, the compu-tational model should match the experimental chemicalcomposition. The size of the complex 1 (208 atoms) ispresently beyond that possible for extensive high-levelDFT calculations. Thus, it was necessary to choose asmaller model system that captures the most salientelectronic and structural features. A straightforwardstrategy was to replace the ArTol portion of the ArTolCO2

–

ligand with a methyl group, giving the computationalmodel systems 1-Me and 2-Me (Scheme 2), which wereused throughout the study. In the first part of our discus-sion, we present computed structures and energies ofobservable and nonobservable isomers of the iron dimerto obtain an in-depth description of the flexibility of thediiron core. The second part of the discussion is dedi-cated to the electronic structure of 1-Me. The iron atomsin both dimers are formally high-spin d6 Fe(II) centers,the unpaired electrons of which are AF coupled. Inprevious work on similar systems, ferromagnetic (F)spin-coupling has been often assumed11j–p,15 to avoid com-plications and technical difficulties associated with the

BS orbital approach. We performed two sets of calcula-tions assuming both F and AF spin-coupling. The BSorbital approach gave rise to localized molecular orbit-als that are less familiar. Thus, we explored the resultsof the F-coupled calculations, which gave familiar mo-lecular orbitals as SALCs of the atomic orbitals, as aguide to derive an intuitive understanding of the BSorbitals. The importance of using the correct spin-cou-pling to compute accurately the structure and energiesof this class of molecules has been demonstratedpreviously.11a,b,16 An intuitive understanding aboutwhich features of the BS orbitals dictate the differentstructure and reactivity properties of the molecule hasthus far been unavailable, however. We derive a basicunderstanding of the iron dimers studied here by sys-tematically comparing the molecular orbitals of the AF-coupled system to that of the F-coupled dimer.

4. STRUCTURES AND ENERGIES

Optimized StructuresTable 1 summarizes key features of the fully opti-

mized geometries using both ferromagnetic (S = 4) andantiferromagnetic (S = 0) spin-coupling between theiron centers. AF spin-coupling notably improved theagreement between theory and experiment. The com-puted iron···iron distance of 2.854 Å in the AF-coupledmodel 1-Me compares favorably with a distance of2.8229(9) Å found experimentally, whereas 2.697 Å ispredicted when ferromagnetic spin-coupling is used.The ferromagnetic coupling overestimates the through-space interaction between the iron centers (vide infra).

The basic structures of 1-Me and 2-Me have ap-proximate D2d and C2h symmetry, respectively, if themethyl groups are neglected. Thus, it is sufficient toexamine the geometry around one iron center. The opti-mized structure of the AF-coupled model 1-Me sug-gests that the four iron–oxygen bonds are not chemi-cally equivalent, as observed experimentally. In thesolid-state structure, the Fe1–O11 and Fe1–O13 dis-tances are, on average, 0.11 Å shorter than the Fe1–O12and Fe1–O14 bonds. The N1–Fe1–O angles also differin an approximately pairwise manner, the shorter Fe–Obonds being accompanied by larger N1–Fe1–O angles.

Scheme 2. Computational models used in this study.

Fig. 1. Visualization of the solid-state structure of [Fe2(µ-O2CArTol)4(4-tBuC5H4N)2]. Two views of the same molecule,related by a 90° rotation around the y-axis, are shown. Thering-carbon atoms of the pyridine ligands are shown as balls.Hydrogen atoms are removed for clarity.

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The angles N1–Fe1–O11 and N1–Fe1–O13 are 102.6°and 102.5°, respectively, whereas smaller angles of98.8° and 93.4° are measured for N1–Fe1–O12 and N1–Fe1–O14, respectively. These Fe–O bond differencesare reliably reproduced in our AF-coupled calculation(Table 1), suggesting that the different characters of theFe–O bonds reflect electronic control by the orientationof the pyridine ligands rather than steric effects imposedby the bulky ArTolCO2

– group. The carboxylate unit in-

teracts more strongly with the metal center in the or-thogonal orientation with respect to the pyridine ligandthan in the coplanar arrangement, as indicated by theshorter bond lengths. The excellent agreement betweenthe model system 1-Me and 1 further indicates that thediiron core in the latter is electronically fully relaxed.That is, the sterically demanding ArTol group does notintroduce significant strain into the diiron core.

Although the F-coupled model of 1-Me gives reason-

Table 1. Optimized structural parameters of the diiron core for the different computational models

1-Me 1-Me 1 2-Me 2-Me 2calc. calc. exp.6b calc. calc. exp6a

spin-coupling F AF AF F AF AFFe···Fe 2.697 2.854 2.823 4.035 4.002 4.220Fe1–O11 2.060 2.030 2.028 2.025 2.030 2.005Fe1–O12 2.051 2.135 2.136 2.081 2.063 2.047Fe1–O13 2.045 2.030 2.031 1.986 1.988 1.957Fe1–O14 2.071 2.135 2.144 — — —Fe1–O22 — — — 2.285 2.268 2.359Fe1–N1 2.270 2.182 2.105 2.175 2.197 2.131angle N1-Fe1-O11 97.0 104.9 102.6 97.2 96.3 98.7angle N1-Fe1-O12 94.7 92.6 98.8 91.6 91.6 90.0angle N1-Fe1-O13 103.0 104.5 102.5 99.9 98.9 96.3angle N1-Fe1-O14 90.4 92.7 93.4 — — —spin-densitiesa Fe1 2.97 3.76 3.79 3.80spin-densitiesa Fe2 2.96 –3.76 3.76 –3.80relative energiesb 19.45 0.00 9.06 9.52

aMulliken spin-density.bThe relative energies (kcal mol–1) are referenced to the AF-coupled model 1-Me.

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able Fe–O distances, averaging 2.067 Å compared to theexperimental average of 2.085 Å, the subtle detail of theapparent Fe–O distance dependence on the orientationof the pyridine ligand is not correctly reproduced. TheF-coupled model predicts essentially equal Fe–O dis-tances of 2.060 Å, 2.051 Å, 2.045 Å, and 2.071 Å. Atleast two structural features are not modeled properly in1-Me, regardless of the spin-coupling scheme em-ployed. One is that the Fe–N bond lengths are overesti-mated by 0.077 Å and 0.165 Å in the AF- and F-coupledmodels, respectively. The other is that the twist of theCO2

– group with respect to the Fe–Fe vector (Fig. 1) isnot reproduced in the simple methyl model. The car-boxylate bridges are orientated parallel to the iron–ironvector in the computational model. When we increasedthe model size by using a phenyl instead of the methylcap, we observed the same effect. Only a m-xylyl-CO2

– (2,6-dimethylbenzoate), a 104-atom model, gavethe experimentally observed twist. These exploratorycalculations on larger model systems, however, did notindicate a substantial enough electronic change to jus-tify the considerable increase in computational cost. Thecomputed energy of the AF-coupled model is 19.45 kcalmol-1 lower than that of the F-coupled model. Althougha substantial energy difference between the AF- andF-coupled models is anticipated from the experimen-tally observed strong coupling, this difference is toolarge for a corresponding AF/F pair in a Heisenberg spinHamiltonian treatment. Notable differences in opti-mized structures, discussed above, similarly cast doubton the complementary nature of the two species. Lastly,whereas the Mulliken spin densities of +3.76/–3.76 forthe AF-coupled model 1-Me are fully consistent withFe(II) centers, we were thus far unable to converge to anelectronic state for the F-coupled case with expectedMulliken spin density of approximately 3.5–4.0. Takentogether, these results indicate that the assumption ofparallel spin orientation of unpaired electrons on theiron centers in 1-Me consistently affords a very differ-ent electronic state for the paddlewheel structure thandoes the AF-coupled model.

The solid-state structure of the doubly-bridged wind-mill structure 26a shows an iron···iron separation of4.219(1) Å. Our calculations underestimate theiron···iron distance by 0.218 Å and 0.185 Å in the AF-coupled and F-coupled models, respectively. Theiron···iron distance is a poor benchmark for the qualityof the calculation, however, because there is no directelectron density overlap between the two iron centersand the distance is governed by the angles at the bridg-ing ligands. Thus, the potential energy surface along theiron–iron vector is expected to be very flat (vide infra).In addition, the steric demands of the ArTol groups will

play a more pronounced role, as the orientation of theArTolCO2

– ligands in the crystal structure suggests(Fig. 2).6a Thus, the structure of the computationalmodel 2-Me is expected to differ from that determinedexperimentally for 2. The solid-state structure indicatesthat the Fe–O bonds of the bridging carboxylate ligands,Fe1–O11 and Fe1–O13, become slightly shorter by anaverage of 0.05 Å, whereas a more pronounced contrac-tion of 0.09 Å is observed for Fe1–O12 compared to thatin the structure of 1. The calculated structural featuresare in fair agreement with the experimental data, with theexception of the length of the newly formed Fe1–O22bond, which is underestimated by 0.09 Å and 0.07 Å inthe AF- and F-coupled models, respectively. As theillustration of the experimental solid-state structure(Fig. 2) demonstrates, this result is most likely a stericconsequence of the ArTol moiety. Unlike the situation in1, the ArTol group forces a notable overall expansion ofthe diiron core from the theoretically most relaxed struc-ture of the bare diiron core composition.

Both AF- and F-coupled models give essentially thesame structure for 2-Me, which is a clear reflection ofthe very weak coupling between the metal centers. Thedifferential effect on the Fe–O bonds observed for 1-Meis not present in 2-Me. The calculations actually gave aslightly lower energy for the F-coupled model of 2-Me(Table 1). The energy difference of 0.5 kcal mol–1 thathas been computed for the AF- and F-coupled models of2-Me, however, is below the usual noise level of theB3LYP method and not physically meaningful. For all

Fig. 2. Solid-state structure of 2 generated using the crystallo-graphic coordinates.6a For clarity, the tolyl moieties of thebridging ArTolCO2

– ligands and all hydrogen atoms are notshown.

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practical purposes, the AF- and F-coupled cases can beconsidered isoenergetic, which is again in good agree-ment with the very weak spin-coupling observed experi-mentally.8 Unlike in 1-Me, the Mulliken spin densitiesare consistent with Fe(II) centers regardless of the spin-coupling scheme used.

Structural IsomersA comparison of our model 2-Me (Table 1) with the

crystal structure of 2 (Fig. 2) reveals that the pyridineligand orientation is different. Whereas the crystal struc-ture reveals a nearly orthogonal arrangement of bothpyridine rings to the plane formed by the metal centersand their respective terminal carboxylate ligands, thelowest energy structure computed indicates a nearly co-planar orientation. To obtain a more quantitative picture ofthe structure–energy relationship between possible iso-mers, we conducted geometry optimization on the mostfeasible isomers of both 1-Me and 2-Me. The results aresummarized in Fig. 3, using the overall lowest energyspecies, the AF-coupled 1-Me, as the zero-point for therelative energy scale. Overall, the three AF-coupledisomers considered for each structural motif, respec-tively, span a range of only 3 kcal mol–1, demonstratingthe electronic compatibility of the diiron core structure

with respect to pyridine orientation. It is somewhat sur-prising that the more open doubly-bridged core arrange-ment does not lead to even greater compatibility andsmaller isomeric energy range. The pyridine arrangementfound in the crystal structure of 2, labeled as 2o-Me inFig. 3, is 3 kcal mol–1 higher in energy than 2-Me. Thus,unlike the situation in 1, the pyridine orientation foundin the solid-state structure of 2 is not electronicallyfavored, but is most likely enforced by the steric demandsof the ArTolCO2

– ligand. In the third isomer considered, 2’-Me, which is isoenergetic with 2-Me, the pyridine ligandsare oriented perpendicular to one another. The chemicaldifference of the Fe–O bonds in 1-Me discussed above asa function of the pyridine ligand orientation makes clearthat there must be an isomeric form where the Fe–Obonds are mismatched, that is, a structure where Fe1–O11is longer than Fe1–O12. This iron–oxygen bond-mis-matched isomer is shown as 1’-Me in Fig. 3 and is 3 kcalmol–1 higher in energy than 1-Me. The product of a 90°rotation of one pyridine ligand around the iron–iron vec-tor, isomer 1h-Me, is 1.9 kcal mol–1 higher in energy than1-Me. This relative energy profile with small energydifference between the isomers suggests that under real-istic conditions, any one of the isomers is accessible anddemonstrates the flexibility of the diiron core structure.

Fig. 3. Relative energies of fully optimized structural isomers of 1-Me and 2-Me. Hydrogen atoms are not shown, for clarity. Fand AF denote ferromagnetic and antiferromagnetic spin-coupling between the iron centers, respectively. The AF-coupled 1-Mewas chosen as the reference zero-point for the relative energy scale.

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Carboxylate ShiftsWith the structure–energy relationship described

above, it is easy to understand the transformation be-tween isomers that involves rotation of the pyridinerings around the iron–iron vector. Interconversion of thepaddlewheel and windmill motifs, required to achievethe architecture suitable for subsequent dioxygen coor-dination, is more difficult to envision, however. In thefollowing discussion, we examine possible pathwaysfor such a transformation. Starting from the lowest en-ergy isomer of 1-Me with the pyridine ligands orthogo-nal to one another, two reaction pathways were exam-ined that would allow interconversion between 1-Meand 2-Me, depending on which of the Fe–O bonds iscleaved first. Intuitively, one would predict that theweakest bond will break first, which would lead to thereaction path shown as Path-a in Fig. 4. Another possi-bility is to break the shorter Fe–O bond first, labeled asPath-b in Fig. 4. The initial carboxylate shift would thenbe followed by a subsequent shift of the second car-boxylate.

To probe these carboxylate-shift reaction pathways,we carried out a series of calculations where theiron···iron distance was reduced in 0.1 Å steps from3.9 Å to 2.9 Å,21 freezing the iron···iron distance and

fully reoptimizing the rest of the molecule. Both thestepwise Fe···Fe distance elongation starting from 1-Meand the Fe···Fe distance contraction starting from 2-Mewere probed. This approach is commonly known as thelinear transit method. Although this approach does notoffer a conclusive evaluation of the true transformationmechanism, it provides an interesting comparison of thetwo reaction pathways. The relative energy profiles ofthe linear transition scans are shown in Fig. 5. Thelowest energy transformation (open circles and solidline) involves cleavage of the initially shorter Fe–Obond. This Fe–O bond, which is orthogonal to the pyri-dine, breaks at the approximate transition state denotedTS-1, in which the iron···iron distance is 3.4 Å. There isa relatively small differential energy despite significantiron···iron distance changes close to both equilibriumstructures 1-Me and 2-Me. This result illustrates the flatpotential energy surface that has been mentioned fre-quently in the literature for similar systems.11 The doubly-bridged windmill structure displays an extremely flatpotential energy surface and a very small activationbarrier of 1.8 kcal mol–1 for the carboxylate shift towardsthe quadruply-bridged paddlewheel structure that corre-sponds to an overall iron···iron distance distortion of0.6 Å. The energy change as a function of the iron···irondistance is more pronounced once the paddlewheelstructure is adopted. The extent of the Fe···Fe distortionwith very small energy penalty (1.2 kcal mol–1) is limited

Fig. 4. Two possible reaction pathways for the carboxylateshifts. Path-a: longer Fe–O bond, labeled A, breaks first. Path-b: shorter Fe–O bond, labeled B, breaks first.

Fig. 5. Computed energy profiles for the carboxylate shiftreaction 1-Me → 2-Me using the iron···iron distance as reac-tion coordinate.

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to 3.1 Å. Elongation of the Fe···Fe distance to 3.2 Årequires approximately 4 kcal mol–1. The most crucialpart of the carboxylate shift reaction occurs between theiron···iron distances of 3.1 Å and 3.4 Å, where theenergy changes dramatically by 10.2 kcal mol–1. Figure6 illustrates the structures of the computed transitionstate TS-1 and the last structure with four intact car-boxylate bridges in our forward scan, 3-Me. In TS-1 theFe2–O22 bond is fully broken at a distance of 3.264 Å,whereas the same bond is clearly elongated, but stillintact, in 3-Me, with an Fe–O22 distance of 2.205 Å.The second carboxylate shift, the cleavage of Fe1–O14and formation of Fe2–O14 that follows the first car-boxylate shift, occurs in a barrierless fashion once theTS-1 has been traversed. The 2.243 Å Fe1–O14 bond isalready substantially elongated in TS-1. This elongationdoes not occur in a stepwise fashion, but is directlyconnected to Fe1–O22 bond formation, since a compari-son with 3-Me indicates no such elongation at anFe1–O12 distance of 2.016 Å.

Obtaining the second reaction pathway was moredifficult because the geometry optimizations readily af-forded the energetically more favorable initial pathwaylabeled Path-b. Only by starting from the optimizedstructures of Path-b series and rotating both pyridineligands by 90° around the Fe–N axis, without allowingthe pyridine ligand adjacent to the elongated bond to

rotate back, could the reaction energy profile be con-structed.22 Path-b was obtained without any such con-straints simply by increasing and decreasing theiron···iron distance in a stepwise manner. The approxi-mate transition state for this alternative carboxylate shiftpathway is 28.5 kcal mol–1 higher in energy and islabeled TS-2 in Fig. 5. The structure of TS-2 shown inFig. 7 reveals the reason for the high energy barrier ofthe carboxylate shift involving initial Fe1–O14 bondcleavage. Although the Fe1–O14 bond is essentiallybroken at a distance of 2.837 Å, the new Fe2–O14 bondis not formed. In addition, the carboxylate bridge thatstays intact shows no sign of support for the initialcarboxylate shift by appropriately elongating the corre-sponding Fe–O bond, as observed in TS-1. BothFe1–O12 and Fe2–O22 are substantially contracted,being 1.916 Å and 1.991 Å, respectively. In summary,our calculations strongly suggest that the carboxylateshift is highly selective towards initial cleavage of theFe–O bond that is orthogonal to the pyridine ring. Thisprocess is followed by a second carboxylate shift thatinvolves cleavage of the Fe–O bond that is coplanarwith the pyridine ring. Whereas the coordinatively un-saturated arrangement is readily formed when the emptycoordination site is orthogonal to the pyridine ring, asseen for Fe2 in TS-1, the corresponding situation withthe empty ligand site coplanar to the pyridine ring,shown for Fe1 in TS-2, is thermodynamically unfavor-able. The low-energy reaction pathway avoids the lattersituation by cleaving the Fe1–O14 bond after the newFe1–O22 bond is formed, so that the coordination site inthe pyridine-ring plane remains fully occupied at all times.

The ArTolCO2– Ligands and Steric Control

A closer inspection of the solid-state structure of 1(Fig. 1) reveals two geometric elements that deservespecial attention. The first is that the ArTolCO2

– ligandscreate a nearly fourfold symmetric cavity, in which thepyridine ligands lie across the diagonals. The second isthat the two pyridine rings are canted at an interplanar

Fig. 6. Computed structures of the critical points on the reac-tion energy profile: (a) TS-1, (b) 3-Me.

Fig. 7. Computed structure of TS-2.

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angle of 70.4°. A CPK representation of solid-statestructure illustrates that the cavity created by theArTolCO2

– ligands might constrain the spatial orientationof the pyridine ligand. This feature makes it desirable toobtain a more quantitative assessment of pyridine rota-tion about the Fe–N bond axis in the ArTol environmentand to explore whether the flexibility described abovefrom core-electronic arguments applies in the realligand environment. The size of the molecule prohibits afull-scale DFT study, whereas the sensitivity of theelectronic structure of the iron core makes low-levelstudies, for example at a semiempirical level, inadvis-able. We therefore performed two separate series ofcalculations, dividing 1 into a ligand part (Fig. 8a), forwhich the semiempirical HF method AM123 was ap-plied, and a diiron core part (Fig. 8b) that employs DFT.Only one pyridine ligand undergoes stepwise rotationaround the Fe–N vector in our approach (Fig. 8). InAM1 calculations, the position of the tolyl fragments ofthe ArTolCO2

– ligand next to the rotating pyridine wasoptimized to avoid van der Waals clashes between therotating pyridine ligand and the methyl group of the

tolyl moiety (Fig. 8a). All other atoms both in the AM1and DFT calculations were maintained at the solid-stategeometry. Figure 8c shows the rotation energy profilesof both parts and the simple sum of both contributions.Structures at the critical points labeled A, B, C, and Dare visualized as CPK models in Fig. 9. Although thisprotocol is far from being truly quantitative, it revealsseveral interesting features of 1. Because structural re-laxation is not allowed in our calculations, the barriersshown in Fig. 8c are most likely overestimated andshould be taken as upper limit estimates.

A most important finding is that the transformationbetween the nearly orthogonal and parallel orientationsof the pyridine ligands, structures A and C, is a veryfeasible process. The transition state between these twoorientations, structure B, occurs at an interplanar angleof approximately 20° and is ~6 kcal mol–1 higher inenergy than the minimum structure found in solid state.The parallel interplanar orientation of the pyridine ringsis disfavored by ~3 kcal mol–1. The iron core flexibilitydescribed above using the simple 1-Me model is thusmaintained in the ArTol environment. The shape of thecavity created by the ArTolCO2

– ligands effectively dis-ables full rotation of the pyridine ring. The structurewith an interplanar angle of 120° (Fig. 9, structure D) is~14 kcal mol–1 higher in energy than A, which is essen-tially all due to the steric energy of the cavity. Theelectronic energy penalty for the core-rearrangement isnegligibly small.

Fig. 8. Relative energy profiles of a 180° rotation of onepyridine ligand around the Fe–N axis.

Fig. 9. CPK representation of 1 at significant pyridine–pyri-dine interplanar angles identified on the rotational energyprofile.

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5. MO DIAGRAMS

Broken-Symmetry OrbitalsIn order to describe AF spin coupling in a quantum

mechanical model, it is necessary in principle to use amultireference method in combination with the unre-stricted spin formalism that takes mixing of excited statewave functions into account. In essence, one is forced toallow different spatial orbital occupation patterns for αand β spin electrons, where the corresponding β-orbitalof an occupied α-orbital remains unoccupied and viceversa. Such an orbital occupation pattern in a single-reference method leads to severe spin-contaminationthat renders the computed energies and the electronicstructure unreliable.24 A working solution has been sug-gested by Noodleman and is widely known as the bro-ken-symmetry (BS) orbital method. Instead of allowingthe d-orbitals of the metal centers to form delocalizedmolecular orbitals according to their local symmetry,localized molecular orbitals are formed by maximizingthe contribution of the respective d-orbital centered oneach of the metal centers. Despite certain limitations,this approach gives a valid description of AF-coupledmultinuclear systems.16 Since including AF spin cou-

pling in computational models is highly non-trivial,however, many studies have used ferromagnetic spincoupling and ignored the experimentally observed anti-ferromagnetic reality.11j–p,15 Above, we described thestructural effects of using ferromagnetic coupling for 1-Me. In the following and final part of our study, weexamine the metal-d-dominated molecular orbitals ofour model compounds, where the only orbitals exam-ined are those that play a role in distributing the 12unpaired electrons of the metal centers. Thus, only thehighest nonbonding and metal–ligand antibonding orbit-als will be mentioned here.

MO Description of Iron(II) DimersThe left-hand side of Fig. 10 shows iconic represen-

tations of the MOs in F-coupled 1-Me. We have severelysimplified the MOs and depict only the metal d orbitals.In addition, we neglect mixing between the dyz and dxz

orbitals; thus the dyz and dxz combinations are improperlyrepresented as pure combinations that would not exist inthe local D2d symmetry. The proper MOs are admixturesof dyz and dxz wave functions that lie between the yz andxz planes. For all practical purposes in this discussion,the simplified pure representations are admissible. The

Fig. 10. MO-diagram of ferromagnetically- and antiferromagnetically-coupled iron-centers.

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β-orbitals are shifted up in energy compared to thecorresponding α-orbitals to form the high spin complexwhere all 10 metal-based α-MOs are occupied. The twohighest occupied β-orbitals are in-phase combinationsof the dz2 and dxy orbitals, respectively. Figure 11 dis-plays isosurface plots of the in-phase and out-of-phasecombinations of the dxy orbitals, MOs <114α> and<121α>. Whereas MO <114α> is essentially a non-bonding orbital due to the mismatched phases with theout-of-phase combinations of the carboxylate lone-pairorbitals (oxygen-p), the full metal-ligand antibondingcharacter is developed in MO <121α>. Here, the phasesof the metal dxy wave functions match those of theoxygen lone-pair orbitals precisely to give a stronglyantibonding orbital. Note that there is a correspondingmetal–ligand bonding combination at a much lowerenergy that is not depicted.25

The right-hand side of Fig. 10 shows the same iconicrepresentations of BS orbitals describing the electronicstructure of AF-coupled 1-Me. Using localized atomicorbitals and disregarding local symmetry has a few sig-nificant consequences. Most importantly, the energiesof the occupied orbitals shift notably to lower energies,which gives an intuitive rationale for the lower totalenergy of the AF-coupled model. A more thoroughinvestigation examining all shifts of all orbitals is re-

quired, however, to understand fully the energy differ-ences and thus the spin-coupling mechanism betweenthe iron centers. Another notable difference betweenAF-coupled and F-coupled models relates to the distri-bution of the two excess electrons that exceed the limitof five d-electrons for each metal center to achieve ahalf-filled metal-d MO-configuration. In the F-coupledmodel the two electrons are placed in two β-MOs,<115β> and <116β>, which are in-phase combinationsof dz2 and dxy orbitals (Fig. 12). Note that <115β> is thecorresponding β-spin orbital of <114α> and has essen-

Fig. 11. Isosurface plots (isodensity = 0.05 au) of the metal dxy-based MOs in 1-Me: (a) SALC-MO, metal–metal in-phase, α-spin, (b) SALC-MO, metal–metal out-of-phase, α-spin.

Fig. 12. Isosurface plots (isodensity = 0.05 au) of the SALC-orbital <115β> of F-coupled 1-Me.

Fig. 13. Isosurface plots (isodensity = 0.05 au) of the BS-orbitals of AF-coupled 1-Me: (a) MO <115β> localized at Fe2(b) MO <120α> localized at Fe1.

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tially the same shape as <114α>. In the AF-coupledmodel, the excess electrons are placed in <120α>, an α-MO that is localized on Fe2, and in <120β>, its corre-sponding β-MO that is localized on Fe1. Figure 13shows an isosurface plot of MO <120α>. The conse-quence of this difference between F-coupling andAF-coupling is that the F-coupled model has an extraelectron in an orbital that promotes through-space iron–iron bonding, as the isosurface plot of the F-coupledMO <115β> shows clearly in Fig. 12. Consequently, thegeometry optimization gave an additional shortening ofthe iron···iron distance compared to the AF-coupledmodel to maximize this favorable interaction. Similarly,the occupation of the MOs <120α> (Fig. 13) and <120β>in the AF-coupled model introduces a repulsive biastowards one set of the Fe–O bonds, namely the Fe–Obonds that are coplanar with the pyridine ring. Thisresult explains the energetic preference of a structurewith correspondingly elongated Fe–O bonds.

6. SUMMARY AND CONCLUDING REMARKSWe have presented theoretical evidence for the struc-tural flexibility of the dinuclear iron(II) complexesrecently prepared as biomimetic constructs for thedioxygen-activating centers in non-heme diiron en-zymes. Such flexibility has been probed experimentallyin previous work by variable temperature NMR meth-ods,8 and plays a crucial role in core rearrangement thatprimes the metal center for subsequent dioxygen bind-ing.9 Our calculations are fully consistent with a highlyflexible, dynamic structure of the diiron(II) complexes.The use of the correct spin-coupling of unpaired elec-trons between the iron centers is necessary to reproducethe experimental solid-state structure of the quadruply-bridged paddlewheel structure, whereas the weaklycoupled windmill structure is less sensitive to the use ofthe wrong spin-coupling scheme in the computationalanalysis. Our calculations suggest that the structuralstrain imposed on the diiron core from the stericallydemanding ArTolCO2

– ligands does not constrain theflexibility of the core. In addition, we have exploredpossible reaction pathways of the carboxylate shifts, thenature of which is dictated by the orientations of thepyridine ligands. Further studies are required to estab-lish the possible generality of this directionally selectivebond shift and whether it might play a role in structur-ally related metalloenzymes in which the imidazolerings of histidine groups bind a diiron center.

The nature of the BS orbitals, which are required todescribe the experimentally observed AF spin-couplingbetween the metal centers, has been examined and com-pared to the classical MOs formed as SALC of atomic

orbitals. Further studies are required to expose fully thegeneral patterns of the orbital splitting and the applica-bility of classical MO-analysis protocols to these local-ized orbitals. We have nonetheless presented evidencethat these localized orbitals can be interpreted in thesame manner as classical SALC-MOs to rationalizestructural features such as the experimentally supporteddifferential effect of the pyridine orientation on theFe–O bonds in the equilibrium structure.

The studies presented here constitute the first step ofa new approach toward a rational design strategy aimedultimately at preparing functionally relevant biomimeticinorganic models. Rather than simply reproducingstructural features found in a metalloenzyme, we wish tounderstand the electronic features that lead to the ob-served reactivity. From this information we plan to buildinorganic analogues duplicating the key electronic char-acteristics that promote the desired reactivity, possiblyin a different ligand environment that might be bettersuited for technical purposes. Understanding the detailsof the electronic structure of the diiron cores in theenvironment of the native enzyme is just as crucial asthe full characterization of the inorganic complexes thathave been prepared so far. The points of immediateinterest in our laboratories are to apply the same proto-col outlined in this paper to analyze reaction pathwaysof model complexes that have been used previously tomimic the reactivity of metalloenzymes.6a,b,d,e,9 Equallycrucial are fundamental studies that aim at a moregeneral understanding of how structural motifs com-monly found in dioxygen-activating systems dictatethe electronic structure and reactivity in a BS-orbitalframework.

Acknowledgments. This work was supported by grants fromthe NIH to R.A.F. (GM40526) and grants from the NationalScience Foundation and National Institute of General MedicalSciences to S.J.L. Computational resources were provided bythe NPACI program under a grant to R.A.F. and by the NCRRdivision of NIH (P41 RR06892).

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(25) The main goal of the orbital analysis presented here is

to highlight the differences between the different cou-pling schemes. The metal–ligand bonding orbitals areof course of essential importance to understand thestructural features discussed in the first part of thispaper. We have studied these orbitals in detail and willreport the results elsewhere in a different framework.