theory of chemical bonds in metalloenzymes. xiv. correspondence between magnetic coupling mode and...

Theory of Chemical Bonds inMetalloenzymes. XIV. CorrespondenceBetween Magnetic Coupling Mode andRadical Coupling Mechanism inHydroxylations with MethaneMonooxygenase and Related Species

TORU SAITO,1 MITSUO SHOJI,1 HIROSHI ISOBE,1

SHUSUKE YAMANAKA,1 YASUTAKA KITAGAWA,1

SATORU YAMADA,1 TAKASHI KAWAKAMI,1

MITSUTAKA OKUMURA,1 KIZASHI YAMAGUCHI2

1Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka,Osaka 560-0043, Japan2Center for Nanomaterial Design, Osaka University, Toyonaka, Osaka 560-8531, Japan

Received 30 April 2010; accepted 21 July 2010Published online 8 September 2010 in Wiley Online Library (wileyonlinelibrary.com).DOI 10.1002/qua.22918

ABSTRACT: Broken-symmetry (BS) and approximate spin-projected (AP) BS hybriddensity functional theory (DFT) calculations were performed to elucidate possiblemechanisms of hydroxylation reactions of methane and alkanes with soluble methanemonooxygenase (sMMO) and related metalloenzymes. The BS HDFT (UB3LYP) methodwas employed to elucidate electronic and spin structures of the key intermediate ‘‘Q’’and to locate transition structures for hydroxylation reactions in the lowest-spin (LS)singlet and the highest-spin (HS) states of sMMO. The spin density populations and

Correspondence to: T. Saito; e-mail: [email protected]

Contract grant sponsor: JSPS [Grants-in-Aid for ScientificResearch (KAKENHI)].

Contract grant numbers: 19750046, 19350070, 18350008.Contract grant sponsor: Ministry of Education, Culture,

Sports, Science and Technology (MEXT).Contract grant number: 19029028.Additional Supporting Information may be found in the

online version of this article.

International Journal of Quantum Chemistry, Vol 110, 2955–2981 (2010)VC 2010 Wiley Periodicals, Inc.

chemical indices obtained by the BS B3LYP calculations were found to be consistentwith orbital interaction models for hydroxylation with MMO. However these indices inturn indicated significant spin contamination errors in the BS LS solution. Theelimination of the errors with the AP procedure indeed reduced the barrier height forthe recombination step of alkyl and hydroxyl radicals in the pure LS singlet state,leading to a rebound process. Then present computational results indicated thathydroxylation reactions proceed through the continuous diradical (diradicaloid)mechanism without discreet free radical fragments in the pure LS singlet state. Thecomputational results are, respectively, compatible with local singlet (SD) and localtriplet (TD) diradical mechanisms for hydroxylation in the LS and HS states; those werealready applied to P450 successfully. Thus magnetic (exchange) coupling modes (LSand HS) in MMO, P450 and related metalloenzymes are directly related to local SD andTD mechanisms for hydroxylation, indicating the correspondence between the magneticcoupling mode and the radical reaction mechanism. These theoretical results enable usto examine recent BS hybrid DFT computational results for hydroxylation reactions withsMMO by several groups. Implications of the present theoretical and computationalresults are also discussed in relation to several experimental aspects of hydroxylationreactions. VC 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2955–2981, 2010

Key words: intermediate Q; sMMO; local singlet and local triplet; diradicaloidmechanism; correlation diagram; hydroxylation; broken symmetry; spin projection;UB3LYP

1. Introduction

B inuclear iron complexes play importantroles in chemistry and biology; many metal-

loenzyme indeed involve these units as activesites as reported previously [1–61]. For example,diiron carboxylate complexes in bacterial multi-component monooxygenases (BMMs) catalyse theselective hydroxylation of hydrocarbons to alco-hols as illustrated in Scheme 1 [25]. Four classesof BMMs have been identified experimentally; (A)methane monooxygenase (MMO), (B) amo alkenemonooxygenase (AMO), (C) phenol hydroxylase(PMO), and (D) alkene/arene monooxygenases(ToMO). Each enzyme contains three proteins,including (a) a hydroxylase, (b) a reductase, and(c) a small regulatory component required for gat-ing [6, 11, 14]. Extensive experimental studieshave been carried out by several groups [1–36],and have provided mechanistic insights into thedioxygen and hydrocarbon activation steps inthese enzymes. For example, soluble methanemonooxygenase (sMMO) isolated from Methylo-coccus capsulatus (Bath) and Methylosinus trichospo-rium OB3b utilizes a carboxylate-bridged diironcenter and dioxygen to catalyze the conversion ofmethane to methanol as shown in A of Scheme 1.The hydroxylase component of toluene/o-xylenemonooxygenase (ToMO) from Pseudomonas sp.OX1 has a similar diiron center to that of sMMO.

The epoxidation of C¼¼C double bond by AMO isalso catalyzed with the diiron center as illustratedin B of Scheme 1. Structure and reactivity of theseenzymes have been investigated extensively.

Many experimental studies revealed the macro-molecular structure of sMMO [6, 11, 14]. Thehydroxylase component (MMOH) contains a bis-l-hydroxo-bridged diiron cluster that is essentialfor oxygen activation and substrate oxidation. Thereductase component (MMOR) in sMMO transferstwo electrons from NAD(P)H to the MMOHdiiron cluster to prepare its Fe(II)AFe(II) state forreaction with molecular oxygen. A small regula-tory protein termed component B (MMOB) plays

SCHEME 1. Selective hydroxylation of hydrocarbonsby diiron carboxylate complexes.

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2956 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI 10.1002/qua VOL. 110, NO. 15

several roles in sMMO catalysis; for example, itbrings about an oxygen-gating effect that acceler-ates the rate of the reaction between the MMOHdiiron cluster and molecular oxygen and rates ofother steps. Scheme 2 illustrates the catalytic cyclefor hydroxylation of alkane with sMMO that isproposed on the experimental grounds. Molecularoxygen appears to interact with the Fe(II)AFe(II)pair to afford a putative complex; then it is con-verted into a terminal superoxo or a briding per-oxo complex (P). The next intermediate Q havebeen trapped and characterized experimentally.Mossbauer and other spectroscopic studies sug-gested that P contains a differric l-peroxo-bridgeddiiron Fe(III)AFe(III) cluster, and Q contains anunprecedented bis l-oxo Fe(IV)AFe(IV) cluster inwhich the two single atom oxygen bridges form aso-called diamond core. The intermediate Q withthe antiferromagnetic exchange interaction [36]has been considered as a key intermediate thatundergoes hydroxylation of alkanes as illustratedin Scheme 2.

Past decades several groups have carried outtheoretical calculations of diiron cores with theoxygen dianion bridges, Fe(X)AOAFe(X) (X ¼ II,III, IV). Early broken-symmetry (BS) computa-tions concluded that the superexchange mecha-nism plays an important role for stabilization ofthe antiferromagnetically (AF) coupled state,namely the low-spin (LS) state of the diiron core[37–40]. In fact, the superexchange mechanism

can be applicable to many other diiron complexesas shown in I of this series of papers [41]. Theeffective exchange interaction for the intermediateQ was negative in sign (J < �30 cm�1), indicat-ing the AF (LS) ground state [42, 43]. However,several BS computations [49–53] assumed thehigh-spin (HS) state, namely ferromagnetic (F),exchange coupling for Q to elucidate possiblemechanisms of hydroxylation reactions in Scheme2, though some of recent BS computations [55–61] exactly reproduced the AF ground state of Qfor the same purpose. However, each groupassumed a possible spin state of Q, and thereforesystematic comparison of both AF and F states ofQ was not performed yet, particularly in relationto the mechanism of hydroxylation of alkaneswith Q.

Therefore, in part XIV of this series, we per-form a systematic hybrid DFT (UB3LYP) compu-tations of both LS and HS states of the key inter-mediates appeared in Scheme 2 to elucidate thenature of their chemical bonds and the exchangecoupling mechanisms in the diiron cores. As acontinuation of parts XII [62] and XIII [63], to-gether with related articles [64–66], the orbitalinteraction schemes in the catalytic cycle ofsMMO are first depicted for qualitative purposeon the basis of the BS molecular-orbital (MO)model; this reveals scope and applicability of thelocal singlet diradical (LSD) and local triplet dir-adical (LTD) mechanisms for hydroxylation withthe LS and HS states of Q. Furthermore, the natu-ral orbital (NO) analysis of the LS BS solutions isperformed to elucidate several chemical indicesfor the key species. The localized molecular orbi-tals (LMO) obtained by the NO analysis are usedto confirm the simple BS orbital interaction pic-tures of hydroxylation reactions with both LS andHS states of Q. The locations of the transitionstructures (TSs) for hydroxylation reactions arealso performed by the energy gradient techniqueof UB3LYP. The energy diagrams before and afterapproximate spin (AP) correction of the BS totalenergies are depicted for estimation of the spincontamination error in the BS LS solution that hasbeen utilized by many groups. Several bond indi-ces are also calculated for key species in Scheme2. Finally we elucidate the correspondencebetween the magnetic coupling mode in thediiron core and radical coupling mechanism ofhydroxylation reaction in the sMMO system likein the cases of the Fe(IV)¼¼O, P450 and relatedspecies.

SCHEME 2. The catalytic cycle of sMMO.

THEORY OF CHEMICAL BONDS IN METALLOENZYMES

VOL. 110, NO. 15 DOI 10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2957

2. Theoretical Backgrounds

2.1. MAGNETISM AND CHEMICAL BONDS INMETAL OXIDES

Past decades active oxygens and oxyradicals[67–70] have been attracted great attention sincethese species play important roles in variousfields of chemistry and biology. Atomic (O) andmolecular oxygen (O2) at the excited singlet stateas well as hydroxyl (OH) and hydroperoxy(OOH) radicals are typical example of such activespecies. In early 1980s, molecular beam experi-ments [71–75] on the atomic oxygen (O) demon-strated different chemical behaviors of singlet(1O) and triplet (3O) states of atomic oxygen; sin-glet O-atom favors the insertion-type reaction intoa RAH bond, whereas triplet O-atom undergoesthe hydrogen abstraction reaction as illustrated inScheme 3. Similarly, abstraction reaction modesare exchange-allowed for oxygen free radicals(OH, OOH, etc.), though the insertion mode isexchange-forbidden. These selection rules are con-sistent with many experiments [76–90]. Scheme 3is also extended to theoretical understanding ofoxygenation reactions with the metal-trappedcompounds of the species [91–111] such as M¼¼O,MOH, MOM, MOO, MOOH and MOOR (M ¼Cr, Fe, Mn, Cu, etc.) (see Fig. 3 below). In fact,these compounds have been interesting and im-

portant target molecules on both experimentaland theoretical grounds because of participationsof various oxygenations reactions. Some of reac-tion modes of these species are reviewed previ-ously [37, 78, 79, 99].

Various active metal-oxides species [a]–[l] havebeen utilized as oxygenation reagents as shown inFigure 1; some of them are indeed used in the cat-alytic cycle of sMMO as illustrated in Scheme 2.The electronic structures of these metal oxides areusually complex because three degrees of free-dom; (a) spin, (b) charge, and (c) orbital, are vari-able as shown in Figure 2, depending on reactionfields such as solvents and protein structures inbiology. This indicates that theoretical descrip-tions of these species [a]–[l] are great challengefor elucidation and understanding of structureand reactivity of these species. Both molecular or-bital (MO) [37, 99] and valence-bond (VB) [106,110] concepts have been introduced and appliedfor the purpose. Shaik and coworkers [106, 110]have already presented the VB-theoretical formu-lation of radical species such as metal oxides withlocal spins. Therefore we do not repeat their VBdescriptions here; the derivation of the VB con-cepts from BS MO calculations is given in theSupporting Information. On the other hand, in theformer MO approach, the extended Huckel MOmethod without spin degree of freedom is notsufficient enough for theoretical descriptions ofactive oxygens and oxyradicals in Figure 1. Onthe other hand, the closed-shell Hartree-Fock andKohn-Sham DFT solutions often suffer the so-called triplet instability [112–114], indicating the

SCHEME 3. The hydroxylation of alkane by (A) tripletoxygen (3P) and (B), (C) singlet oxygen (1Dxy,

1Dxx(yy)).

FIGURE 1. Several transition-metal oxides [a]–[k] gen-erated in oxygenation reactions.

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necessity of more general BS molecular orbitals(MO) such as different orbitals for different spins(DODS) [37–43] and general spin orbitals (GSO)[115, 116]; these MOs can indeed describe varia-tions of spin, charge and orbital degrees of free-dom in such unstable molecules. In fact, BShybrid Kohn-Sham density functional theory(DFT) by the use of DODS and GSO is now a use-ful and handy procedure for qualitative purposeas shown in this series of papers, though furtherrefinements are often necessary for quantitativepurpose.

In early 1980s, we attempted to elucidate scopeand limitation of the BS MO approach to metal-oxo (M¼¼O)þm species [g] (M ¼ Cr, Mn, and Fe)and l-oxo transition-metal dimmer [h](MAOAM)þm (M ¼ Cr, Mn, Fe, Ni, and Cu) withseveral oxidation numbers (m ¼ 0–3) in Figure 1[37–43]. To this end, total energies of several spinand orbital configurations of (M¼¼O)þm were firstcalculated with changing the oxidation number mto elucidate electronic structures of the groundand lower-lying excited configurations. It wasshown that the metal-oxo [g] (M¼¼O)þm speciesexhibit low-(LS), intermediate-(IS), and high-(HS)spin configurations, and the energy differencesamong them are not so large. This characteristicfeature provided a postulate that both ground

and lower-lying excited configurations of thesespecies may participate oxygenation reactions ofvarious substrates. Interestingly, the charge popu-lation on the oxygen site of the high-valent M¼¼Ospecies indicated the electrophilic property. TheBS MO calculations of addition reactions of elec-trophilic [Fe(IV) ¼¼O]þ2 species to ethylene indi-cated that metal 1,4-diradical mechanism wasmore favorable than the metal perepoxide-typepathway because of the diradical character of thecore [37]. The spin crossover from triplet to sin-glet diradical configuration indeed occurred alongthe 1,4-diradical pathway. Recently the radical-type mechanism for oxygenation reactions basedon the experimental [91–96, 100–103] and theoreti-cal [37, 97–99] grounds has been received arenewed interest [106–111].

The magnetic measurements provided impor-tant information on electronic structures of multi-nuclear transition-metal oxides even in early1980s [92]. Therefore development of computa-tional methods to determine the effectiveexchange coupling constants (J) between transi-tion metal ion in the l-oxo transition-metaldimmer [h] (MAOAM)þm was an important theo-retical problem. We developed a practical methodfor the purpose based on the BS computations fol-lowed by the approximate spin projection proce-dure (AP) [37–40]. The J-values were calculated tobe antiferromagnetic in relatively shorter MAObond regions; these are consistent with the experi-ments. The magnitude of the effective exchangeintegral (J) for the [Cu(II)AOACu(II)]þ2 core wasindeed reported to be one-order larger than thatof other MAOAM systems examined [37, 38]. Inthe same year (1986), the high-Tc superconductiv-ity was discovered in copper oxide planes con-sisted of [Cu(II)AOACu(II)]þ2 [117]. The large |J|value for the species was immediately used toconstruct a magnetic (J) model [38] of supercon-ductivity [118] instead of the exciton (charge)mediated model [119]. The charge population ofthe oxygen site at the LS (antiferromagnetic) stateof the high valent [Cu(III)AOACu(III)]þ3 and[Fe(III)AOAFe(III)]þ2 was positive, indicating theelectrophilic property; namely ability of oxygentransfer reactions such as epoxidation [37].

The BS calculations of the metal peroxides andmetal hydroperoxides in Figure 1 have provideduseful information on oxygenation mechanismswith these species [78, 97–99]. Several spin andorbital configurations of [MOO]nþ1 [a] with andwithout model ligands were also examined with

FIGURE 2. Three (orbital, spin and charge) degrees offreedom of strongly correlated electron systems(SCES). Environmental effects such as substituents, sol-vents and protein fields control their electronic struc-tures, properties and chemical reactivity.



variation of the oxidation number (m) to examinestructure and reactivity of the metal peroxides.Several spin-orbital configurations of [MOO]nþ1

were indeed constructed under the BS MOapproximation, and their energy differences arenot so large. Existence of such quasi-degeneratedstates (QDS) involving several configurations wassimilar even in the case of [MOOH]þ [i] with andwithout model ligands [98, 99]. The electrophilicreactivity of theOAO r* orbital of some of[MOOH]þn [i] and [MOOR]þn [j] species wasexplained in analogy with that of organic peracid,oxirane, and carbonyl oxide [78, 98, 99]. The elec-tronic structure and reactivity of the metal oxidesin Figure 1 was qualitatively explained with var-iations of charge and spin density populations,and orbital configurations obtained by the BS MOcalculations. Thus the BS MO method [78, 112–116] was concluded to be useful and handy fortheoretical investigation of transition-metal oxideswith strong electron correlations, though severalprocedures such as the HOMO–LUMO mixing[113] were necessary for constructions and rapidconvergences of appropriate BS solutions underinvestigation.

In early 1980s our BS MO calculations indi-cated that isoelectronic (isolobal and isospin) anal-ogy between organic and inorganic molecules canbe a guiding principle for theoretical understand-ing of chemical bonds in metal oxides. The insta-bility in chemical bonds was indeed a useful crite-rion for high-valent metal oxides [37]. Forexample, carbonyl oxide (R1R2COO) is isoelec-tronic to porphyrine (Por) FeOO species ([a]in Fig. 1) in the singlet state, indicating similardiradical character (y ¼ 40–50%) [78, 79]. Thisimplies that the terminal oxygen in porphyrine(-Por) FeOO species undergoes radical additionreaction to a C¼¼C double bond [97]. In 1980s weperformed ab initio BS MO calculations of modelcomplexes to elucidate the electronic and spinstructures of a, g, and i in Figure 1 [37, 78, 79, 97,98]. It was found that these transition-metal spe-cies have several electronic and spin statesdepending on three degrees of freedom (charge,spin, and orbital) in Figure 2. Recent develop-ments of the computational facilities enabled usto perform the hybrid DFT calculations of realsystems. Closed-shell molecular orbitals of thesespecies often exhibited triplet instability, indicat-ing the existence of BS solutions with metal-dirad-ical structures in a sharp contrast with organome-tallic compounds with zwitterionic character. For

example, the metal diradical character of the por-phyrine(Por)FeOO species with thiolate ligandwas indeed 51.8% in our UB3LYP calculationwith the full geometry optimization [120]. In fact,BS MO computations revealed possible spin con-figurations and charge-spin densities of theground and lower-lying excited states of the metaloxides. Then reaction mechanisms of oxygen-ations of various substrates with a, g, and i wereexamined on the basis of both orbital symmetryconservation and orbital symmetry breaking crite-ria as shown in this series of papers. Several pos-sible models for oxygen-transfer reactions havebeen proposed on theoretical and computationalgrounds as described in review articles [37, 79,99]. Computational results were found to be use-ful for rational explanation and understanding ofmechanisms of oxygenation reactions of alkanes,alkenes and other substrates by the M¼¼O, MOOand MOOR species.

2.2. ISOELECTRONIC ANALOGY ANDMECHANISMS OF HYDROXYLATIONS

In this series of papers [62, 64], we have beenexamining theory of chemical bonds in metalloen-zymes as a systematic development of the BS MOand resonating BS (RBS) methods to unstable mol-ecules such as organic diradicals, transition-metaloxides, and hydroxides (M¼¼O, MOO andMOOH) species [37, 97–99] in Figure 1. Experi-mentally [1–36, 67–70, 92–112], product popula-tion and stereochemistry of oxygenation reactionswith synthetic transition-metal oxide catalysts arevariable with reaction conditions, suggesting thatseveral active oxygens or different electronic andspin states of the same species might be partici-pating. For example, let us consider hydrogenabstraction reactions of alkanes with atomic oxy-gen as shown in Scheme 3 [64, 78, 79]. Singlet ox-ygen atom 1(;O:; 1Dxy) abstracts hydrogen fromHAC bond of alkanes to afford singlet biradical1(;�OHþ :�CR3) followed by the rotation of theOH group for direct exchange coupling of theradical lobes for formation of the OAC bond.Direct coupling of radical lobes is however, spin-forbidden in the case of triplet oxygen atom3(:O;), showing the necessity of spin inversionwith the spin-orbit interaction (ISC) or therebound process of discrete free radicals (�OHand �CR3). On the other hand, direct insertion ofsinglet oxygen atom 1(;O:; 1Dxx(yy)) into a HACbond is both orbital- and spin-symmetry allowed

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[37, 78, 79, 112] in accord with the molecularbeam experiments [71–75].

Similar situation is also found for the isoelec-tronic Fe(IV)¼¼O species in P450 [37, 79, 99]. TheFe(IV)¼¼O species exhibits the complete degener-acy between HOMO and LUMO (:px* and py*:) asshown previously [37, 62]. Then it becomes tripletdiradical at the ground state because of the Hundrule. Previously [37, 79, 62–65], we have proposedsinglet (1Dxy) and triplet (3

Pxy) diradical models

from the view point of the isolobal analogyamong O, O2 and Fe(IV)¼¼O, together with theelectrophilic (1Dxx(yy)) insertion-like closed-shellmodel for oxygenation reactions with theFe(IV)¼¼O core. Isoelectronic, namely both isolobaland isospin, analogy among O, O2 and Fe(IV)¼¼Obased on the generalized MO concept has beenone of our basic ideas for theoretical understand-ing of chemical reactivity of molecular oxygenand the Fe(IV)¼¼O core in heme- and nonhemecomplexes [37, 79, 97–99] since a lot of experimen-tal [67–70] and theoretical studies on oxygenationswith O and O2 have been performed even at thattime (near 1980) and such results are useful forcomparative purpose. Moreover, the BS computa-tions indicated that the internal spin crossoverfrom 3(:Fe(IV)¼¼O:) to 1(:Fe(IV)¼¼O;) within thecomplex often occurs along the radical-abstractiontype pathway of hydroxylation [37, 62]. Thisimplies that spin crossover of the Fe(IV)¼¼O isone of the important factors for regulation ofhydroxylation pathways. Scheme 4 illustratesthree different reaction modes of Fe(IV)¼¼O andCAH bond of alkanes on the basis of the isoelec-tronic analogy [37]; (a) (2þ2)-type four-centeredmechanism, (b) radical abstraction mechanismand (c) insertion-type mechanism. The diironcluster of sMMO can be regarded as a dimer ofthe Fe(X)¼¼O (X ¼ III, IV); this means that ourprevious theoretical models and basic ideas forFe(X)¼¼O can be extended to sMMO as shown inthe following section.

3. Theoretical Studies of theHydroxylation Mechanisms of sMMO

3.1. FOUR MECHANISMS FORHYDROXYLATION REACTIONS WITH sMMO

Recently oxygen transfer reactions with bi-nuclear transition metal complexes and metallo-enzymes involving the MAOAM cores have been

received particular interest [1–61]. As examinedpreviously, the hole is often introduced on the ox-ygen site in the case of high-valent MAOAMsystems [37–41]. For example, the oxidation ofthe Cu(II)AO2�ACu(II) unit provides two possibleVB structures: Cu(III)AO2�ACu(II) and Cu(II)-O1�(�)ACu(II); the extra hole is introduced on thecopper site and oxygen site, respectively. Theexact diagonalization of the Hubbard model [39]indicated that a superposition state of these limit-ing VB structures is appropriate in the case ofcuprates; this picture was indeed important forconstruction of possible models for the high-Tcsuperconductivity of cuprates. Similarly, thehole can be introduced on the manganese siteand/or oxygen site in the case of the high-valentmanganese oxides: Mn(V)AO2�AMn(IV) andMn(IV)AO1�(�)AMn(IV) [39]; the oxygen holeplays an important role for the radical couplingmechanism for oxygen evolution in the oxygenevolution center (OEC) of PSII system as shownin part XV of this series. Therefore, the generationof hole on the oxygen site (or electrophilic site[37]) is also a key step for radical mechanisms ofhydroxylation of alkanes with the Q intermediate insMMO: Fe(IV)AO2�AFe(IV) $ Fe(IV)AO1�(�)AFe(III)$ Fe(III)AO1�(�)AFe(IV) $ Fe(III)AO0AFe(III); it isnoteworthy that the O0 site in the last structure canhave the 1Dxx(yy) configuration in the isoelectronicanalogy [42].

Scheme 4 is utilized for elucidation of possiblereaction models for hydroxylation with sMMO asshown in Figure 3. It shows possible reactionmechanisms (a)-(d) of hydroxylation reactions ofalkanes with sMMO: (a) a direct extension of theforbidden-concerted (2þ2) mechanism in Scheme4, four centered mechanism followed by forma-tion of zwitterionic (ZW) transition structure (TS)is feasible to afford the intermediate T in Scheme2; (b) Hydrogen atom abstraction from the sub-strate followed by radical recombination isanother possibility, in contradiction to the nonrad-ical mechanism; the oxygen hole plays an essen-tial role in the mechanism; (c) Direct insertion of

SCHEME 4. Three reaction modes of metal-oxo spe-cies (M-O) and R-H bond.



the oxygen atom from Q to the CAH bond is alsoconceivable, particularly in the case of the 1Dxx(yy)

configuration of Fe(III)AO0AFe(III); and (d) Elec-tron-transfer mechanism from substrate to Q fol-lowed by formation of cationic species is also fea-sible, depending on environmental conditions.Therefore, proposed mechanisms in Figure 3 areparallel to those of molecular oxygen, Fe(IV)¼¼Oand CpI (P450) as shown in parts XII and XIII ofthis series. The mechanisms in Figure 3 are alsoconsistent with those that are concluded from thevarious experiments [1–36].

3.2. LOCAL SINGLET AND TRIPLETDIRADICAL MECHANISMS OFHYDROXYLATIONS BY SMMO

Figure 3 clearly shows the possible analogybetween P450 and sMMO concerning with theradical mechanisms of hydroxylations of alkanes.As an extension of our previous work (part XIII)on P450 [63], we have investigated correspond-ences between the magnetic coupling mode andthe mechanism of radical coupling in the case ofsMMO. We indeed elucidate that LSD and LTDmechanisms are equally applicable for radicalreactions of these species as illustrated in Figures

4–6. First of all, let us examine orbital interactiondiagrams for hydroxylation reactions of methaneand related compounds with total LS, namelyantiferromagnetic, diiron core (11) that has thehigh-spin configuration at each Fe(IV) ion in thecase of sMMO as shown in Figure 4. As an initialstep, the oxygen hole is generated with the elec-tron transfer from oxygen dianion to the Fe(IV)ion, leading to the formation of the intermediate(12). The radical orbital (LMO) of the oxygenatom in 1[(:Fe(III)(S ¼ 5/2)O2� (;�O1�)Fe(IV)(S ¼�4/2);) (12) abstracts a hydrogen atom from alka-nes to form a radical intermediate (I) 1[(:Fe(III)(S¼ 5/2)O2� (OH1�) (;�CH3)Fe(IV)(S ¼ �4/2);) (13)through the transition structure (1TS1) for hydro-gen transfer. For the rebound (exchange coupling)step to alcohol, the HAO rotation is necessary forthe orbital interaction of a lone pair of the oxygenatom with carbon-radical orbital as shown in 13rotin Figure 4. Furthermore, the radical formation onthe OH group is essential; this entails the chargetransfer from the lone pair of the OH anion groupto dxz orbital of Fe(IV), leading to formation ofthe low spin (LS) complex 1[(:Fe(III)(S ¼ 5/2)O2�

(:�OH)(;�CH3)Fe(III)(S ¼ �5/2);) (14), where thegenerated diradical pair of �OH and �CH3 is localsinglet in nature. Therefore, the radical rebound

FIGURE 3. Four possible reaction mechanisms of hydroxylation of alkanes with sMMO on the basis of theoreticalmodels in Scheme 3 and various experiments [1–36].

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process is facile to afford a product 1[(:Fe(III)(S ¼5/2)O2� (CH3OH)Fe(III)(S ¼ �5/2);) (15) in theLS (singlet) state in accord with the exchange-allowed process. Thus the orbital interactionscheme clearly indicates the correspondencebetween the magnetic coupling mode in Q andthe radical rebound mechanism as shown in Fig-ure 4. Of course, smooth molecular deformationsinstead of the discrete steps for the above qualita-tive explanations occur along the reaction path-ways as shown in later BS calculations (Section 4).

Next, let us examine orbital interaction diagramsfor hydroxylation reactions of methane and relatedcompounds with total high-spin (HS), namely ferro-magnetic, diiron core (91) in the methane-monoxy-genase (MMO) enzyme as shown in Figure 5. Asan initial step, the oxygen hole is generated withthe electron transfer from oxygen dianion to theFe(IV) ion, leading to the formation of the HS inter-mediate (92). The radical orbital (LMO) of the oxy-gen atom in 9[(:Fe(III)(S ¼ 5/2) O2� (;�O1�)Fe(IV)(S¼ 4/2):) (92) abstracts a hydrogen atom from alka-nes to form a radical intermediate (I) 9[(:Fe(III)(S ¼5/2)O2� (OH1�) (;�CH3)Fe(IV)(S ¼ 4/2):) (93)

through the transition structure (9TS1) for hydrogentransfer. For the rebound, namely exchange cou-pling, step to alcohol, the H-O rotation is necessaryfor the orbital interaction of lone pair of oxygenatom with the carbon-radical orbital as shown in13rot in Figure 4. However, the radical formation onthe OH group is essential; this entails the chargetransfer from the lone pair of the OH anion groupto dxz orbital of Fe(IV), leading to formation of thehigh spin (HS) complex 9[(:Fe(III)(S ¼ 5/2)O2�

(;�OH)(;�CH3)Fe(III)(S ¼ 5/2):) (94II), where thegenerated diradical pair of �OH and �CH3 is localtriplet in nature. Therefore, the dissociation of thetriplet radical pair into free radicals is necessary;then the rebound process of them provides thesuper high-spin (SHS) product: 11[(:Fe(III)(S ¼ 5/2)O2�(CH3OH) Fe(III)(S ¼ 5/2):) (115). As ananother possibility, the spin exchange transition(SET1) among dxz orbital in the Fe(III) ion is neces-sary to generate the up spin on the O-atom, leadingto the unstable HS species 9[(:Fe(III)(S ¼ 5/2)O2�

(:�OH) (;�CH3)Fe(III)(S ¼ 3/2):) (94I); in this casethe right Fe(III) ion has the local intermediate spinconfiguration, namely the locally excited

FIGURE 4. The orbital interaction diagrams for hydroxylation reactions with the low-spin (LS) singlet state of solublemethane monooxygenase (sMMO): one to five expresses orbital configurations of several key intermediates (see text).



configuration. However, the radical rebound pro-cess for [(:�OH)(;�CH3)] becomes facile to afford aproduct in the excited state: 9[(:Fe(III)(S ¼ 5/2)O2�

(CH3OH)Fe(III)(S ¼ 3/2):) (95). Thus the orbitalinteraction scheme clearly indicates the correspon-dence between the magnetic coupling mode in Qand the radical rebound mechanism even in thecase of the high-spin state. The orbital interactiondiagram is useful for construction of BS configura-tions in the UB3LYP computations.

As shown in Figures 4 and 5, both orbital andspin configurations play important roles for theorbital interaction schemes for hydroxylationbased on the BS MO approximation [37–43, 78,79, 97–99, 112–116]. Probably this is a merit ofthe BS MO approach for qualitative understand-

ing of radical-type reactions. However, the(2þ2)-type nonradical mechanism in Figure 3 isconceivable as in the case of many organometal-lic (2þ2) reactions if the closed-shell RB3LYP so-lution was utilized for location of the transitionstructure. On the other hand, available EXAFSand Mossbauer experiments [18, 36] have eluci-dated that the Q intermediate exhibits the AFexchange-coupling interaction (J < �30 cm�1)between the local HS irons; Fe(IV) (Sz ¼ 2). Thisindicates that an assumption of the closed-shellstate of Fe(IV) is eliminated from the experimen-tal ground for the Q intermediate in sMMO.Thus, theoretical investigations of the groundelectronic structures of the M-O-M species arenot at all trivial [37]. Therefore we may

FIGURE 5. The orbital interaction diagrams for hydroxylation reactions with the high-spin (HS) singlet state of solublemethane monooxygenase (sMMO): one to five expresses orbital configurations of several key intermediates (see text).

SAITO ET AL.


alternately consider the ferromagneticallycoupled diiron di-l-oxo core, 9[Fe(IV)(Sz ¼2)(O2�)2Fe(IV)(Sz ¼ 2)](91) in Figure 5 as a possi-ble model of an important reactive species Q inthe hydroxylation with sMMO; partly becausethe theoretical construction of this HS BS solu-tion is not so difficult. The mixed-valence struc-ture 92 with the local high-spin iron Fe(III) (Sz ¼5/2) and the oxygen hole with the down-spin inFigure 5 can be generated with the spin delocali-zation (SD) in conformity with the high valency[39–42]. However, the ferromagnetic SD inter-action through O1�� seems weaker than theantiferromagnetic superexchange interactionthrough O2� in the case of 2. In fact, reportedEXAFS and Mossbauer experiments [36] haveelucidated that the Q intermediate exhibits theAF exchange-coupling interaction (J < �30cm�1) between the local HS irons; Fe(IV) (Sz ¼2). This indicates that Q in sMMO is regarded asthe AF coupled diiron di-l-oxo core (11) in Fig-ure 4. The mixed-valence structure 12 with thelocal high-spin iron Fe(III) (Sz ¼ 5/2) and theoxygen hole with the down-spin in Figure 4 canbe similarly generated in the AF state.

The possible configuration correlation diagramcan be depicted on basis of the above theoreticalanalyses based on the experimental and orbital

interaction results; previous Huckel–Hubbard–Hund (HHH) model (see parts XII [62] and XIII[63] in this series) is utilized for depicting the dia-gram as shown in Figure 6. The HHH modelinvolves the resonance integral (b), on-site Cou-lomb repulsion (U) and the on-site exchange inte-gral (K). The generation of the excited mixed-valence state 1,92 is a key factor to determine theactivation barrier for the hydrogen abstractionstep (TS1). This means in turn that the activationbarrier is highly dependent on the functionalsused in the hybrid DFT computations. On theother hand, the energy difference between the LSand HS states should be small at the radical inter-mediate 1,93. The transition structure (TS1) existsin the intermediary state between 1,92 and 1,93 asillustrated in Figure 6. The avoided crossingbetween the diabatically crossing surfaces shouldoccur under the BS calculations. Furthermore,generation of the oxygen radical site 1,94 is an im-portant process for the rebound process (theOHACH3 recombination), since TS2 lies in thecrossing region of potential curves of 1,93 and 1,94as illustrated in Figure 6. Several hybrid DFTcomputations have already been reported tolocate TS1 and TS2 for MMO as shown below.However, at the present stage, BS (U) B3LYPcomputations are popular in this field, becausemore reliable BS(UCCSD), resonating BS(UCCSD)CI and MRCC computations are too heavy. There-fore, future computations may reveal the nonradi-cal nonsynchronous (NN) (namely only <50% dir-adical character) mechanism for stereospecifichydroxylations by MMO [1–36] as illustrated in(c) in Figure 3; it is noteworthy that the abstrac-tion-type insertion reaction was discovered in thecase of the model complex: O¼¼OH2, for the1Dxx(yy) state of sMMO.

3.3. SPIN VECTOR MODELS FOR RADICALSPECIES IN SCHEME 2

As shown in Figures 4–6, we are concernedwith molecular systems with broken chemicalbonds. Diradicals and polyradicals generated inthe course of these hydroxylation reactions aretypical broken-bond(s) species. This means thatthe spin-multiplet spectra should be resulted fromthe spin-symmetry breaking in these species.Since these species indeed have local spins, spinHamiltonian (Heisenberg) models have beenintroduced to describe effective exchange interac-tions between molecular spins as

FIGURE 6. The configuration correlation diagram forhydroxylation reactions with the low-spin (LS) andhigh-spin (HS) states of soluble methane monooxygen-ase (sMMO) on the basis of the Huckel–Hubbard–Hund(HHH) model: one to five expresses orbital configura-tions of several key intermediates (see text).



HðHFBÞ ¼ �2JS1 � S2 (1)

where Si is the spin operator at the site i (i ¼ 1, 2)[37]. Several experimental techniques have beendeveloped to elucidate these exchange interac-tions (J) in molecules-based magnetic materials. Infact, the observed J values are clues for considera-tion of possible ground states of the key inter-mediates in catalytic cycle of sMMO. On the otherhand, the assumption of the Heisenberg-typesplitting for spin multiplets provides an approxi-mate but practical procedure (AP) to eliminate thehigher-spin components in the LS BS solutions asshown previously.

DE ¼ �J ðS� 1ÞS� SðSþ 1Þf g ¼ 2SJ: (2)

Under this approximation, the J-values by theAP procedure are given by the simple equation[37–43]:

J ¼ LSE� HSE� ��

HS S2� �� LS S2

� �� ; (3)

where YE and YhS2i denote, respectively, the totalenergy and total angular momentums by a com-putation method Y. Eq. (3) is also applicable forcomputations of J values even if intermediate spinstates are utilized instead of HS.

The resonating BS (RBS) CI method [121–128]often utilized to confirm the reliability of the APscheme. Furthermore, the spin-optimized (SO)RBS CI is feasible for multicenter polyradicals ifnecessary. The denominators in Eq. (3) are alsorewritten by the difference of spin correlationfunction. The expression of J is applicable forboth single reference (SR) BS after AP, RBS CI, SORBS CI and multireference (MR) symmetry-adapted (SA) methods [121–128]. The energy cor-rection for the LS BS state after AP correction isgiven by the following simple equation;

AP BSEðLSÞ ¼ BS EðLSÞ þ DS2J; (4)

where BSE(LS) denotes the total energy of the LSstate by BS and the second term is the correctionterm for BS errors. Therefore this term becomesmore and more negligible by the use of higher ex-citation operators in the CC scheme. The energygradient (g) and Hessians (H) of the AP BSenergy are also derived for the full geometry opti-mization of open-shell radical species at the LS

state. The errors for the optimized geometrical pa-rameters at the BS LS level have been clarified bythe AP EG optimizations. The local spins in theHeisenberg model are often regarded as axialspin vectors (classical spins) in many cases. Wehave derived both quantum and classical Heisen-berg models for key intermediates in the catalyticcycle in sMMO. The formulations and numericalresults are given in the Supporting Informationfor brevity.

4. Hybrid DFT Calculations ofCatalytic Cycle of Hydroxylationwith sMMO

4.1. COMPUTATIONAL DETAIL

The hybrid DFT (HDFT) calculations of the keyintermediates in Scheme 2 and the transitionstructures for hydroxylation of methane withsMMO were performed to confirm the above the-oretical models. For the purpose, the initial struc-ture of Q in sMMO was taken from the X-raycrystal structure from Methylococcus capsulatus(PDB code: 1MTY) [11]. We constructed the mo-lecular structure model of the intermediate Q;acetic acid and methylimidazole were, respec-tively, employed as model molecules of glutamicacid and histidine residues in sMMO as illus-trated in Figure 7.

We employed the UB3LYP method [129] by theuse of the MIDIþpd [130] basis set for Fe atom

FIGURE 7. The model complex of the active site ofsMMO. [Color figure can be viewed in the online issue,which is available at wileyonlinelibrary.com.]

SAITO ET AL.


and the 6-31G* basis sets for the other atoms. Fullgeometry optimizations were performed for boththe LS (S ¼ 0) and HS (S ¼ 4) states using theenergy gradients of UB3LYP. Frequency analyseswere also carried out at each stationary point tocheck whether the optimized structures wereenergy minima (intermediates) or transitionstructures.

The reactions of triplet and singlet diradicalstates (1Dxy and 3P) of atomic oxygen (O) withCH4 were also examined to confirm the reactionmechanisms in Scheme 2. The geometry optimiza-tions of the transition structures of the reactionswere performed by UB3LYP with cc-pVTZ basissets. We used AP optimization procedure, whichcan optimize stationary points by removingthe high-spin contamination error in the LSBS state [131, 132]. Furthermore, Mukherjee’s mul-tireference coupled cluster singles and doubles(MkMRCCSD) calculation [133] was performedfor single-point energy calculations with (2e,2o)(two electrons in two orbitals) as the active space.The UB3LYP and MkMRCCSD calculations wereperformed by using Gaussian 03 [134] and PSI3program packages [135, 136], respectively.

4.2. OPTIMIZED GEOMETRIES OFKEY SPECIES IN HYDROXYLATIONWITH sMMO

First of all, we examined spin contaminationerror on the Fe2O2 core of Q to confirm whetherthe spin contamination error from the HS statehas serious effects on the reaction coordinate ofsMMO or not. The optimized structural parame-ters, together with EXAFS data, are summarizedin Table I.

The Fe1–Fe2 distances of the LS and HSstates are 2.687 and 2.794 (A), respectively,showing a small difference (0.007 A). However,these are longer than those of EXAFS study [16]by about 0.2 and 0.3 A, respectively. Two ofFeAO distances optimized at the HS state areshort and the other two are long; therefore theunsymmetrical structural parameters D becomelarge as follows.

D1ðHSÞ ¼ RðFe1 �O1Þ � RðFe2 �O1Þ¼ 2:146� 1:665 ¼ 0:481ðAÞ (5a)

D2ðHSÞ ¼ RðFe1 �O2Þ � RðFe2 �O2Þ¼ 1:722� 1:956 ¼ 0:234ðAÞ (5b)

Therefore the molecular structure of Q at theHS state is unsymmetrical and is regarded as adimmer structure of the Fe¼¼O units. On the otherhand, the D parameters for the LS state are givenby the BS and AP BS methods.

D1ðBSÞ ¼ 1:842� 1:733 ¼ 0:109ðAÞ; D1ðAP BSÞ¼ 1:809� 1:742 ¼ 0:067ðAÞ ð6aÞ

D2ðBSÞ ¼ 1:797� 1:796 ¼ 0:001ðAÞ; D2ðAP BSÞ¼ 1:809� 1:775 ¼ 0:024ðAÞ ð6bÞ

Both BS and AP BS calculations have provideda symmetrical diamond core in accord with theexperiment [1–36]. Moreover, the comparisonbetween the BS and AP BS structures indicatesthat the difference between the optimized geome-try and experimental value is not caused by thespin contamination error involved in the BS solu-tion. This in turn indicates that the BS methodwithout AP is useful enough for the geometryoptimizations of the key intermediates.

Therefore, the usual geometry optimizationprocedure was used to locate other stationarypoints in the catalytic cycle in Scheme 2. As men-tioned above, the hydroxylation reaction pro-gresses through hydrogen abstraction via TS1and radical rebound via TS2 (see Figs. 4 and 5).

TABLE IThe optimized structural parameters of Q.

Parameters

Spin state

LS(S ¼ 0)

AP(S ¼ 0)

HS(S ¼ 4) Expt.a

Fe1AFe2 2.687 2.678 2.794 2.46–2.52Fe1AO1 1.842 1.809 2.146Fe1AO2 1.797 1.809 1.722 1.77,2.06Fe2AO1 1.733 1.742 1.665Fe2AO2 1.796 1.775 1.956Fe1AGlu114 2.185 2.195 2.039Fe1AGlu209 1.831 1.833 1.850Fe1AGlu243 2.009 2.015 1.924Fe1AHis246 2.127 2.123 2.186Fe2AGlu114 2.105 2.106 2.098Fe2AGlu144 1.916 1.916 1.919Fe2AHis147 2.110 2.111 2.114Fe2AWat 2.145 2.142 2.143

Comparison among spin states (HS, BS and AP).a From Ref. [16].



The optimized important parameters of TS1, I,and TS2 are shown in Figure 8.

The unsymmetrical structural parameters D atTS1 are given by

D1ðBS LSÞ ¼ RðFe1 �O1Þ � RðFe2 �O1Þ¼ 1:980� 1:917 ¼ 0:063ðAÞ (7a)

D1ðHSÞ ¼ RðFe1 �O1Þ � RðFe2 �O1Þ¼ 1:985� 1:957 ¼ 0:028ðAÞ: (7b)

D2ðBS LSÞ ¼ RðFe1 �O2Þ � RðFe2 �O2Þ¼ 2:129� 1:659 ¼ 0:470ðAÞ (7c)

D2ðHSÞ ¼ RðFe1 �O2Þ � RðFe2 �O2Þ¼ 2:228� 1:657 ¼ 0:571ðAÞ: (7d)

The molecular structure of the Fe1AO1AFe2unit is almost symmetrical at both LS and HSstates, showing that the reactive oxygen O1 issupported with both iron ions. On the otherhand, the molecular structure of the Fe1AO2AFe2unit is largely unsymmetrical at both LS and HSstates; the O2 atom is shifted to provide theFe2¼¼O2 unit like in the HS state of Q. This indi-cates that the mixed valence (MV) state of theFe1AO2AFe2 unit corresponds to the charge-local-ized MV type I structure; the Fe1(III)AO2¼¼Fe2(IV)unit. These characteristic features are also recog-nized for the intermediate (I) and the transititonstructure TS2 as shown in Figure 8. On the otherhand, the BS method by the use of the generalspin orbitals (GSO) will be necessary to describethe charge-delocalized MV structure; theFe1(3.5)AO2AFe2(3.5), as discussed in the Support-ing Information.

4.3. ENERGY PROFILE FOR HS, LS, AND APSTATE

The relative energies of the key compounds inthe catalytic cycle are calculated setting the totalenergy of the intermediate (I) as the reference asshown in Figure 9. The energy gap between TS1and I was 11.4 kcal/mol at the HS state; it wasalmost equivalent to the activation barrier (11.5kcal/mol) for TS1 because the energy gapbetween Q and I was almost zero. On the otherhand, the energy gap between TS1 and I was 8.4kcal/mol at the BS LS state; therefore the activa-tion barrier was 16.4 kcal/mol because the energygap between Q and I was 8.0 kcal/mol at the

state. Furthermore the activation barrier increasedto be 17.2 kcal after the AP correction; the energylowering for Q by AP was 1.9 kcal/mol, whereasit was 1.1 kcal/mol for TS1, and 0.3 kcal/mol forI. Thus the difference of the activation barrierbetween AP BS (LS) and HS states was 5.7 kcal/mol for TS1. The r(CH3AH) of the HS state (1.233A) at TS1 is shorter than that of the LS state(1.291 A), indicating that the HS state goesthrough earlier TS than the LS state. This result isqualitatively in good agreement with those ofMorokuma and coworkers [50] and Siegbahn [53],who located TS1 structures for the HS (S ¼ 4)state. The details will be discussed in Section 5.

The energy gap (activation barrier) between Iand TS2 was 6.5 kcal/mol at the HS state. On theother hand, the gap was 4.2 kcal/mol at the BSLS state; it was further reduced to 3.6 kcal/molafter the spin correction (AP). Then the differenceof the activation barrier of TS2 from I was 2.9kcal/mol between AP BS (LS) and HS states; theAP correction was very important for therebound step. The r(CH3AH) of the HS state(2.428 A) at TS2 is shorter than that of the LSstate (2.573 A); TS2 at the LS state is quite earlyat the rebound step. The low activation barrierand the early TS2 indicate the facile recombina-tion reaction at the LS state. This result is in goodagreement with that of Lippard-Friesner et al.[55].

The activation barriers for hydrogen abstractionreaction by atomic oxygen (O) were also calcu-lated for comparison with sMMO as shown inFigure 10. Those of the triplet O (3P) atom werecalculated to be 8.0, 16.2, and 21.6 (kcal/mol),respectively, by AP UB3LYP, AP UCCSD(T), andMkMRCCSD(2e,2o). The UB3LYP method under-estimated the barrier for the radical reaction asusually in the case. On the other hand, theMRCCSD overestimated it, indicating the neces-sity of the perturbation correction by the inclusionof the triple excitation (T); MRCCSD(T). The spincontamination error is significant because theexperiment shows that the LS (S ¼ 0) state isabout 45 kcal/mol above the HS (S ¼ 1) state inthe case of the O (1Dxy). The energy gap between3P and 1Dxy was 16.1 kcal/mol at the UB3LYPlevel; it increased to be 32.3 kcal/mol at APUB3LYP. However, the gap was still underesti-mated by the UB3LYP calculations despite the APcorrection, while MkMRCCSD(2e,2o) reproducesthe experimental value, 45 kcal/mol as illustratedin Figure 10.

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FIGURE 9. The energy profile of the hydroxylationreaction of CH4 with sMMO for the HS, LS and APstate. [Color figure can be viewed in the online issue,which is available at wileyonlinelibrary.com.]

FIGURE 10. The energy profile of the reaction of CH4

with 1O (1Dxy) and3O (3P). [Color figure can be viewed

in the online issue, which is available atwileyonlinelibrary.com.]

FIGURE 8. Optimized structures at TS1, I, and TS2 for the LS and HS state. Values in parenthesis represent thedata for the HS state. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]



In contrast to the model of sMMO, the activa-tion barrier of hydrogen abstraction is very small(1.0 kcal/mol) at the 1Dxy state of the O atom,and the radical recombination proceeds with nobarrier even in the LS state as shown in Figure10. Since the AP state does not suffer from thespin contamination, it is found that the reactionoccurs spontaneously. This result also agrees wellwith that of MkMRCCSD(2e,2o). Thus the reactionprofiles in Figure 10 indicates that the activationbarrier for the radical recombination in sMMO isreduced [58] if very large basis sets are used forthe UB3LYP calculation and/or high-level calcula-tions such as MRCCSD(T) are performed, thoughsuch computations are impossible at the presentstage.

4.4. NATURAL ORBITAL (NO) ANALYSIS ANDCHEMICAL INDICES

Chemical indices such as effective bond order(b) and diradical character (Y) based on the natu-ral orbital occupation numbers are calculated toclarify the nature of chemical bonds at each sta-tionary point in the catalytic cycle. Their defini-tion, formulation and expression with the occupa-tion numbers are given in the SupportingInformation SI. The calculated chemical indices (b,Y) together with J values are summarized in TableII, and corresponding natural orbitals are depictedin Supporting Information Figs. S6–S9 in SIII.

As shown in these figures, HONO-4 expressesthe orbital interaction in the O1AHACH3 moietyat the TS1 of the LS state. The effective bondorders before (b) and after (B ¼ 1 � Y) AP were0.419 and 0.712, respectively, showing the moder-

ate covalent bonding character. Therefore the dir-adical character Y was 29% for this bond. Sincethe Y value of the HS solution always equals to1.000, this small Y value of the BS solution showsthe relatively strong covalency unlike the result ofthe simplified reaction model in Figure 10 (Y ¼97% in this case). On the other hand, HONO-3indicates the orbital interaction in theO1AHACH3 moiety at I; it was quite isolated likein the case of the HS solution. In fact, the b andY(B) values for I were 0.105 and 0.792 (0.218),respectively. These values at the LS state indicatethe bound radical state instead of the free radical.HONO-4 represents the orbital overlap betweenthe diradical pair [(:�OH)(;�CH3)] at TS2. The band Y(B) values for TS2 were 0.274 and 0.491(0.501), respectively. These values at the LS stateclearly demonstrated the bound radical state inaccord with the prediction on the experimentalgrounds. The computations support the very fastrecombination proposed by Friesner and co-workers [58].

The chemical indices indicated that the weakcovalent bonding remains even at the intermedi-ate I, and the transition structures TS1 and TS2.Therefore, the situation is different from that ofatomic oxygen that indicates the generation of thefree radicals. Then, the J-values for these key spe-cies are indeed negative in sign, showing the anti-ferromagnetic (AF) ground state. The double andsuperexchange mechanisms in the MV configura-tion Mn(III)A(O)2AMn(IV) favor, respectively, theferromagnetic and antiferromagnetic interactions.The negative J-values for the key species in thecatalytic cycle in Scheme 2 indicate that the super-exchange mechanism is stronger than the double

TABLE IICalculated chemical indices (b and Y) and J-values based on magnetic orbitals at Q, TS1, I, and TS2.

State Index

Natural orbital

HONO-4 HONO-3 HONO-2 HONO-1 HONO Ja

Q b – 0.284 0.220 0.187 0.178 �166Y – 0.475 0.581 0.639 0.655

TS1 b 0.419 0.256 0.094 0.086 0.062 �77Y 0.288 0.519 0.813 0.829 0.876

I b 0.241 0.105 0.074 0.071 0.041 �23Y 0.544 0.792 0.852 0.858 0.919

TS2 b 0.274 0.253 0.119 0.042 0.006 �64Y 0.491 0.524 0.766 0.916 0.988

a In cm�1.

SAITO ET AL.


exchange in the diiron clusters in sMMO. Thecomputational results demonstrated the corre-spondence between the magnetism and chemicalbonds.

5. Discussions and ConcludingRemarks

5.1. LOCATIONS OF TRANSITIONSTRUCTURES FOR MMO

In this section, we examine previous computa-tional results on the mechanisms of hydroxylationwith sMMO. For the purpose, we have summar-ized the spin densities on the reaction sitesreported by several groups in Table III. To eluci-date the correspondence between magnetism andreaction mechanism, we first examine the mag-netic interactions in the diiron cores [40–43].Yoshizawa et al. [44–48] has assumed that anactive site of the intermediate Q lies in the closed-shell state consisted of the locally closed-shellirons, 1[Fe(IV)(Sz ¼ 0)O2�

2 Fe(IV)(Sz ¼ 0)](11RB3LYP) under the RB3LYP approximation andthe closed-shell nature holds throughout the oxy-

genation reaction. Such closed-shell constraintentailed that the high-valent Fe(IV) attacks thecarbon atom of CH4 in an electrophilic manner togenerate zwitterionic four centered transitionstructure (TS) without no spin density on all theatoms. Their mechanism is therefore formally sim-ilar to our electrophilic substitution bimolecularmodel, namely (2þ2)-type mechanism in Figure 3,and many other (2þ2)-type organometallic reac-tions. Probably their mechanism is reasonable ifthe Fe(IV) sites [36] are closed-shell as in the caseof organometallic reactions.

However, the energy gap between TS1 andI was 40.5 kcal/mol under the RB3LYP approxi-mation; the activation barrier for TS1 was 31.5kcal/mol because Q was less stable by 9.4 kcal/mol than I. The activation barrier was too large ascompared with the experimental values. Theenergy gap (activation barrier) between I and TS2was 17.9 kcal/mol under the RB3LYP model. Thisvalue was also very large as compared with theactivation barriers reported by several groups[49–53]. Thus the closed-shell RB3LYP modelbreaks down for locations of TS1, I and TS2because of the instability of the closed-shell bondsin the diiron cluster in sMMO.

TABLE IIIMulliken spin density populations on the important atoms at each stationary point.

Structure Spin state

Spin density

Fe1 Fe2 O1 O2 CH3 Ref.

Q 1LS 3.38 �3.30 �0.12 �0.06 – This work9HS 3.29 3.22 0.50 0.31 – This work9HS 3.44 3.55 0.30 0.44 – [50]1LS 1.71 �1.52 �0.57 0.38 – [53]1LS 3.54 �3.49 �0.06 �0.03 – [58]

TS1 1LS 4.06 �3.21 �0.41 �0.38 �0.55 This work9HS 4.09 3.21 �0.26 �0.47 �0.47 This work9HS 4.59 3.54 �0.37 0.40 �0.55 [50]9HS 4.11 1.36 0.63 0.77 0.53 [53]1LS 4.17 �3.39 �0.38 �0.28 �0.43 [58]

I 1LS 4.10 �3.21 0.00 �0.37 �1.09 This work9HS 4.11 3.21 0.24 0.51 �1.09 This work9HS 4.64 3.51 0.08 0.43 �0.99 [50]9HS N.A. N.A. N.A. N.A. N.A. [53]1LS 4.24 �3.38 0.01 �0.26 �0.92 [58]

TS2 1LS 4.08 �3.46 0.11 �0.27 �0.93 This work9HS 4.10 3.13 0.27 0.44 �0.89 This work9HS 4.58 3.23 0.20 0.38 �0.73 [50]9HS 4.13 1.80 N.A. 0.64 0.79 [53]1LS 4.23 �3.49 0.10 �0.22 �0.94 [58]



The above results indicate the necessity of theopen-shell treatments of the key species in thecatalytic cycle. Morokuma and coworkers [49, 50]indeed investigated the HS state of Q with Stotal¼ 5 (2S þ 1 ¼ 11). They showed that the hydro-gen atom abstraction with the oxygen site occursto afford a discrete methyl radical as illustrated in93 of Figure 5. They further located the reboundprocess of CH3 and OH radicals assuming the fer-romagnetic state with Stotal ¼ 5. The spin densitieson the Fe1 and Fe2 atoms in Q(TS1) were3.44(4.59) and 3.55(3.54), respectively. Those ofCH3 and OH at TS1 were �0.55 and �0.37,respectively. Morokuma and coworkers model[49, 50] is therefore regarded as a triplet O-modelin our terminology in Scheme 3 and Figure 5: thehydrogen atom abstraction of p-radical orbital oftriplet O atom to generate OH and CH3 radicalsfollowed by spin inversion for recombination pro-cess. The energy gap between TS1 and I was 11.6kcal/mol under the UB3LYP approximation; theactivation barrier for TS1 was 13.3 kcal/molbecause Q was more stable by 1.7 kcal/mol thanI. Thus the high-spin (HS) UB3LYP model pro-vides a reasonable reaction profile of TS1, I andTS2. The spin densities on Fe1 and Fe2 at TS2were 4.59 and 3.54, respectively, indicating thelocal high-spin configurations of Fe(III) andFe(IV); this means that an extra b-spin wasinduced on another site to generate a local singletdiradical pair (OH and CH3). However, the ferro-magnetic state of the diiron core is hardly con-ceivable for a reactive state in sMMO; the energygap between 1Q and 3Q was 9.7 kcal/mol. Thusthe magnetic coupling of sMMO plays an impor-tant role in oxygenation reactions.

Siegbahn [51–53] has assumed the AFexchange-coupled state of iron ion Fe(IV) withthe intermediate spin (IMS; S ¼ 1), 1[Fe(IV)(Sz ¼1)O2�2Fe(IV)(Sz ¼ �1)](11IMS), for the Q interme-diate at an initial state of methane monooxygen-ation. In fact, the spin densities on Fe1 and Fe2 atQ are 1.71 and �1.52, respectively, indicating theAF coupling. However, Noodleman and co-workers [54] have pointed out that the groundstate of the diiron core becomes triplet if the in-termediate spin state (S ¼ 1) is assumed for theFe(IV) ion, in contradiction to the AF groundstate of Q. One-electron transfer from O2� toFe(IV)(Sz ¼ 1) to generate a ferromagneticallycoupled state via the double exchange mecha-nism, 9[Fe(III)(Sz ¼ 5/2)O2�O1 (Sz ¼ 1/2)Fe(IV)(Sz¼ 1)](92IMS), as an activated Q intermediate,

where oxygen p-radical orbital can abstracthydrogen atom from CH4. The energy gapbetween TS1 and I was 11.0 kcal/mol under themodified UB3LYP approximation; the activationbarriers for TS1 (TS2) was 13.8 (4.8) kcal/molbecause Q was more stable by 2.8 kcal/mol thanI. The spin densities on Fe1 and Fe2 at TS1 (TS2)are 4.11(4.13) and 1.36(1.80), respectively; those ofCH3 and OH at TS1 are 0.53 and 0.63, respec-tively. As a result, Siegbahn model [51–53] is alsoregarded as a triplet (HS) O-model to generatediscrete methyl radical intermediate in agreementwith the reaction profiles in Figure 5. It is how-ever noteworthy that Mossbauer spectroscopy[36] shows the local HS state of iron in Q, and itsoxidation number is consistent with Fe(III) (Sz ¼5/2) or Fe(IV) (Sz ¼ 2).

Friesner and coworkers [55–61] have assumedan AF state of diiron core with local HS (S ¼ 2)state, 1[Fe(IV)(Sz ¼ 2)O2�

2 Fe(IV)(Sz ¼ �2)](11) inFigure 4. The spin densities on Fe1 and Fe2 at Qare 3.54 and �3.49, respectively, indicating the AFcoupling. One-electron transfer from O2� to oneFe(IV) occurs in their model to afford another AFstate, 1[Fe(III)(Sz ¼ 5/2) O2�O1-(Sz ¼ �1/2)Fe(IV)(Sz ¼ �2)], where O1�(Sz ¼ �1/2) site hasin-plane p-radical orbital that can abstract ahydrogen atom from CH4 to generate 1[Fe(III)(Sz¼ 5/2)O2�OH1�(�CH3)(Sz ¼ �1/2)Fe(IV)(Sz ¼�2)]. Next, one-electron transfer from OH anionto the other Fe(IV) iron occurs to afford singletbiradical pair between hydroxyl radical andmethyl radical, 1[Fe(III)(Sz ¼ 5/2)O2�{�OH(Sz ¼1/2)�CH3(Sz ¼ �1/2)} Fe(III)(Sz ¼ �5/2)], whichrapidly collapses to the AF state with CH3OH,1[Fe(III)(Sz ¼ 5/2)O2�{CH3OH}Fe(III)(Sz ¼ �5/2)].The spin densities on Fe1 and Fe2 at TS1 (I andTS2) are 4.17(4.24 and 4.23) and �3.39(�3.38 and�3.49), respectively, showing no remarkablechange; those of CH3 and OH at TS2 are �0.94and 0.10, respectively. The energy gap betweenTS1 and I was 11.5 kcal/mol under the UB3LYPapproximation; the activation barriers for TS1(TS2) was 17.9 (3.9) kcal/mol because Q wasmore stable by 6.4 kcal/mol than I. The key pointof the Friesner and coworkers model [55–61] is ageneration of singlet diradical pair between OHand CH3, followed by very fast recombinationbecause of retention of the AF state throughoutthe oxygenation, in accord with the orbital inter-action model in Figure 4. The Friesner and co-workers model [55–61] is therefore consistentwith a singlet O-model LSD in our terminology

SAITO ET AL.


[37]: singlet O (1Dxy) abstracts a hydrogen atomfrom CH4 to generate singlet biradical (OH (Sz ¼1/2) and CH3 (Sz ¼ �1/2)) followed by the rapidrecombination (see also Scheme 3 and Fig. 4). Atthe present stage there is no report of GSO calcu-lations, though triangular (noncollinear) spin con-figurations may appear in TS1 and TS2, andtherefore the GSO solutions with noncollinearspin structures may be the ground state under theBS approximation.

Our singlet O(1Dxx)-model for sMMO permits anonradical nonsynchronous (NN) mechanism forhydroxylation originally proposed by Lippard[25]. For example, activated Q state generatedwith the back charge transfer from O2� to Fe(IV),1[Fe(III)(Sz ¼ 5/2)O2�O0Fe(III)(Sz ¼ �5/2)], hassinglet O(1Dxx)-site (electrophilic p-orbital LUMO)which can undergo abstraction-type insertion oxy-gen transfer via the NN mechanism; the chargetransfer interaction between the vacant p-orbitalof the O-site with the CAH bond is a drivingforce in this hydrogen transfer process. The BS CIcalculation by the use of AF BS configurationscited above is inevitable for elucidation of thepotential curves. To confirm the NN mechanism,we have examined hydroxylation of CH4 withO¼¼OH2 (water assisted O-atom model), showingthe NN process along the reaction coordinates[42]. This in turn indicates that possibility of theNN mechanism cannot be eliminated for hydrox-ylation with the Q intermediate for MMO; how-ever, at least a polar factor (for example H3O

þ)seems necessary near the reaction site for thismechanism. The reaction of Q with CH4 providesCH3OH, together with the oxidized MMOH state,1[Fe(III)(Sz ¼ 5/2)(OH1�)2Fe(III)(Sz ¼ �5/2)]; (Tintermediate in Scheme 2), which is formally gen-erated from 1[Fe(III)(Sz ¼ 5/2) O2�Fe(III)(Sz ¼�5/2)] and H2O as shown in Scheme 2. Polaraminoacids and/or other environmental effectsseem necessary to stabilize the NN TS1’ [63].However, although the ionic state indeed is highas compared with the DR-type TS [63], its contri-bution in the BS CI is not negligible. In this situa-tion the mixing of singlet DR and ZW configura-tions in the resonating BS CI scheme often occurs,leading to the singlet ‘‘diradicaloid’’ mechanismfor hydrogen transfer step (TS1) at the LS singletstate.

1WRBS�CIð2XÞ ¼ C11W1ð12RÞ þ C2

1W2ð12LÞþ C3

2W3ð12DÞ; (8)

where Ci means the resonating CI coefficient ofthe single determinant BS configurations:Fe(IV)AO1�(�)AFe(III) (12R), Fe(III)AO1�(�)AFe(IV)(12L), and Fe(III)AO0AFe(III) (12D). The key con-cept of the resonating CI effect is the fact that thesinglet diradical character is more or less reducedto afford a continuous diradical (diradicaloid)with partial ZW character, which is essentiallyregarded as a NN state from the viewpoint ofstereochemistry. It is noteworthy that the singlereference (SR) BS approach such as UB3LYP [62–65] may be biased to overestimate the diradicalcharacter at the hydrogen transfer step (TS1).Future CASPT2 calculations may elucidate contri-butions of many other configurations at TS1. Sim-ilarly, the resonating BS CI is necessary for therebound step TS2. Thus, judging from various ex-perimental results, it seem too early to concludethe simple radical mechanism for hydroxylation,showing the necessity of further BS CI and MR-theoretical examination of the TS1 and TS2including environmental effects. In fact, previousBS calculations cited above have indeed shownchameleonic variations of spin, charge and orbitaldegrees of freedom at iron sites in the course ofoxygenation reactions in MMO. The present dis-cussions are equally applicable to pMMO involv-ing Cu(III) oxygen bonds. Many interestingtheoretical problems remain in the case of oxygentransfer reactions from binuclear transition metaloxides.

5.2. THE NATURE OF TRANSITIONSTRUCTURE 1

The first transition state (TS1) is responsiblefor the breakings of the Fe(IV)AOAFe(IV)superexchange coupling (�Fe(III) AO�AFe(IV))and CAH single bond (�HAC�) followed by thecoupling between the O� and �H sites to generatemetal diradical (�Fe(III)AOHAFe(IV) plus �CH3)[71–73]. The TS1 is determined with subtle bal-ance between these bond breaking energies.Therefore we can define the simple geometricalparameter to express early or late transition struc-tures (TS1) [71–73] as

x ¼ rðH� CÞrðH� CÞ þ rðH�OÞf g (9)

where r(X–Y) denotes the optimized X–Y lengthat TS1. Small x-values mean early TS1 in this



definition. Table IV summarizes the x-values forhydroxylation reactions with atomic oxygen andsMMO; the x-values for hydroxylations withCpI and p450 were discussed in part XIII [62].The x-value for the hydroxylation of CH4 withthe LS state (11) of sMMO was 51.4%; it is a littlelarger than that of Lippard and coworkers [58].On the other hand, the corresponding x-value forthe high-spin (HS) state was 48.8%; it is largerthan the value (44.5%) of Morokuma and co-workers [50] and smaller than that (51%) of Sieg-bahn [51].

The x-values for hydroxylation of other alka-nes with the LS state (11) of sMMO are about50–51% as shown in Table IV; these are there-fore compatible with the x-values of CpI andp450, showing a characteristic of their commonradical mechanisms of hydroxylations. Thus thex-values for the ground LS state of sMMO arealso compatible with that (53%) of hydroxylationwith the ground state O-atom. On the otherhand, the x-value for the singlet excited O-atom(1Dxy) was 46.9%, showing an early TS like inthe case of the excited HS state (91) of sMMO;however it was still larger than that (32.7%) ofthe abstraction-type insertion reaction withO¼¼OH2 (1Dxx of the excited O-atom) that was amodel of the Fe(III)AO0AFe(III) (12D); namelythe singlet nonradical model in Scheme 4. Thisin turn indicates that the nonradical insertionmechanism in Scheme 4 is not operative in the

ground state of sMMO without specific polareffects.

5.3. LOCAL SINGLET AND TRIPLETDIRADICAL MECHANISMS FORHYDROXYLATIONS

Scheme 3 illustrates the singlet diradical (SD)and triplet diradical (TD) mechanisms for hydrox-ylation of alkanes with atomic oxygen. Previously[37, 62–66, 78, 79], we employed the isoelectronic(isolobal and isospin) analogy among atomic oxy-gen (O), molecular oxygen (O¼¼O) and iron-oxo(Fe(IV)¼¼O) species. The isoelectronic analogybetween O¼¼O and Fe(IV)¼¼O provided five dif-ferent reaction modes for (2þ2)-type reactions ofthese species to alkenes [37, 79]. Similarly, the iso-electronic analogy among O, O¼¼O and Fe(IV)¼¼Oindicated possible reaction modes in Scheme 4; itcan be extended to reaction modes of sMMO asshown in Figure 3. One of characteristic featuresin these systems is the existence of several elec-tronic states with the near degeneracy. In this sec-tion, possible reaction modes of several electronicstates of some of oxygenation reagents in Figure 1are therefore examined systematically as summar-ized in Table V.

The effective exchange coupling (J) [37]between Fe(II) and O provides triplet and singletspin configurations of Fe(IV)¼¼O; 1(:Fe(IV)¼¼O:)

TABLE IVOptimized geometrical bond length and x-parameters for transition structures (TS1).

System Model Spin state r(HAC) r(HAO) rta x DEb Ref.

O CH4 þ 1O 1Dxy (S ¼ 0) 1.200 1.360 2.56 46.9 1.0 This workCH4 þ 3O 3P (S ¼ 1) 1.327 1.189 2.52 52.7 8.0 This work

O¼¼OH2 CH4 þ 1O¼¼OH21Dxx(yy) (S ¼ 0) 1.824 1.104 2.93 32.7 1.5 [65]

sMMO CH4 þ 91 9HS (S ¼ 4) 1.176 1.465 2.54 44.5 13.3 [50]CH4 þ 91 9HS (S ¼ 4) 1.30 1.24 2.54 51 13.8 [53]CH4 þ 11 1LS (S ¼ 0) 1.259 1.296 2.56 49.2 17.9 [58]CH4 þ 91 1HS (S ¼ 4) 1.233 1.293 2.53 48.8 11.5 This workCH4 þ 11 1LS (S ¼ 0) 1.291 1.218 2.51 51.4 17.2 This workCH3CH3 þ 11 1LS (S ¼ 0) 1.260 1.273 2.53 50.3 15.8 [60]CH3OH þ 11 1LS (S ¼ 0) 1.203 1.258 2.46 51.1 16.6 [60]CH3CN þ 11 1LS (S ¼ 0) 1.284 1.255 2.54 49.4 15.6 [60]CH3NO2 þ 11 1LS (S ¼ 0) 1.256 1.274 2.53 50.4 19.5 [60]CH3F þ 11 1LS (S ¼ 0) 1.286 1.345 2.63 51.1 16.6 [60]

a r(HAC) þ r(HAO).b In kcal/mol.

SAITO ET AL.


(31), and 1(:Fe(IV)¼¼O;) (11) and 1(;Fe(IV:)¼¼O)(11’). These are considered to be reactive spinconfigurations in the three-states model ofFe(IV)¼¼O (31, 11, and 11’) [37, 79, 62–64, 137–150]. Moreover, the d-orbital configuration of theiron-site often becomes triplet, namely 3(:dd*:).Then the exchange coupling of (:dd*:) with 31and 11 (11’) provides quartet and triplet configu-rations; 5[3(1) 3(:dd*:)] (51) and 3[1(1) 3(:dd*:)](31’) (3[1(1’) 3(:dd*:)] (31’’)), respectively. The or-bital interaction diagrams between active reactionorbital(s) and HAC bond of alkanes can bedepicted for each BS configuration as shown inour previous papers [37, 78, 79, 62–66] like inFigures 4 and 5. The LSD and LTD mechanismshave been concluded from these analyses asshown in Table V. From Table V, the singlet dir-adical (SD) and triplet diradical (TD) mecha-nisms are modified with participations of otherspins in Fe(IV)¼¼O; the notations of SET1 andSET2 are the same in Figure 5. SET1 means thatthe spin excitation (SET) is necessary to inducethe LSD configuration for the rebound radicalspair (OH and CH3); SET2 in turn indicates thatthe spin inversion (SI) is necessary for generationof the LSD configuration. The resonating BS CIapproach including 11 and 11’ is also feasible for

quantitative purpose (see part XIII [63]). Thusthe open-shell orbital interaction diagramsrevealed the correspondence between the mag-netic coupling mode and the radical reactionmechanism in hydroxylation reactions of theFe(IV)¼¼O species.

Local singlet and local triplet diradical mecha-nisms are similarly concluded for the hydroxyla-tion of alkanes with sMMO based on the orbitalinteraction diagrams in Figures 4 and 5. A keypoint of the proposed mechanisms is that ferro-magnetic and antiferromagnetic states assumedfor the Q state undergo, respectively, hydrogenabstraction, followed by triplet (discrete) and sin-glet (continuous) diradical recombination proc-esses. Indeed the ferromagnetic and antiferro-magnetic coupling modes in Q are directlyrelated to our LTD and LSD mechanisms forhydroxylation reaction of methane. The BS MOinteraction schemes in Figures 4 and 5 are con-sistent with the computational results available.So-called radical clock and chiral probe experi-ments have been performed to elucidate partici-pation of radical species with short lifetime [20].According to these experiments, discrete freeradical species are not involved in hydroxylationwith soluble MMO (sMMO) in accord with the

TABLE VLocal singlet diradical (LSD) and local triplet diradical (LTD) mechanisms of hydroxylations.a

System States Mechanism

O 3P [31] TD1Dxy [

11, 110] SDFe(IV)¼¼O 3R [31] LSD (3Fe(II))

1Dxy [11, 110] LTD (3Fe(II)) (SET2), LSD (1Fe(II)) (SET1)

5(3R�3(dd*)) [51] LSD (5Fe(II))3(1Dxy �3(dd*)) [310] LTD (5Fe(II)) (SET2), LSD (3Fe(II)) (SET1)[3100] LTD (1Fe(II)) (SET2), LSD (3Fe(II)) (SET1)

�L-Fe(IV)¼¼O 4(3R�2L) [41] LTD (2Fe(III)) (SET2), LSD (4Fe(III)) (SET1)2(3R�2L) [21] LSD (2Fe(III))2(1D�2L) [210] LSD (2Fe(III))[2100] LTD (2Fe(III)) (SET2), LSD (2Fe(III)*) (SET1)6(41�3(dd*)) [61] LTD (4Fe(III)) (SET2), LSD (6Fe(III)) (SET1)4(21�3(dd*)) [410] LSD (4Fe(III))4(210�3(dd*)) [4100] LSD (4Fe(III))4(2100�3(dd*)) [410 0 0] LTD (2Fe(II)*) (SET2), LSD (4Fe(III)*) (SET1)

Fe(IV)2O2 [Q] 1(Fe(IV)AFe(IV)) [11] LSD [1(Fe(III)AFe(III))]9(Fe(IV)AFe(IV)) [91] LTD [9(Fe(IV)AFe(IV))] (SET2)

LSD [9(Fe(III)AFe(III)*)] (SET1)

a SET1 and SET2 (see Fig. 5) and ‘‘*’’ denotes the excited configuration.



LSD mechanism at the ground LS state ofsMMO.

Accumulated experimental results have shownthat the high-valent iron-oxo core in P450 is for-mally regarded as the doublet Fe(V)¼¼O core [92–112], but the charge-transfer from ligand groups(porphyrin and cystein anion) to Fe(V)¼¼O occursto provide the so-called compound I (CpdI) con-sisted to Fe(IV)¼¼O and ligand radical (�L);indeed, hole radical is more or less populatedboth ligand groups [151, 137–158]. We have alsoexamined variations of hole populations overligand groups with change of proximal ligands(cystein(P450), imidazole(peroxidase) or phenoxi-de(catalase)anion) [158]. The exchange coupling(J) [37] between Fe(IV)¼¼O and �L provides quar-tet and doublet spin configurations of CpdI;4[3(:Fe(IV)¼¼O:) 2(�L:)] (41) and 2[3(:Fe(IV)¼¼O:)2(�L;)] (21). These are considered to be reactivespin configurations in the two-states model (41and 21) [137–150]. However, the singlet excitedstate of the Fe(IV)¼¼O core may participatehydroxylation reactions because of the small sin-glet–triplet state [37, 62–65]. This entails anotherdoublet configurations arising from the spincoupling; 2[1(:Fe(IV)¼¼O;) 2(�L:)] (21’) and2[2(;Fe(IV)¼¼O:) 2(�L:)] (21’’). Thus four configura-tions (41, 21, 21’, and 21’’) [62–65] based on the BSMO approximation are feasible for hydroxylationreactions of alkanes as a direct extension of thesinglet and triplet DR models for the Fe(IV)¼¼Ospecies [37, 97–99] in Scheme 3. The resonating BSCI approach including 21, 21’, and 21’’ is also fea-sible for quantitative purpose (see part XIII [63]).Table V summarizes the correspondence betweenthe magnetic coupling mode and the radical reac-tion mechanism revealed [65].

The d orbital part of Fe(IV) in CpdI can beregarded as the closed-shell state in the case ofstrong ligand field discussed previously [137–158]. However, as shown previously [37, 62–65],the dd* excitation becomes feasible under theweak ligand filed, leading to the parallel spinalignment (:dd*:). Then the exchange coupling of(:dd*:) with 41 and 21 provides sextet and anotherquartet configurations; 6[3(:Fe(IV)¼¼O:) 3(:dd*:)2(�L:)] (61) and 4[3(:Fe(IV)¼¼O:) 3(:dd*:) 2(�L;)](41’), respectively. Such variations of the spinstates often occur as illustrated in the reactioncycle of P450. The quasi-degenerate states (QDS)model involve six BS configurations (41, 21, 21,21’’, 61, and 41’) in the case of weak ligand field.Moreover, the spin coupling of (:dd*:) with 21’

and 21’’ gives rise to another excited quartet con-figurations, 4[3(:Fe(IV)¼¼O;) 3(:dd*:) 2(�L:)] (41’’)and 4[3(;Fe(IV)¼¼O:) 3(:dd*:) 2(�L:)] (41’’’). Thusthe spin couplings lead to the QDS model includ-ing eight configurations (41, 21, 21’, 21’’, 61, 41’,41’’, and 41’’’) that covers all the lower-lying radi-cal-type configurations for hydroxylations underthe BS approximation [37–40, 62–65, 78, 79]. Theorbital interaction diagrams of all these configura-tions with a CAH bond of alkanes have beendepicted in part XIII of this series; both LSD andLTD mechanisms were resulted as a continuationof the singlet and triplet diradical mechanisms inScheme 3, showing the clear cut correspondencebetween the magnetic coupling mode and radicalmechanism of hydroxylation reaction as summar-ized in Table V.

The insertion mode or abstraction-type inser-tion mode in Scheme 3 has been out of concern inmany BS B3LYP calculations of hydroxylationreactions by CpI [137–158]. However, it is note-worthy that the electrophilic insertion-like modelfor oxygenation reactions with the doubly occu-pied 1Dxx(yy) configuration of O, O¼¼OH2,Fe(X)¼¼O (X ¼ V, IV) cores and L-Fe(V)¼¼O (X ¼V) is feasible as shown previously [37, 62–65].Interestingly, the Fe¼¼O doubly occupied bond ofthe Fe(V)¼¼O and L-Fe(V)¼¼O often indicated thetriplet instability, leading to the labile bond witha singlet diradical character ; 2(:��Fe(IV)¼¼O�;)and L-2(:��Fe(IV)¼¼O�;) [37, 62]. As the result ofthe non-negligible radical character, these configu-rations favor the hydrogen abstraction mode [62–66] via the LSD mechanism instead of the abstrac-tion-type insertion mode as shown in the case ofO¼¼OH2 [65]. The triplet instability of the Fe¼¼OdpApp bond is, however, dependent on severalenvironmental factors: oxidation number of transi-tion metals, ligand filed splitting energies, Cou-lomb exchange energy, solvation energy, proteinfields, etc. Then, the careful examination of reac-tion modes in each environmental condition isnecessary for theoretical elucidation of reactivityof CpdI and related species.

6. Concluding Remarks

Electronic mechanisms of hydroxylation reac-tions of methane and related species with sMMOhave been investigated on the basis of the BS

SAITO ET AL.


UB3LYP method followed with the AP. First ofall, four possible mechanisms of the hydroxyla-tion reactions are derived based on previous(2þ2), singlet and triplet O-models for hydroxyla-tions in Scheme 4; these mechanisms are illustratein Figure 3. The open-shell orbital interaction dia-grams for the hydroxylation with sMMO aredepicted to elucidate the mechanisms of radicalreactions as shown in Figures 4 and 5. From thesediagrams, the LSD and LTD mechanisms havebeen concluded for the ground LS state and theexcited high-spin (HS) state of sMMO, respec-tively. The LSD and LTD mechanisms for hydrox-ylation reactions are similarly concluded for sev-eral electronic configurations of the iron-oxospecies (Fe(IV)¼¼O) and CpI in p450 (�L-Fe(IV)¼¼Oand/or L-Fe(V)¼¼O); the orbital interaction dia-grams have been shown in previous papers [62–65]. Thus, the open-shell orbital interaction dia-grams have elucidate the correspondence betweenthe magnetic coupling mode and radical reactionmechanism as summarized in Table V.

The BS UB3LYP computations of both theground LS (S ¼ 0) and excited HS (S ¼ 4) stateshave been carried out to elucidate the electronicstructures of key species in the catalytic cycle inScheme 2. The full geometry optimizations of theLS and HS states of the key intermediate Q havebeen performed using the energy gradient of BSand AP BS UB3LYP methods. The optimizedstructural parameters, together with EXAFS data,are summarized in Table I. The molecular struc-ture of Q at the HS state is unsymmetrical and isregarded as a dimmer structure of the Fe¼¼Ounits. On the other hand, both BS and AP BS cal-culations have provided a symmetrical diamondcore in accord with the experiment [1–36]. More-over, the comparison between the BS and AP BSstructures indicates that the difference betweenthe optimized geometry and experimental valueis not caused by the spin contamination errorinvolved in the BS solution. This in turn indicatesthat the BS method without AP is useful enoughfor the geometry optimizations of the key inter-mediates. Therefore, the usual geometry optimiza-tion procedure was used to locate other stationarypoints in the catalytic cycle in Scheme 2.

As mentioned above, the hydroxylation reac-tion progresses through hydrogen abstraction viaTS1 and radical rebound via TS2 (see Figs. 4 and5). The optimized important parameters of TS1, I,and TS2 are shown in Figure 8. The molecularstructure of the Fe1AO1AFe2 unit is almost sym-

metrical at both LS and HS states, showing thatthe reactive oxygen O1 is supported with bothiron ions. On the other hand, the molecular struc-ture of the Fe1AO2AFe2 unit is largely unsymmet-rical at both LS and HS states; the O2 atom isshifted to provide the Fe2¼¼O2 unit like in the HSstate of Q. This indicates that the mixed valence(MV) state of the Fe1AO2AFe2 unit corresponds tothe charge-localized MV type I structure; theFe1(III)AO2¼¼Fe2(IV) unit. These characteristic fea-tures are also recognized for the intermediate (I)and the transititon structure TS2 as shown in Fig-ure 8. The relative energies of the key compoundsin the catalytic cycle are calculated setting thetotal energy of the intermediate (I) as the refer-ence as shown in Figure 9. The activation barriersfor hydrogen abstraction reaction by atomic oxy-gen (O) were also calculated for comparison withsMMO as shown in Figure 10.

In contrast to the model of sMMO, the activa-tion barrier of hydrogen abstraction is very small(1.0 kcal/mol) at the 1Dxy state of the O atom,and the radical recombination proceeds with nobarrier even in the LS state as shown in Figure10. Since the AP state does not suffer from thespin contamination, it is found that the reactionoccurs spontaneously.

Chemical indices such as effective bond order(b) and diradical character (Y) based on the natu-ral orbital occupation numbers are calculated toclarify the nature of chemical bonds at each sta-tionary point in the catalytic cycle in Scheme 2.The calculated chemical indices (b, Y) togetherwith J values are summarized in Table II, and cor-responding natural orbitals are depicted in Sup-porting Information Figures S6–S9 in SIII.

As shown in these figures, HONO-4 expressesthe orbital interaction in the O1AHACH3 moietyat the TS1 of the LS state. The effective bondorders before (b) and after showed, respectively,the moderate covalent bonding character. On theother hand, HONO-3 indicates the orbital interac-tion in the O1AHACH3 moiety at I; it was quiteisolated like in the case of the HS solution. Thechemical indices at the LS state of at I indicatethe bound radical state instead of the free radical.HONO-4 represents the orbital overlap betweenthe diradical pair [(:�OH)(;�CH3)] at TS2. Thechemical indices at TS2 clearly demonstrated thebound radical state in accord with the predictionon the experimental grounds [1–36].

The above computational results have beencompared with previous computational results



on the mechanisms of hydroxylation with sMMOby several groups; the RB3LYPe results by Yoshi-zawa et al., the HS UB3LYP results by Moro-kuma and coworkers [49, 50] and Siegbahn [51–53] and the LS UB3LYP results by Friesner andcoworkers [55–61]. Scope and applicability of theBS UB3LYP method have been elucidated on thebasis of these computational results (see Sections5.2 and 5.3). The necessity of the BS CI usingseveral near degenerated BS configurations hasbeen touched for further refinements of the BScomputational results on the oxygenation reac-tions with Fe(IV)¼¼O, CpI, and sMMO. However,the present and previous BS computations haveclearly revealed the correspondence betweenmagnetic coupling and radical coupling mecha-nism in hydroxylation with sMMO and relatedspecies.

ACKNOWLEDGMENT

T.S. is grateful for the Research Fellowshipsfrom Japan Society for the Promotion of Sciencefor Young Scientists (JSPS).

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