cPCET versus HAT: A Direct Theoretical Method for Distinguishing X–H Bond‐Activation Mechanisms

Abstract Proton‐coupled electron transfer (PCET) events play a key role in countless chemical transformations, but they come in many physical variants which are hard to distinguish experimentally. While present theoretical approaches to treat these events are mostly based on physical rate coefficient models of various complexity, it is now argued that it is both feasible and fruitful to directly analyze the electronic N‐electron wavefunctions of these processes along their intrinsic reaction coordinate (IRC). In particular, for model systems of lipoxygenase and the high‐valent oxoiron(IV) intermediate TauD‐J it is shown that by invoking the intrinsic bond orbital (IBO) representation of the wavefunction, the common boundary cases of hydrogen atom transfer (HAT) and concerted PCET (cPCET) can be directly and unambiguously distinguished in a straightforward manner.

The transfer of an et hydrogen atom as part of ac hemical reaction can proceed in many different ways.D epending on the circumstances,v iewing this process as the coupled but distinct transfer of ap roton and an electron can be more appropriate than viewing it as transfer of an actual hydrogen atom. An umbrella term covering reactions of this type is proton-coupled electron transfer (PCET). [1] Such reactions are of broad relevance in contexts ranging from biological processes,s uch as some of the key steps related to the function of Photosystem II, [2] to hydrocarbon combustion, in for example the engine of ac ar. [3] Their fundamental understanding is therefore vital for future developments in the associated research fields.
Them ost fundamental scenarios to be distinguished are stepwise processes in which electron and proton transfer occur in individual steps,a nd concerted PCET (cPCET), where the proton and the electron are transferred simulta-neously.R eactions in which electron and proton travel together as at rue hydrogen atom will be called hydrogen atom transfer (HAT);t he more general term cPCET will be used only when proton and electron are transferred in concert, but do not travel together,adefinition similar to the one used by Shaik and co-workers. [7a] Scheme 1shows two representative cases,w hich we will discuss in detail below. Unfortunately,the use of these terms is far from consistent in the literature and at times much confusion can arise when these terms are used interchangeably.
Identifying which of the outlined mechanistic scenarios is operational can be challenging,a sa ll scenarios involve the same net transfer of one electron and one proton and therefore cannot be distinguished by knowledge of properties of the reactants and products alone.C onsequently,t he concrete nature of the process effecting this transfer is af requent matter of debate.M echanistic insight is primarily gained by indirect inference,b ased on various physical models of the imagined sub-processes of electron transfer (ET) and proton transfer (PT) and their coupling. [1] In certain cases,d irectly accessible thermodynamic information on model compounds is sufficient to,f or example,r ule out stepwise processes. [1e] Frequently,however, complex physical models must be constructed to provide abasis for comparison to experimentally accessible information [1] (for example, kinetic isotope effects or influences of substrate properties on rate behavior). These models have proven very successful in providing adetailed quantitative physical picture of PCET events in many contexts.F or example,t he Hammes-Schiffer group has employed quantitative and qualitative diagnostics based on 1) electronic transition/proton tunneling times; [4] 2) the nonadiabatic coupling matrix element along the Scheme 1. Representation of the electron flow in HATand cPCET events from C(sp 3 )ÀHbonds to an acceptor (Fe IV =OorF e III ÀOH). Electron flow for single-electron events is depicted in black and blue for the movement of electron pairs. proton coordinate; [4] 3) changes to the charge distribution using indicators such as dipole moment, electrostatic potential, or partial charges; [5] and 4) changes in spin density. [6] An alternative tool is,f or example,t he analysis of deformation energies,a sproposed by the group of Shaik. [7] Nevertheless,i fw eo nly pose the question of how the various PCET processes can be distinguished (for example, regarding sequentiality of electron and proton transfer), and which chemical bond transformations they are accompanied and influenced by,then the construction of such quantitative rate models may not be the most direct way to obtain this information. With modern software and computers it is absolutely possible to determine approximate but qualitatively correct (Kohn-Sham) electronic wave functions for most of the involved species and, based on those,a lso determine all likely intrinsic reaction paths for possible PCET events and compare their barriers.O nce the most favorable reaction path has been determined, it should be possible to simply analyze the obtained trajectory of the ground state Nelectron wave function directly to clarify the concrete nature of the process.A fter all, the N-electron wave function contains all information about the N-electron system which is physically observable.A dditionally,r ecently introduced analytic methods,s uch as the intrinsic bond orbital (IBO) [8] transformation, provide an exact representation of any Kohn-Sham density functional theory (DFT) wavefunction, which is well amenable to the analysis of electronic structure changes in intuitive terms.W ehave previously demonstrated that the changes which IBOs undergo along agiven reaction path can be linked to curly arrows [9] and are indeed suitable for the investigation of C(sp 3 )ÀHa ctivation reactions. [10] These previously investigated reactions were of closed shell nature and only involved the movement of electron pairs.Asaresult, previous investigations did not give rise to the challenges that open shell systems,e specially in homolytic bond cleavage, pose to most computational chemistry methods,a nd in particular to single-reference methods such as DFT. [11] Yet DFT does frequently allow for the qualitative,a nd even quantitative,d escription of complex chemical transformations (including reactions involving PCET) [12] and its software implementations have by now reached as tate of maturity allowing for in-depth studies of large (and more importantly, experimentally accessible) systems.A nalysis of stationary points for ac PCET reaction of an Fe III ÀOH complex with TEMPOH [13] prompted us to explore the possibilities of monitoring electron flow in such PCET transformations using the IBO representation, to reveal their reaction mechanisms directly.
We initiated our studies by analyzing two reactions from the field of bioinorganic chemistry [14] where C(sp 3 )ÀHb ond oxidation occurs either via cPCET,f ollowing the above definition, or aH AT mechanism. Fort he cPCET case,w e selected the well-studied reaction of lipoxygenase, [15] an Fe III À OH active site which breaks one of the C(sp 3 ) À Hb onds of arachidonic acid, and for HATw es elected the C(sp 3 ) À H oxidation event from the oxoiron(IV) intermediate in taurine dioxygenase (TauD-J), [16] which oxidizes aC(sp 3 )ÀHbond of taurine.S tructural depictions for the active sites and transition states for CÀHb ond activation are shown in Figure 1.
Based on these two reactions we will demonstrate that it is indeed possible to differentiate between cPCET and HATin as traightforward and chemically intuitive way using IBOs. Our approach therefore provides at ool for unambiguous mechanism assignment with the potential for very broad applicability.
Fort he cPCET reaction of lipoxygenase,w eu sed the model system previously employed by Soudackov and Hammes-Shiffer [6] consisting of ah igh-spin (S = 5/2) Fe III À OH unit ligated by three imidazoles mimicking histidine residues,acarboxylate residue mimicking an isoleucine,a nd an amide mimicking an asparagine residue.The substrate was mimicked as a1 ,4-diene with as imple hydrocarbon framework (see Figure 1, bottom right). This reaction has not only been identified to follow ac PCET mechanism, but also provided ap latform for the evaluation of theoretical methods. [3,7,17] Fort he HATr eaction of the high-valent oxoiron(IV) intermediate TauD-J,w es elected am odel system studied previously by Ye and Neese. [18] This consists of ah igh-spin (S = 2) Fe IV =Ounit ligated by two imidazoles and one acetate mimicking a2 -His-1-carboxylate facial triad [19] and one additional acetate mimicking the coordination of decarboxylated a-ketoglutarate.W enote that several reaction channels have been discussed for oxoiron(IV) complexes for HAT reactions [20] and we will focus on the s-pathway associated with the S = 2s pin state which has been judged to be energetically most favorable in the present case by Ye and Neese.
We first computed the transition states for the C À Hbond breaking events at the B3LYP [21] /def2-SVP [22] level of theory in the gas phase.W eselected the B3LYP functional, as it has ap roven track record for reactions of this type and provides satisfactory results even for challenging Fe-based systems, [23] Figure 1. a) Lewis structure depictions of active sites for a-KG-dependent iron dioxygenases and lipoxygenase. [14] b) Computed transition states for CÀHbond oxidation by models for TauD-J and lipoxygenase. despite its many known shortcomings.The def2-SVP basis set is well balanced and has also been used successfully in several instances for related systems. [24] To cross-check, we also evaluated how the choice of functional and basis set affects our conclusions.All tested combinations produced consistent classification of cPCET vs.HAT and therefore these data are given in the Supporting Information, Figures S1 and S2.
We begin by demonstrating how IBOs can be used to identify HATinthe case of TauD-J,which may be regarded as the simpler case.Webegin our analysis by producing IBOs for the a and b spin manifold;n ext, we identify the localized orbitals of the CÀH s-bond, and then follow the changes that they undergo along the IRC.I nF igure 2a we show how the a and b spin IBOs of the CÀHb ond evolve along the IRC. This in principle allows us to categorize C À Hb ond breaking reactions in ac hemically intuitive way.A so utlined above,i f the C À Hb ond is broken via HAT, it would be expected that one of the localized IBOs would be transformed from aC ÀH s-bond into apart of the OÀHbond in the present case.This is indeed what is observed:t he IBO belonging to the a spin manifold becomes part of the newly formed OÀH s-bond, whereas the IBO of the b spin manifold remains on the carbon atom of the substrate.T his scenario is consistent with the expected s-pathway previously described for HATreactions of oxoiron(IV) complexes.Ahigh-spin Fe III À OH intermediate is formed, which is antiferromagnetically coupled to the radical on the substrate. [20] In short, we can see that the electron pair of the CÀHb ond in the substrate is cleaved homolytically,w here one electron travels together with the proton and the second electron is left behind forming as ubstrate radical. As the proton and the electron are transferred together,t he newly formed O À Hb ond should consist of one (here a)electron from the C(sp 3 ) À Hbond and one electron from the Fe IV =Ounit. This does indeed happen and the O-centered s-lone pair, which provides the b electron is shown in Figure 2c.
Thus far, this procedure would require as tep by step analysis of every individual point of the IRC and then would require us to estimate by how much agiven IBO has changed. In previous studies of closed-shell reactions, [25] including C(sp 3 )ÀHa ctivation processes, [10] we have simplified the process of identifying the IBOs which undergo changes by computing the root-mean-square deviation of every IBO from the initial partial charge distribution along the intrinsic reaction coordinate.Aplot of these values (orbital change, plotted in units of e À )g ives immediate insight into which IBOs are participating in bond making and bond breaking along the reaction path. IBOs not involved in this process do not undergo significant changes and in principle do not require inspection (we only show the changes to the CÀH bonds in Figures 2b and 3b;all other changes are not shown for clarity). Thec orresponding plot for the HATr eaction studied here is shown in Figure 2b.F urthermore,t his plot clearly demonstrates that the electron flow associated with HATi sc ontinuous and thus that our description truly captures how the reaction occurs.
Forthe second reaction we studied the cPCET reaction of lipoxygenase and followed the same procedure.F irst, we followed the changes of the a and ßelectrons of the C(sp 3 ) À H bond along the IRC (Figure 3a). As outlined above,f or ac PCET reaction we would expect the proton and the electron to not travel together,but rather take separate paths. In line with this anticipation, we do observe this very behavior along the reaction path of the lipoxygenase model with the 1,4-diene model substrate.T he a electron remains on the substrate along the entire IRC,w hereas the ße lectron is transferred to the iron center,r endering its transfer independent of the proton. This independent proton transfer is confirmed by inspecting the electron pairs on the oxygen of the FeÀOH unit. As expected, the proton is forming anew OÀ Hb ond with alone pair on the oxygen atom, supporting the observation of proton transfer rather than hydrogen atom transfer (Figure 3c). This behavior is characteristic for cPCET.T his clean distinction between HATa nd cPCET mechanisms demonstrates how powerful the analysis of the electron flow by IBOs can be,including both closed and open shell pathways.T he plot shown in Figure 3b shows that the electron flow for cPCET is also captured as ac ontinuous process.
In summary,wehave used two prototypical model systems that cleave C(sp 3 ) À Hbonds to demonstrate that the electron flow of open shell reactions can be readily studied using IBOs. This simple and straightforward tool is apparently capable of differentiating electronic mechanisms even in challenging scenarios,such as occurring in HATand cPCET reactions.W e therefore believe this approach may shed light into many other challenging transformations.