Kinetic Isotope Effect Determination Probes the Spin of the Transition

Article Cite This: Acc. Chem. Res. XXXX, XXX, XXX−XXX

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Kinetic Isotope Effect Determination Probes the Spin of the Transition State, Its Stereochemistry, and Its Ligand Sphere in Hydrogen Abstraction Reactions of Oxoiron(IV) Complexes Published as part of the Accounts of Chemical Research special issue “Hydrogen Atom Transfer”. Debasish Mandal,† Dibyendu Mallick,‡ and Sason Shaik* Institute of Chemistry, The Hebrew University of Jerusalem, Givat Ram Campus, 91904 Jerusalem, Israel S Supporting Information *

CONSPECTUS: This Account outlines interplay of theory and experiment in the quest to identify the reactive-spin-state in chemical reactions that possess a few spin-dependent routes. Metalloenzymes and synthetic models have forged in recent decades an area of increasing appeal, in which oxometal species bring about functionalization of hydrocarbons under mild conditions and via intriguing mechanisms that provide a glimpse of Nature’s designs to harness these reactions. Prominent among these are oxoiron(IV) complexes, which are potent H-abstractors. One of the key properties of oxoirons is the presence of close-lying spin-states, which can mediate H-abstractions. As such, these complexes form a fascinating chapter of spin-state chemistry, in which chemical reactivity involves spin-state interchange, so-called two-state reactivity (TSR) and multistate reactivity (MSR). TSR and MSR pose mechanistic challenges. How can one determine the structure of the reactive transition state (TS) and its spin state for these mechanisms? Calculations can do it for us, but the challenge is to find experimental probes. There are, however, no clear kinetic signatures for the reactive-spin-state in such reactions. This is the paucity that our group has been trying to fill for sometime. Hence, it is timely to demonstrate how theory joins experiment in realizing this quest. This Account uses a set of the H-abstraction reactions of 24 synthetic oxoiron(IV) complexes and 11 hydrocarbons, together undergoing H-abstraction reactions with TSR/MSR options, which provide experimentally determined kinetic isotope effect (KIEexp) data. For this set, we demonstrate that comparing KIEexp results with calculated tunneling-augmented KIE (KIETC) data leads to a clear identification of the reactive spin-state during H-abstraction reactions. In addition, generating KIEexp data for a reaction of interest, and comparing these to KIETC values, provides the mechanistic chemist with a powerful capability to identify the reactive-TS in terms of not only its spin state but also its geometry and ligand-sphere constitution. Since tunneling “cuts through” barriers, it serves as a chemical selectivity factor. Thus, we show that in a family of oxoirons reacting with one hydrocarbon, the tunneling efficiency increases as the ligands become better electron donors. This generates counterintuitive-reactivity patterns, like antielectrophilic reactivity, and induces spin-state reactivity reversals because of differing steric demands of the corresponding 2S+1TS species, etc. Finally, for the same series, the Account reaches intuitive understanding of tunneling trends. It is shown that the increase of ligand’s donicity results in electrostatic narrowing of the barrier, while the decrease of donicity and increase of bond-order asymmetry in the TS (inter alia due to Bell−Evans−Polanyi effects) broadens the barrier. Predictions are made that usage of powerful electron-donating ligands may train H-abstractors to activate the strongest C−H bond in a molecule. The concepts developed here are likely to be applicable to other oxometals in the d- and f-blocks. the gas-phase reaction of FeO+ with H2 is an example of what a good theory may achieve.3d But this achievement still requires a huge effort, even for this small system. There exist spectroscopic probes for spin and structure of the transition-metal complexes in their ground states.4 There are also ways to characterize the reactive-spin-states in the gas phase by coupling infrared spectroscopy and mass spectrometry.4b,c By contrast, clear kinetic signatures for reactive-spin-states in metallo-enzymatic and biomimetic reactions is rare. It is this paucity that our group has been trying to fill in by exploring

1. INTRODUCTION Spin states play major roles in metalloenzymes and their synthetic models,1 as well as in catalysis by transition metal complexes.1b The spin states of a given complex influence structure, spectroscopy, bonding, and reactivity. The field is surging2 and interesting to a broad community of chemists. As such, it is timely to demonstrate how theory can be a partner of experiment in the quest to identify the reactive-spin-state in a chemical reaction. A fascinating branch of spin-state’s chemistry is reactivity of oxometal complexes, where spin states interchange during the reaction.1a,d,e Theoretical treatments of spin-state crossings have been done for small systems,3 and the recent treatment for © XXXX American Chemical Society

Received: September 9, 2017

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DOI: 10.1021/acs.accounts.7b00442 Acc. Chem. Res. XXXX, XXX, XXX−XXX

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Accounts of Chemical Research

Figure 1. (a) Schematic energy profiles for H-abstraction by 6-coordinate [FeIV(O)(L)] non-heme− and heme−Cpd II complexes. Alongside are the typical d-block orbitals. The S = 1 profile is drawn in red, while S = 2 in black. 3,5TSH are transition states, and 3,5IH are intermediate products, with indicators of the d-orbital that gains one electron during this oxidative step (c, d). The energy ordering within each spin-state-manifold depends on the specific system. (b) Electron-shift diagrams from σCH of the hydrocarbon to the oxoiron(IV) orbitals during H-abstraction. (c) Shifting the electron to π*xz/yz generates bent 2S+1TSH,π structures, while (d) shifting to σ*z2 generates upright 2S+1TSH,σ structures with a Fe−O−H angle of ∼180°.

present only the low-lying spin-states and indicate the corresponding spin multiplicities 2S+1 using superscripts. Figure 1 shows the two-state reactivity (TSR) scenario during H-abstraction reactions involving synthetic non-heme [FeIV(O)(L)] complexes or analogous [FeIV(O)(Por)] hemecomplexes,7 sometimes known as Compound II (Cpd II).7c Most of these complexes have a triplet (S = 1) ground state and a slightly higher-lying quintet (S = 2) state, due to the promotion of an electron to the stongly antibonding σ*xy orbital.1a,8 Both spin states can in principle participate in H-

trends of tunneling-corrected kinetic isotope effects (KIETC) for H-abstraction reactions of oxometal complexes.5,6 As this Account shows, comparing the experimental KIE with the calculated KIETC values for various spin states identifies the reactive-spin-state and, in addition, characterizes the transition state (TS) structure and its ligand sphere constitution. 1.1. Preamble

To articulate the scope of the problem, we consider archetypical energy profiles for H-abstraction reactions by oxoiron(IV) complexes from a hydrocarbon (R−H). We B


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Figure 2. (a) Energy profiles for H-abstraction by Cpd I, alongside the d-block orbitals and the singly occupied a2u orbital. The doublet-state profile is drawn in red and the quartet in black (energy-order is system-dependent). 2,4TSH are transition states, and 2,4IH are intermediate products. There are PorFeIVOH and Por•+FeIIIOH types for each spin-state. (b) Electron-shift diagrams from σCH of the hydrocarbon to the orbitals of Cpd I during the H-abstraction.

Although the great majority of the complexes treated here are the oxoiron(IV) types in Figure 1, for the sake of outlining a broader perspective, Figure 2 shows also the TSR scenario for a porphyrin-radical-cation−-iron(IV)-oxo species, [FeIV(O)(Lax)(Por•+)], known as Compound I (Cpd I) in analogy to the active species of cytochromes P450.7c Here, the two lowest lying spin-states are doublet (S = 1/2) and quartet (S = 3/2), which may both participate in H-abstraction. Most calculations9 show that the two energy profiles are close throughout the Habstraction phase and may both contribute to products.9b Additionally, Figure 2b shows that there are options to create Por•+FeIIIO···H···R and PorFeIVO···H···R states, which are close in energy and sensitive to the ligand sphere.9a Is there any kinetic probe that can tell us the spin and electromeric nature of the reactive state? Recently, we addressed the challenge using experimentally studied systems that exhibit TSR and MSR situations during C−H bond activation.5,6 Our studies showed that calculated KIEs could be compared with experimentally determined values to provide the following information on the TS under experimental conditions: its spin-state, its structure, and the constitution of the ligand sphere of its transition metal. As such, the interplay between theory and experiment, which we describe in this Account, provides a tool that uncovers the

abstraction via two structural varieties each, leading to four transition states (TSs) in Figure 1a. To comprehend the origins of these TSs, we recall that Habstraction is an oxidative step, in which oxoiron(IV) gains one electron and transforms to hydroxo-iron(III). Figure 1b shows four options to shift an electron from the σCH orbital to the dblock of oxoiron(IV). The so resulting TSs are labeled as 2S+1 TSH,σ and 2S+1TSH,π. The Greek subscripts indicate the identity of the d-orbital that gains the electron during oxidation; σ refers to the σ*z2 orbital, and π refers to the π*xz/yz orbital. Furthermore, as seen in Figure 1c,d, these orbitals determine the structure of 2S+1TSH: π*xz/yz leads to structures with a bent Fe−O−H angle, whereas σ*z2 enforces upright geometries with a Fe−O−H angle of ∼180°. Furthermore, the relative ordering of these TSs is system-dependent,1a,5c,7d and a few of them are close in energy. For example, in certain non-heme complexes, the 5TSH,σ and 3TSH,π species are close,6c while 3TSH,σ is significantly higher lying.1a Similarly, in Cpd II species with weakly bound axial ligands, 5TSH,σ and 3TSH,σ are close.5c Is there any kinetic probe that might enable the experimentalist to distinguish these varieties of transition states and identify the reactive-spin-state, the structure, and the coordination sphere of the TS? The answer given later is “yes”. C


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Equation 1 shows that tunneling cuts the barrier by ΔΔE⧧tun (Scheme 1), which depends on κ and the temperature T:5a,b

fine details of C−H bond activation by oxoiron(IV) compounds. Insights into the tunneling trends and their impact on chemoselectivity are discussed.5a

ΔΔE ⧧ tun = −RT ln κ(T )

2. CALCULATIONS OF TUNNELING Tunneling is a quantum-mechanical phenomenon, in which atoms behave as waves and propagate from reactant to product states, while bypassing the high energy of the TS.10 This can be represented by the cartoon in Scheme 1. The H-transfer is seen

(1)

R is the universal gas constant. The corresponding tunneling-corrected KIE (KIETC) is then evaluated by eq 2, KIE TC = (κH/κD)KIE EY

(2)

where κH/κD is the ratio of the transmission coefficients of the two isotopomers and KIEEY is the semiclassical Eyring value.

Scheme 1. Barrier Cartoon Being Tunneled through by H/D Species during H-Abstractiona

2.1. Calculated versus Experimental KIE Values

Being one-dimensional, the Eckart method does not take advantage of alternative tunneling pathways (e.g., by “cornercutting”). There are more sophisticated models,10 for example, based on multidimensional tunneling, which are time-extensive. Scheme 2 shows the systems we treated, and each one has several spin states, thus generating a large data set, which requires 107 tunneling calculations, making the multidimensional calculations impractical. Nevertheless, despite its simplicity, the Eckart model performs reliably,14 giving values close to multidimensional calculations.5b,c,6c For the set of Habstractions in Scheme 2, the model has been proven to be invaluable. For example, for 11/S7 (Scheme 2), the multidimensional model6c led to KIETC = 53 and the Eckart model to KIETC = 49,5b,c while KIEexp = 55 ± 5.6c The Eckart model reproduced the KIE dependence on temperature for a reaction of 15 with S4 down to ∼200 K5b,c as seen in the SI accompanying this paper.

a

The tunneling lowers the observed barrier relative to the semiclassical TS. The equation outlines the relationship between the observed (ΔE⧧eff) and semiclassical (ΔE⧧) barriers.

to propagate through the barrier at a point that depends on the temperature and at which the de Broglie wavelength of H matches the width of the barrier.10a The top of the energy barriers of H-abstraction reactions is narrow enough to allow ambient-temperature tunneling.10a−c As the scheme illustrates, the tunneling lowers the semiclassical barrier, ΔE⧧, by a quantity ΔΔE⧧tun, to yield an effective barrier, ΔE⧧eff. Due to its greater mass, deuterium (D) has a smaller de Broglie wavelength. While D can also tunnel, this occurs at a higher energy point near to the TS. Consequently, the resulting KIE at room temperature will exceed the classical limit and will exhibit other characteristics, such as energy barrier difference that exceeds the zero-point energy (ZPE) difference for H and D, nonclassical temperature-dependence, etc.10a,b As tunneling lowers the barrier by as much as10b 4 kcal/mol at ambient temperature, the involvement of tunneling in a chemical reaction acts as a reactivity and selectivity factor.11 Such a tunneling-induced counterintuitive reactivity pattern is the “antielectrophilic” trend observed12 a few years back in H atom abstraction reactions by a variety of oxoiron(IV) complexes of varying electrophilicity.5a Being sensitive to the width of the barrier, tunneling also acts as a filter for spin states that are close in energy and as a probe of the ligand sphere of the iron. This Account will discuss some of these trends. To address these issues, we use the Eckart-based method,13 which employs an analytical potential-energy function along the adiabatic minimum-energy path (AMEP), namely, the intrinsic reaction coordinate (IRC) in mass weighted coordinates. This function is fitted by the computed ZPE-corrected energies of reactants, products, and TS, as well as by the imaginary frequency. The transmission coefficient, κ, due to tunneling is calculated by integration of the barrier “penetration” probability as a Boltzmann averaged function of the energy.

Figure 3 shows a general correlation between KIETC and KIEexp for 23 reactions, involving selected-spin-states using the match of KIETC values, for different spin multiplicities, to KIEexp for a given reaction. The KIEexp values were determined in several groups, with different reaction conditions (temperature and solvent), and different error margins.

3. TUNNELING AS A PROBE OF THE REACTIVE-SPIN-STATE AND TRANSITION STATE 3.1. Probing Reactive-Spin-States

The investigated H-abstraction reactions of oxoiron(IV) complexes show that KIE measurements identify the reactivespin-states in potential TSR situations. The many cases are relegated to the SI, while Figure 4 uses four cases as examples. Figure 4a shows a reaction of [FeIV(O)(N4Py)]2+ with CHE (S7) that was investigated using both multidimensionaltunneling calculations6c and Eckart modeling.5b,c For this system, the large tunneling for S = 1 brings 3TSH,π to within 0.74 kcal/mol higher than 5TSH,σ.6c Even-though 3TSH,π is still higher in energy, the matching KIETC(S = 1, π)/KIEexp in Figure 4a allows us to unequivocally assign the reactive spin state as S = 1. As such, instead of TSR, the reaction proceeds primarily via single-state reactivity (SSR), and this choice reflects a combination of the poor tunneling on S = 2 and a possible nonunity spin-inversion probability from S = 1 to S = 2, which tips the balance in favor of S = 1.6c Figure 4b−d shows three other reactions with complexes based on tetramethylcyclam (TMC) ligands and differing axial ligands. Here, the KIEexp values5d,12 are matched only with the KIETC(S = 2,σ) values, while S = 1 values are too huge to match. Thus, all these reactions are genuine TSR cases wherein D


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Accounts of Chemical Research Scheme 2. (a) Oxoiron(IV) complexes and (b) Substrates Used in This Account and Their Numbering Systemsa

a

See SI for Abbreviations.

drops significantly15b now matching only the KIETC(S = 2,σ). Figure 5c,d depicts the corresponding TSs structures; the steric repulsion caused by the meta-positions of the pyridine rings destabilizes 3TSH,π (by 6.1 kcal/mol). Figure 5, panel f vs panel c, shows that the destabilization manifests as elongation of the C−H bond and opening of the Fe−O−H angle in 3TSH,π (12+S5) vs 3TSH,π (11+S5), resulting in a larger distortion energy1a of 3TSH,π (12+S5), and a larger barrier (by 6.1 kcal/ mol, Table S5). Now, the efficient tunneling for S = 1 is insufficient, and 5TSH,σ (12+S5) becomes the reactive TS. Similar low KIEexp values (11−14) were observed15c for the reaction of N4Py derivatives in which benzene rings were fused to the nitrogen ligands of N4Py. It is apparent that matching KIEexp to KIETC identifies this transformation, from SSR to TSR, as well as the TS’s geometric change.

the reaction proceeds by crossover from S = 1 to S = 2. Note that thiolate, as the best electron-donating axial ligand in the [FeIV(O)(TMC)(Lax)]z+ set, gives rise to a particularly high KIE for S = 2, which is the highest among all the non-heme oxidants and in line with KIEexp data.5a,d The next subsection projects the utility of KIETC by demonstrating that it can probe the reactivity switches from SSR to TSR, when steric effects prefer the upright 5TSH,σ species over the bent 3TSH,σ. 3.2. Reactive-Spin-State Switching Due to Steric Effects

Because 5TSH,σ and 3TSH,π have different geometries (Figures 1c,d), the bent 3TSH,π is more sensitive to steric effects, which may raise it well above 5TSH,σ. Indeed, Figure 5 demonstrates that when steric effects are built into [FeIV(O)(N4PyMe,OMe)]2+, reactivity toward benzyl alcohol (S5) changes from SSR to TSR. Thus, Figure 5a illustrates that for the unsubstituted [FeIV(O)(N4Py)]2+, KIEexp reasonably matches only KIETC(S = 1,π), whereas for N4PyMe,OMe in Figure 5b, the KIEexp value15a E


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Figure 3. Plot of KIETC vs KIEexp for 23 reactions of various non-heme oxoiron(IV) complexes [FeIV(O)(L5)]z [z = 2+,1+], heme−Cpd II, and Cpd I species. Here and elsewhere, the labels of the oxidants and substrates are taken from Scheme 2. Reactive spin states are colorcoded (S = 2 red, S = 1 blue, and S = 1/2 black).

Figure 5. (a, b) H-abstractions for cases prone to TSR. Shown are the KIEexp values15a,b and KIETC values for both S = 1,π and S = 2,σ. The matching KIETC value is framed in red. (c,d) Corresponding 2S+1TSH structures for the identified matching pathways. (e,f) The 2S+1TSs for the nonreactive pathways.

reaction of [FeIV(O)(TPFPP)] with xanthene (S3),5c KIEexp7a matches only KIETC(S = 1,σ). This match is consistent with 3 TSH,σ being the lowest energy species. Figure 6b shows the reaction of the same oxidant with DHA (S2). Once again, KIEexp reasonably matches only KIETC(S = 1,σ), which is in accord with the ordering of the various TSs.5c However, since the reaction in Figure 6b is conducted in acetonitrile with water traces, we tested the impact of these solvents as axial ligands (Figure 6c). By comparing the corresponding KIETC values to KIEexp,7a it becomes apparent that for H2O both KIETC(S = 1,σ) and KIETC(S = 1,π) values are now much higher, while KIETC(S = 2,σ) is still too low. However, the KIETC(NCCH3) for S = 1,σ reasonably matches KIE exp , but the CH 3 CN ligand is dissociated in the corresponding TS (RFe−N = 4.05 Å; Figure S6). Thus, in the presence of an axial ligand, KIEexp and KIETC values are mismatched, hence indicating that in the actual reaction,7a the aqua or acetonitrile ligands are absent or dissociated en route to the TS. Furthermore, in the case of a strongly bonded axial

Figure 4. H-abstractions for non-heme reactions, which may proceed by TSR. KIEexp values5d,12 are presented along with theoretical KIETC values for both S = 1 and 2. The matching KIETC value is framed in red.

3.3. KIETC Probes TS Structure During H-Abstraction by Heme−Cpd II Complexes

In heme−Cpd II, in addition to the S = 2,σ and S = 1,π pathways (Figure 1), the S = 1,σ pathway is energetically accessible,5c,7d which becomes the lowest in energy when the porphyrin lacks an axial ligand to Fe(IV). KIETC is a sensitive probe of these features. Figure 6 shows recently studied H-abstraction reactions by meso-substituted Cpd II species.5c Figure 6a shows that for the F


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ing KIEexp(T = 295 K) is 47 ± 4.17b The calculations revealed two Por•+FeIII type TSs, for which S = 1/2 is below S = 3/2 (Figure 2), with KIETC values of 44 for S = 1/2 compared with 78 for S = 3/2. As such, the match of KIEexp to KIETC (S = 1/2) identifies the doublet state as the main reactive-spin-state. Let us now discuss the role of tunneling as a chemoselectivity factor. 3.5. Counterintuitive Reactivity Patterns

The [FeIV(O)(TMC)(Lax)]z+ set of non-heme oxidants (1−10, Scheme 2), wherein the Lax ligands differ in their electrondonating capability to the FeIVO electrophilic center, posed an intriguing dilemma.12 Thus, experimentally, O-transfer reactions to phosphines followed the relative electrophilicity of the oxidants, making [FeIV(O)(TMC)(CH3CN))]2+ more reactive than the poorest electrophile, [FeIV(O)(TMC)((CH2)2S−)]1+. On the other hand, the H-abstraction reactivity toward DHA displayed an antielectrophilic trend, where the poorest electrophile, [FeIV(O)(TMC)((CH2)2S−)]1+, was more reactive than the best one, [FeIV(O)(TMC)(CH3CN)]2+. KIETC calculations showed that the factor that concocts this counterintuitive reactivity trend is tunneling.5a Figure 7a shows properties of the oxidants, alongside the effect of tunneling on the activation free energies of the two Habstraction reactions. Thus, the LUMO of [FeIV(O)(TMC)((CH2)2S−)]1+ is higher than that of [FeIV(O)(TMC)(CH3CN)]2+. Similarly, the amount of charge transferred

Figure 6. (a,b) H-abstraction cases with potential TSR, along with the KIEexp values,7a and KIETC values5c for S = 1 and 2 σ and π pathways. The matching KIETC values are framed in red. (c) The effect of potential axial ligands H2O/NCCH3 on KIETC for 22/23+S2. The data are given as KIETC(H2O)/KIETC(NCCH3), respectively. (d) Predicted KIEs5c for the reaction of 21+S2. The question mark signifies a prediction awaiting testing.

ligand like imidazole, the lowest energy TS is 3TSH,π, and such a case7c is predicted to have a very large KIETC. Finally, Figure 6d predicts KIETC values for the reaction of [FeIV(O)](TMP)] with DHA. Here after tunneling correction, the lower energy species are 3TSH,σ and 5TSH,σ, the latter is lowered by only 0.8 kcal/mol, which is within the error margins of DFT. However, the respective spin-state pathways have very different KIETC, 50.9 for S = 1 vs 9.2 for S = 2. Determining the KIEexp and matching it to one of the KIETC values for this reaction will, therefore, reveal if the reaction proceeds via S = 2 and exhibits TSR, or SSR via S = 1. An exciting scenario would be that both S = 2 and S = 1 pathways contribute to products and exhibit mixed KIE value.9b Clearly therefore, examining the H-abstraction reactions of Cpd II complexes shows that KIEexp can nimbly spot the reactive-spin-states, the geometry of the TS (upright like in the σ or bent as in the π pathway), and the constitution of the oxidant’s ligand sphere in the TS. 3.4. KIETC Probes the Reactive-Spin-State in H-abstraction by a Heme−Cpd I Complex

KIEs for reactions of Cpd I in P450 enzymes are not easy to interpret since there are competing steps in the catalytic cycles that may mask the KIE16 though the reported value of 12.5 for CYP119 implies tunneling.16 However, synthetic Cpd I species, with donor groups,17 either on meso positions of porphyrin (Scheme 2)17b or as axial ligands,17a appear to exhibit tunneling. As a proof of principle that KIETC-matching applies also for Habstractions by Cpd I, we investigated the reaction of 24 ([FeIV(O)(TMP•+)(Cl−)]) with S4, for which the correspond-

Figure 7. (a) Properties and relative reactivities of [FeIV(O)(TMC)((CH2)2S−)]1+ (10) vs [FeIV(O)(TMC)(CH3CN)]2+ (1) toward DHA (S2).5a Shown are the LUMO energies, the amount of charge transfer from the axial ligand (ΔQCT), and the relative free-energy barriers, calculated without tunneling (ΔG⧧rel), including tunneling (ΔG⧧rel,eff), and experimental ones (ΔG⧧rel,exp). (b) Corresponding Eckart barriers plotted against the IRC. Adapted with permission from ref 5a. Copyright 2015 American Chemical Society. G


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Accounts of Chemical Research from the ligand to the rest of the oxidant, ΔQCT, is much higher for thiolate than for acetonitrile. Both factors would have normally made [FeIV(O)(TMC)((CH2)2S−)]1+ the poorer Habstractor of the two oxidants. Indeed, without tunneling the DFT calculations showed5a that the free-energy barrier with thiolate was higher than that with acetonitrile. However, when tunneling was included, it was found that the barrier-cutting effect (ΔΔE⧧tun) for the reaction of [FeIV(O)(TMC)((CH2)2S−)]1+ was 2 kcal/mol larger than that of [FeIV(O)(TMC)(CH3CN)]2+. This effect reverses the reactivity order,5a making the free-energy barrier of [Fe IV (O)(TMC)((CH2)2S−)]1+ lower by 1.5 kcal/mol vs 2.0 kcal/mol experimental value.12 As such, tunneling inverts the relative reactivity in favor of the poorer electrophile, thus acting as a chemoselectivity factor. Furthermore, as temperature decreases, this antielectrophilic trend is predicted to become increasingly more significant. Note that in the absence of tunneling, in Otransfer reactions, the best electrophile, [FeIV(O)(TMC)(CH3CN)]2+, is clearly superior.5a Figure 7b shows the Eckart potentials plotted against the IRC for the two reactions. It is seen that thiolate, the better electron-donating ligand, has a narrow barrier throughout its height. Such a slim barrier enables tunneling well below the TS (3.5 kcal/mol), whereas for acetonitrile, the poorer electron donor, the barrier is broader and nonsymmetric, leaving a small energy space for tunneling closer to the semiclassical TS. The reasons for these different features are discussed in section 4.

4. TRYING TO MAKE SENSE OF TUNNELING TRENDS Narrow barriers bring about efficient tunneling.10a,c,18 The main factor that determines the narrowness of the barrier is the imaginary frequency (IF). High IF (>1300 cm−1) slims down the barrier, such that a significant fraction of it, from the TS downward, becomes available for tunneling, thus leading to a large transmission coefficient and high KIETC value. There are other factors, like the height of the barrier and its asymmetry5b,18 (e.g., due to reaction endothermicity or exothermicity or simply TS bonding asymmetry), as seen above in Figure 7b, which modulate the transmission coefficient. A reaction series that exhibits all these factors is the set of [FeIV(O)(TMC)(Lax)]z+ oxidants reacting with a single hydrocarbon, DHA (S2). Figure 8a shows a plot of the absolute magnitude of the IF vs the natural logarithm of the corresponding transmission coefficients (κ) for the series at one temperature, while Figure 8b shows a similar plot but against KIETC. In both plots, the data show some scatter, but the general trend is apparent: larger IFs generally lead to higher transmission coefficients and higher KIETC values. Let us now try to formulate a chemically intuitive rationale for the behavior displayed in Figure 8. Thus, if we reflect the barrier through a mirror passing perpendicular to the plane of the page, the barrier will “become an energy well”, allowing us to think of IF (for 5TSH) as though it were a real frequency of a stable structure located in an energy minimum.10a Doing so, we can link the barrier slimness to physical properties of the O··· H···C moiety in 5TSH,σ. In this moiety, H has a positive charge, while O and C carry negative charges; hence one property is the electrostatic potential (V) that governs the movement of this moiety along the reaction coordinate, and the other is the bond-order asymmetry. Equation 3a shows the electrostatic potential (V) across the OQ−···HQ+···CQ− moiety:

Figure 8. (a) Plot of absolute values of imaginary frequencies (ν, in cm−1) for H-abstractions by [FeIV(O)(TMC)(Lax)]z+ from DHA vs the natural logarithm of the transmission coefficients (κ). Lax varies from acetonitrile (CH3CN, 1) to thiolate ((CH2)2S−), 10), in increasing donicity. (b) Plot of ν vs corresponding KIETC values for the same series (T = 273 K).

V=−

|Q O| × |Q H| R O−H

−

|Q C| × |Q H| R C−H

+

|Q C| × |Q O| R C−O (3a)

Here QO, QH, and QC are NBO charges (au), R are corresponding distances (Å) at the 5TSH,σ geometry. Assuming other interactions are nearly constant, the second derivative of V, with respect to movements along the reaction coordinate R, will dominate the force constant (k) of the OQ−··· HQ+···CQ−moiety of the TS. The second derivative is shown in eq 3b. d2V 1 |Q O| × |Q H| 1 |Q C| × |Q H| ; ≈k=− − 2 3 2 R O−H 2 R C−H3 dR R = R C−H − R O−H

(3b)

With a little algebra, this second derivative links to the square of the IF (ν2) in the TS and, hence, with the slimness of the barrier (see SI for details). Figure 9a shows the variation of ν2 with the second derivative of V. The good correlation implies electrostatic narrowing of the barrier. Thus, as the axial ligand’s donicity increases, the H


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distinguishes between transition-state structures, which differ in their spin states, geometries, and ligand spheres. As we mentioned briefly, our preliminary investigation shows that KIETC probes also the reactive-spin-state in C−H bond activations by Cpd I in the reaction 24+S4. As such, KIE measurement constitutes a kinetic signature of the reactivespin-state, thus providing mechanistic research with a capability to identify the reactive-TS in terms of its spin, geometry, and ligand-sphere constitution. In addition, the Account shows that tunneling has a significant barrier-cutting effect, which increases with the augmented ligand donicity, thus leading to counterintuitive reactivity patterns, like antielectrophilic reactivity.5a,12 Steric control of S = 2/S = 1 reactivity reversals was demonstrated (Figure 5). Tunneling drives D- and H-abstractions to proceed via different spin states or have different regioselectivities, for example, C−H cleavage versus CC epoxidation in cyclohexene.6c Another intriguing mechanistic phenomenon brought about by tunneling was the observation19 of spiked KIE plots versus BDE(C−H) for two series of C−H bond-cleavage reactions by ([FeIV(O)(N4Py)]2+ and [FeIV(O)(Bn-TPEN)]2+ with different hydrocarbons. As we argued,5b these Melander− Westheimer look-alike plots of KIETC values reflect the bondorder asymmetry (Figure 9c) of the TS and hence the expansion of the energy profile, which reduces the tunneling efficiency in relation to the most symmetric profile in the series. A challenge is to find an oxidant that would be driven by tunneling to cleave selectively the strongest C−H bond. In principle, tunneling allows that to happen via augmenting the ligand donicity. The concepts described above are portable and applicable to other oxometal complexes and their superoxo and hydroxo derivatives.1,2 Investigating tunneling patterns in reactions of oxometals in the d and f blocks will extend the horizons of the seminal idea.

Figure 9. Correlations of (a) ν2 with the second derivative of the electrostatic potential (V) for 5TSH,σ and (b) ν with the difference of the C···H and H···O Wiberg bond orders in 5TSH,σ. (c) Eckart barriers of a few of the reactions along the IRC for reactions of [FeIV(O)(TMC)(Lax)]z+ complexes with S2.

electrostatic interaction across OQ−···HQ+···CQ− becomes more stable and the corresponding ν2 becomes larger. As such, the oxoiron(IV) having the best electron-donating axial ligand, [FeIV(O)(TMC)((CH2)2S−)]1+, will possess the highest ν2 and the narrowest barrier, which is the most conducive to tunneling. Figure 9b further shows that ν depends on the bond order (BO) difference between C−H and O−H bonds in the TS. The larger the BOCH−OH is, the smaller the ν and hence the lower the transmission coefficient and the KIE are. Figure 9c shows that the TS bonding asymmetry causes the barrier to expand in a given direction of the IRC, thereby minimizing the narrow part of the barrier that is available for tunneling. Extrapolating the line in Figure 9b to BOCH−OH = 0 shows that at fully symmetric TS the ν would be 2334 cm−1. In summary, as the axial ligand of [FeIV(O)(TMC)(Lax)]z+ becomes a better electron donor, it increasingly narrows the barrier by electrostatic interactions and reduces the bonding asymmetry of the H in transit, thereby leading to a higher tunneling efficiency and KIE. In this study of various complexes abstracting H from DHA, [FeIV(O)(TMC)((CH2)2S−)]+1 (10) is the ideal oxoiron(IV) for tunneling controlled reactivity, as witnessed from the very large KIEexp value.5d A more powerful donor is a selenolate ligand, as in [FeIV (O)(TMC)((CH2)2Se−)]+1, if such a putative complex could be made. The dependence of tunneling on the donor capability of the ligand is also known for H-abstraction reactions of Cpd I.17

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.accounts.7b00442. Abbreviations used, computational details, KIEs, detailed derivation of electrostatic contribution to frequency, and Cartesian coordinates. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel +972 (0)2 658 5909, fax +972 (0)2 658 4033, e-mail [email protected]. ORCID

Dibyendu Mallick: 0000-0002-0650-1872 Sason Shaik: 0000-0001-7643-9421 Present Addresses

5. PROSPECTS This Account demonstrates that usage of tunneling-augmented KIE (KIETC) identifies the reactive-spin-state during Habstraction reactions by oxoiron(IV) complexes, of nonheme- and heme-types, hence providing important mechanistic clues on two- or multistate reactivity situations. Thus, KIETC

†

D. Mandal, Computational Toxicology Facility, CSIR-Indian Institute of Toxicology Research, Lucknow-226001, India. ‡ D. Mallick, School of Chemistry and Biochemistry, Thapar Institute of Engineering and Technology, Patiala 147 004 Punjab, India. I


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Accounts of Chemical Research Funding

Abstraction by Heme Compound II Complexes. J. Am. Chem. Soc. 2017, 139, 11451−11459. (d) Klein, J. E. M. N.; Mandal, D.; Ching, W.-M.; Mallick, D.; Que, L.; Shaik, S. The Privileged Role of the Thiolate Ligand in HAT Reactions by Oxoiron(IV) Complexes in Shaping the Potential Energy Surface and Inducing Significant HAtom Tunneling. J. Am. Chem. Soc. 2017, 139, 18705−18713. (6) (a) England, J.; Prakash, J.; Cranswick, M. A.; Mandal, D.; Guo, Y.; Münck, E.; Shaik, S.; Que, L., Jr. Oxoiron(IV) Complex of the Ethylene-Bridged Dialkylcyclam Ligand Me2EBC. Inorg. Chem. 2015, 54, 7828−7839. (b) Bigelow, J.; England, J.; Klein, J. E. M. N.; Farquhar, E. R.; Frisch, J. R.; Martinho, M.; Mandal, D.; Münck, E.; Shaik, S.; Que, L., Jr. Oxoiron(IV) Tetramethylcyclam Complexes with Axial Carboxylate Ligands: Effect of Tethering the Carboxylate on Reactivity. Inorg. Chem. 2017, 56, 3287−3301. (c) Kwon, Y. H.; Mai, B. K.; Lee, Y.-M.; Dhuri, S. N.; Mandal, D.; Cho, K.-B.; Kim, Y.; Shaik, S.; Nam, W. Determination of Spin Inversion Probability, HTunneling Correction, and Regioselectivity in the Two-State Reactivity of Nonheme Iron(IV)-Oxo Complexes. J. Phys. Chem. Lett. 2015, 6, 1472−1476. (7) (a) Jeong, Y. J.; Kang, Y.; Han, A. R.; Lee, Y. M.; Kotani, H.; Fukuzumi, S.; Nam, W. Hydrogen Atom Abstraction and Hydride Transfer Reactions by Iron(IV)−Oxo Porphyrins. Angew. Chem., Int. Ed. 2008, 47, 7321−7324. (b) Fertinger, C.; Hessenauer-Ilicheva, N.; Franke, A.; van Eldik, R. Direct Comparison of the Reactivity of Model Complexes for Compounds 0, I, and II in Oxygenation, HydrogenAbstraction, and Hydride-Transfer Processes. Chem. - Eur. J. 2009, 15, 13435−13440. (c) Ji, L.; Franke, A.; Brindell, M.; Oszajca, M.; Zahl, A.; van Eldik, R. Combined Experimental and Theoretical Study on the Reactivity of Compounds I and II in Horseradish Peroxidase Biomimetics. Chem. - Eur. J. 2014, 20, 14437−14450. (d) Kupper, C.; Mondal, B.; Serrano-Plana, J.; Klawitter, I.; Neese, F.; Costas, M.; Ye, S.; Meyer, F. Nonclassical Single-State Reactivity of an Oxo-Iron(IV) Complex Confined to Triplet Pathways. J. Am. Chem. Soc. 2017, 139, 8939−8949. (8) (a) Shaik, S.; Chen, H.; Janardanan, D. Exchange-Enhanced Reactivity in Bond Activation by Metal-Oxo Enzymes and Synthetic Reagents. Nat. Chem. 2011, 3, 19−27. (b) Geng, C.; Ye, S.; Neese, F. Analysis of Reaction Channels for Alkane Hydroxylation by Nonheme Iron(IV)-Oxo Complexes. Angew. Chem., Int. Ed. 2010, 49, 5717− 5720. (9) (a) Shaik, S.; Cohen, S.; Wang, Y.; Chen, H.; Kumar, D.; Thiel, W. P450 Enzymes: Their Structure, Reactivity, and Selectivity Modeled by QM/MM Calculations. Chem. Rev. 2010, 110, 949−1017. (b) Wang, Y.; Kumar, D.; Yang, C.; Han, K.; Shaik, S. Theoretical Study of N-Demethylation of Substituted N,N-Dimethylanilines by Cytochrome P450: The Mechanistic Significance of Kinetic Isotope Effect Profiles. J. Phys. Chem. B 2007, 111, 7700−7710. (10) (a) Caldin, E. F. Tunneling in Proton-Transfer Reactions in Solution. Chem. Rev. 1969, 69, 135−156. (b) Truhlar, D. G.; Gao, J.; Alhambra, C.; Garcia-Viloca, M.; Corchado, J.; Sánchez, M. L.; Villa, J. The Incorporation of Quantum Effects in Enzyme Kinetics Modeling. Acc. Chem. Res. 2002, 35, 341−349. (c) Kästner, J. Theory and Simulation of Atom Tunneling in Chemical Reactions. WIREs 2014, 4, 158−168. (d) Layfield, J. P.; Hammes-Schiffer, S. Hydrogen Tunneling in Enzymes and Biomimetic Models. Chem. Rev. 2014, 114, 3466−3494. (11) Ley, D.; Gerbig, D.; Schreiner, P. R. Tunneling Control of Chemical Reactions − the Organic Chemist’s Perspective. Org. Biomol. Chem. 2012, 10, 3781−3790. (12) Sastri, C. V.; Lee, J.; Oh, K.; Lee, Y. J.; Lee, J.; Jackson, T. A.; Ray, K.; Hirao, H.; Shin, W.; Halfen, J. A.; Kim, J.; Que, L., Jr.; Shaik, S.; Nam, W. Axial Ligand Tuning of a Nonheme Iron(IV)−Oxo Unit for Hydrogen Atom Abstraction. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 19181−19186. (13) Eckart, C. The Penetration of a Potential Barrier by Electrons. Phys. Rev. 1930, 35, 1303−1309. (14) (a) Maity, D. K.; Bell, R. L.; Truong, T. N. Mechanism and Quantum Mechanical Tunneling Effects on Inner Hydrogen Atom Transfer in Free Base Porphyrin: A Direct ab Initio Dynamics Study. J.

Supported by the Israel Science Foundation (ISF Grant 1183/ 13). Notes

The authors declare no competing financial interest. Biographies Debasish Mandal is a postdoctoral associate in Jerusalem and a former Graduate of Jadavpur University, Kolkata (2013). His major interests are in quantum catalysis. Dibyendu Mallick is a postdoctoral associate in Jerusalem and a former graduate of IISc Bangalore (2013). His major interest is in biomimetic reactions. Sason Shaik is a Professor in Jerusalem. Among his interests are concepts for bonding and reactivity. His most recent award is the Gold Medal of the Israel Chemical Society.

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Kinetic Isotope Effect Determination Probes the Spin of the Transition

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