Kinetic Isotope Effect Probes the Reactive Spin State, As Well As the

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Kinetic Isotope Effect Probes the Reactive Spin State, As Well As the Geometric Feature and Constitution of the Transition State during H‑Abstraction by Heme Compound II Complexes Dibyendu Mallick and Sason Shaik* Institute of Chemistry and the Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel S Supporting Information *

ABSTRACT: What do experimentally measured kinetic isotope effects (KIEs) tell us about H-abstraction reactions with multispinstate reactivity options? Using DFT calculations with tunneling corrections for experimentally studied H-abstraction reactions of porphyrin-Compound II species (Chem.-Eur. J. 2014, 20, 14437; Angew. Chem., Int. Ed. 2008, 47, 7321) with cyclohexane, dihydroanthracene (DHA), and xanthene (Xan), we show here that KIE is a selective probe that identifies the experimentally reactive spin state. At the same time, comparison of calculated and experimental KIE values permits us to determine the structural orientation of the transition states, as well as the presence/absence of an axial ligand, and the effect of porphyrin substituents. The studied compound II (Cpd II) species involve porphine, and porphyrin ligands with different meso-substituents, TPFPP (tetrakis(pentafluorophenyl)porphyrin dianion) and TMP (tetramesitylporphyrin dianion), with and without imidazole axial ligands. The DFT calculations reveal three potential pathways: quintet and triplet σ-pathways (5Hσ and 3Hσ) that possess linear transition state (TS) structures, and a triplet π -pathway (3Hπ) having a bent TS structure. Without an axial ligand, the 5Hσ pathways for these Cpd II complexes cross below the triplet states. The axial ligand raises the barriers for the quintet and triplet σ-pathways and quenches any chances for two-state reactivity, thus proceeding via the 3Hπ pathway. All of these pathways exhibit characteristic KIE values: very large for 3Hπ (48−200), small for 5Hσ (3−9), and intermediate for 3Hσ (23−51). The calculated KIEs for (TPFPP)FeIVO without an axial ligand reveal that 3Hσ is the only pathway having a KIE that matches the experimental values, for the reactions with DHA and Xan (Angew. Chem., Int. Ed. 2008, 47, 7321). Indeed, theory shows that tunneling significantly lowers the 3Hσ barrier rendering it the sole reactive state for the reaction. A prediction is made for the reactivity and KIE of (TMP)FeIVO complex, and a comparison is made with the analogous nonheme complexes.

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INTRODUCTION

(S = 1) ground states with modest reactivities as compared to their Cpd I counterparts. Nevertheless, several experimental studies by Groves,4a Nam,4b−d and van Eldik,4e,f and their co-workers, have demonstrated the competence of various synthetic mimics of Cpd II species in different oxidative processes toward a variety of substrates. Thus, for example, Groves et al. showed that the iron(IV)-oxo porphyrin complex (TMP)FeIVO (TMP = tetramesitylporphyrinate) epoxidizes olefins.4a Similarly, Nam and co-workers demonstrated that the usage of the electrondeficient porphyrin ligand TPFPP (tetrakis(pentafluorophenyl) porphyrin dianion) generates an iron(IV)-oxo complex that carries out hydroxylation of alkanes and epoxidation of olefins with considerable efficiency.4b−d In a comparative reactivity study on the model complexes of Cpd 0, Cpd I, and Cpd II, van

In heme-iron enzymes, high-valent iron(IV)-oxo species, such as iron(IV)-oxo porphyrin π-radical cations, are referred to as compound I (Cpd I), while the one-electron reduced forms, iron(IV)-oxo porphyrins, are referred to as compound II (Cpd II).1 Because of their high biological significance, the reactivity of Cpd I species toward the oxygenation of alkanes and olefins has been widely studied both experimentally and theoretically.2,3 In contrast, less attention has been devoted to the biomimetic studies of Cpd II analogous.3j,m,4 Moreover, as compared to the corresponding nonheme iron(IV)-oxo complexes that exhibit two-state reactivity (TSR)5 and exchange-enhanced reactivity (EER) in the high-spin states (S = 2) during the C−H and CC bond activation reactions,6 the analogous heme iron(IV)-oxo complexes do not seem to exhibit these unique reactivity features. Density functional theoretical (DFT) calculations3m,4e,f further show that the reactions of Cpd II species seem to proceed solely via the triplet © 2017 American Chemical Society

Received: April 26, 2017 Published: July 24, 2017 11451

DOI: 10.1021/jacs.7b04247 J. Am. Chem. Soc. 2017, 139, 11451−11459

Article

Journal of the American Chemical Society

reactive spin states, triplet (S = 1), which is the ground state, and a relatively low-lying quintet excited state (S = 2). These two spin states may interchange their energy order at the transition state and hence exhibit a TSR scenario.5c,d,6 In addition, each one of these spin states can react via either a linear or a bent TS, respectively, called the σ-pathway or the πpathway. These labels depend on the iron-d orbital that controls the geometry of the TS.6b,c,12 The accessibility of the two states depends on the axial ligand to the iron that gauges the spin states energy gap.10c,13 Thus, our major focus here is the development of a standard probe that can be used experimentally to characterize the reactive spin state, the structure of the transition state (TS), as well as the effect of the axial ligand to iron. As shall be demonstrated, a comparison of the computed KIE values including tunneling corrections with the experimentally determined KIE values9b,10,11 enables one to pinpoint the reactive spin state, the orientation of the TS, as well as the presence/absence of an axial ligand, and the effect of meso-substituents on the porphyrin. Furthermore, it will be shown that while in the absence of an axial ligand TSR is available to these systems, still this reactivity scenario will often be quenched by tunneling, which lowers the triplet TS below the quintet congeners. Nevertheless, the special electronic features of the porphyrin ligand enable Cpd II to proceed via a linear triplet TS that is endowed by EER.6c,12a

Eldik and his co-workers have demonstrated that Cpd II is the most efficient oxidant in the hydride transfer process.4e This rising interest in the reactivity patterns of Cpd II4b−g has prompted us to use theory to derive the conditions under which the heme Cpd II species proceed via TSR and exhibit EER, and also to find probes that can be used by the experimentalists to identify the reactive spin state under experimental conditions. In the studies of Cpd I reactivity, it was noted that kinetic isotope effects (KIEs) provide information about the structure of the transition state7 and may even probe its reactive spin state5c,d,8 during H-abstraction. Recently, our group has demonstrated that the tunnelingcorrected KIEs are excellent probes for the reactive spin states for the H-abstraction reaction by various nonheme FeIVO complexes.9 This idea has been successfully tested by experimental10 and computational11 studies. Indeed, as shall be seen later, KIEs with tunneling corrections9−11 can efficiently identify the reactive spin state during H-abstraction by heme Cpd II species. Moreover, the tunneling corrected KIEs9−11 will also be shown to probe the structure of the transition state and its ligand sphere constitution, and may thereby guide the experimentalists in their quest to characterizing the transition state (TS) structures and spin-state selectivities.

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TARGET STUDIES AND GOALS Scheme 1 displays the target Cpd II species and substrates studied here. Scheme 1a depicts the Cpd II species, 1−3, which

COMPUTATIONAL DETAILS

All of the structures were optimized with UB3LYP14 using the Gaussian 09 package.15 The robustness of B3LYP for FeIVO systems has been established in various benchmark studies.16 It has been found that B3LYP reproduces the triplet−quintet gap and the relative barriers between triplet and quintet states against the high-level RCCSD(T)-F12 method for H-abstraction reactions from CH4 by model nonheme Fe(IV)-oxo systems with good accuracy.16a Thiel, Neese et al. performed an extensive benchmark of the spin states of FeO+ and its H-abstraction reactions16b and showed that B3LYP is the best functional for iron-oxo systems, and its results are as good as, if not better than, those of high-level ab initio results. The calculated singlet−triplet splitting by B3LYP for the iron-superoxide species was shown to be in excellent match with the CASSCF/MM calculations for the oxy-myoglobin system.16c The two lowest-lying spin states of Compound I (Cpd I) of P450 are reproduced by B3LYP with experimental accuracy. Other spin states of Cpd I for P450 and chloroperoxidase (CPO) show that B3LYP is good with respect to CASPT2 results.16d,e Pierloot and her co-workers showed that for the spin states of MnVO(corrole) and MnVO(corrolazine) complexes, especially, the singlet−triplet splitting values are reproduced by B3LYP with an error bar of 0.01−0.1 eV with respect to CASPT2 calculations.17 Moreover, B3LYP reproduces the identity of the ground state of Cpd II according to experiment.18 These results show the appropriateness of B3LYP functional for the FeIVO systems and give us confidence in using B3LYP for the current study. The first basis set (B1) used for geometry optimization involves LACVP* for Fe and 6-31G* basis set for the rest of the atoms except F, for which the 6-31+G* basis set was used. The optimizations were performed in an implicit solvent using PCM solvent model,19 with parameters corresponding to acetonitrile, which is the solvent utilized in the experimental studies. The nature of stationary points was characterized by frequency calculations at the same level of theory (using B1). Single-point energy evaluations were carried out at the UB3LYP/ Def2-TZVP20 level (B2) including the solvent. Free energies were evaluated at 298.15 K unless otherwise specified, and the corresponding free energies of activation (ΔG⧧cal) for H-abstraction were calculated relative to the separated reactants. The resulting ΔG⧧cal values were further corrected with a factor of −RT·ln[24.45] for changes in standard state from 1 mol gas phase to 1 M in a

Scheme 1. (a) Iron(IV)−oxo Porphyrins (Cpd II) and (b) H-Abstraction Reaction and Different Substrates Studied in This Work

involve a pristine porphine (R = H), 2, and two mesosubstituted porphyrins, TPFPP (1) and TMP (3).4a−d These three complexes are used as either devoid of an axial ligand to the iron (1a−3a) or having an axial imidazole ligand (ImH),4e,f 1b−3b. Using these oxidants, we employed DFT and tunneling calculations to study the corresponding H-abstraction reactivity patterns toward the substrates in Scheme 1b. Cpd II has two 11452


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Journal of the American Chemical Society solvent.21 Because there are four equivalent hydrogens on DHA, the HAT reaction barriers were adjusted by a factor −RT·ln(4) to account for 4 times faster rate. Similarly, for the HAT reaction from xanthene, which has two equivalent hydrogens, the energy barriers were corrected by a factor of −RT·ln(2). Dispersion corrections were evaluated using Grimme’s D3 with Becke−Johnson damping (GD3BJ) algorithm22 at the B2 basis set. The dispersion-corrected values exhibit the same trends as those found in the uncorrected B3LYP barriers, albeit the absolute numbers differ. The dispersion corrected values are given in Tables S1−S3. The use of a multidimensional tunneling method to calculate the tunneling effect is impractical for the present study. This would involve KIE calculations for a total of 12 reactions for systems that involve a minimum of 104 and a maximum of 140 atoms, which would require enormous computational power [which we do not possess] and a long time. Instead, we use one-dimensional Eckart tunneling model,23 which was found before to produce KIEs that are compatible with experimental KIEs for various Fe(IV)-oxo systems.9,10a,c In our recent study,9b we showed that the temperature (T) dependence on Eckartbased KIE is in excellent agreement with the temperature dependence deduced from the experiment by Klinker and Que.24 Moreover, a comparison of Eckart-based KIEs and the experimental KIEs for 18 different H-abstraction reactions was made, and the results are given in Table S5, which demonstrates that the so calculated KIEs match the experimental KIEs quite well. To further check the accuracy of the Eckart method for FeIVO species, we calculated the Eckart-based KIE values for the reactions of [(N4Py)Fe IVO] 2+ (N4Py = N,N-bis(2-pyridylmethyl)-N-bis(2pyridyl)methylamine) with cyclohexene (CHE), using the same protocol as that used here for the reactions of Cpd II. These KIE values were compared to available multidimensional tunneling calculated KIE values for the same reaction.11a The comparison shows a good match between Eckart-based KIEs and multidimensional KIEs for both S = 1 and S = 2 spin states (see Table S6). Moreover, both methods identify S = 1 as a reactive state for this reaction with KIEs of 49 (Eckart), 53 (multidimensional), and 55 (exp). The Rate program25 is used to carry out the tunneling calculations. The Eckart model evaluates an approximate adiabatic ground-state potential energy curve that is computed by fitting to an Eckart potential with the zero-point energy (ZPE) and solvent-corrected energies of the reactants, products, and TS, as well as the imaginary frequency along the intrinsic reaction coordinate (IRC) in massweighted coordinates. The temperature-dependent transmission coefficient, κ(T), due to tunneling at a given temperature T, is calculated by the integration of the barrier “penetration” probability as a function of the energy.25 The energy lowering of the barrier due to tunneling is given by the following equation: ⧧ ΔΔEtun = − RT ·ln[κ(T )]

Figure 1. Optimized geometries of different Cpd II species with (1b− 3b) or without (1a−3a) axial ligand. Relative energies of the triplet and quintet states (in parentheses) calculated at UB3LYP/B2// UB3LYP/B1 level of theory are given.

the two spin states (S = 1 and S = 2) for all of the Cpd II species, (TPFPP)FeIVO (1a), (Por)FeIVO (2a), (TMP)FeIVO (3a), (TPFPP)(ImH)FeIVO (1b), (Por)(ImH)FeIVO (2b), and (TMP)(ImH)FeIVO (3b). All of these Cpd II species (1a−3a and 1b−3b) were found to have S = 1 (triplet, 2S+1 = 3) ground states. The excited S = 2 (quintet, 2S +1 = 5) states are higher lying (see energy values in parentheses) than the triplet states in different magnitudes that depend upon the nature of the meso-substituents as well as the presence or absence of the axial ligand. Irrespective of the nature of the meso-substituent, in the absence of the axial ligand, the quintet states are higher in energy than the triplet states, by 7.5−8.6 kcal mol−1. The introduction of the axial imidazole ligand increases the triplet−quintet (T−Q) gaps to 12.1−12.6 kcal mol−1, for all of the Cpd II species. Note that the S = 2 spin states of axially ligated Cpd II species are much higher lying as compared to the six coordinated nonheme Fe(IV)-oxo complexes,6a,b,9a,12c which exhibit TSR and EER.6b In fact, the heme Cpd II species place the quintet state higher in energy, relative to the triplet state, even without an axial ligand to iron. The larger triplet−quintet gap in heme Cpd II species as compared to nonheme complexes reflects the strong antibonding interaction in the σ*x2−y2 orbital, due to the rather tight ligating core of the macrocycle. In the presence of imidazole axial ligand, the σ*x2−y2 orbital is further destabilized, as the iron-oxo moiety almost nestles into the porphyrin plane (Figure 2). Thus, the S = 2 state for the Cpd II species is relatively high lying and more so for the axially ligated species. As such, it might be expected that, if at all, only the complexes devoid of axial ligands are potential candidates for TSR and EER. B. Hydrogen Atom Transfer (HAT) Reactivity of Heme Cpd II Species. Hydrogen atom transfer (HAT) by Cpd II species can occur in two different pathways, σ- and π-pathways, depending upon the nature of iron-d orbitals, which accept the shifted electron during the H-abstraction reaction, for both S =

(1)

Here, R is the universal gas constant and T is the absolute temperature. As can be seen from eq 2, the tunneling correction effectively cuts the barrier by the negative quantity ΔΔE⧧tun. The effective free energy barrier is given accordingly as ⧧ ⧧ ⧧ ⧧ ΔGeff = ΔGcal + ΔΔEtun (ΔΔEtun < 0)

(2)

The KIE calculations employed the frequencies of the reaction of the iron(IV)-oxo complexes with the substrates and their deuterated isotopologues. The KIEs were calculated using the semiclassical Eyring equation,26 followed by tunneling corrected values, using the following expression:

KIEcal = (κH/κD)·KIE EY

(3)

where the ratio of κH/κD is the Eckart tunneling corrections of the two isotopologues.

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RESULTS AND DISCUSSION A. Electronic Structure and the Spin States. Figure 1 displays the optimized geometries and the relative energies for 11453


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Scheme 2. (a) Electron-Shift Diagrams for H-Abstraction Reactions from Cyclohexane by Cpd II Species, in Various Pathways for the S = 1 and S = 2 States;a Orbital−Overlap Cartoons Predicting the Orientations in (b) π-Pathway TS and the Corresponding TS Structure, 3TS-Hπ; and (c) σPathway and the Corresponding TS Structures, 3TS-Hσ and 5 TS-Hσ, Occur for All Other Substrates

Figure 2. Optimized geometries and corresponding σ*x2−y2 orbitals of (a) 52a and (b) 52b. Without an axial ligand in 52a, the Fe atom lies above the porphyrin plane somewhat more than in 52b, thus reducing the antibonding interaction in the σ*x2−y2 orbital.

1 and S = 2 spin states. Scheme 2 shows the predicted structural orientations using electron-shift diagrams.27 As found for many nonheme cases, here too the quintet state prefers the σ-pathway due to its exchange enhanced reactivity (EER) as compared to the exchange-depleted π-pathway.6c,12c We shall, therefore, restrict our attention to this low energy pathway for the S = 2 manifold. However, because the triplet state is considerably lower than the quintet in heme Cpd II complexes, both σ- and π-pathways are potentially low in energy for S = 1 and will be considered for their HAT reactivity. Cyclohexane (S1) has been used as a substrate to compare the HAT reactivity of all of the Cpd II complexes in Scheme 1a. The key findings are summarized below and discussed with reference to Figures 3 and 4. Figure 3a summarizes the HAT barriers for the Cpd II species that are devoid of an axial ligand to iron (1a−3a), while Figure 3b does so for the complexes possessing axial ligands (1b−3b). In each part of the figure, the energy data are given in the order 1/2/3. As shown in Figure 3a, the quintet states have the lowest barriers for all Cpd II species that are devoid of axial ligands, and hence these reactions may potentially follow TSR, whereby 5 TS-Hσ crosses below all of the triplet pathways. On the other hand, for the species with an axial ligand in Figure 3b, the triplet states possess the lowest energy path, and no TSR should take place. The comparison of the barriers between the Cpd II species with or without axial ligand reveals (Figure 3a vs b) that the introduction of an axial ligand decreases the reactivity for all three oxidants, that is, 1b < 1a, 2b < 2a, and 3b < 3a. As such, the presence of an axial ligand decreases the HAT reactivity of a heme Cpd II species. Furthermore, the most reactive channels for the axially ligated systems differ from those without axial ligand. Without axial ligands, the σ-pathways via 3TS-Hσ and 5 TS-Hσ are favored in both spin manifolds, due to EER,6 whereas the π-pathway via 3TS-Hπ, which is devoid of EER, is preferred for those Cpd II species with an imidazole axial ligand. Thus, an axial ligand quenches the σ-pathways by raising the σ*z2 orbital due to an additional antibonding interaction imparted by the axial ligand (see also Figure S1).

a

The Greek labels of the orientations correspond to the d orbitals, which accept the shifted electron during the H-abstraction.

The effect of the axial ligand on the activation energy barrier for the σ-pathway is displayed in Figure 4a, which reveals an excellent linear correlation between the HAT barrier and the energy of the σ*z2 orbital for both quintet and triplet σpathways. Such a linear correlation has been found by Sautet et al., who have studied the H-abstraction barrier for 55 different oxidants.28 In the absence of an axial ligand, the energy of the σ*z2 orbital is lowered due to the removal of an antibonding interaction between the ligand and iron (see Figure 4b and c). This reduced antibonding interaction renders the σ-pathway the preferred pathway in both spin manifolds. Further stabilization of the σ*z2 orbital (as we go from 2a to 1a as illustrated in Figure S1) is imparted by the high electronwithdrawing meso-substituent in 1a, which makes this Cpd II species the most reactive among all of the complexes studied in 11454


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Figure 4. (a) Correlation between the ZPE corrected barrier heights for the σ-pathways of C−H abstraction (y-axis), and the σ*z2 orbitalenergy of the corresponding Cpd II species (x-axis), for complexes 1a−3a and 1b−3b. The line in black is for the 5Hσ-pathway, while the one in red is for the 3Hσ-pathway. (b) The σ*z2 orbital of 52b with the imidazole-iron antibonding, and that of (c) 52a showing the reduced antibonding interaction due to the absence of the axial ligand.

Figure 3. Zero-point energy (ZPE) corrected energy profiles for the H-abstraction reactions by the Cpd II species 1−3 from cyclohexane (S1), where the barriers are given in the order of 1/2/3. (a) The reactions of Cpd II species without axial ligands (1a−3a), showing that the quintet σ-pathway has the lowest barrier for all cases irrespective of the nature of meso-substituents, and (b) the reactions of axially ligated Cpd II species (1b−3b), showing that the axial ligation destabilizes both triplet and quintet σ-pathways and makes the triplet π-pathway the most favorable one. The relative energies are calculated at the UB3LYP/B2//UB3LYP/B1 level of theory.

3

Hπ-pathway exhibits by far the highest H atom tunneling probability, whereas the 5Hσ-pathway involves negligible tunneling. The contrasting tunneling probabilities for the different reaction channels (5Hσ, 3Hσ, and 3Hπ) can be understood by analyzing the respective energy profiles along the intrinsic reaction coordinates (IRCs) of the H-abstraction processes for 1a + DHA, as shown in Figure 5. Figure 5 shows that the potential energy profile along the reaction coordinate of the H-abstraction reaction by 1a from DHA via 3Hπ-pathway is sharp and narrow (high imaginary frequency of the corresponding TS, 1739i cm−1; see Figure 6), and hence this pathway provides a large energy space and narrower barrier to tunnel through at 288 K. The large hydrogen atom tunneling probability for the 3Hπ-pathway is reflected in the largest computed KIEcal value (67.7) at 288 K. A large computed KIEcal value (47.5) for the 3Hπ-pathway is also found for xanthene. These high values mismatch the experimentally observed KIEobs values (20−21) for DHA and xanthene. This mismatch in KIE values rules out the 3Hπpathway as the reactive one. This conclusion is further supported by the fact that, even after tunneling correction, the effective free energy barriers in Table 1 (ΔG⧧eff; see eq 2) place the 3Hπ-pathways as the least favorable among all of the pathways for HAT. Considering now the 5Hσ-pathway, it is seen that the low imaginary frequency of this TS (500i cm−1, Figure 6) and its small barrier create a very broad and flat energy profile, which leaves less of an energy space to tunnel through the barrier. The

this work. This higher reactivity of 1a is in agreement with the experimental finding by Nam and his co-workers.4d C. Kinetic Isotope Effect Is a Probe of Spin-State Reactivity, Structure of TS, and Ligand-Sphere Constitution. Since we found in the previous section that Cpd II species, devoid of an axial ligand, may follow the TSR scenario, it will be interesting to see whether we can identify the reactive channel by comparing the calculations to an appropriate experimental probe. In 2008, Nam and co-workers reported that the hydrogen abstraction reactions by the iron(IV)-oxo porphyrin complex, (TPFPP)FeIVO (1a), from 9,10dihydroanthracene (DHA) and xanthene (Xan) and their deuterated counterparts ([D4]-DHA and [D2]-Xan) exhibit large deuterium KIE values, 20 and 21, respectively, at 288 K.4d These large KIE values indicate the involvement of hydrogen atom tunneling. To characterize the reactive pathway for the above-mentioned reactions, we calculated the KIE values for all possible pathways: the σ- and π-pathways for S = 1 state and the σ-pathway for S = 2 state of the species 1a. The data are collected in Table 1, which contains the calculated free energy barriers and tunneling-corrected KIEs for both S = 1 and S = 2 spin states in various reaction channels for both substrates DHA and xanthene. Analysis of the transmission coefficient values at 288 K for all three pathways in Table 1 (5Hσ, 3Hσ, and 3Hπ) reveals that the 11455


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Table 1. UB3LYP/B2//UB3LYP/B1-Based Free Energies of Activation before Tunneling Corrections (ΔG⧧cal) and after the Tunneling Corrections (ΔG⧧eff) at 288 K, for H-Abstraction Reactions from DHA and Xanthene (Xan) by 1a for All Possible Pathwaysa subs DHA

Xan

spin state S S S S S S

= = = = = =

2 1 1 2 1 1

mechm 5

Hσ Hσ 3 Hπ 5 Hσ 3 Hσ 3 Hπ 3

ΔG⧧calb

ΔΔE⧧tun

ΔG⧧eff

ΔGr

imag freq in TS (in cm−1)

κ at 288 Kc

KIEcal

KIEobs

17.6 18.5 23.3 18.3 18.8 22.9

−0.2 −2.0 −2.7 −0.1 −1.8 −2.4

17.4 16.5 20.6 18.2 17.0 20.5

−9.6 −5.9 2.7 −10.5 −5.5 0.8

500i 1624i 1739i 310i 1550i 1661i

1.41 35.10 120.0 1.20 23.10 71.0

4.0 32.6 67.7 2.8 23.3 47.5

20

21

a

Also shown are free energies of reaction (ΔGr), imaginary frequencies of TSs, transmission coefficients (κ), and calculated and observed KIE values at 288 K. bAll energies are in kcal mol−1. cTransmission coefficient for H atom at 288 K.

tunneling the 5Hσ pathway has a smaller barrier than the 3Hσ pathway (Table 1 and Figure 3a), the higher tunneling energy correction in the latter pathway reverses the order, leading to lower ΔG⧧eff values for the 3Hσ-pathways for both DHA and Xan as compared to the respective 5Hσ pathways. For the case of Xan, the tunneling-corrected barrier is 17.0 for 3Hσ versus 18.2 kcal mol−1 for 5Hσ, while for DHA, the barriers are 16.5 and 17.4 kcal mol−1 for the 3Hσ- and 5Hσ-pathways, respectively. The tunneling corrected H-abstraction barriers of 16.5 and 17.0 kcal mol−1 via 3Hσ pathway for DHA and Xan, respectively, are in good agreement with the experimentally observed barriers (15.9 and 15.8 kcal mol−1 for DHA and Xan, respectively). Thus, while the tunneling corrected barriers are quite similar for the 3Hσ- and 5Hσ-pathways, the comparison of the experimentally observed KIEobs with the calculated KIEcal values clearly identifies the 3Hσ-pathway as the primary reactive channel (Table 1). It is noted that the 3Hσ-pathway exhibits EER (see Scheme 2a), and this is the reason why its uncorrected free energy barrier (Figure 3a) lies significantly below the exchangedepleted 3Hπ-pathway, such that the subsequent significant tunneling correction makes 3Hσ the reactive pathway. Kinetic Isotope Effect in the Presence of an Axial Ligand. One might have argued that there exists a possibility that during the reaction, 1a + DHA, that was carried out in the presence of a small amount of H2O in a solvent mixture of CH3CN and CH2Cl2 (9:1) at 288 K, the actual constitution of the oxidant involves an axial ligation of iron by H2O. To test this possibility, we calculated the H-abstraction barriers and the KIE values for all possible pathways discussed above for the reaction 1b(H2O) + DHA. The full results are given in Table S4, while here we follow with the key results. As expected, the free energy barriers for all of the pathways are found to be higher than the same for the reaction 1a + DHA in the absence of an axial ligand (in

Figure 5. Energy profiles versus intrinsic reaction coordinates for the H-abstraction reaction by 1a from DHA for all possible pathways.

very small KIEcal = 4 is far off the experimental datum, which rules out the operation of this pathway in the experiment. We, therefore, remain with the 3Hσ-pathway as a potential mediator of the HAT in the reactions of 1a with DHA and Xan. Having a substantial imaginary frequency and a sizable barrier, the 3Hσ-pathway exhibits moderately large KIEcal values (32.6 and 23.3 for DHA and Xan, respectively), which are, respectively, in reasonable and good agreement with the experimentally observed ones (KIEobs = 20 and 21). Thus, the 3 Hσ-pathway exhibits KIEcal values that are the best match to the experimental KIEobs values. This conclusion is further supported by the relative free energies of activation for the three pathways. Thus, while without considering the effect of

Figure 6. UB3LYP/B1 optimized transition state structures (distances in Å and angles in degrees) and imaginary frequencies (Imag Freq) in i cm−1 for H-abstraction from DHA by 1a in the S = 1 and S = 2 spin states for σ- and π-pathways (3,5TS-Hσ and 3TS-Hπ). 11456


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Table 2. UB3LYP/B2//UB3LYP/B1-Based Free Energies of Activation before Tunneling Corrections (ΔG⧧cal) and after the Tunneling Corrections (ΔG⧧eff) at 288 K, for H-Abstraction Reaction from DHA by 3a for All Possible Pathwaysa subs DHA

spin state S=2 S=1 S=1

mechm 5

Hσ 3 Hσ 3 Hπ

ΔG⧧calb

ΔΔE⧧tun

ΔG⧧eff

ΔGr

imag freq in TS (in cm−1)

κ at 288 Kc

KIEcal

KIEobs

20.3 22.8 29.8

−0.8 −2.5 −3.8

19.5 20.3 26.0

−4.0 −2.9 4.0

1218i 1734i 1900i

4.1 84.3 802

9.2 50.9 200.0

NA

a Also shown are free energies of reaction (ΔGr), imaginary frequencies of TSs, transmission coefficients (κ), and calculated and observed KIE values at 288 K. bAll energies are in kcal mol−1. cTransmission coefficient for H atom at 288 K.

bound to iron, this ligand will dissociate to benefit from the lower energy of 3Hσ or 5Hσ pathways as has been found in the 3 TS-Hσ structure of the reaction of DHA with acetonitrile ligated 1a complex (see Figure S9). Thus, we found that the ZPE corrected binding energies of CH3CN and water as axial ligands to 1a complex are quite small, 1.09 and 1.15 kcal mol−1, respectively, as compared to the difference in the free energy barriers between the 3Hσ and 3Hπ-pathways (4.7 and 2.5 kcal mol−1 in favor of 3Hσ for axially ligated CH3CN and water, respectively) for the H-abstraction reaction from DHA, which support our prediction. Finally, let us point out that the 3Hσ-pathway, which is operative in the Cpd II species that are devoid of any axial ligand, is quite unique and is not observed for the nonheme complexes.12c This pathway involves EER and is enabled here because, unlike synthetic nonheme iron(IV)-oxo complexes, which have generally six coordination, the present Cpd II iron(IV)-oxo are penta-coordinated. The missing sixth ligand produces a relatively low-lying σ*z2 orbital and opens a new pathway for the H-abstraction in the triplet state. Our comprehensive comparison of the various possibilities for six oxidants and three substrates makes a strong case that the 3Hσ pathway should control the reactivity of the heme Cpd II species. In some cases, the competition between the 3Hσ and 5 Hσ pathways is likely.

Table 1). Furthermore, the H2O ligation causes a significant increase in the KIEcal values too, which become 5.9 (5Hσ), 74.0 (3Hσ), and 83.8 (3Hπ). Now, all of these KIEcal values are far away from the observed one (KIEobs = 20). Hence, on the basis of the calculated high barrier and the mismatching KIEcal and KIEobs values, we can also rule out the possibility of axial ligation by iron. As such, the KIE probe shows in a rather convincing manner that the oxidation pathways in the experiments of Nam et al.,4d with (TPFPP)FeIVO (1a), proceed via the triplet σ-pathway (3Hσ), in which the corresponding TS has a linear Fe−O−H moiety, and the iron does not possess an axial ligand. Predicting the Expected Kinetic Isotope Effect for (TMP)FeIVO (3a). Having successfully determined the actual Habstraction pathway that is operative for the reactions of 1a with DHA and xanthene, let us now make a prediction by exploring the KIE probes for the reaction of (TMP)FeIVO (3a) with DHA, for which no experimental KIE is reported. Table 2 shows all of the relevant results. In comparison to 1a (Table 1), here the KIEcal values for 3a are substantially higher in accord with the larger imaginary frequencies that trim the width of the energy profiles.9a The comparison of the free energies of activation for various pathways in Table 2 shows that the 3Hπ-pathway exhibits the highest barrier (26.0 kcal mol−1) even after significant energy reduction (3.8 kcal mol−1) due to high tunneling correction. Hence, this path can be ruled out as before. On the other hand, the 3,5Hσ-pathways have rather close tunneling-corrected barriers, with some preference for 5Hσ. We can, therefore, make a testable prediction that if KIE is measured for this reaction, it will enable one to specify whether the reaction follows the 3Hσ or 5Hσ-pathway: a low KIE value (ca. 9) will reveal the operation of the 5Hσ pathway in a TSR scenario, while a large KIE value, of ca. 50, will single out the 3Hσ pathway. We note that the synthetic Compound I (Cpd I) analogue of 3a also exhibits high KIE value of 54 at 283 K (and a very large KIE of 190 at 263 K) for H-abstraction reaction from benzyl alcohol,29 which lends some support to the calculated high KIE value found for the 3Hσ-pathway for the reaction 3a + DHA. Our study leads then to an important deduction, that KIE not only can be used to identify the reactive spin state but also to specify the constitution of the TS in terms of the axial ligation to iron. In addition, KIE measurement will differentiate between various reactive pathways (σ- or π-pathways). With a strong axial ligand, the favored pathway would be the traditional 3Hπ path as shown in Figure 3b. However, because axial ligation of iron raises the barrier significantly due to the rise in the energy of the σ*z2 orbital (Figure 4), such Cpd II species (e.g., 1b−3b in Scheme 1) would be sluggish oxidants in HAT reactions with alkanes. In the context of axial ligation, one should make an important note that whenever the axial ligand is weakly

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CONCLUSIONS Density functional studies are reported for H-abstraction reactions by six different Cpd II model complexes from cyclohexane, DHA, and xanthene (Scheme 1). The calculations suggest that Cpd II species without axial ligands to iron are ideal candidates for undergoing TSR and EER, via the 3Hσ- and 5 Hσ-pathways. Both 3Hσ- and 5Hσ-pathways proceed via linear transition state structures, but with different spin states. On the other hand, those Cpd II species with strongly bound axial ligands would be sluggish oxidants that proceed via the traditionally accepted 3Hπ-pathway with the transition states that are exchange-depleted and have bent structures. The mesosubstituents (as in 1 and 3) that are investigated in this study do not play a dominant role in deciding the TSR scenario, although the donor substituents in (TMP)FeIVO (3a) increase the barriers for all of the pathways as compared to the electron-withdrawing substituents in (TPFPP)FeIVO (1a). The major find of this study is that KIE is a reliable probe of the reactive spin state, the structure of the transition state, and its ligand-sphere constitution. As such, by comparing the calculated KIEcal to the observed ones (KIEobs) for the reaction of (TPFPP)FeIVO with DHA and Xan, we are able to argue that the only pathway with a good fit between the calculation and experiment is the 3Hσ-pathway in which the oxidant is devoid of an axial ligand to iron. We also found that the KIEs 11457


Article


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are very sensitive to axial ligation and hence can be used to determine the presence/absence of axial ligation in the transition state of a given system. The axial ligation significantly raises the tunneling contributions to all of the pathways but will tend to prefer 3Hπ pathway for strongly ligated cases. This study also makes a testable prediction of the KIE value to be expected for the H-abstraction reaction from DHA by (TMP)FeIVO complex. Thus, an observation of a small KIE (9.2, Table 2) would identify the reactive channel as the 5Hσpathway, which proceeds via both TSR and EER, whereas a large KIE (51) would fit 3Hσ, and a very high KIE (200) would indicate a 3Hπ-pathway. Which one will it be? This is a challenge for the experiment. Finally, the ability of significant tunneling to lower the transition state of a given spin state below others shows that tunneling is a selectivity-promoting factor in chemistry, as discovered by Schreiner et al.30

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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/jacs.7b04247. Energy profiles with or without dispersion corrections, geometries of TSs, orbital correlation diagram, KIEEckart versus KIEexp, KIEEckart versus KIEMultidimensional, Mulliken spin densities, and optimized Cartesian coordinates for all of the stationary points (PDF)

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AUTHOR INFORMATION

Corresponding Author

*[email protected] ORCID

Sason Shaik: 0000-0001-7643-9421 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research is supported in part by the Israel Science Foundation grant to S.S. (ISF grant 1183/13). D.M. thanks the Israeli PBC for the postdoctoral fellowship.

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REFERENCES

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NOTE ADDED IN PROOF A recent study of H-abstraction by a tetracarbene iron(IV)-oxo complex gave KIE = 32 at 233 K through an upright S = 1 TS: Kupper, C.; Mondal, B.; Serrano-Plana, J.; Klawitter, I.; Neese, F.; Costas, M.; Ye, S.; Meyer, F. J. Am. Chem. Soc. 2017, 139, 8939−8949.

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Kinetic Isotope Effect Probes the Reactive Spin State, As Well As the

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