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Analysis of Hydrogen Atom Abstraction from Ethylbenzene by an FeVO(TAML) Complex Longzhu Q. Shen, Soumen Kundu, Terrence J. Collins, and Emile L. Bominaar* Department of Chemistry, Carnegie Mellon University, 4400 Fifth Avenue, Pittsburgh, Pennsylvania 15213, United States S Supporting Information *

ABSTRACT: It was shown previously (Chem. Eur. J. 2015, 21, 1803) that the rate of hydrogen atom abstraction, k, from ethylbenzene (EB) by TAML complex [FeV(O)B*]− (1) in acetonitrile exhibits a large kinetic isotope effect (KIE ∼ 26) in the experimental range 233−243 K. The extrapolated tangents of ln(k/T) vs T−1 plots for EB-d10 and EB gave a large, negative intercept difference, Int(EB) − Int(EB-d10) = −34.5 J mol−1 K−1 for T−1 → 0, which is shown to be exclusively due to an isotopic mass effect on tunneling. A decomposition of the apparent activation barrier in terms of electronic, ZPE, thermal enthalpic, tunneling, and entropic contributions is presented. Tunneling corrections to ΔH⧧ and ΔS⧧ are estimated to be large. The DFT prediction, using functional B3LYP and basis set 6-311G, for the electronic contribution is significantly smaller than suggested by experiment. However, the agreement improves after correction for the basis set superposition error in the interaction between EB and 1. The kinetic model employed has been used to predict rate constants outside the experimental temperature range, which enabled us to compare the reactivity of 1 with those of other hydrogen abstracting complexes.

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of activating C−H bonds, including FeIV species16,19−25 and FeV species,26−28 the latter supported by tetraamido macrocyclic ligands (TAML, Figure 1).29−31 With molecular weights around

INTRODUCTION The inertness of the carbon−hydrogen bond makes its functionalization a challenge to biology and chemistry. Nature achieves the hydroxylation of C−H groups through employing heme-type metalloenzymes such as cytochrome P4501−4 and chloroperoxidase (CPO)5 as well as non-heme oxygenases.6−8 Apart from its biological importance, this transformation is of interest for a wide array of industrial applications, for instance by converting saturated hydrocarbons into more functionalized molecules.9 Various FeIIIOOH, FeIVO, FeIVO−P•+ (P = porphyrin), and, inter alia, FeVO compounds have been proposed as the intermediates in the reaction cycles of oxygen activating enzymes. An extensive literature is devoted to the reactivity of FeIVO intermediates with organic substrates.1,3,10−15 Nonheme enzymes typically cycle between FeII/FeIV and heme enzymes between FeIII/FeIVO−P•+, both with additional intermediate oxidation states being involved.3,10,16 Even one of the least stable metalloprotein reactive intermediates, CPO Compound I, has yielded to EPR and Mössbauer spectroscopic characterization to reveal an FeIVO−P•+ species that is common to the reaction cycles of the widely studied horseradish peroxidase and peroxidase enzymes in general.17 Compound I species act also as key reactive intermediates in the catalytic cycles of the vast family of cytochrome P450 enzymes; spectroscopic validation has been achieved here as well.4,18 FeVO (isoelectronic with FeIVO−P•+) has been proposed to be the active intermediate of Rieske dioxygenases.10,13 To elucidate the role of high-valent iron−oxo species, chemists have designed biomimetic model complexes capable © 2017 American Chemical Society

Figure 1. Structure of the [FeV(O)B*]− activator, 1. Hydrogens are not show for clarity. Color code: C (gray), Fe (light blue), N (blue), O (red).

500 Da, i.e., at only less than 1% the size of oxygen and peroxide activating enzymes, iron−TAML activators are functional mimics of the peroxidase and short-circuited cytochrome P450 enzymes.32,33 TAML systems support multiple FeIV34−37 and the first spectroscopically characterized FeVO complex.38 This FeVO TAML species is demonstrably more reactive than FeIV TAML complexes.38,39 Since the report of the TAML-supported FeVO complex, a second FeVO species, supported by the TMC ligand, has been spectroscopically characterized: [FeVO(TMC)(NC(O)CH3)]+ Received: November 23, 2016 Published: April 3, 2017 4347

DOI: 10.1021/acs.inorgchem.6b02796 Inorg. Chem. 2017, 56, 4347−4356

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Inorganic Chemistry

spin SFe = 5/2 FeIII(OH) species that is coupled to the substrate radical to give system spin S = 2 or 3, states that require one or two spin crossovers to be accessed from the initial S = 1 state. The reaction kinetics for FeIVO have been analyzed by Shaik and co-workers, using a model coined the two (spin) state reactivity (TSR) model.65−68 In contrast, in the case of the S = 1/2 FeVO TAML species 1, the hydrogen atom abstraction results in an intermediate-spin SFe = 1 FeIV(OH) species that is coupled to the substrate radical to give S = 1/2 or S = 3/2 states, of which the former spin state, which has the lowest energy, requires no spin crossover to be accessed from the initial state. Thus, the barrier calculations for the FeVO case can be safely confined to the potential surface for S = 1/2, simplifying matters considerably (single state reactivity model). In the course of the present analysis we became aware that our DFT calculations underestimated the electronic contribution to the activation barrier for the hydrogen abstraction reaction by ∼11 kJ mol−1. Underestimates of this magnitude are not unprecedented in the DFT literature on TS calculations,77−80 and are consistent with the error margin of 8−20 kJ mol−1 reported for the performance of the B3LYP functional used in the present study.80 However, in other studies B3LYP is found to overestimate barrier energies,65a signaling that the basis set choice affects the barrier height. Self-interaction energy has been viewed as a major error source in DFT estimates of reaction barriers.80−83 The delocalization of the transient electron over several atoms reduces the self-repulsion, thereby lowering the TS energy relative to the energy of the initial state in which the electron is localized in a C−H bond. To address this issue, several palliatives have been proposed, for example, by implementing dynamic density in the definition of the functional, such as in the BMD functional.84 Unfortunately, the BMD functional gives for complex 1 a spurious FeIVO TAMLradical (Compound I type) ground state instead of the spectroscopically established FeVO state.38 Large scale multiconfigurational ab initio calculations for the activation energy, in which self-energy terms are absent, indeed improve the agreement with experiment.85 However, these calculations are computationally too expensive for studying the reaction of EB and 1. The agreement with experiment of the activation energy obtained with the help of our small-scale DFT calculations improves considerably by correcting for basis set superposition errors (BSSE)86,87 in the interaction between EB and 1.

(TMC = 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane).40 In ref 27 we explored the activation of C−H bonds by the TAML complex [FeV(O)B*]−, 1 (Figure 1), in a series of chemicals at temperatures ranging from −30 °C to −40 °C. As a special case, the kinetic isotope effect (KIE) on the abstraction rate of a methylene hydrogen atom in ethylbenzene (EB, DC−H = 87 kcal/mol) was analyzed by comparing the rates for EB and its isotopologue EB-d10, yielding a KIE ratio of 25.7 at −40 °C, which exceeded the KIE ratio of ∼8 expected to arise from isotope-dependent zero-point energy (ZPE) differences alone. Even higher KIE ratios (>100) have been reported for C−H bond activations catalyzed by enzymes such as lipoxygenases41 and methane monooxygenase42,43 and by heme oxo−iron(IV)−cation radicals.25 Large KIE ratios such as those measured here have been rationalized by considering the mass dependence of nuclear tunneling.41−43 Nuclear tunneling has been detected in the transfer of protons,44,45 hydrogen atoms,46−48 hydrides,49,50 and carbons51,52 and is the subject of many theoretical and experimental studies.53−58 According to some reports nuclear tunneling accounts for 60%49 and 85%59 of the reactive flux in enzymatic hydride transfers. Although the relative importance of tunneling, a quantum effect, diminishes when the temperature is raised, significant hydrogen tunneling may persist at room temperature60 and even up to 65 °C in alcohol dehydrogenases.61 In addition, nuclear tunneling was also found as a critical parameter in the control of chemical reactions.62,63 The presence of tunneling raises an intriguing problem: According to classical transition-state (TS) theory, on which the analysis of the rate of the reaction between EB and 1 given in ref 27 was based, the activation enthalpy (ΔH⧧) and entropy (ΔS⧧) are, respectively, obtained as the slope and the intercept (apart from a constant) at T−1 → 0 of the ln(k/T) vs T−1 plot. However, this interpretation is inaccurate in the presence of nuclear tunneling, in which case the values for ΔH⧧ and ΔS⧧ can only be accessed after removal of the tunneling contributions to slope and intercept. A procedure for the removal of tunneling contributions will be presented and applied to the reactions between 1 and EB and its isotopologue EB-d10. The selection of the tunneling model, among many alternatives,64−71 was guided by our DFT calculations using density functional B3LYP.72−76 Because the electronic coupling between donor (EB) and acceptor (1) at the TS is strong, these calculations produce a well-defined activation barrier, approximating a parabolic potential near the top (TS), which prompted us to adopt Bell’s tunneling model.64 Compared to purely computational approaches, the Bell model has the advantage that it provides a simple parametrization for the tunneling induced modifications of Eyring plots. Obviously, the simplicity comes at a cost in terms of accuracy. A more rigorous treatment would require the inclusion of vibrational energy changes along the reaction coordinates and a more general barrier shape, providing curved reaction paths that allow rate increase by corner cutting tunneling.71 The analysis presented here will also provide an estimate of the extent to which tunneling persists in the atom abstraction from the deuterated substrate, EB-d10. Hydrogen atom abstraction by the S = 1/2 FeVO species 1 is a much less convoluted process than a similar reaction carried out by an S = 1 FeIVO non-TAML species. The reason for the difference is that the process for FeIVO usually results in a high-

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METHODS

The DFT calculations were performed with Gaussian 09, revision B.01,72 using Becke’s three parameter hybrid functional (B3)73,74 along with the Lee−Yang−Parr correlation functional (LYP)75 and triple-ζ basis set 6-311G. The effect of the acetonitrile solvent on the electronic states and optimized geometries was evaluated using the SMD continuum model.76 The geometries for 1, EB, the reaction complex, 1−EB at the TS, and the broken-symmetry (BS) product state (H atom reduced 1/EB radical) were optimized using the default convergence criteria. The spin multiplicity (2S + 1) of the FeVO species was set to 2 on the basis of previous spectroscopic characterization.38 The TS structure for the hydrogen atom abstraction reaction was obtained from a relaxed potential energy surface scan and confirmed by TS optimization and frequency analysis (one imaginary frequency).

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RESULTS AND DISCUSSION For EB and EB-d10, the Gibbs free energies of activation (ΔG⧧), including electronic, vibrational, rotational, and translational contributions, were calculated using the thermochemical 4348


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Figure 2. Ln(knθ) vs θ plot. (A) Simulated kinetic curves in the θ range (0−8 × 10−3 K−1). (B) Linear extrapolations of the simulated kinetic curve from the experimental temperature range in the θ range (0−5 × 10−3 K−1) with the inset zooming into the θ range (0−1 × 10−3 K−1). kn is the normalized rate constant obtained from DFT calculations. Color coding: blue, kinetic curve for 1H transfer from EB including nuclear tunneling; red, kinetic curve for 2H transfer from EB-d10 including nuclear tunneling; cyan, classical kinetic curve for 1H transfer excluding tunneling; purple, classical kinetic curve for 2H transfer excluding tunneling; dashed vertical bars enclosing the experimental temperature range; solid curves, theoretical results from DFT calculations; broken lines, linear extrapolations.

properties facility of the Gaussian 0972 software package and compared with the values deduced from the slopes of the experimental Eyring (ln(k/T) vs T−1) plots (hereafter referred to as “kinetic curves”) for the two isotopologues. The comparison reveals two major differences. First, the calculated KIE ratios at different temperatures, which are essentially determined by the difference between the zero point energies (ZPEs) for EB and EB-d10, are about three times smaller than the experimentally observed values. Second, linear extrapolation to T−1 → 0 of the kinetic curves, calculated in the experimental temperature range of 233−243 K, yields only a small positive difference between the intercepts for the two isotopologues, ΔInt = Int(EB) − Int(EB-d10) > 0, which is at odds with the experimental kinetic data that extrapolate to a large negative value (−34.5 J mol−1 K−1) for this difference. This disagreement triggered further theoretical analysis. Intercepts of Kinetic Curves and Criterion for Nuclear Tunneling. In quasiclassical TS theory the expression for the rate of a thermally activated reaction has been written as k(T ) = (kBT /h) exp[−ΔG⧧/RT ]

activation enthalpy, we have modeled the abstraction of the methylene hydrogens from EB and EB-d10 by 1 with DFT calculations (see the next section). The results for the kinetic curves have been presented in Figure 2A by the cyan (proton) and purple (deuteron) curves. Figure 2B shows the tangents of these curves taken in the experimental range in corresponding colors. These tangents intersect each other at the vertical axis of Figure 2B, which has been drawn at a slightly negative value of θ, implying a positive intercept difference at θ = 0, ΔInt > 0 (see inset of Figure 2B). The positive sign of ΔInt can be undestood from the approximate relationship ΔInt ≈ ΔS⧧(EB) − ΔS⧧(EB-d10), by using the definition ΔS⧧ = STS − SRC (RC, reaction complex) and the relations SRC(EB) < SRC(EB-d10), which reflects the larger vibrational entropy for the deuterated RC due to hνC−H > hνC−D, and STS(EB) ≈ STS(EB-d10). It should be noted that this derivation of the inequality ΔInt > 0 tacitly assumed that ΔS⧧ contributes only a θ-independent term to ΔInt. However, a closer examination of the kinetic curves in Figure 2A reveals that the cyan and purple graphs are slightly curved as a result of the θ-dependences of ΔS⧧ and ΔH⧧. As these quantities introduce θ-dependent terms to the tangent with values depending on the isotope, it is conceivable that these terms also contribute to the intercept difference ΔInt. However, it can be shown that, even when these dependencies are included, the inequality ΔInt > 0 rigorously holds in the harmonic approximation (cf. the Supporting Information). To determine the size of this additional contribution, we have evaluated the difference between the intercepts of the cyan and purple tangents of Figure 2B with the vertical θ = 0 axis and compared this number with the difference between the entropies of EB and EB-d10 obtained from DFT thermochemical property calculations at 233 K. The comparison of the two numbers obtained, +0.86 J mol−1 K−1 and +0.90 J mol−1 K−1, respectively, shows a close agreement, leading to the conclusion that the θ-dependence of the activation entropy has, under the conditions prevailing in our system, only a minor impact on ΔInt. In contrast to the small, positive value for ΔInt predicted in the foregoing analysis, the linear extrapolation of the experimental data obtained for 233 K ≤ T ≤ 243 K yields a large, negative intercept difference, ΔInt = Int(EB) − Int(EBd10) = −34.5 J mol−1 K−1. [Note that the experimental temperature range is too narrow for resolving the curvature of

(1)

where T is the temperature, kB is the Boltzmann constant, h is Planck’s constant, ΔG⧧ is Gibbs free energy of activation, and R is the gas constant.88,89 In the interpretation of the kinetic data, we considered the quantity ln[k(T)/T]. This quantity is conventionally plotted as a function of the reciprocal temperature T−1, denoted θ, yielding a ln[θk(θ)] vs θ graph that we have called above a kinetic curve. The tangent of a kinetic curve at a given reciprocal temperature θ intersects the vertical axis at θ = 0 with the intercept (cf. the Supporting Information) ⎛k ⎞ θ 2 ⎛ dΔG⧧ ⎞ ⎟ ⎜ Int = ln⎜ B ⎟ + ⎝h⎠ R ⎝ dθ ⎠

(2)

This expression simplifies to the well-known expression Int ≈ ln(kB/h) + ΔS⧧/R, which features the intercept as a measure of the activation entropy, by treating the activation enthalpy and entropy, ΔH⧧ and ΔS⧧, in ΔG⧧ = ΔH⧧ − TΔS⧧ as temperature-independent quantities. To estimate the magnitude of the isotope effect on the intercept difference ΔInt as it may arise through the dependence of this quantity on the activation entropy and 4349


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and EB-d10. As the magnitude of the fourth term in eq 6 is larger for EB than for EB-d10 (see Table 1), the tangents of the kinetic curves for EB and EB-d10 give a negative intercept difference, ΔInt < 0, as inferred from the kinetic data.

the kinetic curves; the extrapolations of the observed linear relationships represent the tangents of the kinetic curves at θ ≈ 233−1 K−1.] Considering the low mass of the transient atom (1H or 2H), we will now explore the possibility that quantum mechanical tunneling is the source of the discrepancy between the observed and predicted intercept differences. The inclusion of Bell’s tunneling factor64,90 converts eq 1 into the expression46,47

Table 1. DFT-Based Decomposition of Eapp in Experimental Temperature Range state

⎛ ΔG⧧ ⎞ ⎟ k(T ) = κQ t exp⎜ − ⎝ RT ⎠

⧧

ΔEele ΔECP ΔEZPE⧧ ΔEtherm⧧ θ ΔΔEtherm⧧/Δθ −ΔΔS⧧/Δθ subtotal −(RΔQt)/(QtΔθ)

(3)

where κ = kBT/h and Qt is the tunneling factor, ∞

1 Q t (T , ε) = kBT

∫ 0

( )

exp

ε−w kBT

(

1 + exp 2π

ε−w hν

⧧

)

dw (4)

−R/θa totalb total + ΔECP ΔERC total + ΔECP + ΔERC exptc

⧧

ε is the energy width of the tunneling range, and iν is the imaginary frequency at the transition state. The values for iν⧧ and ε have been estimated from DFT calculations, and κ in eq 3 has been treated as a temperature-independent constant since hν ≫ kBT. Due to the presence of tunneling factor Qt, the rate constant k(θ) in eq 3 decays more slowly than exponential as a function of θ. As a consequence, logarithmic expressions, such as ln[θk(θ)], give convex kinetic curves, with the function for the EB-d10 substrate being less curved and running at more negative values than the corresponding function for EB (shown as the red and blue solid curves in Figure 2A). Although the classical curves, shown in cyan and purple, also show some curvature (see above), the nonlinearity is much smaller than when tunneling is included. The various contributions to the slope of a kinetic curve can be obtained by evaluating the derivative given in the left-hand side of eq 5. By using the rate expression given in eq 3 we obtain

EB-d10 (kJ mol−1)

43.1 10.2 −15.7 3.0 −2.9 2.9 30.5 −13.4 −16.8b 1.9 15.7 25.9 1.0 26.9 25 ± 1

43.1 10.2 −11.6 3.2 −3.3 3.4 34.7 −6.7 −10.5b 1.9 26.1 36.3 1.0 37.3 39 ± 3

θ was taken as 243.15 K. bUsing CP corrected ν⧧; cf. Figure S2. Reference 27.

a c

The intercepts and crossing of the tangents and their relationship with the curvatures of the kinetic curves for the two isotopologues are illustrated in Figures 2A and 2B. As noticed before, the kinetic curves excluding tunneling show only slight curvature (Figure 2A), with the EB curve only marginally more curved than the EB-d10 curve. The introduction of tunneling results in substantial curvature, with the nonlinearity for EB being greater than for EB-d10 (Figure 2A). This gives rise to an intercept for EB that is more negative than for EB-d10, as shown by the intercepts of the blue and red dash-dotted lines in Figure 2B. Consequently, the large negative difference between the intercepts, ΔInt < 0, results from tunneling and is not an isotope effect on the activation entropy as suggested by the conventional analysis of Eyring plots, according to which the intercept with the θ = 0 axis gives the activation entropy. Although tunneling and zero-point energy both contribute to the KIE, among the two contributions only tunneling contributes to ΔInt. This property can be readily understood from eq 6 which shows that the intercept depends on dΔG⧧/ dθ. This dependency implies that among the terms that constitute ΔG⧧ only those that are functions of temperature (or, equivalently, θ) influence the intercept. Since ZPE is independent of temperature, this quantity does not affect the intercept. In contrast, the temperature-dependent terms, − TΔS⧧ and ΔH⧧, do affect the intercept. However, as it was shown above, the isotopic dependency of these two terms leads only to minor changes in the intercept. By far the largest contribution to the isotopic dependency of the intercept comes from tunneling (dQt/dθ term in eq 6) as can be seen from Figure 2B. As the “classical” description (including contributions for ZPE) predicts a small and positive value for the difference ΔInt (see above), tunneling is left as the only viable explanation for the large negative intercept difference inferred from the experimental kinetic data. Thus, the observation of a ΔInt < 0 can be considered as a signature of tunneling, and the larger this difference, the more extensively are tunneling

d ln[θk(θ)] 1⎛ R dQ t dΔH ⧧ dΔS ⧧ R⎞ = − ⎜⎜ΔH ⧧ − +θ − − ⎟⎟ θ⎠ R⎝ dθ Q t dθ dθ dθ

(5)

where the thermodynamical variables have their conventional meanings. The temperature-dependent terms in eq 5 lead to the nonlinearity of the kinetic curves. The second term on the right-hand side of eq 5 originates from the tunneling factor and is the principal source of the curvatures in the blue and red curves of Figure 2A. The tangent at θ of the kinetic curve obtained for the rate expression given in eq 3 intersects the vertical θ = 0 axis at the intercept Int = ( − 1 + ln(θκ )) +

EB (kJ mol−1)

θ 2 ⎛ dΔG⧧ ⎞ θ dQ t ⎜ ⎟ + ln(Q t) − R ⎝ dθ ⎠ Q t dθ (6)

A comparison of eq 6 with eq 2 reveals two additional terms due to the tunneling factor in eq 3. The first term of eq 6 (in parentheses) is almost identical for EB and EB-d10 and contributes little to the intercept difference, ΔInt. The second, third, and fourth terms are positive, positive, and negative, respectively. As the fourth term is dominant among the latter three in the experimental temperature range, they yield together a negative contribution to the intercepts for both EB 4350


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Inorganic Chemistry phenomena contributing to the KIE. This criterion provides an experimentally based protocol for determining the extent to which tunneling controls the magnitude of the KIE. Decomposition of the Slopes of the Kinetic Curves. This section presents the results of a computational DFT analysis of the slopes of the kinetic curves for the hydrogen atom abstractions from EB and EB-d10 by FeVO complex 1 in terms of electronic and ZPE contributions to the activation energy, the thermal energies of vibration, rotation, and translation, the entropy, and tunneling. The analysis is based on the DFT results for both the initial RC and the TS (for details, see the next section). To facilitate the discussion, the decomposition is given in terms of contributions to the apparent activation energy, Eapp. Eapp = −R

d ln(θk) dθ

(7)

The definition implies that a negative contribution to the slope of the kinetic curve converts into a positive contribution to the effective activation energy, and vice versa. The DFT-based decomposition of Eapp in the experimental temperature range is given in Table 1. Comparison of the data for EB and EB-d10 reveals both similarities and differences. The electronic energies for EB and EB-d10 are equal because they are independent of the nuclear masses. As usual, the electronic contribution, ΔEele, is the largest component of Eapp. The second largest contribution, ΔEZPE⧧, is determined primarily by the ZPE of C−H/C−D bond stretching for the abstracted hydrogen/ deuterium, which raises the ground state energy relative to the energy of the transition state in which this mode is converted into a mode with an imaginary frequency. The third largest contribution derives from nuclear tunneling, −(RΔQt)/ (QtΔθ), and has a negative sign, because a lowering in temperature (increase in θ) leads to a lowering of the energies of the levels at which the tunneling predominantly occurs. The two thermal energy terms, θΔΔEtherm⧧/Δθ and ΔEtherm⧧, nearly cancel, as predicted when the classical limit of equipartition, where their sum is zero, is approached. The entropic term, −ΔΔS⧧/Δθ, is small but becomes increasingly important at higher temperatures. These entropic and thermal terms contribute to the slight curvature of the classical kinetic curves shown in Figure 2A. In the experimental temperature range the kinetic curve for EB is more horizontal than the corresponding curve for EB-d10 primarily because the tunneling contribution to Eapp for EB is twice that for EB-d10. Electronic Structure and Counterpoise Correction. The hydrogen atom abstraction reaction starts with the formation of a RC (O24···H65 = 2.74 Å, H65−C59 = 1.09 Å, and Fe−O24 = 1.60 Å; the labeling used is defined in Figure 3). The energy of the RC is ∼3 kJ mol−1 lower than the sum of the energies of EB and 1 calculated in isolation (see below). Subsequently, the S = 1/2 FeVO complex 1 evolves into an FeIV(OH) species with spin SFe = 1, which is antiferromagnetically coupled to a singly dehydrogenated substrate radical, SR = 1/2 (EB-H)•, to give system spin S = 1/2. The process passes through a TS, in which the transient proton is closer to the donor than the acceptor (H65···C59 = 1.24 Å vs O24···H65 = 1.34 Å) and with an elongated iron−oxo bond (Fe−O24 = 1.72 Å). The TS structure is shown in Figure 3 together with a contour plot of the α-LUMO, which has significant amplitudes at C59, O24, and Fe but is nearly vanishing at transient H. The orbital is an antibonding linear combination of the C−H σbond donor orbital and the antibonding O(py)−Fe(dyz)

Figure 3. α-LUMO at transition state. H atoms have been omitted for clarity except for the transient proton.

acceptor orbital combination. The corresponding transient αelectron containing orbital, which is bonding between C−H and O−Fe, is much lower in energy (α-HOMO−9) and substantially admixed with other orbitals on EB and 1. The RC and TS correspond, respectively, to the leftmost point and the maximum of the potential energy barrier shown in Figure 4 as a

Figure 4. Solid curve: Potential energy surface obtained by a relaxed scan of the distance between the transient H and the recipient axial O of 1. Dots: Activation barrier evaluated with energies corrected for the BSSE by means of the counterpoise method. The CP corrected curve has been vertically shifted to match to the uncorrected curve (solid) at the leftmost point (RC) by subtracting the CP correction (4.0 kJ mol−1) at the RC.

solid curve, which was obtained by performing a relaxed scan along the H65···O24 coordinate. The electronic energies for the TS and RC differ by ∼43 kJ mol−1 (ΔEele in Table 1). A comparison of the values for Eapp obtained experimentally (25 kJ mol−1 and 39 kJ mol−1, cf. Table 1) and theoretically (15.7 kJ mol−1 and 26.1 kJ mol−1, cf. Table 1) shows that the experimental values are on the average ∼11 kJ mol−1 larger than the theoretical ones, suggesting that the DFT calculations have underestimated the isotope-independent electronic contribution, ΔE ele, by about the same amount. The discrepancy can be explained as a basis set superposition error (BSSE) in the interaction between EB and 1.86,87,91,92 The BSSE can be understood as follows. When EB and 1 are placed in each other’s vicinity, the DFT calculation will improve the 4351


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barrier by 3.4 kJ/mol relative to the CP-corrected TZVP value for ΔEele. The moderate increase in ΔEele obtained with the larger basis set (def2-QZVP) cannot be accounted for as a BSSE in the result for ΔEele obtained with the smaller basis set (TZVP), as it was the case for TZVP and 6-311G. Quasiclassical Activation Parameters for EB and EBd10. Conventional kinetic analysis extracts the activation enthalpy (ΔH⧧) and activation entropy (ΔS⧧) from the slope and intercept of the ln(k/T) vs T−1 plot. However, since nuclear tunneling affects both the slope and the intercept, these quantities have to be corrected for tunneling to obtain accurate values for these thermodynamic activation parameters. The tunneling-corrected activation enthalpies have been referred to as the “quasiclassical” or “substantial” enthalpies of activation in the literature.96,97 The apparent activation enthalpies, deduced from the experimental slopes, are 25 kJ mol−1 (EB) and 39 kJ mol−1 (EB-d10).27 As these numbers contain contributions of −16.8 kJ mol−1 (EB) and −10.5 kJ mol−1 (EB-d10) due to nuclear tunneling (cf. Table 1), one arrives after tunneling correction at the values ΔH⧧ = 42 kJ mol−1 (EB) and 50 kJ mol−1 (EB-d10). The intercepts obtained for the normalized rates used in Figure 2B have the values Int(NT) ≈ 0 for both EB-d10 and EB in the case of no tunneling (NT), and Int(EB-d10) = −3.5 and Int(EB) = −5.2 in the presence of tunneling. The latter two theoretical intercepts correspond with Intexp(EB-d10) = −119 J K−1 mol−1 and Intexp(EB) = −152 J K−1 mol−1 obtained from the experimental Eyring plot analysis given in ref 27. The quantity of interest, ΔS⧧ = Intexp(NT), can be obtained by linear extrapolation,

wave function of 1 by using the basis orbitals of EB and, vice versa, EB will improve its state by using the basis orbitals of 1. Together these improvements lead to an artificial lowering of the energy of the EB···1 system. To correct for this error we have performed a counterpoise (CP) treatment, in which one calculates the energy lowering of 1 by extending its basis set with the basis orbitals of EB, but without adding the nuclei and electrons of EB, and the energy lowering of EB by extending its basis set with the basis orbitals of 1.86,87 The sum of the two corrections constitutes the counterpoise (CP) correction. When EB and 1 are far apart, the orbitals of the complementary fragment will only improve the small amplitude in the far out regions of the wave function in a small solid angle, leading to a small correction to the energy. However, the BSSE increases when the distance between EB and 1 is reduced. Thus, the net effect of the BSSE is to decrease the activation barrier and, consequently, the CP correction for this error increases the barrier height as obtained by DFT. This prediction is borne out by the CP corrected activation barrier presented in Figure 4 by blue dots. There is some ambiguity in the definition of the fragments in the vicinity of the TS, arising from the assignment of the transient atom. In our calculations the transient proton was assigned to EB before the TS and to 1 after the TS. The CP corrected potentials for the two regions match reasonably well as can be seen in Figure 4 (for details, see Figure S2). The CP correction adds energy ΔECP ≈ 10 kJ mol−1 to the height of the activation barrier (see Figure 4). Inclusion of the CP correction dramatically improves the agreement between the apparent activation energies obtained from theory and experiment: Eapp = 25.9 kJ mol−1 (25 ± 1 kJ mol−1, experimental) for EB and Eapp = 36.3 kJ mol−1 (39 ± 3 kJ mol−1, experimental) for EB-d10 (Table 1). The CP correction to the RC energy, which is ∼4 kJ mol−1, raises its value by about 1 kJ mol−1 above the sum of the energies for EB and 1 calculated in isolation. The latter sum represents the system energy for EB···1 distances approaching infinity where the CP correction vanishes. If one takes the sum of the isolated energies as reference for defining the barrier height, the apparent activation energies have to be raised by an additional ΔERC ≈ 1 kJ mol−1 (Table 1), yielding Eapp = 26.9 kJ mol−1 for EB and Eapp = 37.3 kJ mol−1 for EB-d10 (Table 1). The CP correction of the activation barrier also affects the imaginary frequency at the TS. In particular, the correction is expected to increase the value of ν⧧ by sharpening the barrier top (Figure 4), thereby enhancing the role of tunneling. This expectation is confirmed by a quantitative analysis (Table 1) which shows that the CP correction to the tunneling lowers Eapp by 3.4 kJ mol−1 (EB) and 3.9 kJ mol−1 (EB-d10). The BSSE can be reduced by improving the basis sets for the fragments. To analyze the reduction associated with the addition of polarization functions we have performed single point calculations for the B3LYP/6-311G geometries of RC and TS, using B3LYP in combination with the triple-ζ valence polarized basis set TZVP.93a The basis change reduces the CP correction to 3 kJ mol−1 but raises the uncorrected activation energy by 9 kJ mol−1. The net result is that the CP corrected activation energies obtained for TZVP and 6-311G differ by as little as 2 kJ mol−1. Although the Boys procedure adopted here may overestimate the counterpoise correction,94,95 the good agreement suggests that in the present case the correction is rather accurate. We have also performed single-point calculations with the large “default” basis set def2-QZVP.93b These calculations increased the electronic contribution to the

Intexp(NT) = Intexp(EB‐d10) − Int(EB‐d10)

Intexp(EB‐d10) − Intexp(EB) Int(EB‐d10) − Int(EB)

(8)

Substitution of the aforementioned values for the experimental (Intexp) and theoretical (Int) intercepts into eq 8 yields ΔS⧧ = Intexp(NT) ≈ −49 J K−1 mol−1 for the activation entropies of both EB and EB-d10. The above example shows that the tunneling corrections that have to be applied to the conventional ΔH⧧ and ΔS⧧ values extracted from the ln(k/T) vs T−1 plot are sizable: the corrections for ΔH⧧ are 11 kJ mol−1 (EB-d10) and 17 kJ mol−1 (EB), and those for ΔS⧧ are 70 J K−1 mol−1 (EB-d10) and 103 J K−1 mol−1 (EB). Although, as expected, the tunneling corrections for EB-d10 are smaller than those for EB, they are by no means small. The activation enthalpies (ΔH⧧) of closely related bond breaking/formation reactions are often found to correlate linearly with the associated bond dissociation energies. As this type of correlation has been rationalized on the basis of the relationship between classical barrier height and driving force (ΔH°),90 it seems plausible to use quasiclassical values for ΔH⧧ for establishing such correlations in the case of hydrogen atom transfer reactions. As tunneling depends on both the height and the width of the reaction barrier, one anticipates that there is a relationship between nuclear tunneling and C−H bond dissociation energy. This type of relationship has been explored in a recent study.65d Comparative Analysis. A number of high-valent iron−oxo complexes that perform hydrogen atom abstraction reactions from EB have been listed in Table 2. With three exceptions, the rate constants for these reactions, listed in the third column of Table 2, have been determined at ambient temperatures (see 4352


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EB and EB-d10 by TAML activator [FeV(O)B*]−. The analysis can be summarized as follows: (1) Nuclear tunneling combined with the isotope effect on the ZPE leads to 52- and 5-fold increases in the hydrogen abstraction rates at −40 °C from EB and EB-d10, respectively. (2) Nuclear tunneling is the origin of the large negative difference found between the intercepts of the tangents of the kinetic curves at −40 °C for EB and EB-d10. The negative sign of the intercept difference, ΔInt < 0, is an indicator of nuclear tunneling. (3) The nuclear tunneling factor contributes a significant term to the apparent activation energy deduced from the slope of ln(k/T) vs T−1 plots. The apparent activation energies calculated at the B3LYP/6311G level for the hydrogen atom abstraction from EB and EBd10 by 1 are in good agreement with experiment, provided the electronic contribution to the activation energy is corrected for the BSSE. According to some accounts80 the B3LYP functional underestimates systematically the energy of C−H bond activation by high-valent metal−oxo species. The counterpoise correction may bridge part of the discrepancy, particularly in calculations using small basis sets. However, in the case of larger basis sets, when the counterpoise corrections are smaller, alternative sources for the discrepancy, such as dispersion energies,80 have to be considered.

Table 2. Rate Constants for the Oxidation of EB by Various Iron−Oxo Complexes Compared with Those for 1 at Corresponding Temperatures iron complexesa IV

2+

[Fe (O)(N4Py)] [FeIV(O)(BnTPEN)]2+ [FeIV(O)(BQEN)]2+ [FeIV(O)(Me3NTB) (NCMe)]2+ [FeIV(O)(TQA) (NCMe)]2+ [FeIV(O)(TMP+•)]− [FeV(O)(TPP)]− [FeV(O)(TMP)]− [FeV(O)(OEP)]− [FeV(O)B*]−, 1

T/°C

k/M−1 s−1 for complexes

kextra/M−1 s−1b for 1

ref

25 25

0.004 0.069

3.16 3.16

16 16

0 −40

0.026 1.5

1.08 0.145c

24 23

−40

2.1

0.145c

98

22 22 22 22 −40

1.64 7.7 × 104 1.4 × 105 2.9 × 105 0.145

2.79 2.79 2.79 2.79 0.145

25 99 99 99 this work

a

N4Py = N,N-bis(2-pyridylmethyl)-N-bis(2-pyridyl)methylamine; BnTPEN = N-benzyl-N,N′,N′-tris(2-pyridylmethyl)ethane-1,2-diamine; BQEN = N,N′-dimethyl-N,N′-bis(8-quinolyl)ethane-1,2-diamine; Me3NTB = tris((N-methylbenzimidazol-2-yl)methyl)amine; TQA = tris(2-quinolylmethyl)amine); TMP = 5,10,15,20-tetramesitylporphyrin; TPP = 5,10,15,20-tetraphenylporphyrin; OEP = 2,3,7,8,12,13,17,18-octaethylporphyrin. bRates for 1 obtained by extrapolation to the temperature indicated in the same row (cf. Figure S3). cExperimental value for 1 at −40 °C.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b02796. Activation entropy analysis (Table S1, Figure S1), counterpoise correction analysis (Figure S2), decomposition of apparent activation energy and reaction rate prediction (Tables S2−3, Figure S3), and coordinates of DFT structures and spin populations (PDF)

second column). To allow a meaningful comparison of these rate constants with those for complex 1, which were recorded between −30 °C and −40 °C,27 the rates for 1 have been extrapolated to the temperatures at which the rates for the complexes in Table 2 were recorded. Obviously, a reliable extrapolation can only be achieved by adopting a description that provides an accurate representation of the observed rate constants. To this end, we first fitted the experimental data for the reaction of 1 with EB using eq 3, treating ΔEele, κ, and ν⧧ as adjustable parameters (for details, see the Supporting Information), and subsequently used the resulting parameter set for evaluating the extrapolated rates. Accurate fits for the slopes of the experimental ln(k/T) vs T−1 plots (shown in the Supporting Information) required only moderate adjustments in the parameters of Table 1. The rate constants for the hydrogen abstraction from EB by 1 obtained by the extrapolation have been listed in the fourth column of Table 2. Comparison of the rate constants in columns 3 and 4 shows that the S = 1/2 FeVO complex 1 is more reactive than the S = 1 FeIVO species supported by the N4Py, Bn-TPEN, and BQEN ligands by as much as 2 to 3 orders of magnitude. However, 1 is 1 order of magnitude less reactive than S = 1 [FeIV(O)(Me 3 NTB)(NCMe)] 2+ and S = 2 [Fe IV (O)(TQA)(NCMe)]2+.23,98 The lower half of Table 2, which lists the results reported for a number of porphyrin species, reveals that complex 1 has a reactivity similar to that of the Compound I type TMP-radical−FeIVO complex but is 4 to 5 orders of magnitude less reactive than the three photogenerated, shortlived intermediates supported by the TPP, TMP, and OEP ligands, which have been proposed to be FeVO species on the basis of their high reactivities.99

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Emile L. Bominaar: 0000-0002-5125-265X Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS T.J.C. thanks the Heinz Endowments for support. L.Q.S. and S.K. thank CMU for Presidential Fellowships. REFERENCES

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CONCLUSIONS Theoretical analysis of the KIE shows that nuclear tunneling plays an important role in the hydrogen atom abstraction from 4353


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