Quantum Chemical Modeling of the Oxidation of Dihydroanthracene

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J. Phys. Chem. C 2007, 111, 12397-12406

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Quantum Chemical Modeling of the Oxidation of Dihydroanthracene by the Biomimetic Nonheme Iron Catalyst [(TMC)FeIV(O)]2+ Adam Johannes Johansson,* Margareta R. A. Blomberg, and Per E. M. Siegbahn Department of Physics, Stockholm UniVersity, SE 106 91, Stockholm, Sweden. ReceiVed: April 19, 2007; In Final Form: June 19, 2007

Hybrid density functional theory has been employed to model the oxidation of dihydroanthracene (DHA ) C14H12) to anthracene (C14H10) by the biomimetic iron complex [(TMC)FeIV(O)]2+ (TMC ) 1,4,8,11tetramethyl-1,4,8,11-tetraazacyclotetradecane). Experimentally, the reaction has been studied in a solution of the reactants and the counterion trifluoroacetate (CF3CO2 ) in the solvent acetonitrile (CH3CN). Depending on the concentration of trifluoroacetate, different coordination situations have been observed by NMR spectroscopy. The complexity of the chemical environment offers a challenging modeling problem, and five different models were initially considered. The effects of the coordination of either a counterion or a solvent molecule were found to be rather small. The reaction was found to be a two-step process in which the first step is rate-limiting. The free energy of activation (∆G q ) for the first H-abstraction was found to be between 14.5 and 16.9 kcal mol-1 depending on the model, in reasonable agreement with experimental data. The second step has a much lower free-energy barrier, found to be completely entropic in origin. In all models, the system is found to have a triplet ground state in the FeIV(O) reactant. A spin-crossing of the triplet and quintet potential energy surfaces occurs before the first transition state, and the system is found to end up in the FeII quintet state, releasing a water molecule and the anthracene product. Because of the formation of the aromatic anthracene molecule, the reaction is very exothermic.

1. Introduction Mononuclear nonheme iron enzymes have been found to catalyze a number of important oxidative biochemical processes. Several studies have suggested the active oxidants to be high valent iron-oxo intermediates, resulting from dioxygen cleavage.1 This has been verified spectroscopically only for the monoiron enzyme TauD and for the di-iron enzymes MMO and RNR. Que and co-workers have characterized and reported the first examples of synthetic mononuclear nonheme iron (IV)-oxo complexes. These complexes show interesting catalytic activities that mimic the chemistry performed by mononuclear nonheme iron enzymes, which supports the hypothesis that iron (IV)oxo intermediates could be responsible for the oxidative activities in the corresponding enzymes. The study of biomimetic complexes is not only an important complement to direct studies of enzymatic mechanisms but there are also potential applications for synthetic complexes to be used industrially. The oxidation of dihydroanthracene (DHA ) C14H12) to anthracene (C14H10) by the biomimetic iron complex [(TMC)FeIV(O)]2+, has been studied experimentally by Que and Rohde.2 The reaction was investigated in acetonitrile (CH3CN) and in the presence of the counterion trifluoroacetate (CF3CO2 ). In the absence of substrate, the complex is stable enough to be crystallized. Under stoichiometric concentration (1:2) of the counterion CF3CO2 , X-ray diffraction revealed a structure in which an acetonitrile molecule is coordinated to iron. This could also be confirmed by NMR spectroscopy of the complex in solution. To mimic the biological situation in which a carboxylate (Asp or Glu) is coordinated to iron, a salt of the counterion (NEt4CF3CO2) was added until NMR data revealed a structure in which the coordinated CH3CN molecule was replaced by a CF3CO2 ion. The DHA substrate was added to the solutions of

both stoichiometric and higher concentration of CF3CO2 , and the half-life times of the FeIV(O) complexes were measured. For the complex coordinating a CH3CN molecule, the measured half-life time corresponds to an activation free energy of 20.1 kcal mol-1, whereas in the case of CF3CO2 coordination, the free energy of activation was lowered to 18.6 kcal mol-1. The present study is an application of the hybrid DFT (density functional theory) functional B3LYP, to model the H-abstraction from DHA by [(TMC)FeIV(O)]2+ as occurring in solution. Because the system contains not only the iron complex and substrate but also counterions and the solvent, the quantum chemical modeling is a challenge. The effects of coordination and total charge of the model have been investigated systematically by considering five models of different total charge and with different coordination situations. In the simplest model (Figure 1; model E) including only [(TMC)FeIV(O)(CH3CN)]2+ and the DHA substrate, severe errors reflected by an artificial electron distribution were encountered, which is why this model was abandoned. Although unexpected for the present system, this is an effect of the well-known self-interaction error of DFT methods. This problem was removed completely when the total charge was reduced by the inclusion of counterions in the models. The entire reaction mechanism was investigated for two + models with a total charge of +1; [(TMC)FeIV(O)(CF3CO2 )] (A), and [(TMC)FeIV(O)(CH3CN)]2+(CF3CO) (B), and for 2 two models of total charge 0; [(TMC)FeIV(O)(CH3CN)]2+ - + IV (CF3CO2 )2 (C), and [(TMC)Fe (O)(CF3CO2 )] (CF3CO2 ) (D) (Figure 1). In all models, the first H-abstraction was found to be the ratelimiting step, with ∆Gq in the range of 14.5 to 16.9 kcal mol-1 depending on the model. Because the accuracy of the B3LYP

10.1021/jp0730444 CCC: $37.00 © 2007 American Chemical Society Published on Web 07/27/2007

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Figure 1. Optimized structures used to model the [FeIV (TMC)(O)]2+ complex and the counterion CF3CO2 in the solvent CH3CN. Model E has a total charge +2, models A and B has a total charge +1, and models C and D are neutral. The substrate DHA is shown for each model. The Lewis structure of the TMC ligand is shown in the figure.

functional is expected to be within 3-5 kcal mol-1, the calculated barriers are in reasonable agreement with experimental data. However, the observed difference in free energy of activation of 1.5 kcal mol-1, depending on the coordination situation, is too small to be reproduced. Instead, the purpose of the present study is to gain insight into the reaction mechanism and to investigate how the mechanism is affected by the choice of model. A common feature of all models is that the FeIV(O) intermediate has a triplet (S ) 1) electronic ground state, which is in agreement with experimental observations. The first transition state is lower on the quintet (S ) 2) surface, which indicates a spin-crossing preceding the first barrier. The second H-abstraction occurs on the quintet surface and the system is found to end up in the FeII (d 6 ) quintet (S ) 2) state. Because of the formation of the aromatic anthracene molecule, the reaction is very exergonic, ∆G being about -60 kcal mol-1. Finally, it should be mentioned that near completion of our work, Shaik and co-workers published a DFT study of the hydroxylation of cyclohexane by (TMC)FeIV(O).3 The first step in the hydroxylation is a H-abstraction quite similar to the first step of the reaction studied in the present work, differing mainly in the substrate.

2. Computational Details a. Methods. Quantum mechanical calculations have been performed employing density functional theory with the hybrid exchange-correlation functional B3LYP (including the Becke three-parameter exchange functional and the Lee, Yang, and Parr correlation functional).4-6 The software package Jaguar 5.57 has been used to optimize molecular geometries at the B3LYP/lacvp level of theory, and for single-point calculations of the energy at the B3LYP/lacv3p(d,p) level of theory. Lacvp is a basis set of double-ζ quality, whereas lacv3p(d,p) is of triple-ζ quality with polarization functions on all atoms; both include an effective core potential to describe the iron atoms.8 The methodology to perform geometry optimization with a double-ζ basis set, followed by single-point evaluation of the energy using a triple-ζ basis set, has been proven reliable many times for DFT calculations on transition-metal-containing systems.9 Also, the self-consistent reaction field (SCRF) method implemented in Jaguar has been used to evaluate electrostatic solvation effects.10,11 This method describes the solvent as a polarizable dielectric continuum in which the quantum model of the solute system is contained in a cavity. The continuum and the quantum model polarize each other in an iterative process until convergence is reached. The

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+ Figure 2. Free-energy profile for the reaction in model A [(TMC)FeIV(O)(CF3CO2 )] . In the schematic drawings of the FeTMC complex, Q denotes a counterion (CF3CO2 ). The table shows the Mulliken spin population on iron, oxygen, and on the substrate molecule.

continuum is characterized by a temperature-dependent dielectric constant, . For acetonitrile (CH3CN),  has been experimentally determined to be 36.6 at T ) 298 K.12 Different empirical values can be found for the dielectric constants of solvents, for acetonitrile ranging between 36 and 38. It should be emphasized that such a small difference has no significant effect on the results of the present type of calculations. Hessian matrices, that is, force constant matrices, were computed using the Gaussian 03 package.13 The Hessian is used to calculate thermodynamic parameters and guide the search for transition states. Initial guesses for the transition states were obtained by constrained optimization of minima for different distances of the O-H bonds to be formed. For the structure and electronic probability density corresponding to the highest energy on the potential energy surface, a Hessian was calculated and the vibrational frequencies were analyzed to ensure that the guess for the TS optimization has one dominating imaginary frequency that corresponds to the reaction coordinate of interest. Transition-state optimizations were then performed using Gaussian 03. Thermodynamic parameters and changes in Gibbs free energy (∆G), enthalpy (∆H), and entropy (∆S) were computed at 298.15 K. Because in all models the constrained optimization scan of the reaction coordinates indicated that the first H-abstraction is the rate-limiting step, transition states were optimized for this step in all models. For the second H-abstraction, a TS was optimized only for model C. The zero-point and entropy effects calculated for the second step in model C was then added to the electronic activation energies in the other models to estimate the free-energy barriers also for the second step. For the models of total charge +1 (Figure 1; models A and B), no electronic energy barriers were found for the second H-abstraction on the quintet surface. To estimate the free-energy barriers, structural parameters were taken from the corresponding triplet states, for

which electronic energy barriers were found to exist. Constrained optimization was performed at an O-H distance of 1.65 Å and a C-H distance of 1.17 Å. To the electronic energies in these points, a zero-point and entropic correction of 4.5 kcal mol-1 derived from model C was added to estimate the free energy. Several benchmark tests have been done in order to evaluate the accuracy of the B3LYP functional. From comparisons with experimental thermodynamic data for a wide diversity of molecules including radicals, nonhydrogen systems, hydrocarbons, substituted hydrocarbons, and inorganic hydrides, it could be concluded that an average error of 3.11 kcal mol-1 can be expected.14,15 For transition-metal-containing systems, the deviation between computed and measured bond dissociation energies for the M-R bonds in a number of MR+ systems (M ) firstrow transition metal, R ) H, CH3, CH2, OH), is in the range 3.6-5.5 kcal mol-1.16,17 There are indications that the reparametrized B3LYP* functional, which uses 15% Hartree-Fock exchange as compared to the 20% used in the original functional, could be a better description of the exchange-correlation part of the energy in transition-metal-containing systems.18 As a comparison, the B3LYP* functional has been used to evaluate the electronic energy of activation and the splitting of different electronic spin states in models A and B. The spin population referred to in the discussion and shown in Figures 2-5, is a qualitative measure of the amount of unpaired R-spin (+sign) or β-spin (-sign) on each atom. This was computed according to the standard Mulliken population analysis. It is known by experience that high-spin states of Fe complexes typically have some of the spin delocalized to the ligands so that the Fe ion obtains a spin population that is lower than that for a free Fe ion. Although B3LYP and some other DFT functionals in general perform well for transition-metal systems, they all utilize

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Figure 3. Free-energy profile for the reaction in model B [(TMC)FeIV(O)(CH3CN)]2+(CF3CO2 ). In the schematic drawings of the FeTMC complex, S indicates a solvent molecule (CH3CN), whereas Q denotes a counterion (CF3CO2 ). The table shows the Mulliken spin population on iron, oxygen, and on the DHA substrate molecule.

approximative exchange-correlation functionals, resulting in an artificial interaction of an individual electron with itself. In wavefunction-based methods like Hartree-Fock, such interactions disappear because the Coulomb and exchange integrals cancel exactly. In DFT methods, because the exchange part is not exact, the resulting nonzero difference between the Coulomb and exchange contributions leads to a nonzero self-interaction. DFT functionals including corrections for the self-interaction error have been developed but are so far found to perform worse in benchmark tests.19-22 The self-interaction error results in artificial stabilization of delocalized electronic states,23 as illustrated by the dissociation of H2+ into H(1/2)+ + H(1/2)+ instead of the physical dissociation limit H + H+. Effects of the self-interaction error on the electron distribution in transitionmetal complexes are unusual but did appear for one of the models in the current investigation. b. Models. The oxidation of dihydroanthracene (DHA ) C14H12) by [FeIV (TMC)(O)]2+ studied experimentally takes place in a solution of acetonitrile (CH3CN) and in the presence of the counterion trifluoroacetate (CF3CO2 ). X-ray diffraction and NMR data have revealed different coordination situations depending on the concentration of the CF3CO2 ion. Thus, it is not obvious how a realistic model of the reacting system should be constructed. In total, five different models have been considered. The models are shown in Figure 1 together with the substrate dihydroanthracene (C14H12). To investigate systematically the effects of charge and coordination, we included CH3CN molecules and CF3CO2 ions in different ways. In the simplest model, model E, only a single CH3CN molecule is coordinated to iron, which is why this model has the highest charge of +2. Although this model was found to behave normal in the triplet state, in the quintet state it was

found to suffer from severe errors in the electronic distribution between the iron complex and the DHA molecule. According to the Mulliken population analysis, one electron is shared between the iron complex and the closed-shell DHA molecule, even at a large distance (13 Å). Furthermore, no barrier was found for the first H-abstraction on the quintet surface. Because of this artifact, model E was abandoned at an early stage of the investigation. It is important to note that this problem was eliminated completely in the other models, by the inclusion of counterions. This is discussed further in the next section of this paper. Both models B and C correspond to the coordination situation for a stoichiometric concentration of the CF3CO2 ion, as indicated by NMR spectroscopy. In both models, a CH3CN molecule is coordinated to iron. In addition, model C includes two CF3CO2 ions outside the first coordination sphere, whereas model B includes only one CF3CO2 ion. Model C is thus electrostatically neutral, whereas model B has a total charge of +1. Both models A and D reflect the coordination situation for an increased concentration of the CF3CO2 ion, also indicated by NMR data. In both models, a CF3CO2 ion is coordinated to iron. Model D includes an additional CF3CO2 ion outside the first coordination sphere. Thus, model D is neutral, whereas model A has a total charge of +1. Although the electronic energy and entropy of activation are calculated relative to the infinitely separated reactant species, the dielectric solvation effects could not be modeled in this way because there is a large unphysical dielectric effect originating from differences in the solvation model cavities. Instead, the solvation effects on the activation energies were calculated

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Figure 4. Free-energy profile for the reaction in model C [(TMC)FeIV(O)(CH3CN)]2+(CF3CO2 )2. In the schematic drawings of the FeTMC complex, S indicates a solvent molecule (CH3CN), whereas Q denotes a counterion (CF3CO2 ). The table shows the Mulliken spin population on iron, oxygen, and on the DHA substrate molecule.

relative to the reactant complex. The dielectric solvent effect on the activation energy in model C is only 2.2 kcal mol-1 obtained in this way. However, for models A and B the dielectric solvent effects on the activation energies are quite large, 6.2 kcal mol-1 in model A and 5.0 kcal mol-1 in model B. These comparatively large dielectric effects make the activation energies a bit uncertain. However, it should be noted that dielectric effects of the same magnitude were reported also in a recent work by Shaik et al. on a similar reaction.3 Model D is left out of the discussion because it was found to be problematic for the continuum solvation model employed. The solvation effects on the reaction in this model differ so much from the effects in models A-C that the second H-abstraction would be rate-limiting, in contrast to what was found in models A-C where the first step is rate-limiting. The solvent effects are very irregular, probably because the continuum model is sensitive to the position of the noncoordinated counterion. As can be seen in the structure of model D in Figure 1, the noncoordinated counterion gets a position much closer to the substrate molecule than in models B and C, also including noncoordinated ions. This could not be avoided, and the qualitative differences in the solvation effects are believed to be related to these structural differences. 3. Results and Discussion Density functional theory has been applied to investigate the oxidation of dihydroanthracene (DHA ) C14H12) to anthracene (C14H10) by the biomimetic nonheme iron complex [(TMC)FeIV(O)]2+. The reaction is modeled to occur in a solution of acetonitrile (CH3CN) and in the presence of the ion trifluoroacetate (CF3CO2 ). Because different coordination situations

have been suggested experimentally, five models with different charges and coordinations, described in the previous section and shown in Figure 1, have been considered. It is found for models A-C that the reaction is a two-step process for which the first step is rate-limiting. Furthermore, the first step is found to be a hydrogen-atom transfer, that is, a process in which the proton and electron are transferred simultaneously. The calculated free energies of activation are 14.5 to 16.9 kcal mol-1, depending on the model. This is in reasonable agreement with the experimental results for which the corresponding barriers are 18.6 to 20.1 kcal mol-1. Also in agreement with experimental results, it is found that the FeIV(O) intermediate has a triplet (S ) 1) electronic ground state. The differences between solvent or counterion coordination are found to be rather small, about 2 kcal mol-1 for the thermodynamics of both steps and for the free energy of activation of the rate-limiting step. The reaction is found to be exergonic by about 60 kcal mol-1. Most of this exergonicity (45 kcal mol-1) comes from the second step in which a radical substrate intermediate is transformed into the completely aromatic dihydroanthracene molecule. The free-energy profiles in Figures 2-4 summarize the results obtained for models A-C. These profiles show the Gibbs free energy at the B3LYP/lacv3p(d,p) level of theory and includes electrostatic solvation effects on the energy. Optimized transition states for the rate-limiting steps in models A-C, and for the second step in model C, are shown in Figure 5. Zeropoint vibrational effects and entropic effects are summarized in Table 1. + Both models A [(TMC)FeIV(O)(CF3CO2 )] and B [(TMC)FeIV(O)(CH3CN)]2+(CF3CO) have a total charge of +1 (Fig2

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Figure 5. Optimized transition-state structures for the first H-abstraction in models A-C (TS1) and for the second step in model C (TS2).

TABLE 1: Computed Thermodynamic Parameters for the First and Second H-abstraction from DHA by Three Different Models of (TMC)FeIV(O)a model

point

∆Eel

∆H

-T∆S

∆G

A A A A B B B B C C C C

TS1 I TS2 P TS1 I TS2 P TS1 I TS2 P

+11.7 -9.3 -14.9 -52.4 +10.5 -8.8 -18.7 -51.0 +11.5 -10.4 -12.2 -53.0

+6.6 -13.1 -19.1 -56.2 +5.2 -12.6 -22.9 -53.5 +5.7 -13.3 -16.4 -56.0

+10.3 -4.0 +8.7 -6.1 +9.3 -2.2 +8.7 -6.7 +9.6 -3.1 +8.7 -6.2

+16.9 -17.1 -10.4 -62.3 +14.5 -14.8 -14.2 -60.2 +15.3 -16.4 -7.7 -62.2

a For each model, the energy of the initial FeIV(O) reactant is set to zero. Point I refers to the energy of the FeIII (OH) intermediate, and point P refers to the final product. All energies are given in kcal mol-1.

ure 1). Model B corresponds to the coordination situation observed experimentally under stoichiometric concentration of the counterion CF3CO2 , whereas model A reflects the coordination situation that has been achieved experimentally by adding 10 equiv of NEt4CF3CO2 to the solution of the reacting system. In agreement with experimental data, the FeIV(O) intermediate is found to be in the ferromagnetically coupled triplet (S ) 1) state, having formally one R-spin on iron and one R-spin on the oxo group. However, a ferromagnetically coupled quintet state with formally three R-spins on iron and one R-spin on the

oxo group was found to be only 4.1 kcal mol-1 higher in model A and 2.6 kcal mol-1 higher in model B. Antiferromagnetically coupled states of the same spin multiplicities, the triplet having three R-spins on iron and one β-spin on the oxo group, and the quintet having five R-spins on iron and one β-spin on the oxo group, were found to be higher than the corresponding ferromagnetically coupled states. For the first H-abstraction, the free energy of activation is 16.9 kcal mol-1 in model A and 14.5 kcal mol-1 in model B, whereas for the second step it is 6.7 kcal mol-1 in model A and only 0.6 kcal mol-1 in model B (Figure 2-3). Thus, the first H-abstraction is found to be the rate-limiting step in both models. The triplet/quintet splitting in the first transition state is 6.1 kcal mol-1 in model A and 9.8 kcal mol-1 in model B. In both models, the quintet state is lower than the triplet in the TS region, which is opposite of the situation in the FeIV(O) intermediate. It is well known that spin-orbit coupling in transition-metal systems is large enough to allow spin-crossings,24 and a transition state was therefore optimized for the first rate-limiting H-abstraction on the quintet surface. The transition state is found at an O-H distance of 1.45 Å in model A and 1.52 Å in model B (Figure 5). The spin-crossing found here was also identified in a recent DFT study of the hydroxylation of cyclohexane by (TMC)FeIV(O).3 From the Hessian matrix of the optimized transition-state structures, zero-point and thermal effects on the barriers were evaluated (Table 1). The entropic effect (-T∆Sq) on the free

Biomimetic Nonheme Iron Catalyst [(TMC)FeIV(O)]2+ energy of activation of the first step is 10.3 kcal mol-1 in model A and 9.3 kcal mol-1 in model B. The major part of this effect originates from the loss of translational entropy in the formation of the FeIV (TMC)(O)-DHA complex. Alternatively, the zeropoint effects act in the opposite direction, giving (thermal effects included) an enthalpy of activation of 6.6 kcal mol-1 in model A and 5.2 kcal mol-1 in model B. For the second step, the free energy of activation is completely entropic in origin because in the quintet state no electronic energy barrier was found on the potential energy surface. Because of the formation of the aromatic anthracene product, the second step is very exergonic, ∆G° being about -45 kcal mol-1 in both models. According to the Mulliken spin population (Figures 2, 3, and 5), the spin on the substrate changes gradually during the first H-abstraction. The spin population is zero for the closed-shell singlet DHA molecule and one on the substrate radical formed after H-abstraction. In the transition state, the spin population on the substrate is -0.4 (0.4 β-spin) on the quintet surface in both models. Thus, the first step can be described as a H-atom transfer, that is, the proton and electron are transferred together. On the triplet surface, a β-spin electron is transferred from the substrate molecule to the FeIV(O) complex and forms a bonding pair with the unpaired R-spin electron on the oxo group, resulting in a ferromagnetic coupling between the unpaired electron on the substrate radical and the single unpaired electron on iron (low-spin iron) (Figure 6; S ) 1). Another triplet state having formally three R-spins on iron (intermediate-spin iron) and one β-spin on the substrate radical was found to be 2.3 kcal mol-1 higher in the TS region and 6.0 kcal mol-1 higher than the ferromagnetic triplet in the FeIII (TMC)(OH) intermediate. On the quintet surface, the same mechanism as that on the triplet surface would lead to a state with formally three R-spins on iron (intermediate-spin iron) and one R-spin on the substrate radical (Figure 6; S ) 2). However, when transferring the first hydrogen atom of DHA to FeIV (TMC)(O) in the quintet state with formally three R-spins on iron and one R-spin on oxygen, the antiferromagnetically coupled quintet state described above is mixed in, as reflected by the β-spin on the substrate in the transition state. The resulting FeIII (TMC)(OH) intermediate automatically ends up in a state with formally five R-spins on iron (high-spin iron) and one β-spin on the substrate radical (Figure 6; S ) 2). Because of the relatively weak spin-coupling between the substrate radical and iron, the ground state is determined by the spin on Fe, which is S ) 5/2 (high-spin iron). It should be noted that part of the spin on iron is delocalized to the coordinated ligand atoms and to the hydroxo group. The spin population on iron in the quintet state is therefore lower than it should formally be. Thus, as indicated in Figure 6, the reactions in both the triplet and quintet states proceeds in such a way that FeIII avoids the high-energy intermediate spin state with S ) 3/2 on iron. The product of the first H-abstraction is a stable complex of FeIII (TMC)(OH) and the substrate radical with the radical carbon directed toward the hydroxo group of FeIII (TMC)(OH). The substrate radical thus has to be moved and rotated in order to position the second hydrogen atom to be transferred. In calculating the free energy of the intermediate, the iron complex and the substrate radical are assumed to be noninteracting, verified by that calculations on the unbound complex between the same species gave a very small change in the electronic energy. For the second step, the population analysis indicates differences between the two spin surfaces. In the quintet state (for

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Figure 6. Electronic mechanisms for the first H-transfer. In the quintet, state the transfer of an R-spin electron from DHA leads to high spin iron in the FeIII intermediate. In the triplet state, the transfer of a β-spin electron leads to low-spin FeIII. The high-energy intermediate spin state is thus avoided on both the triplet and quintet spin surface.

which no electronic energy barrier was found in models A or B), the spin on the substrate is zero already at an O-H distance of 1.65 Å, corresponding to the O-H distance in the transition state on the triplet surface. The spin on the substrate in the transition state is thus the same as in the product, the closedshell anthracene molecule (Figures 2, 3, and 5). This result suggests an early electron transfer on the quintet surface. However, on the triplet surface the substrate radical has a spin population of +0.9 in the transition state, thus almost unchanged compared to the spin on the substrate radical, indicating a late electron transfer. The product of the second step is an anthracene molecule and a FeII complex coordinating a water molecule. The FeII complex is found to have a quintet ground state with S ) 2 on iron. A triplet state with S ) 1 on iron was found to be 14.9 kcal mol-1 higher than the ground state in model A and 11.3 kcal mol-1 higher in model B. A singlet state with zero spin on iron was found to be about 10 kcal mol-1 higher than the triplet in both models. On the quintet surface, the second H-abstraction consists of the formation of a bonding electron pair by a coupling of the β-spin electron on the substrate radical and an R-spin electron on iron (Figure 7). On the triplet surface, an R-spin electron is

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Figure 7. Electronic mechanisms for the second H-transfer. The lowest triplet and quintet states of the FeIII and FeII intermediates are shown. The electronic energy of FeII in the singlet state (not shown) is about 10 kcal mol-1 higher than that in the triplet state.

transferred from the substrate radical to iron. In both states, the proton binds to the lone pair on the hydroxo group. As discussed above, no enthalpic energy barrier was found for the second H-abstraction on the quintet surface in these models. The free-energy barrier for the second H-abstraction in model B is much lower than that in model A. It can be seen in Table 1 that the electronic energy of the second TS in model A is 5.6 kcal mol-1 lower than the preceding intermediate. In model B, the electronic energy of the second TS is even lower, 9.9 kcal mol-1 below the preceding intermediate. This is mainly a combination of solvent effects, destabilizing the intermediate but stabilizing the TS structure. For both H-abstractions, the internal free-energy barriers are much lower in the quintet state than in the triplet state (Figures 2 and 3). Because the H-abstraction involves an electron transfer from the substrate molecule to the iron complex, a possible explanation for this difference in activation energy could be that the electron affinity (EA) of the iron complex is higher in the quintet state. For the first step in model B, the free energy of activation is 24.3 kcal mol-1 on the triplet surface, but only 11.9 kcal mol-1 on the quintet surface. The EA for the FeIV(O) intermediate in the quintet state is -105.3 kcal mol-1, whereas it is only -88.4 kcal mol-1 in the triplet state. For the second step, the free-energy barrier is 12.7 kcal mol-1 on the triplet surface, whereas it is only 0.6 kcal mol-1 on the quintet surface. The EA for the FeIII (OH) intermediate is -98.7 kcal mol-1 in the quintet state but only -85.5 kcal mol-1 in the triplet state. Both H-abstractions are found to involve a significant entropy change (Table 1). For the first step, -T∆S is 2-4 kcal mol-1 depending on the model. For the second step, -T∆S is even larger, 6-7 kcal mol-1. An analysis of the various partition functions contributing to the total entropy, revealed that the major part of these entropy changes are vibrational in origin (there is also a minor change in the electronic entropy). Although it is sometimes assumed that ∆S for H-atom transfer is very small, the computed values are in agreement with a recent experimental study of H-atom transfer to an iron complex.25 The reparametrized B3LYP* exchange-correlation functional, which includes a reduced amount of Hartree-Fock exchange (15%), was also employed to calculate the triplet/quintet splitting in models A and B. For the initial (TMC)FeIV(O) complex, the

Johansson et al. triplet/quintet splitting in the electronic energy is 2.2 kcal mol-1 in model A and 3.6 kcal mol-1 in model B using the original B3LYP functional. With the B3LYP* functional, the same splitting is 4.9 kcal mol-1 in model A and 6.0 kcal mol-1 in model B. This is expected because reducing the amount of exact exchange has a larger destabilizing effect on states with a larger exchange contribution to the total energy, that is, in this case the quintet. Furthermore, reducing the amount of exact exchange increases the internal barriers. On the triplet surface in model A, the barrier of the first step increases from 12.5 to 14.3 kcal mol-1, and on the quintet surface it increases from 3.3 to 7.5 kcal mol-1. In model B, the barrier on the triplet surface increases from 14.0 to 14.4 kcal mol-1, and on the quintet surface it increases from 1.9 to 3.0 kcal mol-1. Combining these effects of reducing the amount of Hartree-Fock exchange increases the electronic activation energy (B3LYP/lacv3p(d,p), no solvent effects included) in model A from 5.5 to 12.5 kcal mol-1, and in model B from 5.5 to 9.0 kcal mol-1. Addition of zero-point and entropic effects (calculated by B3LYP) to these electronic activation energies gives ∆Gq )23.9 kcal mol-1 in model A and ∆Gq)18.0 kcal mol-1 in model B. As mentioned above, decreasing the amount of Hartree-Fock exchange increased the intrinsic barriers for H-abstraction. This can be understood in terms of the spin and oxidation state of the metal. In iron (III) the exchange integral is a larger part of the total electronic energy than in iron (IV) because iron (III) has one more d electron and thus one more pair of d electrons involved in exchange interactions. Thus, when the amount of Hartree-Fock exchange is reduced, the iron (III) intermediate is affected more than and destabilized relative to the iron (IV) reactant. In the present case, the iron (III) intermediate was destabilized by 4-5 kcal mol-1 relative to the iron (IV) reactant, depending on the spin state. Accordingly, the barrier for H-abstraction from DHA to (TMC)FeIV(O) is increased. Although earlier studies have reported that reducing the amount of Hartree-Fock exchange in general decreases the barriers, those results are not in conflict with the present study because they refer to processes in which iron is being oxidized.26 When iron is oxidized, the number of d electrons is lower in the product, which is why decreasing the amount of Hartree-Fock exchange destabilizes the reactant relative to the product. Consequently, the barrier is then lowered. The fact that the computed barriers in the present investigation are somewhat bit low compared to experimental data is the result of two different effects. First of all, the system changes spin state between the reactant and the transition state, which is why the energetic splitting of the spin states affect the barrier. Second, the effects on the intrinsic barriers by reducing the amount of Hartree-Fock exchange are quite small (0.4-1.8 kcal mol-1), except for the quintet state in model A for which the effect is 4.2 kcal mol-1. Model C [(TMC)FeIV(O)(CH3CN)]2+(CF3CO2 )2 reflects the same coordination situation as model B, observed experimentally under stoichiometric concentration of the trifluoroacetate ion. The difference between models C and B is that an additional counterion has been added in model C, making the system overall electrostatically neutral. The free energy of activation of the first H-abstraction is 15.3 kcal mol-1, thus intermediate to the activation energies found for models A and B. For the second step ∆Gq is 8.7 kcal mol-1. Although the main picture of the mechanism in this model is very similar to the mechanisms of the charged models, there are two differences worth to be noted. Opposite to what was found in models A and B, model C has an electronic activation energy of 3.6 kcal mol-1

Biomimetic Nonheme Iron Catalyst [(TMC)FeIV(O)]2+ for the second H-abstraction on the quintet surface. Thus, although the barriers of the second step in models A and B are mainly the results of dielectric solvation effects and entropy, the barrier of the second step in model C is partly electronic in origin. However, the dielectric solvent effects stabilizes the transition state with 5.4 kcal mol-1 and thus no activation enthalpy remains. The Mulliken spin population of the transition state of the second step indicates a H-atom transfer on the quintet surface; thus, a later electron transfer than in models A and B for which the spin on the substrate is the same in the transition state as in the product. Model D is left out of the discussion because of problems with the modeling of solvation effects. This was explained at the end of the previous section. At an early stage of investigation, the highly charged model E [(TMC)FeIV(O)(CH3CN)]2+ was considered. As for all of the other models, the triplet state of (TMC)FeIV(O) was found to lie lower than the quintet state, in this model by 6.2 kcal mol-1. For the first H-abstraction in the triplet state, an approximate transition state was found at an O-H distance of 1.4 Å, giving an electronic energy barrier of 13.5 kcal mol-1. However, on the quintet surface no electronic energy barrier was found for the first step. Inclusion of the [(TMC)FeIV(O)(CH3CN)]2+ complex and the DHA molecule in the same geometry optimization with a fixed O-H distance of 2.7 Å, followed by a release of this constraint, led directly to the products (TMC)FeIII (OH) and C14H11. Although having a normal electronic distribution in the triplet state, in the quintet state this model suffered from severe errors in the electronic distribution between the closedshell DHA molecule and the iron complex. At a fixed distance of 2.7 Å between the iron complex and the DHA molecule, the total spin population on DHA is -0.20 and the total charge population is +0.25, indicating that an electron has been partially transferred from the DHA molecule to the iron complex. To investigate the model further, we increased the distance between the iron complex and the DHA molecule to 13 Å. At this distance, there is no orbital overlap between the iron complex and the DHA molecule. However, according to the Mulliken population analysis the total spin population on DHA is -0.61 and the total charge population is +0.59. Thus, one electron is shared almost equally between the iron complex and the DHA molecule. Although this error was rather unexpected in the present system, it is a typical reflection of the well-known selfinteraction error of density functional theory, in general leading to artificial delocalization of electron density. The delocalization of the unpaired electron further leads to an artificial stabilization of the system, making it approximately 15 kcal mol-1 lower in energy than the infinitely separated species, the [(TMC)FeIV(O)(CH3CN)]2++DHA asymptote. Alternatively, the [(TMC)FeIV(O)(CH3CN)]++DHA+ asymptote, corresponding to an electron transfer from DHA to iron, lies about 28 kcal mol-1 below the [(TMC)FeIV(O)(CH3CN)]2++DHA asymptote. However, at a distance of about 13 Å the Coulomb repulsion of two point charges of equal magnitude +1 is roughly 26 kcal mol-1. Thus, the energy of the [(TMC)FeIV(O)(CH3CN)]++DHA+ asymptote would be only about 2 kcal mol-1 lower than that for the [(TMC)FeIV(O)(CH3CN)]2++DHA asymptote at 13-Å separation when the Coulomb repulsion is included. Thus, the lower energy obtained for the [(TMC)FeIV(O)(CH3CN)(DHA)]2+ complex at 13 Å does not indicate that the DHA molecule is being oxidized by iron but rather reflects the presence of the self-interaction error. This can probably also explain why no barrier was found for the first H-abstraction on the quintet surface in this model.

J. Phys. Chem. C, Vol. 111, No. 33, 2007 12405 It should be emphasized that reducing the total charge by the inclusion of CF3CO2 ions, as in all other investigated models, completely eliminates this effect of the self-interaction error. The total charge population of the DHA molecule in the models A-D is thus zero as it should be. Interestingly, Shaik et al. recently used model E for the hydroxylation of cyclohexane by (TMC)FeIV(O) without any encounter of the self-interaction error. Most likely, this is explained by that cyclohexane has a much higher ionization potential than dihydroanthracene (220 vs 180 kcal mol-1). 4. Summary and Conclusions The oxidation of dihydroanthracene (DHA ) C14H12) to anthracene (C14H10) by the biomimetic nonheme iron complex [(TMC)FeIV(O)]2+ has been investigated by quantum chemical modeling. Although minor differences are found depending on the choice of model, the mechanisms share the same general characteristics. In all investigated models, the FeIV(O) intermediate is found to have a triplet (S ) 1) electronic ground state, in agreement with experimental results. Before the transition state of the first H-abstraction, a spin crossing occurs from the triplet (S ) 1) to the quintet (S ) 2) state, the system then remains in the quintet state all the way to the final product. In all models, the first H-abstraction is found to be the ratelimiting step. The calculated free energy of activation for the first step is between 14.5 and 16.9 kcal mol-1, depending on the model. This is in reasonable agreement with the experimentally obtained barriers, which are between 18.6 and 20.1 kcal mol-1. The first step is found to be a H-atom transfer, that is, a process in which the proton and electron are transferred simultaneously. Furthermore, it is found to have an exergonicity of between 14.8 and 17.1 kcal mol-1, depending on the model. The second step is very exergonic because of the formation of the aromatic anthracene molecule; ∆G° for this step is about 45 kcal mol-1. The free energy of activation for the second step is much lower than that for the first step. In fact, for the second step the free energy of activation is completely entropic in origin, whereas for the first step ∆Gq consists of both enthalpy and entropy. Concerning the coordination of either a counterion or a solvent molecule, no significant difference was found. The first rate-limiting barrier differs no more than 2.4 kcal mol-1 between models A-C. The differences in the calculated thermodynamics are even less dependent on the model. No qualitative differences in the mechanism were found between models A-C. The other two models considered were subjected to methodological problems in different ways. In the case of model D, having one coordinated counterion and one noncoordinated ion outside the first coordination sphere, the solvent effects were found to be very irregular and thus unreliable. In model E, including no counterions and thus having a total charge of +2, severe errors in the electronic distribution were encountered. This was found to be an effect of the selfinteraction error of DFT methods. By including counterions in the models, this error could be removed. This paper shows that, although being a nontrivial task, reactions involving transition metals and a complex solvent environment can be modeled by the application of B3LYP and a careful choice of models. References and Notes (1) Costas, M. U.; Mehn, M. P.; Jensen, M. P.; Que, L., Jr. Chem. ReV. 2004, 104, 939.

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