Theoretical Analysis of the Mechanism for the Oxidative Carbonylation

Jan 23, 2008 - The Growing String Method (GSM) developed by Peters et al.19 was used to locate the transition state (TS) connecting two minimum energy...
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J. Phys. Chem. C 2008, 112, 2129-2136

2129

Theoretical Analysis of the Mechanism for the Oxidative Carbonylation of Toluene to p-Toluic Acid by Rhodium Complexes Xiaobo Zheng and Alexis T. Bell* Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720 ReceiVed: October 12, 2007; In Final Form: NoVember 12, 2007

Density functional theory has been used to investigate the mechanism and kinetics of the liquid-phase, oxidative carbonylation of toluene to p-toluic acid (C7H8 + CO + 1/2O2 f p-C7H6COOH + H2O) catalyzed by Rh(III) cations. In toluene solution containing trifluoroacetic acid and dissolved CO, Rh(III) is coordinated to three trifluoroacetate (TFA) anions and two CO molecules as Rh(CO)2(TFA)3. The oxidative carbonylation of toluene is initiated by the addition of toluene across one of the Rh-O bonds of Rh(CO)2(TFA)3 to form (C7H7)Rh(CO)2(TFAH)(TFA)2. The latter species undergoes isomerization and CO migration to produce (C7H7CO)Rh(CO)(TFAH)(TFA)2, which then coordinates another molecule of CO. The mixed anhydride of toluic and tirfluoroacetic acid, C7H7C(O)O(O)CCF3 and Rh(CO)3(TFA), are produced by reductive elimination from (C7H7CO)Rh(CO)2(TFAH)(TFA)2. Para-toluic acid is then formed by hydrolysis of C7H7C(O)O(O)CCF3. The proposed reaction mechanism explains many of the observations reported in our previous experimental work (Zakzeski, J. J.; Bell, A. T. J. Mol. Catal. A 2007, 276, 8) and, in particular, the effect of temperature on the ratio of p- to m-toluic acid, the effects of H2O and the partial pressure of CO on the loss of catalyst activity, and the effect of Rh concentration on the formation of a catalytically inactive Rh dimer species.

Introduction Para-toluic acid is an intermediate in the production of terephthalic acid, a monomer used for the synthesis of polyethyleneterephthalate (PET).1 At present, p-toluic acid is made by the selective oxidation of p-xylene; however, because toluene is a less-expensive feedstock than p-xylene, there is an interest in assessing whether p-toluic acid can be made by the oxidative carbonylation of toluene. Several studies have shown that this reaction can be catalyzed by either Rh(III) or Pd(II) cations.2-8 One component of the reaction medium used in all of these investigations is trifluoroacetic acid (TFAH). Because the concentration of TFAH is high, it is believed that trifluoroacetate anions are the ligands associated with the catalyst in its active state. It has also been observed that during the reaction Rh(III) is reduced to Rh(I) and Pd(II) is reduced to Pd(0). Consequently, the reduced metal species must be reoxidized in order to complete the catalytic cycle. Different oxidizing species have been investigated for this purpose. In the case of Pd, reoxidation can be achieved using Cu(II) cations together with O2 in a Wacker-type process.6 FeC2O4, (NH4)6Mo7O24, (NH4)VO3, and V2O5 in combination with O2 have also been shown to work effectively as oxidants for both Pd and Rh.7 The reoxidation of Pd has also be achieved using MnO2 but in the absence of O2.5 More recently, it has been demonstrated that toluic acid can be produced using [(acac)Rh(CO)2] in TFAH by first oxidizing rhodium thoroughly with hydrogen peroxide and then conducting the oxidative carbonylation of toluene in the presence of K2S2O8.9 Studies with Rh have shown that reoxidation of Rh(I) to Rh(III) can become rate-limiting when the concentration of oxidizing species is low.9,10 We have recently investigated the effects of reaction conditions on the oxidative carbonylation of toluene to toluic acid * To whom correspondence should be addressed: E-mail: bell@ cchem.berkeley.edu.

using Rh(III) cations as the catalyst and NH4VO3/O2 as the oxidant.11 The solvent was toluene containing a mixture of TFAH and TFAA. This system was chosen because it gives a higher selectivity to p-toluic acid than does Pd(II), however at a lower rate. A mechanism for the overall reaction was presented based on the experimental evidence acquired and the earlier work of Kalinovskii and co-workers.8 It was shown that under most conditions the activation of the C-H bond at the para position of the aromatic ring of toluene is the rate-limiting step. The aim of the present investigation was to assess the extent to which the proposed mechanism is reasonable and to establish a better understanding of the elementary processes that limit the activity of the catalyst and the selectivity for forming p- versus m-toluic acid. The influence of CO pressure, H2O content, and Rh loading was analyzed with the aim of determining their effects on the oxidative carbonylation of toluene to p-toluic acid. Theoretical calculations of the thermodynamics of all of the elementary reactions believed to be involved in the oxidative carbonylation of toluene were carried out using density functional theory and statistical mechanics. Calculations were also performed to determine the Gibbs free energy of activation for those steps that could limit the rate of reaction. Theoretical Methods Electronic structures and energies of reactants, products, and transition states were determined using density functional theory (DFT). The B3LYP functional12 was used to describe electron exchange and correlation, and the 6-31G* basis set was used to locate optimized ground-state and transition-state structures. The LANL2DZ effective core potential was used to describe the Rh atom. All geometry optimizations were done using Gaussian 03.13 Molden,14 a freeware, was used for visualization of the geometries and vibrational frequencies. After a particular molecular structure was optimized to a stationary point (transition state or minimum energy structure), its energy was further

10.1021/jp709934u CCC: $40.75 © 2008 American Chemical Society Published on Web 01/23/2008

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Figure 1. Rh(TFA)3 and CO/TFAH complexes.

refined by a calculation at a higher level of accuracy using the LACV3P**++ basis set as implemented in the Jaguar software.15 Rhodium was treated using effective core potentials within the LACV3P**++ basis set. All stationary points were found on the basis of gas-phase calculations, and then their energy in solution was calculated using the Poisson-Boltzmann continuum (PBC) model,16,17 which is available in the Jaguar suite of programs. Free energies were determined within the rigid-rotor, harmonic-oscillator approximation. Standard free energies were calculated by including translational, rotational, and vibrational partition functions. Details concerning the calculations of free energies in the liquid phase and the assessment of the accuracy of PBC calculation were shown in the previous study of our research group.18 The Hessian matrix required for vibrational analysis was calculated with the LANL2DZ/6-31G* basis set. All of the energies reported here are for the liquid phase. In making these calculations, the solvation energy of the dissolved species was described by the PBC model. The symbol ∆E0 is used to denote the change in electronic energy, and the symbol ∆G° is used to denote the change in

the Gibbs free energy. Values of ∆E0 and ∆G0 were evaluated at 353 K, the temperature of the reaction.12 The standard state for all species present in solution is 1 mol/L, and the standard state for the gas-phase species is 1 atm. The symbols ∆E0a and ∆G0a refer to the energy of activation and the Gibbs free energy of activation, respectively. The energy reported here includes the interaction between the extended solvent and the solute, which is handled implicitly. The zero-point energy (ZPE) is also included in ∆E0 and ∆E0a . The Growing String Method (GSM) developed by Peters et al.19 was used to locate the transition state (TS) connecting two minimum energy structures. In this method, a minimum energy path connecting the reactant and product is estimated without making an initial guess for the reaction path. The point with the highest energy on this reaction path is taken to be the transition state. This point is further converged to the exact saddle point by the transition-state-finding algorithm implemented in the Gaussian 03 software. However, because of the large degrees of freedom (over 100) of the system, locating transition states was still very difficult even with the GSM. In

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TABLE 1: Summary of Reactionsa reac. no. 1 2 3 4 5 6 7 8 9 10 11 12

Rh(TFA)3 + TFAH f Rh(TFAH)(TFA)3 Rh(TFA)3 + CO f Rh(CO)(TFA)3 Rh(TFAH)(TFA)3 + TFAH f Rh(TFAH)2(TFA)3 Rh(TFAH)(TFA)3 + CO f Rh(CO)(TFAH)(TFA)3 Rh(CO)(TFA)3 + TFAH f Rh(CO)(TFAH)(TFA)3 Rh(CO)(TFA)3 + CO f Rh(CO)2(TFA)3 Rh(TFAH)2(TFA)3 + TFAH f Rh(TFAH)3(TFA)3 Rh(TFAH)2(TFA)3 + CO f Rh(CO)(TFAH)2(TFA)3 Rh(CO)(TFAH)(TFA)3 + TFAH f Rh(CO)(TFAH)2(TFA)3 Rh(CO)(TFAH)(TFA)3 + CO f Rh(CO)2(TFAH)(TFA)3 Rh(CO)2(TFA)3 + TFAH f Rh(CO)2(TFAH)(TFA)3 Rh(CO)2(TFA)3 + CO f Rh(CO)3(TFA)3

13 14′ 14′ 15

Rh(CO)2(TFA)3 (I) + C7H8 f (C7H8)Rh(CO)2(TFA)3 (II) (C7H8)Rh(CO)2(TFA)3 (II) f p-(C7H7)Rh(CO)2(TFAH)(TFA)2 (III) (C7H8)Rh(CO)2(TFA)3 (II) f m-(C7H7)Rh(CO)2(TFAH)(TFA)2 (III′) p-(C7H7)Rh(CO)2(TFAH)(TFA)2 (III) f p-iso-(C7H7)Rh(CO)2 (TFAH)(TFA)2 (IV) p-iso-(C7H7)Rh(CO)2(TFAH)(TFA)2 (IV) f p-(C7H7CO)Rh(CO) (TFAH)(TFA)2 (V) p-(C7H7CO)Rh(CO)(TFAH)(TFA)2 (V) + CO f p-(C7H7CO) Rh(CO)2(TFAH)(TFA)2 (VI) p-(C7H7CO)Rh(CO)2(TFAH)(TFA)2 (VI) f Rh(CO)2(TFAH) (TFA) + p-(C7H7CO)(TFA) (VII) p-(C7H7CO)(TFA) (VII) + H2O f TFAH + p-C7H7COOH (VIII) Rh(CO)2(TFA)3 + H2O f Rh(CO)2(H2O)(TFA)3 Rh(CO)3(TFA) + Rh(CO)2(TFA)3 T Rh2(CO)2(TFA)4 + 3CO

16 17 18 19 20 21 a

reaction

∆E0

∆G0

-12.1 -19.0 -12.5 -18.7 -11.8 -1.65 -13.8 -16.9 -10.7 -16.0 -11.3 -7.9

1.7 -8.3 1.6 -7.7 2.3 -3.7 9.9 -6.3 2.9 -3.9 2.1 2.9

0.2 0.9 0.7 -8.0

13.3 -0.8 -0.6 -6.3

-12.6

-15.2

-4.5

-4.6

-20.1

-35.7

-14.2 -14.4 -12.5

-14.6 -2.3 -7.5

The thermochemistry of all reactions mentioned in the text is summarized here. The energies are in kcal/mol and refer to 353 K.

order to solve this difficulty, we developed and applied an Iterative Partial Optimization Approach (IPOA) in this work. The atoms of the reactant/product are first divided into two groups: the first group includes a small number of atoms whose coordinates are expected to change significantly between reactant and product; the second class includes a large group of atoms whose coordinates are not expected to change significantly. The product structure is then partially optimized with the second group of atoms fixed. A GSM calculation is now started with the second group of atoms fixed. By fixing geometric parameters, the degrees of freedom in the GSM calculation are greatly reduced. The point with the highest potential energy in the GSM calculation is taken to be the initial guess of the transition state, which is then refined using the software in Gaussian 03 with the same fixed atoms as in the GSM calculation. Next, the partially optimized transition state is re-optimized with previously fixed atoms freed and previously free atoms fixed. Finally, the partially optimized transition-state structure is fully optimized with all atoms now free to move. If the last step fails, then another transition-state optimization with several of the fixed atoms freed is initiated and the other fixed atoms are then gradually released during each optimization until a full optimization of the saddle point is converged. Use of the IPOA in combination with the GSM enabled the successful location of transition-state structures for systems with large degrees of freedom, such as the ones reported in this work. Each of the transition states reported here was verified to have only one imaginary frequency. Results and Discussion Three issues are discussed in this section. The first is the structure of the catalyst prior to its interaction with toluene. Next we examine the energetics of the elementary processes involved in the oxidative carbonylation of toluene to toluic acid. The theoretical turnover frequency (TOF) and p- to m-toluic acid ratio were calculated and compared with our experimental study. Finally, we examine the energetics of several elementary processes that can contribute to a loss in catalyst activity.

State of the Active Catalyst. Zakzeski and Bell11 have found that the activity of Rh(III) is independent of whether RhCl3 or Rh(acac)3 was used to introduce Rh(III) into solution. This suggests that in the presence of a high concentration of TFAH the precursor reacts to form Rh(TFA)3. In the case of Rh(acac)3 as the starting material, the reaction can be envisioned to be Rh(acac)3 + 3TFAH f Rh(TFA)3 + 3H(acac). Because Rh(III) coordination compounds prefer to have octahedral coordination, each of the TFA anions will exhibit bidentate coordination with the Rh(III) cation. This structure and all others considered in this study are taken to be cation-anion pairs because the dielectric coefficient of toluene is low. The calculated structure of Rh(TFA)3 is shown in Figure 1a. Because the reaction system contains a high concentration of TFAH and dissolved CO, it is anticipated that Rh(TFA)3 could react with these species to form other products, such as Rh(CO)(TFA)3, Rh(CO)2(TFA)3, Rh(CO)3(TFA)3, Rh(CO)2(TFAH)(TFA)3, Rh(CO)(TFAH)2(TFA)3, Rh(CO)(TFAH)(TFA)3, Rh(TFAH)(TFA)3, Rh(TFAH)2(TFA)3, and Rh(TFAH)3(TFA)3. The structures of these complexes are shown in Figure 1b-j. To identify which Rh(III) species predominates in solution, we calculated the free energies of formation of reactions 1-12 for each of the species listed above and collected them in Table 1. Figure 2 illustrates that these species could possibly be formed through the reaction of Rh(TFA)3 with TFAH and CO along with the change in Gibbs free energy for each transformation. Solid arrows represent the addition of TFAH, whereas dotted arrows represent the addition of CO. Dashed-dotted arrows represent the addition of CO and the elimination of TFAH. The ∆G0 values are negative for all of the steps leading to the formation of Rh(CO)2(TFA)3, indicating that this is the thermodynamically preferred product. Thus, assuming that all of the reaction steps shown in Figure 2 are in chemical equilibrium, Rh(CO)2(TFA)3 will be the dominant Rh(III) species in solution. There remains, however, the question of whether the addition of CO to Rh(TFA)3 is limited kinetically. The transition-state structures for CO insertion to Rh(TFA)3 to form Rh(CO)(TFA)3

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Figure 2. Rh(TFA)3 complex formation reaction free energy map.

Figure 3. Transition-state structures for Rh(CO)2 (TFA)3 formation.

(C7H8)Rh(CO)2(TFA)3 (II) f p-(C7H7)Rh(CO)2(TFAH)(TFA)2 (III) (14)

in the standard state at 353 K is ∆G0 ) -0.8 kcal/mol. The structure of the calculated transition state for Reaction 14 is shown in Figure 5. A six-membered H-C-Rh-O-C-O ring is formed in the transition state. One of the TFA ligands rotates so as to become proximate to the H atom in the para position of toluene. In the transition state, the H atom moves away from the para-C atom of the aromatic ring, and the C-H bond distance increases from 1.09 Å in toluene to 1.30 Å. The H-O distance is 1.35 Å, indicating the onset of breakage of the C-H bond and formation of an O-H bond with the TFA anion present in the transition-state complex. The C-Rh distance is 2.20 Å, which is less than the corresponding bond distance of 2.46 Å in species II and larger than the corresponding bond distance of 2.05 Å in species III, indicating the formation of a C-Rh bond. The calculated values of ∆E0a and ∆G0a are 7.7 and 7.9 kcal/mol, respectively. The geometry of the transition state for Reaction 14 is virtually the same as that determined by Ziatdinov et al.20 for C-H activation of benzene by Pt(pic)(TFA) (pic ) η2-N,O picolinate). The authors of that work reported an activation energy of 21.0 kcal/mol, which is higher than our calculated activation energy of C-H activation of toluene by Rh(III) catalyst, 16.0 kcal/mol. This difference in activation energies is likely due to two factors. Fujiwara et al. have pointed out that Rh is more active than Pt fpr C-H bond activation and that the reactivity of toluene is higher than that of benzene.4,21,22

This step is also close to being thermo-neutral with ∆E0 ) 0.9 kcal/mol, and the change in the Gibbs free energy of reaction

The next step in the mechanism shown in Figure 4 is the isomerization of species III to form species IV via Reaction

and subsequently Rh(CO)2(TFA)3 are shown in Figure 3a and b. For the reaction Rh(TFA)3 + CO f Rh(CO)(TFA)3, ∆E0a is calculated to be 9.0 kcal/mol, whereas for the reaction Rh(CO)(TFA)3 + CO f Rh(CO)2(TFA)3, ∆E0a is calculated to be 12.1 kcal/mol. Because the activation barriers for both reactions are relatively low, the formation of Rh(CO)2(TFA)3 should be facile. Reaction Mechanism for the Oxidative Carbonylation of Toluene. The proposed reaction mechanism for the oxidative carbonylation of p-toluic acid formation is illustrated in Figure 4. The sequence of individual reaction steps illustrated in this scheme is suggested by the experimental work of Kalinovskii and co-workers5,7 and the subsequent work of Zakzeski and Bell.11 The energy changes and the Gibbs free energy changes for each of these steps are given in Table 1. Reaction 13 involves the coordination of toluene by Rh(CO)2(TFA)3 (I) to form the complex (C7H8)Rh(CO)2(TFA)3 (II).

Rh(CO)2(TFA)3 (I) + C7H8 f (C7H8)Rh(CO)2(TFA)3 (II) (13) This step is virtually thermo-neutral, ∆E0 ) 0.2 kcal/mol, and the Gibbs free energy change is ∆G0 ) 13.3 kcal/mol. In Reaction 14, the C-H bond of toluene at the para position is activated to form (C7H7)Rh(CO)2(TFAH)(TFA)2 (III).

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Figure 4. Proposed reaction mechanisms.

Figure 6. TS structure of CO migration step (TS2). Figure 5. TS structure of C-H activation of p-toluene (TS1).

15. In the course of this reaction, the coordinated TFAH rotates in order to hydrogen bond with a TFA ligand.

p-(C7H7)Rh(CO)2(TFAH)(TFA)2 (III) f p-iso-(C7H7)Rh(CO)2(TFAH)(TFA)2 (IV) (15) This reaction step is exothermic, ∆E0 ) -8.0 kcal/mol. The structure of the transition state could not be located for this reaction step because of computational difficulties. However, it is reasonable to assume that the activation barrier for this step would be small because it is favored thermodynamically. Reaction 16 involves the migration of CO to form (C7H7CO)Rh(CO)(TFAH)(TFA)2 (V).

p-iso-(C7H7)Rh(CO)2(TFAH)(TFA)2 (IV) f p-(C7H7CO)Rh(CO)(TFAH)(TFA)2 (V) (16)

This reaction step is exothermic, ∆E0 ) -12.6 kcal/mol, and has a negative change in the Gibbs free energy, ∆G0 ) -15.2 kcal/mol. The transition-state structure is shown in Figure 6. The carbonyl group has moved away from its original position in order to get closer to the benzene ring. The C2-C1 distance is reduced to 1.82 Å, indicating the formation of a C-C bond. The C1-Rh distance is slightly elongated to 2.18 Å in order to accommodate the insertion of CO. The calculated energy and free energy of activation are ∆E0a ) 11.9 kcal/mol and ∆G0a ) 13.9 kcal/mol. (C7H7CO)Rh(CO)(TFAH)(TFA)2 is five-coordinated and readily coordinates additional CO to form the six-coordinated (C7H7CO)Rh(CO)2(TFAH)(TFA)2 complex (VI).

p-(C7H7CO)Rh(CO)(TFAH)(TFA)2 (V) + CO f p-(C7H7CO)Rh(CO)2(TFAH)(TFA)2 (VI) (17) Reaction 17 is thermodynamically favorable with ∆E0 ) -4.5 kcal/mol, and ∆G0 ) -4.6 kcal/mol and is barrierless. Complex

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Figure 7. TS structure of toluic acid production step CH3-C6H4CO(TFA) + H2O f CH3-C6H4-COOH + (TFA)H (TS3).

VI then undergoes a reductive elimination to produce Rh(CO)2(TFAH)(TFA) and the mixed anhydride of toluic and trifluoroacetic acid, C7H7C(O)OC(O)CF3 (VII).

(C7H7CO)Rh(CO)2(TFAH)(TFA)2 (VI) f Rh(CO)2(TFAH)(TFA) + p-(C7H7CO)(TFA) (VII) (18) This step is highly favorable thermodynamically, ∆E0 ) -20.1 kcal/mol and ∆G0 ) -35.7 kcal/mol. In the course of this reaction, Rh(III) is reduced to Rh(I). Because Reaction 18 is highly exothermic, it is reasonable to assume that the activation barrier for this step would be relatively low and, hence, that the rate of this reaction will be relevant to the overall kinetics. Reoxidation of Rh(I) to Rh(III) must occur for the reaction sequence shown in Figure 4 to be completed. A number of oxidants for this process have been described in the experimental literature.2,4,10,11,21,23,24 The mixed anhydride of toluic acid reacts further with H2O to produce the product, p-toluic acid (VIII).

p-(C7H7CO)(TFA) (VII) + H2O f TFAH + p-C7H7COOH (VIII) (19) The thermodynamics of Reaction 19 are favorable with ∆E0 ) -14.2 kcal/mol, ∆G0 ) -14.6 kcal/mol. The transition-state structure of this reaction is shown in Figure 7. One H-O bond of H2O is extended to 1.04 Å and ready to be broken. At the same time, the H atom of the extended H-O bond interacts with an O atom in TFA, so that the H-O bond distance is 1.50 Å. The second OH group of H2O moves close to the carbon atom of the carbonyl group bonded to the benzene ring, such that the O-C bond distance is 1.87 Å. The calculated energy and free energy of activation for Reaction 19 are ∆E0a ) 2.5 kcal/mol and ∆G0a ) 15.8 kcal/mol, respectively. This low activation energy agrees very well with our experimental observation that p-toluic acid is formed immediately once H2O is added to the reaction mixture.12 The energy and Gibbs free energy profiles of the reaction network presented in Figure 4 are illustrated in Figure 8. Activation of the C-H bond in the para position of toluene is the rate-limiting step, and the apparent energy is simply the sum of the coordination energy for toluene (Reaction 13) and the activation energy for the C-H bond activation of coordinated toluene (Reaction 14). The apparent energy and Gibbs free energy of activation are calculation to be 7.9 and 21.2 kcal/ mol, respectively. The turnover frequency, TOF, can be determined from the 0 expression TOF ) KI,IIkII,III[Rh(CO)2(TFA)3], where KI,II ) GI,II0

e(-∆ /RT) is the equilibrium constants for Reactions 13 and kII,III ) kT/h e(-∆GII,III0/RT) is the rate coefficient for Reaction 14. Using these relationships and the reaction temperature of the

Zheng and Bell experimental studies of Zakzeski and Bell11 (T ) 353 K), one obtains a value of TOF ) 5.9 × 10-1 s-1, which is over 12 times higher than the experimental turnover frequency of 5 × 10-2 s-1.11 A possible reason for the higher value of the calculated TOF could be that not all of the Rh present in the experimental work is present as Rh(III) due to inadequately rapid reoxidation of Rh(I) to Rh(III). This interpretation is suggested by the observation of a linear increase in the rate of toluene conversion to toluic acid with increasing concentration of V(V), the oxidant used to reoxidize Rh(I) to Rh(III).11 Ratio of p/m-Toluic Acid. As noted in the Introduction, experimental studies by Kalinovskii and co-workers7 and Zakzeskii and Bell11 indicate that the formation of p-toluic acid is favored over the formation of m-toluic acid when toluene undergoes oxidative carbonylation in the presence of Rh(III); however, the ratio of p-toluic acid to m-toluic acid decreases with increasing temperature. Assuming that either p- or m-toluic acid could form from species II, then the selectivity will be determined by whether the p- or m-C-H bond of coordinated the toluene is activated.

(C7H8)Rh(CO)2(TFA)3 (II) f m-(C7H7)Rh(CO)2(TFAH)(TFA)2 (III′) (14′) The thermodynamics of the m-C-H bond activation is very similar to that of p-C-H bond with ∆E0 ) 0.7 kcal/mol, ∆G0 ) -0.6 kcal/mol. The calculated transition-state structure for m-C-H bond activation of toluene (TS1′) is shown in Figure 9. The C-H and O-H distances are 1.29 and 1.36 Å, which are similar to the values found for TS1 (see Figure 5). The C-Rh distance in TS1′ is 2.22 Å slightly longer that that in TS1. Because of the steric hindrance of the methyl group, activation of m-C-H bond of toluene is more difficult than that of the p-C-H bond. The calculated energy and Gibbs free energy of activation are 9.3 and 9.1 kcal/mol, respectively. The apparent energy and free energy of activation for m-toluic acid conversion are then 9.5 and 22.5 kcal/mol. The selectivity ratio of for forming p- versus m-toluic acid is, therefore, given by the ratio of the rate coefficients for Reactions 14 and 14′, which can be expressed as

S)

exp(-∆Gap,p/RT) rp ) rm exp(-∆Gap,m/RT)

0 0 and ∆Gap,m are the apparent Gibbs free energy where ∆Gap,p for p-C-H activation and m-C-H activation, respectively. The difference between the Gibbs free energies of activation for 0 0 - ∆Gap,m ) -1.2 kcal/mol at T Reactions 14 and 14′ is ∆Gap,p 0 0 ) 353 K, and ∆Gap,p - ∆Gap,m ) -0.8 kcal/mol at T ) 373 K. The value of S is then calculated to decrease from 6.0 to 3.0 as the temperature increases from 353 to 373 K. Over the same temperature range, the experimental value of S decreases from 3.5 to 1.5. Thus, the calculations reported here successfully explain the decrease in p/m selectivity with increasing temperature seen experimentally.11 Factors Inhibiting the Activity of Rh(III). Experimental studies of the oxidative carbonylation of toluene by Rh(III) dissolved in a mixture of TFAH and TFAA has shown that the presence of H2O, an excessively high CO partial pressure, and high Rh concentrations can lead to a loss of catalyst activity.5,7,11 Each of these factors was examined in the course of the present study.

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Figure 8. Energy profile for the proposed reaction mechanism.

Figure 9. TS structure of C-H activation of m-toluene (TS1′).

Figure 10. Structures of Rh(CO)2 (TFA)3 and H2O complex, Rh(CO)2(H2O)(TFA)3.

The interaction of H2O with Rh(CO)2(TFA)3 leads to the formation of Rh(CO)2(H2O)(TFA)3 product as shown in Figure 10 and can be represented by the following reaction:

Rh(CO)2(TFA)3 + H2O f Rh(CO)2(H2O)(TFA)3

(20)

The binding of water is strongly favored thermodynamically, with ∆E0 ) -14.4 kcal/mol, ∆G0 ) -2.3 kcal/mol. Because the thermodynamics of toluene binding are not favorable (∆E0 ) 0.2 kcal/mol, ∆G0 ) 13.3 kcal/mol) by comparison to those for water, even very small concentrations of H2O will deactivate

the catalysts by binding the sites required for the coordination of toluene. This finding explains why trifluoroacetic anhydride (TFAA) is added to the reaction mixture in order to control the level of water present.11 Zakzeski and Bell11 have shown that the activity of Rh(III) for the oxidative carbonylation of toluene is sensitive to the partial pressure of CO. Below 0.345 MPa, the rate of reaction increased with the partial pressure of CO, but above this level, the catalyst activity declined with increasing CO partial pressure. The reason for these observations can be explained with the aid of the calculations presented here. At low CO partial pressures, the catalyst will be present predominantly as Rh(TFA)3 and Rh(CO)(TFA)3, the proportion of the latter species rising with the CO pressure. If more CO would coordinate with the complex, then the site need for the coordination of toluene will be occupied. This is what will occur if CO reacts with Rh(CO)2(TFA)3 to form Rh(CO)3(TFA)3. The Gibbs free energy change, ∆G0, for this reaction is 2.9 kcal/mol, which is lower than that for the coordination of toluene, 13.3 kcal/mol. Therefore, at high CO partial pressures, the activity of Rh(III) will be inhibited by the formation of Rh(CO)3(TFA)3. The negative effect of high Rh concentration on the specific activity of Rh(III) has been noted in several studies.5,7 It has been proposed that this could be due to the formation of Rh(I) complexes to react with Rh(III) complexes to form Rh2(TFA)4, which is not catalytically active in the solution.7,10 Our calculation show that in the presence of CO, the product of this dimerization is Rh2(CO)2(TFA)4, for which the optimized structure is shown in Figure 11.

Rh(CO)3(TFA) + Rh(CO)2(TFA)3 T Rh2(CO)2(TFA)4 + 3CO (21) The dimer complex has C4V symmetry; the Rh-O bond distances are all identical, 2.08 Å, and both Rh-C distances are the same, 2.16 Å. The calculated free energy for the reaction is -7.5 kcal/mol, indicating that the reaction is favored thermodynamically. Formation of dimeric Rh species can be limited, though, by maintaining the presence of an adequate pressure of CO and a moderate concentration of Rh, as shown in the experimental study by Zakzeski and Bell.11

2136 J. Phys. Chem. C, Vol. 112, No. 6, 2008

Zheng and Bell at the University of California, Berkeley. Supercomputer time on the NCSA HP/Convex Exemplar SPP-2000 at the University of Illinois at Urbana-Champaign was provided by the National Computational Science Alliance. References and Notes

Figure 11. Optimized Rh2(CO)2(TFA)4 structure.

Conclusions The results of this investigation have shown that Rh(III) cations dissolved in toluene containing trifluoroacetic acid and dissolved CO are stabilized in the form of Rh(CO)2(TFA)3. The C-H activation of toluene occurs via addition of toluene across one of the Rh-O bonds of a trifluroacetate ligand. The migration of the carbonyl into the Rh-C7H7 bond of this species leads to the formation of (C7H7CO)Rh(CO)(TFAH)(TFA)2. This species then undergoes CO addition and reductive elimination to form the Rh(I) complex and the mixed anhydride of toluic and trifluoroacetic acid, C7H7C(O)O(O)CCF3 and Rh(CO)3(TFA). Para-toluic acid is then formed by hydrolysis of C7H7C(O)O(O)CCF3. The Rh(I) complex is reoxidized to Rh(III) by NH4VO3. The rate-limiting step is found to be the activation of C-H bonds on the benzene ring of toluene. The apparent activation energy and activation free energy for C-H activation at the para position are 7.9 and 21.2 kcal/mol, respectively, and the corresponding values for C-H activation at the meta position are 9.5 and 22.5 kcal/mol. On the basis of these values, the ratio of p- to m-toluic acid is predicted to decrease by a factor of 2 as the temperature rises from 353 to 373 K in good agreement with experimental observation. The effects of H2O, the partial pressures of CO, and Rh loadings on the catalyst activity were investigated. When H2O is present in the reaction mixture, it can coordinate with Rh(CO)2(TFA)3, thereby inhibiting the adsorption of toluene. High CO partial pressures have a similar effect, leading to the formation of Rh(CO)3(TFA)3. High Rh concentrations can lead to the formation of the Rh dimer, Rh2(CO)2(TFA)4, which is inactive catalytically, as a consequence of the reaction of Rh(CO)2(TFA)3 and Rh(CO)4(TFA); however, the extent of dimerization is reduced at elevated CO pressure. Acknowledgment. This work was supported by the Methane Conversion Corporative Program funded by BP. Computations were carried out on a Dell cluster maintained by the Molecular Graphics and Computation Facility in the College of Chemistry

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