Direct Methane Oxidation to Methanol by N - American

Feb 4, 2010 - Department of Chemical Engineering, Yuzuncu Yil UniVersity, Van, 65080, Turkey. ReceiVed: October 11, 2009; ReVised Manuscript ...
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Direct Methane Oxidation to Methanol by N2O on Fe- and Co-ZSM-5 Clusters with and without Water: A Density Functional Theory Study Mehmet Ferdi Fellah†,‡ and Isik Onal*,† Department of Chemical Engineering, Middle East Technical UniVersity, Ankara, 06531, Turkey, and Department of Chemical Engineering, Yuzuncu Yil UniVersity, Van, 65080, Turkey ReceiVed: October 11, 2009; ReVised Manuscript ReceiVed: January 5, 2010

Density functional theory (DFT) calculations were carried out in a study of oxidation of methane to methanol by N2O on the Fe- and Co-ZSM-5 clusters. The catalytic cycle steps have been studied on model clusters ((SiH3)4AlO4M) (where M ) Fe, Co). Calculations indicate very low methanol selectivity without water and increasing rate of methanol formation with water. These results are in qualitative agreement with the experimental literature. The methanol formation step is also found to be the rate-limiting step, and this result is in agreement with other theoretical work. Co-ZSM-5 cluster has a lower activation barrier when compared to that of Fe-ZSM-5 cluster (49 kcal/mol vs 53 kcal/mol). Activation barrier values decrease to 48 and 39 kcal/mol for Fe- and Co-ZSM-5 clusters, respectively, in the presence of water molecule adsorbed after the formation of a hydroxy group on the ZSM-5 surface. The methanol formation step is the most difficult reaction for both clusters with and without water. Introduction During the past two decades, C-H bond activation of small alkanes, especially of methane,1 has received a great deal of attention both experimentally and theoretically. The direct conversion of methane to methanol is considered to be an important chemical process in this century, since methanol has traditionally been used as a solvent and as a feedstock for bulk organic chemicals (primarily formaldehyde), with modest growth potential.2 Several experimental studies3-11 have demonstrated that Fe-ZSM-5 could be used to produce methanol from CH4 and N2O as the oxidant. Bell et al.10 have investigated the methanol formation reactions on Fe/Al-MFI via the oxidation of methane by nitrous oxide and reported that methanol selectivity is less than 2% at temperatures above 523 K. They also reported that, when H2O is introduced at these reaction temperatures, the rate of methanol formation from the surface methoxy species increases. Water was added to catalyst after formation of surface radicals which are generated with interaction of N2O and CH4 on the surface.10 It is experimentally12-20 and theoretically21-26 known that Fe- or Co-exchanged ZSM-5 is an active catalyst for the stoichiometric decomposition of N2O to N2 and O2. It is also reported that the R-form of the surface oxygen (extra-framework oxygen) plays an important role in direct oxidation of methane on Fe-ZSM-5 in both experimental3-5,8-11 and theoretical27-30 literature. Panov and co-workers3-5,8,9 have reported that methane is oxidized to methanol at room temperature over the interaction with the R-form of the oxygen produced on Fe-ZSM-5 zeolite by N2O decomposition. Schro¨der and Schwarz31-33 have reported that the bare FeO+ complex that is generated from Fe+ and N2O reacts with methane in the gas phase to produce methanol. The following reactions have also been proposed for direct oxidation of methane by N2O3,4,11 * Corresponding author. Phone: +90 312 210 2639. Fax: +90 312 210 2600. E-mail: [email protected]. † Middle East Technical University. ‡ Yuzuncu Yil University.

N2O + ( )R f (O)R + N2

(1)

(O)R + CH4 f CH3OH + ( )R

(2)

A surface oxygen on Fe-ZSM-5 is demonstrated by (O)R in reaction 1, and it is responsible for the formation of methanol from methane (reaction 2). It has been reported that extra framework Fe species in the zeolite micropores can be present as mononuclear, binuclear, and oligonuclear cationic species, neutral iron oxide species, or mixed oxide phases combining Fe and Al.34 Yoshizawa et al.28 studied the reaction pathways and the energetics for direct methane oxidation to methanol on Fe-ZSM-5 zeolite simulated as a ((SiH3)2AlO2(OH)2(FeO)) cluster. They reported that surface oxygen species are responsible for the catalytic reactivities of the Fe-ZSM-5 zeolite. Limtrakul and co-workers30 investigated the selective oxidation of methane to methanol on Fe-ZSM-5 zeolite simulated as a ((OFeO)-ZSM-5) cluster by use of the ONIOM method. The direct methane oxidation to methanol on Fe-ZSM-5 has been studied on ((SiH3)2AlO2(OH)2(FeO2) and (OFeO)) clusters via DFT calculations by Bell et al.29 However, methane oxidation to methanol by N2O on Co-ZSM-5 has not been studied in experimental or theoretical literature. We have theoretically reported that the R-oxygen formation reaction by N2O (reaction 1) occurs on Fe- and Co-ZSM-5 with a high exothermic relative energy through a very small activation barrier.26 The aim of this study is to investigate and compare methane oxidation to methanol by nitrous oxide and to identify the mechanistic steps via which these reactions occur on Fe- and Co-ZSM-5 clusters with mononuclear metal sites by use of density functional theory (DFT) calculations. The water effect on methanol formation will also be investigated. ZSM-5 is modeled as a ((SiH3)4AlO4M) (M ) Fe, Co) cluster. DFT calculations with the B3LYP formalism using 6-31G(d,p) as a basis set for all atoms involved are utilized to obtain energy profiles and equilibrium geometries.

10.1021/jp9097292  2010 American Chemical Society Published on Web 02/04/2010

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Figure 1. (a) ZSM-5 zeolite, (b) ZSM-5 channel, and (c) optimized geometries for 5T M-ZSM-5 cluster (where M ) Fe, Co).

Surface Models and Calculation Method 35

All calculations in this study are based on DFT as implemented in the Gaussian 03 suite of programs.36 In order to take into account the exchange and correlation, Becke’s37,38 three-parameter hybrid method involving the Lee, Yang, and Parr39 correlation functional (B3LYP) formalism is used in this study. The 6-31G(d,p) basis set is used for all atoms including iron and cobalt atoms. It has already been demonstrated40 that the hybrid B3LYP method is a high-quality density functional method certainly for organic chemistry. The ZSM-5 structure shown in part a of Figure 1 was constructed by using the Cartesian coordinates reported by Lermer et al.41 Only small differences between cluster and periodical system calculations were observed in the earlier works where Fe-ZSM-5 and FeFerrierite were used by Kachurovskaya et al.42,43 They studied the adsorption of a complex involving benzene, phenol, keto tautomer of phenol on iron exchanged zeolite structure by using cluster and periodic DFT calculations. It is reported that similar results such as atomic distances and adsorption energies were obtained by using both types of calculation systems. Moreover, qualitative differences for chemical reactions were not in general observed between the cluster approach and periodic DFT modeling on zeolites.44-46 It is reported in experimental literature3-5,8-11 that extra-framework oxygen attached to Fe ((FeO)R) plays an important role in direct oxidation of methane on Fe-ZSM-5; therefore, a (MO) center was used for all methane oxidation reactions for both Fe-ZSM-5 and Co-ZSM-5 clusters. Consequently, a 5T ZSM-5 cluster including five Si and four O atoms is cut from inside a channel (see part b of Figure 1) as reported in our recent theoretical studies26,47,48 about ZSM-5. The 5T ZSM-5 clusters used in this study were modeled as ((SiH3)4AlO4M) (M ) Fe, Co) clusters, as shown in part c of Figure 1. An Al atom is placed in the T12 site of the framework surrounded by O and Si atoms. The dangling bonds of the terminal silicon atoms are terminated with H atoms to obtain a neutral cluster. There was also a neutral total charge value for all catalytic reaction steps involved. The effect of relaxation of terminating H atoms of the ZSM-5 cluster was studied with all

the other atoms being relaxed. All of the reactant and product molecules were also kept relaxed. Energy profile and equilibrium geometry (EG) calculations were in general performed for determination of activation barriers and relative energies. All energy values and energy differences in this study include zeropoint energy (ZPE) corrections which are obtained by using frequency calculations at a temperature of 298 K, since there is no experimental thermochemistry data for methane oxidation to methanol by N2O. Computed 〈S2〉 values confirmed that the spin contamination was very small (after annihilation). Vibrational analysis was performed by using single point frequency calculation for all transition states to confirm that they have only one imaginary mode of vibration and for ground states to confirm that they have no imaginary mode of vibration. Natural bond orbital (NBO)49 analysis has been used to obtain the electronic configuration of metal atoms. Convergence criteria which are gradients of maximum force, rms force, and maximum displacement and rms displacement in the Gaussian 03 software are 0.000450, 0.000300, 0.001800, and 0.001200, respectively. The computational strategy employed in this study is as follows: Initially, the correct spin multiplicity (SM) of the cluster and adsorbing molecule is determined by single point energy (SPE) calculations. SPEs are calculated with different SM numbers for each cluster system, and the SM number which corresponds to the lowest SPE is accepted as the correct SM. The cluster and the adsorbing molecules, N2O and CH4, are then fully optimized geometrically by means of EG calculations. The adsorbing molecule is first located over the active site of the cluster at a selected distance and a coordinate driving calculation is performed by selecting a reaction coordinate in order to obtain the variation of the relative energy with a decreasing reaction coordinate to get an energy profile as a function of the selected reaction coordinate distance. These energy profiles help us also to find the transition state geometry and final equilibrium geometry by using the geometry which has the highest energy and the geometry which has the final minimum energy, respectively. Single point energy calculations were also performed where necessary by locating the adsorbing

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molecule in the vicinity of the catalytic cluster. Coordinate driving calculations result in an energy profile. The resulting relative energies for the cluster and reactant molecule complex are plotted against the reaction coordinate. The relative energy is defined as the following formula:

∆E ) ESystem - (ECluster + EAdsorbate) where ESystem is the calculated energy of the given geometry containing the cluster and the adsorbing molecule at any distance, ECluster is the energy of the cluster, and EAdsorbate is that of the adsorbing molecule, e.g., N2O or CH4 in this case. After obtaining the energy profile for the reaction step, the geometry with the minimum energy on the energy profile is reoptimized by means of EG calculations to obtain the final equilibrium geometry for the particular reaction step. In this reoptimization calculation, the reaction coordinate is not fixed. Additionally, the geometry with the highest energy from the energy profile is taken as the input geometry for the transition state geometry calculations. Starting from these geometries, the transition state structures with only one negative eigenvalue in the Hessian matrix are obtained. Transition states have been calculated using the synchronous quasi-Newtonian method of optimization, QST3.50 Results Optimization of Clusters and Reactant Molecules. EGs for Co- and Fe-ZSM-5 clusters were obtained taking the total charge as neutral, and the spin multiplicities as 5 and 6 corresponding to the lowest SPEs, respectively. A spin multiplicity value for Fe-ZSM-5 cluster containing one Al atom was also reported as 6 by other theoretical studies28,29 in the literature. The spin multiplicity numbers were also determined as 5 (quintet) for Co-ZSM-5 and 6 (sextet) for Fe-ZSM-5 clusters including N2O, methane, and water molecules. These values were used for all catalytic reactions. Figure 1c shows geometries of a ZSM-5 cluster with a single M site (M ) Fe, Co). The effect of relaxation of terminating H atoms of the ZSM-5 cluster was studied with all of the other atoms being relaxed. Si-O distances for relaxed Fe-ZSM-5 clusters range from 1.63 to 1.68 Å. Si-O distances of Fe-ZSM-5 cluster having fixed terminating H atoms are between 1.68 and 1.69 Å. The corresponding distances reported in the experimental literature are between 1.55 and 1.65 Å.41 The average Si-H distance was calculated as 1.485 Å for all clusters. Furthermore, the positions of terminating H atoms for Fe-ZSM-5 clusters with relaxed and fixed H atoms are close to each other. Interaction energies for Fe and Co sites on the Fe-ZSM-5 and Co-ZSM-5 clusters are calculated to be -139.93 and -108.65 kcal/mol, respectively. Mulliken atomic charges on iron and cobalt ions are +0.450 and +0.435, respectively. EGs for N2O and CH4 as reactant molecules were obtained by taking the total charge to be neutral and with a singlet spin multiplicity. The optimized linear N2O molecule has a distance of 1.134 Å for N-N length and 1.192 Å for N-O length. The corresponding values are reported to be 1.128 and 1.185 Å in the experimental literature.51 A linear (N-N-O) N2O molecule was used for decomposition reaction calculations. The calculated C-H bond distance value of 1.093 Å for methane molecule is very close to the reported experimental52 value of 1.096 Å. Methane Oxidation on M-ZSM-5 (M ) Fe, Co) Clusters. The proposed reaction steps3,4,11 for the cycle of methane oxidation with N2O on a mononuclear site on M-ZSM-5 are

Fellah and Onal

(Step 1, N2O decomposition)

M-ZSM-5 + N2O f MO-ZSM-5 + N2

(3)

(Step 2, C-H bond activation of CH4)

MO-ZSM-5 + CH4 f M-(OH)-ZSM-5 + CH3•

(4)

(Step 3, hydroxy complex formation)

M-(OH)-ZSM-5 + CH3• f M-(OH)-(CH3)-ZSM-5

(5) (Step 4, methanol formation) M-(OH)-(CH3)-ZSM-5 f M-(CH3OH)-ZSM-5

(6)

(Step 5, methanol desorption)

M-(CH3OH)-ZSM-5 f M-ZSM-5 + CH3OH

(7)

A Test for the Effect of Relaxation of Terminating H Atoms of ZSM-5 Cluster. In the theoretical literature, methane oxidation to methanol by N2O was studied by using Fe-ZSM-5 clusters either with all relaxed atoms28 or with fixed terminating H atoms.29 In order to see this effect, the second and third steps (C-H bond activation of CH4 and hydroxy complex formation, respectively) were investigated. For step 2, activation barrier values (peak values of the relative energy profiles) for all atoms relaxed and fixed terminating H atoms clusters are 20 and 21 kcal/mol, respectively. Activation barrier values for step 3 were calculated to be 62 kcal/mol for all atoms relaxed cluster and 62 kcal/mol for fixed terminating H atoms cluster. These calculations indicate that these results are the same. On the other hand, calculations for fixed terminating H atoms cluster need much more computational time. Thus, all atoms relaxed M-ZSM-5 clusters were used for direct methane oxidation to methanol by N2O. Methane Oxidation on Fe-ZSM-5 Cluster. Decomposition of the N2O molecule and formation of R-oxygen on Fe-ZSM-5 cluster is the first reaction (step 1) reported in our previous study.26 Mulliken atomic charges on iron and oxygen (O5) for FeO-ZSM-5 cluster were +1.009 and -0.563, respectively. The second and third steps (C-H bond activation of CH4 and hydroxy complex formation, respectively) occur simultaneously on FeO-ZSM-5 cluster. A reaction coordinate is the distance between the hydrogen atom (H) of the CH4 molecule and O atom (O5) adsorbed on the cluster. The relative energy profile obtained is shown in part a of Figure 2 to illustrate the methodology in obtaining relative energy profiles. This reaction occurs with an exothermic relative energy difference of -20 kcal/mol through an activation barrier (TS) of 16 kcal/mol. The calculated imaginary frequency related to the transition state mode is 1680i cm-1. The corresponding O-H distance for the transition state is 1.266 Å. The TS geometry and the EG of the product are represented in parts b and c of Figure 2, respectively. For EG geometry, Mulliken atomic charges on iron, oxygen (O5), hydrogen atom adsorbed on O5, and carbon are +1.107, -0.706, +0.331, and -0.735, respectively. Mulliken atomic charges on hydrogen atoms of carbon atom adsorbed are +0.140, +0.147, and +0.153. Spin contamination 〈S2〉 values for TS and EG are calculated as 8.7501 and 8.75, respectively. The next reaction is the formation of methanol on FeO-ZSM-5 cluster. For this step, a reaction coordinate is the distance between the oxygen atom (O5) adsorbed and C atom of adsorbed CH3 group. This reaction has an endothermic relative energy difference of 36.35 kcal/mol through a higher TS barrier (53 kcal/mol) than those of steps 1, 2, and 3. ∆G# for this reaction

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Figure 2. (a) Relative energy profile, (b) transition state geometry, and (c) equilibrium final geometry for C-H bond activation of CH4 and hydroxy complex formation (steps 2 and 3) on FeO-ZSM-5 cluster.

Figure 3. (a) Transition state geometry and (b) equilibrium final geometry for methanol formation reaction (step 4) on FeO-ZSM-5 cluster.

is computed as 50 kcal/mol. The calculated imaginary frequency related to the transition state mode is 641i cm-1. The corresponding C-O distance for the transition state is 1.851 Å. The TS geometry and the EG of the product are represented in parts a and b of Figure 3, respectively. Mulliken atomic charges on iron, oxygen (O5), hydrogen on O5, and carbon and hydrogen atoms of carbon are +0.451, -0.556, +0.352, and -0.104, +0.131, +0.131, and +0.162, respectively. Spin contamination

〈S2〉 values for TS and EG are calculated as 8.75. Finally, for the last reaction step, desorption of methanol (step 5) formed on the cluster, a reaction coordinate is the distance between the oxygen atom (O5) of the methanol molecule and Fe atom of the cluster. This step has a relatively small desorption barrier of 14 kcal/mol for Fe-ZSM-5 cluster. The electron configurations of iron atoms of all TS and EG for all steps are reported in Table 1.

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Fellah and Onal

TABLE 1: Electron Configuration of Metal Atoms of TS and EG for Reactions of Fe-ZSM-5 and Co-ZSM-5 Clusters geometry electron configuration of metal atom Fe-ZSM-5 cluster FeO-ZSM-5 (Step1) Step2&3 Step4 Step4′ Step5′

Co-ZSM-5 cluster CoO-ZSM-5 (Step1) Step2 Step3 Step4 Step4′ Step5′

EG EG EG TS EG TS EG EG TS

Fe-ZSM-5 [core]4S1.073d6.004p0.09 [core]4S0.323d5.924p0.075p0.01 [core]4S0.343d5.744p0.03 [core]4S0.343d5.884p0.035p0.01 [core]4S0.983d6.054p0.10 [core]4S0.703d6.004p0.115S0.01 [core]4S0.343d5.714p0.025p0.01 [core]4S0.923d6.034p0.155p0.01 [core]4S0.513d6.104p0.115S0.015p0.01

EG EG EG TS EG EG TS EG EG TS

Co-ZSM-5 [core]4S1.033d7.044p0.10 [core]4S0.323d7.054p0.065p0.01 [core]4S0.433d7.074p0.045p0.01 [core]4S0.383d7.114p0.04 [core]4S0.353d6.904p0.035p0.01 [core]4S0.993d7.064p0.09 [core]4S0.363d7.124p0.07 [core]4S0.343d6.894p0.035p0.01 [core]4S0.953d7.054p0.12 [core]4S0.483d7.114p0.105S0.025p0.02

Methane Oxidation on Co-ZSM-5 Cluster. The first reaction (step 1), the decomposition of the N2O molecule on CoZSM-5 cluster, was reported similarly in our previous study.26 Mulliken atomic charges on cobalt and oxygen (O5) for CoOZSM-5 cluster were +0.878 and -0.492, respectively. For the second step, the C-H bond activation of methane molecule, a reaction coordinate is the distance between the hydrogen atom (H) of the CH4 molecule and O atom (O5) adsorbed on the cluster during the first step. This reaction occurs with an endothermic relative energy difference of 9 kcal/mol through an activation barrier (TS) of 15 kcal/mol. The calculated imaginary frequency related with the transition state mode is 1689i cm-1. The corresponding O-H distance for the transition state is 1.187 Å. The TS geometry and the EG of the product are represented in parts a and b of Figure 4, respectively. For EG geometry, Mulliken atomic charges on cobalt, oxygen (O5), and hydrogen atom adsorbed on O5 are +0.717, -0.686, and +0.330, respectively. Spin contamination 〈S2〉 values for TS and EG are calculated as 6.0. The third step is the reaction between CH3 radical and Co atom of the cluster. For this reaction, a

Figure 5. Final equilibrium geometry for hydroxy complex formation reaction (step 3) on CoO-ZSM-5 cluster.

reaction coordinate is the distance between the C atom of the CH3 radical and Co atom of the Co-ZSM-5 cluster. This reaction occurs on the cluster with an exothermic relative energy difference of -21 kcal/mol, and its final equilibrium geometry is represented in Figure 5. Mulliken atomic charges for this geometry on cobalt, oxygen (O5), hydrogen atom adsorbed on O5, and carbon are +0.911, -0.669, +0.339, and -0.634, respectively. Also, Mulliken atomic charges on hydrogen atoms of carbon atom adsorbed are +0.146, +0.149, and +0.164. Spin contamination 〈S2〉 values for EG are calculated as 6.0. The next reaction is the formation of methanol on CoO-ZSM-5 cluster. For this step, a reaction coordinate is selected as the distance between the oxygen atom (O5) and C atom of adsorbed CH3 group. This reaction has an endothermic relative energy difference of 24 kcal/mol through a higher TS barrier (49 kcal/mol) than those of steps 1, 2, and 3. ∆G# for this reaction is calculated to be 43 kcal/mol. The calculated imaginary frequency related to the transition state mode is 774i cm-1. The corresponding C-O distance for the transition state is 1.859 Å. The TS geometry and the EG of the product are represented in parts a and b of Figure 6, respectively. For EG geometry, Mulliken atomic charges on cobalt, oxygen (O5), hydrogen on O5, and carbon and hydrogen atoms of carbon are +0.452, -0.611,

Figure 4. (a) Transition state geometry and (b) equilibrium final geometry for C-H bond activation of CH4 (step 2) on CoO-ZSM-5 cluster.

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+0.383 and -0.085, +0.128, +0.131 +0.145, respectively. Spin contamination 〈S2〉 values for TS and EG are calculated as 6.0. Finally, the last reaction, step 5, is desorption of methanol formed on the cluster. A reaction coordinate is the distance between the oxygen atom (O5) of the methanol molecule and Co atom of the cluster for this step. This reaction has a small desorption barrier (19 kcal/mol). The electron configurations of cobalt atoms of all TS and EG for all steps are reported in Table 1. Water Effect on Methane Oxidation. The reactions below were studied in order to see the water effect on methanol formation, since Bell et al.10 have reported that, when H2O is introduced during the methane oxidation, the rate of methanol formation from the surface methoxy species increases. Water is adsorbed to the cluster after step 3 to simulate a particular experimental study by Bell et al.10 where water was added to the reactant stream after the formation of surface radicals on the catalyst which are generated with interaction of N2O and CH4 on the surface. Methanol then forms on the surface. Formed methanol and adsorbed water then desorb.

(Step 4′, water adsorption)

M-(OH)-(CH3)-ZSM-5 + H2O f M-(OH)-(CH3)-H2O-ZSM-5

(8)

(Step 5′, methanol formation) M-(OH)-(CH3)-(H2O)-ZSM-5 f M-(H2O)-(CH3OH)-ZSM-5

(9)

(Step 6′, water desorption) M-(H2O)-(CH3OH)-ZSM-5 f M-(CH3OH)-ZSM-5 + H2O

(10)

(Step 7′, methanol desorption)

M-(CH3OH)-ZSM-5 f M-ZSM-5 + CH3OH

(11)

For step 4′, water adsorption, a reaction coordinate is the distance between the metal atom of the cluster and O atom of the water molecule. This reaction occurs with exothermic relative energy difference values of 10 kcal/mol for Fe-ZSM-5 and 12 kcal/mol for Co-ZSM-5 without an activation barrier. Final equilibrium geometries are depicted in parts a and b of Figure 7. For EG geometry, Mulliken atomic charges on iron, oxygen (O5), oxygen (O6) of water, and carbon on Fe-ZSM-5 are +1.117, -0.710, -0.601, and -0.738, respectively. Similar charges on Co-ZSM-5 are +0.903, -0.723, -0.597, and -0.619, respectively. Spin contamination 〈S2〉 values for EG are calculated as 8.75 and 6.0 for Fe-ZSM-5 cluster and CoZSM-5 cluster, respectively. The next reaction (step 5′) is the formation of methanol on clusters. For this step, a reaction coordinate is selected as the distance between the oxygen atom (O5) and C atom of adsorbed CH3 group. These reactions have endothermic relative energy difference values of 41 kcal/mol for Fe-ZSM-5 and 32 kcal/mol for Co-ZSM-5. TS barrier values are 48 and 39 kcal/mol for Fe- and Co-ZSM-5 clusters, respectively. ∆G# values of these reactions are calculated to be 45 and 33 kcal/mol for Fe-ZSM-5 and Co-ZSM-5 clusters,

Figure 6. (a) Transition state geometry and (b) equilibrium final geometry for methanol formation reaction (step 4) on CoO-ZSM-5 cluster.

Figure 7. Equilibrium geometries for water adsorption (step 4′) on (a) Fe-ZSM-5 cluster and (b) Co-ZSM-5 cluster.

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Figure 8. (a) Transition state geometry and (b) equilibrium final geometry for methanol formation reaction with water (step 5′) on Fe-ZSM-5 cluster.

Figure 9. (a) Transition state geometry and (b) equilibrium final geometry for methanol formation reaction with water (step 5′) on Co-ZSM-5 cluster.

respectively. The calculated imaginary frequencies related to the transition state modes are 631i and 628i cm-1, respectively. The corresponding C-O distances for the transition states are 1.854 Å for Fe-ZSM-5 and 1.853 Å for Co-ZSM-5. The TS geometry and the EG are represented in parts a and b of Figures 8 and 9 for Fe- and Co-ZSM-5 clusters, respectively. For EG geometry, Mulliken atomic charges on iron, oxygen (O5) of methanol, and oxygen (O6) of water on Fe-ZSM-5 are +0.410, -0.558, and -0.581, respectively. Those charges on Co-ZSM-5 are +0.371, -0.554, and -0.588, respectively. Spin contamination 〈S2〉 values for TS and EG are calculated as 8.75 and 6.0 for Fe-ZSM-5 cluster and Co-ZSM-5 cluster, respectively. After these reactions, methanol formed on the clusters or water will desorb from the surfaces. If methanol desorbs from the surface, desorption barrier values are 13 kcal/mol for Fe-ZSM-5 and 9 kcal/mol for Co-ZSM-5. The desorption barriers are calculated to be 9 and 4 kcal/mol for Fe- and Co-ZSM-5 clusters, respectively, if water desorbs from the surface. When water is absent on the surface, desorption barrier values are lower (14 kcal/mol for Fe-ZSM-5 and 19 kcal/mol for Co-ZSM-5). These are the same values as in step 5. The electron configurations of iron and cobalt atoms of all TS and EG for all water effect steps are reported in Table 1. Discussion A comparison of the activation energy barriers of the direct methane oxidation to methanol cycle steps on Fe-ZSM-5 cluster

with available theoretical literature is given in Table 2. Table 2 has also activation energy barriers of reactions on Co-ZSM-5 cluster. Figures 10 and 11 summarize the energy diagrams of reaction steps of the methane oxidation cycle for Fe- and CoZSM-5 clusters with and without water, respectively. Since extra-framework oxygen attached to Fe is responsible for the formation of methanol from methane,3,4,11 the reaction of surface oxygen formation by N2O on a cluster is a key step for methane oxidation. The activation barrier (TS) for step 2 (C-H bond activation of CH4) and step 3 (hydroxy complex formation) occurring simultaneously was calculated to be 16 kcal/mol for Fe-ZSM-5 cluster. This is close to the other theoretical values of 17 kcal/mol,28 16 kcal/mol on (OFeO) center,29 and 15 kcal/ mol on (OFeO) center.30 It is also smaller than the value of 37 kcal/mol on (FeO2) center reported in the literature.29 A hydroxy complex is formed on Fe atom without difficulty due to the low activation barrier. This situation is supported by an experimental study10 which reports that the active sites in the oxidation of CH4 to hydroxy species by N2O are extra framework Fe atoms associated with framework Al. The most difficult step which has the highest activation barrier is the methanol formation from hydroxy complex formed on the cluster. The TS barrier for this step was calculated to be 53 kcal/mol. This is somewhat higher than the other theoretical values (51 kcal/mol,28 40 kcal/mol on (OFeO) center,30 and 39 kcal/mol on (OFeO) center29) reported in the literature. In view

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TABLE 2: Comparison of the Activation Energy Barriers of Methane Oxidation to Methanol by N2O on Fe-ZSM-5 Cluster and Co-ZSM-5 Cluster with Literature Values activation barrier (kcal/mol) Fe-ZSM-5 reactions without water

with water

Step Step Step Step Step Step Step Step

this study

1 (N2O decomposition) 2 (C-H bond activation of CH4) 3 (hydroxy complex formation) 4 (methanol formation) 5 (methanol desorption) 4′ (water adsorption) 5′ (methanol formation) 6′ (water desorption)

a

other theoretical b

c

4 16

3, 3 17,d 6,e,f 37,e,g 5h,g

53 14 0 48 9

51,d 39,e,f 40h,f 11,d 19,e,f 29h,f

Co-ZSM-5 this study

other theoretical

a

6 15 0 49 19 0 39 4

a Fellah and Onal26 (Gaussian/DFT/B3LYP/((SiH3)4AlO4Fe and Co) Cluster). b Yoshizawa et al.25 (Gaussian/DFT/B3LYP/ ((SiH3)2AlO2(OH)2(FeO)) Cluster). c Heyden et al.23 (TURBOMOLE/DFT/B3LYP/Cluster). d Yoshizawa et al.28 (Gaussian/DFT/B3LYP/ ((SiH3)2AlO2(OH)2(FeO)) Cluster). e Bell et al.29 (Q-Chem/DFT/B3LYP/((SiH3)2AlO2(OH)2(FeO2) and (OFeO))Cluster). f Reaction occurs on the (OFeO) center of ZSM-5 Cluster. g Reaction occurs on the (FeO2) center of ZSM-5 Cluster. h Limtrakul et al.30 (Gaussian/ONIOM/QM:DFT/ B3LYP-MM:UFF).

Figure 10. Summary energy diagram showing a comparison of all of the steps (without water) of methane oxidation to methanol by N2O on Fe-ZSM-5 cluster and Co-ZSM-5 cluster.

of the fact reported in the experimental literature3-5,8-11 that extra-framework oxygen attached to Fe ((FeO)R) plays an important role in direct oxidation of methane on Fe-ZSM-5, (FeO) center was used for all methane oxidation reactions on Fe-ZSM-5 cluster. Since there are some significant differences such as using a smaller cluster,28,29 different basis set for cluster and reactant atoms,28-30 and different active sites such as FeO2 and OFeO29,30 between this study and the other theoretical studies, they are not directly comparable. In other words, the methanol formation step from hydroxy complex formed on FeZSM-5 is a difficult reaction. Bell et al.10 have already experimentally reported this difficulty. In their study, small amounts of methanol with less than 2% selectivity were observed when CH4 and N2O reacted over Fe/Al-MFI. Methanol desorption (step 5) has a lower barrier value of 14 kcal/mol as compared to values calculated for other steps of Fe-ZSM-5 cluster. This is also consistent with the corresponding theoretical value of 11 kcal/mol reported in the literature.28 Bell et al.10 reported that, when H2O is introduced during the methane oxidation reaction, the rate of methanol formation from the surface methoxy species increases. Water is adsorbed to the cluster after step 3 to simulate a particular experimental study

by Bell et al.10 where water was added to the reactant stream after formation of surface radicals on catalyst which are generated with interaction of N2O and CH4 on the surface. After this exothermic reaction, methanol is formed on the surface with an activation barrier value of 48 kcal/mol which is lower than the value of 53 kcal/mol found without water. The energy decrease of the activation barrier for methanol formation step is the same as the Gibbs free energy (∆G#) loss through the water effect. In other words, the activation barrier and Gibbs free energy (∆G#) have both been decreased 5 kcal/mol. After the formation of methanol, water desorbs with a desorption barrier value of 9 kcal/mol from the surface, since methanol desorption from the surface has a higher desorption barrier (13 kcal/mol). Finally, methanol desorption is the same with step 5. Similar considerations would be valid for the entire catalytic cycle results for Co-ZSM-5 cluster given in Table 2. As mentioned before, there are no activation barrier data for the methane oxidation reactions by N2O on Co-ZSM-5 in both experimental and theoretical literature. While steps 2 and 3 (C-H bond activation of methane, hydroxy complex formation, respectively) occur simultaneously on Fe-ZSM-5 cluster, these

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Figure 11. Summary energy diagram showing a comparison of all of the steps for the water effect on methane oxidation to methanol by N2O on Fe-ZSM-5 cluster and Co-ZSM-5 cluster (it starts from point A in Figure 10).

steps occur consecutively on Co-ZSM-5 cluster. The activation barrier (TS) value for step 2 (C-H bond activation of CH4) was calculated to be 15 kcal/mol for Co-ZSM-5 cluster. This is very close to the value (16 kcal/mol) for the Fe-ZSM-5 cluster. Hydroxy complex (step 3) was formed on the cluster without a barrier. The TS barrier for step 4 (methanol formation, the most difficult step) was calculated to be 49 kcal/mol which is lower that that of Fe-ZSM-5 cluster. Methanol desorption (step 5) has a little higher barrier value of 19 kcal/mol as compared to the value of 14 kcal/mol calculated for Fe-ZSM-5 cluster. Calculations to see the effect of water show that methanol is formed on the surface with an activation barrier value of 39 kcal/mol which is lower than the value of 49 kcal/mol found without water. The energy decrease of activation barrier for the methanol formation step is the same as the Gibbs free energy (∆G#) loss through the water effect. In other words, the activation barrier and Gibbs free energy (∆G#) have been decreased 10 kcal/mol. After the formation of methanol, water desorbs with a desorption barrier value of 4 kcal/mol from the surface, since methanol desorption from the surface has a higher desorption barrier (9 kcal/mol). Finally, methanol desorption from the surface is the same as step 5. As a summary, similar activation barrier trends are valid for both Fe-ZSM-5 and Co-ZSM-5 clusters. In general, however, it can also be concluded from Table 2 that for all of the catalytic cycle steps calculated results indicate somewhat lower activation barrier values for Co-ZSM-5 in comparison to Fe-ZSM-5 cluster. Figure 10 also summarizes the energy diagrams of reaction steps of methane oxidation cycle for Fe- and Co-ZSM-5 clusters. The step which has the highest activation barrier, the most difficult step, is the methanol formation reaction from hydroxy complex formed on the clusters. The TS barrier for this step for CoZSM-5 cluster was calculated to be 49 kcal/mol which is lower than the TS value of 53 kcal/mol obtained for Fe-ZSM-5 cluster. Figure 11 shows the water effect on methanol formation on Feand Co-ZSM-5 cluster. Calculations to see the effect of water show that water decreases the activation barrier for methanol formation on the surfaces. The activation barrier trends of somewhat lower activation barrier values for Co-ZSM-5 in comparison to Fe-ZSM-5 cluster are valid with the water effect.

The energy decrease of activation barrier for the methanol formation step is the same as the Gibbs free energy (∆G#) loss through the water effect for both Fe-ZSM-5 and Co-ZSM-5 clusters. There seems to be good consistency between the overall heat of reaction values for Fe-ZSM-5 and Co-ZSM-5 clusters with and without water (-41 and -39 kcal/mol, respectively). Conclusions Density functional theory (DFT) calculations were carried out in a study of the oxidation of methane to methanol by N2O on the Fe- and Co-ZSM-5 clusters. The catalytic cycle steps have been studied on model clusters ((SiH3)4AlO4M) (where M ) Fe, Co). These results are in qualitative agreement with experimental literature. The methanol formation step is also found to be the rate-limiting step, and this result is in agreement with other theoretical work. Co-ZSM-5 cluster without water has a lower activation barrier when compared to that of FeZSM-5 cluster without water (49 vs 53 kcal/mol). Activation barrier values are decreased to 48 and 39 kcal/mol for Fe- and Co-ZSM-5 clusters, respectively, in the presence of a water molecule. The methanol formation step is the most difficult reaction for both clusters with and without water. There is also good consistency between the overall heat of reaction values for the direct methane oxidation to methanol by N2O on FeZSM-5 and Co-ZSM-5 clusters with and without water. Acknowledgment. This research was supported in part by ¨ BI˙TAK through TR-Grid e-Infrastructure Project. TR-Grid TU ¨ BI˙TAK ULAKBI˙M and Middle East systems are hosted by TU Technical University. Visit http://www.grid.org.tr for more information. References and Notes (1) Fellah, M. F.; Onal, I.; Turk, J. Chem. 2007, 31, 415–426. (2) Wallace, J. Kirk-Othmer Encyclopedia of Chemical Technology, 3rd ed.; Wiley: USA, 2005; Vol. 16, p 299. (3) Sobolev, V. I.; Dubkov, K. A.; Panna, O. V.; Panov, G. I. Catal. Today 1995, 24, 251–252. (4) Dubkov, K. A.; Sobolev, V. I.; Talsi, E. P.; Rodkin, M. A.; Watkins, N. H.; Shteinman, A. A.; Panov, G. I. J. Mol. Catal. A 1997, 123, 155– 161.

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