Analysis of the Thermochemistry of NOx Decomposition over CuZSM

Oct 31, 1996 - CuZSM-5 is the most active catalyst known for the direct decomposition of NOx. We have performed first-principles quantum mechanical ca...
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J. Phys. Chem. 1996, 100, 17582-17592

Analysis of the Thermochemistry of NOx Decomposition over CuZSM-5 Based on Quantum Chemical and Statistical Mechanical Calculations Bernhardt L. Trout, Arup K. Chakraborty,* and Alexis T. Bell Center for AdVanced Materials, Materials Science DiVision, Lawrence Berkeley National Laboratory, and Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720 ReceiVed: May 21, 1996; In Final Form: August 16, 1996X

CuZSM-5 is the most active catalyst known for the direct decomposition of NOx. We have performed firstprinciples quantum mechanical calculations to evaluate the electronic and structural properties of species adsorbed to Cu sites that might be involved in NOx decomposition. Using statistical mechanics, we have calculated ∆U°, ∆H°, and ∆G° of possible elementary reactions in order to evaluate the stability of adsorbates on Cu sites and the ease of their interconversion. On the basis of these calculations, we propose a reaction pathway for NOx decomposition. This scheme involves only single, isolated copper sites, is internally consistent, and is consistent with experimental observations.

1. Introduction Catalysts capable of facilitating the direct decomposition of NOx, a mixture of NO and NO2, to N2 and O2 are being sought for the control of emissions from automobiles using lean-burning engines and stationary sources such as power plants. Copper ion-exchanged ZSM-5 zeolites (CuZSM-5) are the most active catalysts found to date. For this reason, there has been significant interest in characterizing the active sites in CuZSM-5 and determining the mechanism by which NOx is decomposed. Despite a large number of experimental studies,1-41 many key questions remain unanswered: What are the active sites of the catalyst? What species are bound to the copper sites during the reaction process, and how stable are these species? How facile is the interconversion of these species? What are the elementary steps of the mechanism of NOx decomposition, and in particular, how are the N-N and the O-O bonds formed? What particular steps in the reaction pathway effect catalyst activity and what steps hinder it? Below, we summarize the state of knowledge concerning the forms of copper in CuZSM5, the species formed upon adsorption of NO on CuZSM-5, and the mechanism of NOx decomposition. Physical characterization of CuZSM-5 suggests that most of the copper is present as isolated cations. EPR measurements show that all of the copper in freshly exchanged CuZSM-5 is present as Cu2+, presumably as either Cu2+(OH)- associated with isolated tSi-O-Alt sites or Cu2+ associated with pairs of tSi-O-Alt sites located in close proximity. Heating freshly prepared CuZSM-5 results in the appearance of Cu+ cations in a process referred to as autoreduction.6,8,11,18,32 Direct evidence for Cu+ cations has been obtained by XANES15,35 and photoluminescence37,39 and more recently by 65Cu NMR.42 The interconversion of Cu2+(OH)- and Cu+ has been proposed to occur via the process 2ZCu2+(OH)- h ZCu+ + ZCu2+O- + H2O.32,43 Quantum chemical calculations have recently confirmed that each of the species in the proposed reaction are stable and have calculated the Gibbs free energy of the reaction at 773 K to be +18 kcal/mol.43 The presence of Cu-Cu pairs has also been suggested, but the evidence for such species is less certain. For example, using EXAFS, Yamashita et al.37 found no detectable evidence for Cu-Cu pairs, while Gru¨nert et al.36 did see evidence for Cu-Cu pairs in some of their * To whom all correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, October 1, 1996.

S0022-3654(96)01470-0 CCC: $12.00

samples depending on the manner of copper exchange and subsequent pretreatment of the catalyst. In the latter case, the average Cu-Cu distance was about 2.96 Å, which is typical of Cu-O-Cu bonds in copper oxides, raising the possibility that the observed Cu-Cu scattering was due to small particles of copper oxides rather than [Cu2+-O2--Cu2+]2+ cations located at anion-exchange positions within the zeolite. This possibility is supported by the work of Beutel et al.,28 who have shown that depending on preparation and pretreatment, small particles of copper oxide can be formed on CuZSM-5. Liu and Robota and Wichterlova´ et al. have suggested that isolated Cu+ cations associated with single framework Al atoms are the active centers for NO decomposition,15,39 based on correlations between concentration of these cations and the turnover frequency of NO consumption. By contrast, Shelef has proposed that NO decomposition occurs on Cu2+ cations associated with two framework Al atoms,16 and Sachtler and co-workers have proposed that [Cu2+-O2--Cu2+]2+ sites are required.27,28 Indirect evidence supporting the role of isolated Cu+ cations has also come from studies of NO decomposition conducted with zeolites differing in Si/Al and Cu/Al ratios.2,4,6,11-13 The interactions of NO with CuZSM-5 are complex and can result in a variety of adsorbed species. Infrared investigations at room temperature reveal the coexistence of the following: Cu+(NO), Cu+(NO)2, Cu2+(NO), and Cu2+O-(NO), as well as adsorbed N2O, NO2, N2O3, and NO3-.30,31,40 Recent in situ observation of the species present at temperatures between 673 and 773 K shows only small concentrations of Cu+(NO), Cu2+O-(NO), together with adsorbed NO2 and NO3-.20,40 Infrared observations of the interactions of NO2 with CuZSM-5 result in evidence for the presence of adsorbed NO2, N2O4, and NO3-.20,40 Two alternative views of the mechanism of NO decomposition have been proposed. In the first, Cu+(NO)2 decomposes to form N2O and Cu2+O-.4,18,19,29,30,31,40 N2 is produced by the reaction of of N2O with ZCu+.40 O2 is hypothesized to be formed via the desorption of O atoms which then react with ZCu2+O- or via a process in which ZCu2+O- reacts with oxygen in the zeolite lattice.23,40 In the second mechanism, a nitrosonitrosyl complex, ZCu2+(NO2-)(NO), is envisioned, which decomposes to produce N2 and O2 directly.20,30,31,41 Several computational studies have recently appeared describing the electronic and structural properties for a few of the © 1996 American Chemical Society

Thermochemistry of NOx Decomposition species thought to be involved in NOx decomposition over CuZSM-5.44-46 Schneider et al.45 have modeled the zeolite as water species coordinated to Cu atoms with various net charges. They have calculated binding energies of NO and CO for their models in addition to minimum energy geometries, Mulliken charges, and molecular orbital diagrams and have shown that both the coordination number and the net charges of their structures influence NO binding. Hass and Schneider46 have compared their water cluster models to more realistic models of CuZSM-5, for nominal Cu(0) and Cu(I) oxidation states, the qualitative predictions of the water-cluster model are consistent with those of the more realistic model, as are quantitative aspects of NO binding. Yokomichi et al.44 have used very small models of CuZSM-5 and calculated the energy of interconversion of five species thought to exist during NO decomposition. Our work is aimed at determining the structure and thermodynamic properties of various species that have been proposed as participants in the decomposition of NO, N2O, and NO2 over CuZSM-5. The majority of our work focuses on isolated copper cationic sites associated with single Al atoms. A significantly smaller set of calculations is performed on Cu2+ cations associated with two Al atoms. Using a first-principles quantum mechanical approach, we determine the electronic and structural properties of all species, and combining results from quantum mechanics with statistical mechanics, we estimate the standardstate internal energy, entropy, enthalpy, and Gibbs free energy (i.e., U°, S°, H°, and G°) for each species. These calculations are used to evaluate the stability of structures proposed in the experimental literature, and to determine the standard-state change in internal energy, enthalpy, and Gibbs free energy for the interconversion of species. On the basis of this analysis, it is shown that a pathway for NOx decomposition over CuZSM-5 can be constructed, which involves only isolated Cu sites and modest changes in Gibbs free energy.

J. Phys. Chem., Vol. 100, No. 44, 1996 17583

Figure 1. Minimum energy structure of ZCu. Bond lengths are given in angstroms.

2. Methods We have performed first-principles quantum chemical calculations in order to determine the structure, energetics, and vibrational frequencies of various copper species believed to be involved in NOx decomposition over CuZSM-5. The results of these calculations are used to evaluate the change in Gibbs free energy for a variety of elementary steps. The methodology used to determine structure and energetics, vibrational frequencies, and thermodynamics are described below. 2.1. Quantum Energy Calculations. Local spin density functional theory (LSDFT) was used to determine the structure and energetics of species adsorbed to copper sites. Copper sites associated with single lattice Al atoms are represented with the associated portion of the zeolite by a 34-atom cluster at the center of which is an Al-substituted T-12 site. We have previously shown43 that copper-containing cationic species having a net +1 charge (e.g., Cu+, Cu2+O-, Cu2+OH-) are coordinated to two O atoms adjacent to the Al. Outward from the Al site are a shell of O’s, a shell of Si’s, and another shell of O’s. The cluster is terminated by a shell of H’s. Each of the outermost O atoms is located at its crystallographic position in silicalite. Figure 1 illustrates the structure of this cluster with copper present as Cu+. A 43-atom cluster was used to study Cu2+ associated with two Al sites in a five T-site ring. The structure of this cluster is shown in Figure 2. All atoms in each cluster, except for the terminating two atoms are relaxed. We have calculated the effect of including the long-range Madelung potential and found, consistent with other studies, that embedding leads to only minor perturbations of important properties.43-48 Thus, we ignore the effect of the Madelung potential in this study.

Figure 2. Minimum energy structure of Cu2+ in a five T-site ring. Bond lengths are given in angstroms.

The choice of a cluster model in which the Al atom is situated in only one of the 12 possible T-sites is based on the following reasons. Previous studies performed in our group have shown that both the proton affinity of HZSM-5 and the energetics of ammonia adsorption on HZSM-5 calculated with a model similar to that used in the present study lie within the range of values observed experimentally.48,49 More recently, we have used the cluster model shown in Figure 1 to establish the structure and properties of Cu+ cations present in CuZSM-5. From these calculations, we determined that the Cu-Al distance in CuZSM-5 is 2.4 Å. This value is in excellent agreement with the value of 2.3 ( 0.2 Å determined from an 27Al-65Cu SEDOR NMR experiment.42 Finally, we note that previous experience with zeolite cluster models similar to that used here have led to descriptions of the structure of adsorbed alcohols and olefins that are in good agreement with experimental observations.47,50,51 Details of our LSDFT code have been presented previously.43 Gaussian basis sets are used for the wave function, all electrons are treated explicitly, Gaussian fitting functions are used for the electron density and for the exchange-correlation (XC) potential, analytical gradients are used for the geometry minimization, and the Perdew-Zunger (PZ) XC functional52 is used. All of our calculations are performed using a mixed basis set, i.e., minimal basis set for the terminating protons which

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Figure 3. ZCu(NO) cluster used for frequency evaluations.

substitute for silicon atoms and fuller basis sets for the rest of the atoms. For the protons, they were chosen from Pople and for the other atoms for the other atoms from Huzinaga as follows:53,54 Hterminating, STO-3G; O, (33/3/1); N, (33/3/1); Al, (333/333/1); Si, (333/33/1); Cu, (5333/53/5). Details of the notation can be found in the references. We have calculated the basis set superposition error for representative diatomic molecules using the counterpoise method55 and have found that in all cases, this error is 0.12 eV or less. We are aware of the tendency of the PZ XC functional to predict overbinding, so that the calculated bond energies are larger than those measured experimentally. We can make only a few direct comparisons of our results with experimental data, since there have been few measurements of the energetics of characteristic reactions involving copper species. The binding energy of O2 to a Cu atom has been measured56 and found to +10 kcal/mol. It has been calculated using coupled clusbe 15-5 ter methods by both Hrusˇa´k et al.57 and Bauschlicher et al.,58 who report values of 9.7 and 14 kcal/mol, respectively, without including corrections for computational errors. We calculate it to be 14.2 kcal/mol, which falls within the experimental range and near the theoretical range. Such close agreement, however, may be fortuitous. In addition, we calculate a binding energy of NO to a Cu atom forming a bent species to be 26.2 kcal/ mol, close to the value of 25.9 kcal/mol calculated by Schneider et al.45 using the BP8659,60 functionals. Using Hartree-Fock theory, Yakomichi et al.44 have calculated this binding energy to be 16.3 kcal/mol, and using coupled cluster theory, Hrusˇa´k et al.57 have calculated it to be 10.4 kcal/mol. In the absence of experimental data, however, it is impossible to determine the errors in the calculation. In the Discussion section, we compare our LSDFT results to experimental results on CuZSM-5 in order to gain a measure of overbinding in the systems we study. 2.2. Frequency Calculations. Our goal in calculating vibrational frequencies is to determine the vibrational contribution of adsorbed species to the Gibbs free energy. This contribution is a fairly insensitive function of the vibrational frequencies. For example, the difference in contribution between a 20 cm-1 mode and a 30 cm-1 mode is only 0.6 kcal/ mol, and that between a 500 cm-1 mode and a 700 cm-1 mode is only 0.5 kcal/mol. Differences of about 1 kcal/mol or less are well within the tolerance of acceptable error. Since the vibrational frequencies are not a strong function of the environment of adsorbed species, we were able to use smaller clusters for the frequency calculations than for the energy calculations.61 A representative structure is illustrated in Figure 3. We tested the effects of calculating only the

Trout et al. vibrational frequencies of adsorbed species and using smaller basis sets than those used for the energy calculations. Vibrational frequencies of adsorbed species were calculated in all but one case using Gaussian-94 unrestricted Hartree-Fock theory. As discussed below, we calculated the vibrational frequencies only for modes associated with the adsorbate and we used a 3-21G basis set. Specific comparisons of calculated versus measured vibrational frequencies are made in section 3. To evaluate the effect of calculating only the vibrational modes associated with the adsorbed species, we calculated all of the vibrational modes of our ZCuNO cluster (Figure 3) and then visually identified each of the six modes associated with the adsorbed NO. We then compared the value of TS° (773 K) determined from those six modes with that determined from the six modes calculated by freezing all of the atoms in the cluster except for the adsorbed NO. The difference in energy is only 0.6 kcal/mol. To determine the effects of our choice of basis set on the value of TS° (773 K), we calculated vibrational frequencies for a cluster similar to that shown in Figure 3, but with SiH3 groups replaced by H. The difference in TS° (773 K) from the vibrational frequencies of the adsorbed NO calculated using 3-21G basis sets and 6-311G basis sets is only 0.9 kcal/mol. Similar results were obtained by Hehre et al.,62 who showed that for a series of molecules, the difference in vibrational frequencies calculated using 3-21G basis sets and 6-31G** basis sets is not large. We compared the geometry of the optimized structures used for the frequency calculations with those from our LSDFT runs. In all cases but one, the geometries matched within a few tenths of an angstrom. The exception was the ZCu(O)(NO) species, in which the Cu-N bond length was about 50% longer than that calculated using LSDFT. Within the framework of Gaussian-94, we recalculated the structures of these species using LSD and B-P59,60 functionals. The former run did not converge, but the latter run returned geometries with bond lengths within 10% of those of our LSDFT geometries. We used the latter structure and wave function to calculate the frequencies of the adsorbed species of ZCu(O)(NO). Vibrational frequencies calculated in the manner described in this section should be accurate enough to obtain entropic contributions to Gibbs free energy with errors of no more than a few kcal/mol. 2.3. Thermodynamic Calculations. The Gibbs free energy for species j is defined as

Gj ) Uj + PVj - TSj

(1)

where Uj is the internal energy of species j, PVj is the pressure times the molar volume of species j, and TSj is the temperature times the entropy of species j. All quantities are defined as intensive. The determination of Uj and Sj for each species follow the development given in McQuarrie.63 For the zeolite-adsorbed species, there are no rotational or translational degrees of freedom, and we assume that the equation of state of each zeolite-absorbed species is the same. Thus

Ujz kT Sjz k

3n

)∑ i)1

(

3n

)∑ i)1

(

hνi

2kT

hνi/kT hνi/kT

e

-1

+

hνi/kT

)

+

ehνi/kT - 1

Ejz kT

)

- ln(1 - e-hνi/kT) + ln(ωe1j)

(2)

(3)

where Uzj , Ezj , and Szj are respectively the internal energy, the electronic energy, and the entropy of zeolite species j at

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J. Phys. Chem., Vol. 100, No. 44, 1996 17585

temperature T. The symbols h and k are Planck’s constant and Boltzman’s constant; n is the number of atoms in the adsorbed species; νi is the vibrational frequency of mode i in the adsorbed species; and ωe1j is the spin degeneracy of species j. Ezj is taken directly from our LSDFT calculations. Note that we take into account only the 3n vibrational frequencies of the species adsorbed to the Cu associated with the zeolite cluster, where n is the number of atoms in the adsorbed species. The harmonic approximation becomes less valid for very low values of νi; however, because of the insensitivity of thermodynamic properties to the values of νi (vide supra), we do not expect this approximation to lead to an error in Gi of more than a few kcal/ mol. Our assumption in treating only the vibrational frequencies of the adsorbed species is that the presence of the adsorbed species does not significantly alter the vibrational frequencies of the Cu-zeolite as described in section 2.2. We assume that the gaseous species are ideal. For these species

Ujg kT Sjg k

)

m

(

hνi

hνi/kT

)

Ejg

+ ) + +∑ + 2 kT kT i)1 2kT ehνi/kT - 1

g Sj,trans

k

g Uj,rot

3

+

g Sj,rot

k

m

+∑ i)1

(

hνi/kT hνi/kT

e

-1

Figure 4. Minimum energy structure of ZCuO. Bond lengths are given in angstroms.

(4)

)

- ln(1 - e-hνi/kT) + ln(ωe1j) (5)

where symbols are defined as above with superscript g replacing z to designate gaseous species. For linear molecules, g g /kT ) 1, and for nonlinear molecules, Urot /kT ) 3/2. The Uj,rot additional entropy terms are given by the following expressions: g Sj,trans

k

[(

) ln

g Sj,rot

k

) ] ( )

2πmkT h2

) ln

3/2

Ve5/2

Te σθr

(6)

(7)

for diatomic molecules and g Sj,rot

k

[ (

) ln

π1/2e3/2 T3 σ θAθBθC

Figure 5. Minimum energy structure of ZCu(NO). Bond lengths are given in angstroms.

3. Results and Discussion

)] 1/2

(8)

for polyatomic molecules, where σ is the symmetry factor, and the θ’s are the rotational temperatures. In the case of NO, which has a low-energy, first-excited electronic state, a contribution of (∆ωe2NOe-∆/kT)/qe is added to Ugj , and the spin degeneracy contribution, ln(ωe1j), is replaced by [(∆ωe2NOe-∆/kT)/qe + ln(qe)], where ωe1NO and ωe2NO are the spin degeneracies of the ground state and first excited state of NO, and ∆ is the difference in energy between the first excited state and the ground state of NO ((∆)/k ) 178 K64), and qe ) (ωe1NO + ωe2NOe-∆/kT). All vibrational energies and rotational temperatures of gaseous species are taken from Huber and Herzberg.64,65 The standard-state change in Gibbs free energy for an elementary reaction is defined as ∆G° ) ∆H° - T∆S°, where ∆H° ) ∆U° + ∆(PV). ∆U° and ∆S° are determined by subtracting the sum of Uj’s and Sj’s, calculated in the standard state, of products from the corresponding sum of reactants. Since the zeolite and zeolite-adsorbate adducts are assumed to be incompressible, and all gases are ideal, ∆(PV) is given by ∆nRT, where ∆n represents the difference between the number of moles of gaseous products and reactants.

3.1. Energetics, Geometry, and Mulliken Populations of Adsorbed Species. In this subsection and the next, we focus on results pertaining to individual species adsorbed on copper sites. In subsection 3.3, we discuss the thermodynamics of interconversion of these species, and in subsection 3.4, we outline a plausible reaction pathway for NOx decomposition. The clusters discussed in this sections are depicted in Figures 1, 2, and 4-12. Selected Mulliken populations and partial charges are presented in Table 1. 3.1.1. ZCu and ZCuO, Species Present before Introduction of NOx. Copper species associated with a single Al-substituted T-site are thought to exist as ZCu(OH) in as-exchanged ZSM5. Previously, we have shown that upon heating and dehydration, these species are converted to ZCu and ZCuO.43 The structures of these species are shown in Figures 1 and 4. Our minimum energy ZCuO structure has a singlet ground state, which is 7.5 kcal/mol lower in energy than the triplet state. We note that the ZCuO species is stable and that the value of ∆U° (0 K) for the dissociation of an O atom is approximately +75 kcal/mol. 3.1.2. ZCu(NO), ZCu(NO)2, and ZCu(O)(NO). Figures 5-7 illustrate the structures of ZCu(NO), ZCu(NO)2, and ZCu(O)(NO). The binding energies of NO for these species (i.e.,

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Trout et al.

Figure 6. Minimum energy structure of ZCu(NO)2. Bond lengths are given in angstroms.

-∆U°) at 773 K, the temperature of maximum catalytic activity, are given in Table 4a. Adsorbed NO, depicted in Figure 5, has an N-O bond length 0.03 Å longer than the calculated gas-phase N-O bond length. This increased bond length is to be expected, since adsorption results in the transfer of electron density from the d-orbitals of Cu+ to the π* orbital of NO. Note, however, that 0.03 Å is within the uncertainty of the calculation. The Cu-N-O bond angle is 178°, from which we conclude that the three atoms are almost linear. The occurrence of a linearly adsorbed form of NO is consistent with results of infrared studies which assign

Figure 7. Minimum energy structure of ZCu(O)(NO). Bond lengths are given in angstroms.

the N-O stretching vibration at 1810 cm-1 to linearly adsorbed NO,9,20,29,30,31,40 since generally, NO frequencies >1720 cm-1 correspond to linear species.66 We note that Schneider et al.45 have shown that the difference in energy between linear and bent NO is negligible for adsorption to Cu coordinated to water molecules. NO bonds to ZCu with a binding energy of 41.3 kcal/mol. The binding energy of the isonitrosyl is only 23.2 kcal/mol. Thus, bonding of NO to Cu+ via the nitrogen atom is preferred. In ZCu(NO)2, depicted in Figure 6, both N-O bonds are 0.05 Å larger than those in ZCu(NO), and the Cu-N-O bond angles are both 180°. The calculated ON-Cu-NO bond angle is 104°,

TABLE 1: Mulliken Populations and Partial Charges for Atoms and Species in Different ZSM-5 Clusters species ZCu (Figure 1) ZCuO (Figure 4) ZCu-NO (Figure 5) ZCu(NO)2 (Figure 6)

ZCu

NO

ZCuO

ZCu

N O′ (Figure 9)

O O

ZCu–N

ZCu

(Figure 7)

O′

O O

N (Figure 9)

O

(Figure 10)

O

N O′ (Figure 11)

ZCuO2 (Figure 12)

atom

spin up

spin down

total

Cu Cu O Cu N O Cu N O N O Cu O′ N O Cu O N O′ Cu O N O Cu O N O Cu O N O O′ Cu O O

14.116 14.064 4.205 14.124 3.833 4.197 13.972 3.794 4.142 3.331 3.899 14.190 4.381 3.516 4.016 14.273 4.202 3.459 4.200 14.283 4.147 3.405 4.257 14.218 4.184 3.532 4.176 14.247 4.187 3.272 4.247 4.126 14.047 4.073 4.048

14.116 14.073 4.110 14.052 3.276 3.842 13.969 3.342 3.883 3.784 4.159 13.847 3.899 3.487 4.032 13.901 4.117 3.300 3.974 13.882 4.101 3.385 3.959 13.935 3.975 3.414 3.992 13.828 4.070 3.291 3.997 4.056 14.062 4.030 4.074

28.231 28.137 8.315 28.176 7.109 8.039 27.942 7.136 8.025 7.115 8.058 28.038 8.280 7.003 8.048 28.174 8.319 6.759 8.174 28.166 8.248 6.791 8.215 28.153 8.159 6.947 8.168 28.075 8.257 6.562 8.244 8.182 28.110 8.102 8.122

(NO)δ; δ ) -0.148 (NO)δ; δ ) -0.161 (NO)δ; δ ) -0.173

(NO)δ; δ ) -0.051 (NO2)δ; δ ) -0.331 (NO2)δ; δ ) -0.252

(NO2)δ; δ ) -0.254

(NO2)δ; δ ) -0.203

(NO3)δ; δ ) -0.245

(O2)δ; δ ) -0.224

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J. Phys. Chem., Vol. 100, No. 44, 1996 17587

Figure 9. Minimum energy structure of 2. Bond lengths are given in angstroms. Figure 8. Minimum energy structure of 1, ZCuO-N-O. Bond lengths are given in angstroms.

which agrees quite well with measurements of between 102° and 104°.2,20,30 As presented in Table 1, the NO partial charge calculated via a Mulliken population analysis is -0.148 for ZCu(NO), whereas it is -0.161 and -0.173 for ZCu(NO)2. The binding energy of NO interacting with ZCu(NO) to form ZCu(NO)2 is 7.9 kcal/mol at 773 K. ZCu(O)(NO), depicted in Figure 7, has an N-O bond length 0.06 Å longer than that of the corresponding bond in ZCu(NO), but the Cu-N-O bond angle is about the same. From the Mulliken population analysis, the partial charge of NO is -0.051, more positive than -0.148, the partial charge of NO in ZCu(NO). This suggests that the N-O bond of ZCu(O)(NO) is stronger than that of ZCu(NO) and that its bond length should be shorter. The difference of 0.06 Å is likely a consequence of the uncertainty of the calculation. The ELOCu-N bond angle is 60°, where ELO stands for extra lattice oxygen. The calculated binding energy of NO in ZCu(O)(NO) is 52.0 kcal/mol. The fact that this is greater than the binding energy of NO in ZCu(NO) is expected, since the NO in ZCu(O)(NO) can contribute electron density from its antibonding orbital to the bonding orbital of the ELO. The calculated NO bonding energies for ZCu(NO), ZCu(NO)2, and ZCu(O)(NO) can be compared with values determined from temperature-programmed desorption (TPD) measurements reported by Li and Armor17 and Schay and Guczi.38 Both sets of authors found that NO desorbed over a range of temperatures. We have calculated NO binding energies from these results only for the highest temperature desorption peak. Using a first-order Redhead analysis and estimating the preexponential factor to be 1013-1015 s-1, we calculate the NO binding energy from Li and Armor to be 43.9-49.5 kcal/mol17 and that from Schay and Guczi to be 47.6-53.8 kcal/mol.38 Hence, our calculated binding energies of 41.3 and 52.0 kcal/ mol for NO associated with ZCu(NO) and ZCu(O)(NO) are close to the experimentally observed values. It should be noted that infrared observations made during TPD show the concurrent loss of NO from ZCu(NO) and from ZCu(O)(NO).40 3.1.3. Cu2+ Associated with Two Al’s in a FiVe T-Site Ring. Previously, we have evaluated the stability of Cu2+ associated with two Al-substituted T-sites in ring structures with five or six T-sites.43 We found that Cu2+ is stable in the five T-site ring but is not stable in the six T-site ring. In this study, we

Figure 10. Minimum energy structure of 3. Bond lengths are given in angstroms.

have calculated the binding energy of NO to the Cu2+ in the five T-site ring depicted in Figure 2 and found it to be negative. Thus, our calculation indicates that NO will not bind to this site, and from this we can infer that such sites will not be active for NO decomposition. There may, however, exist other Cu2+ containing ring structures in the zeolite to which NO can bind. 3.1.4. Structures 1-4. Figures 8-10 depict various isomers of adsorbed NO2 species. In order of appearance, they are N O ZCu ZCuO 1

O

O N ZCu–N

O 2

O 3

referred to as nitrito, bidentate nitro, and monodentate nitro. The N-O bond lengths in all three species are nearly identical (1.25-1.27 Å) and similar to those measured for gas-phase NO2- (1.24 Å).67 The O-N-O bond angles lie between 115° and 117°, also similar to that for gas-phase NO2- (115°). Consistent with the similarities in geometry, partial charges of tbe NO2- ligands in Figures 8-10 are -0.252, -0.254, and

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Trout et al. TABLE 2: Vibrational Frequencies of Adsorbed Species frequencies (cm-1)

cluster ZCuO ZCu(NO) NO ZCu O N O ZCuO O ZCu–N O O ZCu N O ZCu(NO)2 ZCuO2 O ZCu N O O

111, 159, 930 48, 56, 306, 441, 507, 1776 33, 56, 129, 138, 275, 305, 524, 707, 1452 29, 35, 52, 77, 175, 443, 758, 854, 1104 31, 47, 65, 211, 266, 492, 632, 789, 1281 37, 60, 65, 318, 326, 356, 926, 1066, 1297 41, 58, 66, 89, 177, 272, 290, 341, 515, 630, 1578, 1646 87, 123, 146, 598, 624, 1150 26, 45, 69, 154, 272, 323, 653, 744, 749, 893, 1147, 1633

TABLE 3: Frequencies and Normal Modes of Adsorbed NO frequency (cm-1)

Figure 11. Minimum energy structure of 4. Bond lengths are given in angstroms.

48 56 306 441 507 1776

Figure 12. Minimum energy structure of ZCuO2. Bond lengths are given in angstroms.

-0.203, respectively, as shown in Table 1. The binding energies of NO2 at 773 K are as follows: nitrito, 12.2 kcal/mol; bidentate nitro, 42.6 kcal/mol; and monodentate nitro, 26.8 kcal/mol. An adsorbed nitrato species is depicted in Figure 11. This species is quite stable (e.g., ∆G° ) -56.0 kcal/mol for it to O ZCu

N O O 4

decompose to ZCuO and NO2) and might be a significant inhibitor to catalysis (see section 3.3). The nitrato species has a geometry similar to that of the nitrate ion (D3h with bond lengths of 1.22 Å) but is slightly asymmetric. The Mulliken population analysis presented in Table 1 shows that the partial charge of the nitrato species is about the same as that of the nitro and nitrito species. 3.1.5. ZCu(O2). The structure of ZCu(O2) is depicted in Figure 12. This structure is in a singlet ground state, which is 6.0 kcal/mol lower in energy than the triplet state. The O-O

normal mode vv ZCu-NO vv ZCu-NO v ZCu-NO V ZCurNrO v ZCu-NO V ZCurN-Of

name out-of-place wag in-plane wag in-plane rock Cu-NO vibration out-of-plane rock N-O vibration

bond length in this structure is 1.21 Å, identical with that calculated for gas-phase O2. This similarity is to be expected, since this species is adsorbed symmetrically by both O atoms, and the O-O bond is quite strong. We have calculated that the energy to break this bond to form two nonbonded O atoms coordinated to the Cu is 80.4 kcal/mol. Thus, we conclude that this O-O bond remains intact and is not likely to be broken once formed. The partial charge on the O2 is -0.224. The calculated binding energy of O2 at 773 K is 39.0 kcal/ mol. This figure is 8-15 kcal/mol smaller than that determined from the experiments of Valyon and Hall.23 A first-order Redhead analysis of the TPD data obtained by these authors, assuming a preexponential factor of 1013-1015 s-1, gives an O2 binding energy of 47.1-53.2 kcal/mol. Valyon and Hall obtained a value of 54 kcal/mol by measuring the temperature dependence of the partial pressure of O2 over CuZSM-5 and using the Clausius-Clapeyron equation. Note that they obtained smaller values at lower temperatures and that 54 kcal/mol at 773 K would result in a considerable fraction of sites bound by O2 for even very small O2 partial pressures. 3.2. Vibrational Frequencies. All of the calculated frequencies of adsorbed species are listed in Table 2, and illustrations of the normal modes associated with adsorbed NO are given in Table 3. As described in the Methods section, our calculations of vibrational frequencies were undertaken for the purpose of determining the vibrational contribution to the entropy of each adsorbed species, and consequently, a high level of agreement with experimentally observed frequencies was not sought. For reasons noted earlier, we expect that our calculated Gibbs free energy will not be substantially affected by errors in vibrational frequencies. To support this conclusion, we compare calculated frequencies to those observed experimentally, where these are known, and then project the anticipated

Thermochemistry of NOx Decomposition error in TS° (773 K). Unless otherwise noted, our vibrational frequency data is taken from Aylor et al.40 The calculated frequency for the Cu-O stretching mode in ZCuO is 930 cm-1. This value is very close to 935 cm-1, attributed by Valyon and Hall to the vibrations of ELO.21 We note, though, that the authors suggest that their observed mode may be due to Cu-O vibrations in a structure more complex than ZCuO. In the case of ZCuO2, we calculate a frequency of 1150 cm-1 for the O-O stretch, in close agreement with the frequency of 1143 cm-1, observed for O2-61 in transition-metal complexes. Agreement to within 2% is found between the calculated and observed frequency for the N-O stretching bond of ZCu(NO). In this case, we calculate a frequency of 1776 cm-1, and the experimentally observed value is 1810 cm-1. The two N-O stretching bands for ZCu(NO)2 are calculated to be 1578 and 1646 cm-1, an average of 9% lower than the measured frequencies of 1733 and 1824 cm-1. Our calculated value of the N-O stretching frequency in ZCu(O)(NO) is 1452 cm-1. This is 31% lower than the value of 1910 cm-1 for the band attributed in experimental studies to ZCu(O)(NO). The asymmetric, symmetric, and bending modes of the bidentate chelating nitro species are calculated to have frequencies of 1297, 1066, and 926 cm-1. These values differ between 1 and 11% from the values of 1283, 1201, and 854 cm-1, corresponding to averages of modes in similar nitro species occurring in organometallic complexes.61 We note that in all cases except ZCu(O)(NO), the vibrational frequencies were calculated using unrestricted Hartree-Fock theory (see section 2.2). Normally this technique gives vibrational frequencies that are about 10% larger than those measured. All of our calculated frequencies, however, are lower than experimental frequencies. We speculate that this is a result of using small basis sets. It is difficult to calculate exactly the extent to which errors in our estimations of the vibrational frequencies of adsorbed species affect the vibrational contribution to the molar entropy of that species, because it is not known whether the discrepancy between the calculated and observed frequency for a single mode will be the same for all modes. Heuristically, however, calculated vibrational frequencies are often scaled by a constant factor.68,69 If we assume that the average error between observed and calculated frequencies is 10-20%, then the corresponding error in ∆G° at 773 K will be 1-2 kcal/mol. 3.3. Thermodynamics of Elementary Reactions. We present the thermodynamics of elementary steps believed to be relevant to the decomposition of NOx over CuZSM-5 in Table 4a-d. These tables are divided into steps which deal with NO adsorption, N2O formation, NO2 formation, and N2 and O2 formation. For each elementary step, values are given for ∆U (0 K), ∆U° (773 K), ∆H° (773 K), and ∆G° (773 K). 3.3.1. NO Adsorption. The first step in the decomposition of NO is the adsorption of NO onto Cu sites. As shown in Table 4a, the Gibbs free energy for NO adsorption to form ZCu(NO) is -16.2 kcal/mol. While the enthalpy of adsorption of a second molecule of NO is negative, the standard-state Gibbs free energy is +18.5 kcal/mol. Thus, under normal operating conditions, where PNO is in the range 10-1000 ppm (10-510-3 atm), the equilibrium fraction of ZCu(NO)2 will be negligible compared to that of ZCu(NO) at 773 K. On the other hand, if the temperature is lowered to 298 K, ∆G° for reaction 2 becomes +1.3 kcal/mol, and the equilibrium fraction of ZCu(NO)2 becomes more significant. The predicted stability of ZCu(NO)2 with temperature is qualitatively consistent with infrared observations which show the presence of ZCu(NO)2 at 298 K, but its complete absence at 773 K.40

J. Phys. Chem., Vol. 100, No. 44, 1996 17589 The adsorption of NO by ZCuO leads to ZCu(O)(NO) or one of the three isomers of ZCu(NO2). All three species are predicted to be stable at 773 K, with stability increasing in the following order: N O ZCuO

NO < ZCu

O < ZCu–N

O

O < ZCu

O

N

(9)

O

Consistent with the predicted order of stability shown above, infrared observations demonstrate that bidentate nitro species are significantly more stable at 773 K than the other three structures.40 3.3.2. N2O and O2 Formation. Table 4b shows four different paths to N2O that can be envisioned (reactions 7-10). These reactions are listed in order of descending ∆G°. Reaction 8 is unlikely to participate in N2O formation, since at 773 K, the concentration of ZCu(NO)2 is predicted to be small. While the value of ∆G° for reaction 7 is positive, this reaction is very important in explaining how ZCuO is regenerated from ZCu sites as discussed in more detail below. 3.3.3. NO2 and Nitrato Formation and Reaction. CuZSM-5 is known to catalyze the oxidation of NO to NO2.70 NO2 can be formed as a consequence of NO reacting with O2 in the feed or O2 produced as a product of NO decomposition. Table 4c lists thermodynamics of reactions involving NO2. The most likely pathway to NO2 from a thermodynamics standpoint is via reaction 11 or 12. Desorption of NO2 from ZCu(O)(NO) or ZCu(NO2) as shown in reactions 14 and 15 is less favorable, particularly in the case of the bidentate nitro species. Reactions 16-20 illustrate ways in which nitrato species can be formed. The nitrato species, like the bidentate nitro species, is quite stable and, as will be discussed in section 3.4, can contribute to an inhibition of the activity of CuZSM-5 for NO decomposition. The most thermodynamically favorable pathway for the decomposition of the nitrato species is by reaction with NO as in the reverse of reaction 17 to form NO2 and the bidentate nitro species. This bidentate nitro species can then react with NO to form N2O and ZCuO2 as in reaction 9 in Table 4b. These results are consistent with infrared studies,40 which show that nitrate groups are readily observed upon exposure of CuZSM-5 to NO or NO2. Reactions 21 and 22 are thermodynamically favorable paths for the decomposition of NO2. 3.3.4. N2 and O2 Formation. The elementary processes for the formation of N2 and O2 are listed in Table 4d. N2 can be formed via several alternate pathways, each involving decomposition of N2O. The most thermodynamically favorable ones are reactions 23-25, in particular reaction 25, decomposition of N2 by ZCuO. Reaction 26 is less favorable but could be spontaneous, depending on the ratio of concentration of products to reactants. Decomposition of N2O by ZCu is thermodynamically unfavorable at normal reaction conditions. O2 is produced by desorption from ZCu(O2), formed via decomposition of NO and N2O, as shown in reaction 28. At 773 K, ∆G° is positive, implying that large partial pressures of O2 will inhibit the catalyst. 3.4. Reaction Pathway for NO Decomposition. Figure 13 illustrates a possible reaction pathway for the decomposition of NO over CuZSM-5. This reaction pathway is assembled from the elementary steps presented in Table 4a-d and is based on the minimum change in standard-state Gibbs free energy for each stage in the decomposition of NOx. In the case of the net reaction of ZCuO with NO to form ZCuO2, we could have chosen any of the four isomers of ZCuONO as the intermediate, since the net ∆G° is the same regardless of the intermediate.

17590 J. Phys. Chem., Vol. 100, No. 44, 1996

Trout et al.

TABLE 4a ∆U (0 K)

reaction (1)

ZCu + NO h ZCuNO

(2) (3)

ZCuNO + NO h ZCu(NO)2 NO ZCuO + NO ZCu O N O ZCuO + NO ZCuO O ZCuO + NO ZCu–N O O ZCuO + NO ZCu N O

(4) (5) (6)

(7) (8) (9) (10)

-42.8

-16.2

-7.9 -52.0

-9.5 -53.5

+18.5 -28.6

-48.4

-45.8

-47.4

-25.3

-62.6

-60.4

-61.9

-36.8

-77.9

-76.2

-77.7

-50.6

+4.8

+11.2

+17.0 -18.8

+12.7 -20.6

+14.2 -20.6

-7.3 -13.3

-42.2

-44.8

-44.8

-35.3

(21) (22)

ZCuO + NO2 h ZCuNO + O2

(13) (14) (15) (16) (17) (18) (19) (20)

(23) ZCuNO + N2O

(24) ZCu

O

ZCu

N + N2O

O O

ZCu

-31.6

-33.0 -20.6 +1.5 -4.5 +17.6 -27.4 -5.3 -56.0 -30.0 -24.7 -26.0

-30.6

-31.3

-16.5

-17.8

-23.6

-22.4

-22.4

-21.7

-43.6 +5.2

-41.9 +7.7

-41.9 +7.7

-42.3 +4.3

+16.4

+18.4

+18.4

+16.7

+39.5

+37.4

+39.0

+10.8

N O + N2

(27)

O O ZCuO + N2O h ZCuO2 + N2 NO + N2 ZCuNO + N2O ZCu O ZCu + N2O h ZCuO + N2

(28)

ZCuO2 h ZCu + O2

(25) (26)

-30.6

(d) Energetics of Elementary Reactions Involving N2 Formation -18.2 -16.5 N + N2 O

∆G° (773 K)

-10.4 -54.5

(b) Energetics of Elementary Reactions Involving N2O Formation ZCuNO + NO h ZCuO + N2O +6.6 +4.8 ZCu(NO)2h ZCuO + N2O O ZCuO2 + N2O ZCu N + NO O NO + NO ZCuO2 + N2O ZCu O

∆H° (773 K)

(c) Energetics of Elementary Reactions Involving NO2 and NO3- Formation and Decomposition ZCuO + NO h ZCu + NO2 -32.1 -33.6 -33.6 -20.9 -22.9 -22.9 NO + NO ZCuNO + NO2 ZCu O +2.4 +1.3 +1.3 O ZCuNO + NO2 ZCu N + NO O +22.4 +18.4 +19.9 NO ZCu + NO2 ZCu O +45.8 +42.6 +44.1 O ZCu + NO2 ZCu N O -31.2 -31.4 -31.4 NO O + NO2 ZCu ZCu N O + NO O O -7.8 -7.2 -7.2 O O ZCu N + NO2 ZCu N O + NO O O -85.7 -83.4 -85.0 O ZCuO + NO2 ZCu N O O -57.9 -56.7 -58.2 O ZCuO2 + NO ZCu N O O -54.1 -52.8 -54.4 O ZCuNO + O2 ZCu N O O ZCuO + NO2 h ZCuO2 + NO -27.9 -26.7 -26.7

(11) (12)

a

∆U° (773 K)

(a) Energetics of Elementary Reactions Involving NO Adsorption -43.3 -41.3

All energies are in kcal/mol.

The arbitrary choice was made of depicting ZCu(O)(NO). In Figure 13, we include pathways for the decomposition of NO2 and N2O, in addition to NO. The pivotal zeolite intermediate is ZCuO. In the proposed reaction pathway, there are no elementary steps that are highly thermodynamically unfavorable. This pathway offers a plausible explanation for the formation of N2 and O2 over isolated copper cations.

Several authors have proposed that N2O is formed by the reaction ZCu(NO)2 ) ZCuO + N2O.30,31,40,41 Our calculations demonstrate that the concentration of dinitrosyl species will be very small at 773 K and, hence, that the concentration of ZCu(NO)2 will be extremely low. This conclusion is consistent with recent in situ infrared studies that show that even when the concentration of NO is 5%, bands characteristic of ZCu(NO)2

Thermochemistry of NOx Decomposition

J. Phys. Chem., Vol. 100, No. 44, 1996 17591 steps ZCuO h ZCu + O• and ZCuO + O• h ZCu + O2. A more plausible sequence of elementary steps would be

∆G° (773K)

Figure 13. Proposed pathway for NOx decomposition over CuZSM5. Arrows in the diagram depict the progress of each reaction in the forward direction. Numbers are ∆G° (773 K) in kcal/mol.

are not observed above 673 K.40 Our calculations suggest that, instead, gas-phase NO reacts with adsorbed NO or NO2 to release gas-phase N2O. This proposal is consistent with the kinetics of NO decomposition reported by Li and Hall,18 who find that the rate of NO decomposition is proportional to the partial pressure of NO. Another proposed pathway to N2O is via decomposition of ZCu(N2O3)40 or ZCu(NO)(NO2).30,31,41 We have considered the energetics of formation for each of these species via the following reactions: O

O N + NO

ZCu

O

NO O

O

NO

+ NO

ZCu

∆U(0 K) = +21.3

N N

ZCu

O ZCu

O

∆U(0 K) = +58.8

N O

While we have not calculated ∆G° at 773 K for these processes, we can anticipate that it will be very large and positive in both cases. Thus, our calculations suggest that neither ZCu(N2O3) nor ZCu(NO)(NO2) will be stable enough at 773 K to be present in sufficient concentration to sustain the process of NO decomposition. It has been proposed that N2 is formed by reaction of N2O with ZCu to produce N2 and ZCuO and that O2 is formed by reaction of O• with ZCuO.40 Our calculations show that for the first of these processes ∆G° (773 K) ) +16.7 kcal/mol, which is significantly greater than ∆G° (773 K) ) -42.3 kcal/ mol for the reaction ZCuO + N2O h ZCuO2 + N2, shown in Figure 13. For O2 to form via the sequence ZCuO + O• h ZCuO2 and ZCuO2 h ZCu + O2, it would be necessary for O atoms to desorb from ZCuO. Our calculations show that ∆U° (0 K) ) +74.9 kcal/mol for this process, suggesting that desorption of O atoms is very unlikely to occur. It has been observed that O2 inhibits NO decomposition and that the rate of decomposition is a function of the partial pressure of O2 to the -1/2 power.18 Li and Hall attribute this partial pressure dependence to the existence of an equilibrium between ELO and gas-phase O2:18 ZCuO h ZCu + 1/2O2. For the reason discussed above, our calculations suggest that it is unlikely that the pathway for achieving this equilibrium is comprised of the

ZCuO + NO2 h ZCuO2 + NO

-26.0

ZCuO2 h ZCu + O2

+10.8

NO + 1/2O2 h NO2

-8.9

ZCuO h ZCu + 1/2O2

-24.1

Thus, the observed inhibition of NO decomposition by O2 could be a consequence of the equilibrium between NO, O2, and NO2. Both Shelef et al. and Petunchi and Hall have shown that at 773 K, the reaction NO + 1/2O2 h NO2 is at equilibrium over CuZSM-5.70,71 Valyon and Hall propose an equilibrium between nitrogen and oxygen containing surface species and gas phase O2:20 ZCu(NO2) + 1/2O2 h ZCu(NO3). Again, our calculations suggest that such an equilibrium could exist at 773 K but that it is more likely that the following set of elementary processes are involved: ∆G° (773K) O

O N + NO2

ZCu O

NO + 1/2O2

N O + NO

ZCu

NO2

-8.9 O

O N + 1/2O2

ZCu

-5.3

O

O

ZCu

N O

-14.2

O

The decomposition of NO over CuZSM-5 is also known to be inhibited by H2O.72 While the interactions of H2O with CuZSM-5 were not considered in this study, we have shown previously that ∆G° (773 K) for the reaction ZCu + ZCuO + H2O h 2ZCu(OH) is approximately -18 kcal/mol. From this we deduce that H2O could inhibit the decomposition of NO by reducing the concentrations of ZCu and ZCuO, two species which are envisioned to be essential for NO decomposition (see Figure 13). 4. Conclusion Using first-principles quantum mechanical calculations, we have determined structural, electronic, and vibrational properties of species believed to participate in the decomposition of NO over CuZSM-5. Where experimental information is available, comparison of calculated and experimentally observed properties shows good agreement. The results of our quantum mechanical calculations have been used in conjunction with statistical mechanics to determine U°, H°, and G° of each species. From these calculations, we have been able to evaluate the stability of individual species and the thermodynamics (i.e., ∆U°, ∆H°, and ∆G°) of their interconversion. On the basis of the thermodynamics of elementary steps, we have been able to identify a possible reaction pathway for NO decomposition (see Figure 13). The first step is NO adsorption onto ZCu to form ZCu(NO). Reaction of the latter species with additional NO produces ZCuO and gas-phase N2. O2 is produced by desorption from ZCu(O2). This pathway is consistent with a number of experimental observations and demonstrates the plausibility of a pathway for NO decomposition over Cu cations associated with single Al

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