Local Spin Density Functional Theory Study of Copper Ion

J. Phys. Chem. 1996, 100, 4173-4179

4173

Local Spin Density Functional Theory Study of Copper Ion-Exchanged ZSM-5 Bernhardt L. Trout, Arup K. Chakraborty,* and Alexis T. Bell Center for AdVanced Materials, Lawrence Berkeley National Laboratory, and Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720 ReceiVed: August 23, 1995; In Final Form: NoVember 12, 1995X

We have used local spin density functional theory to investigate the electronic and structural properties of Cu species (Cu+, Cu2+O-, and Cu2+OH-) interacting with isolated tAl-O--Sit sites CuZSM-5. We have also evaluated the thermodynamic stability of these species and the thermodynamics of a proposed scheme for the autoreduction of Cu2+ to Cu+. We have found all of the species studied to be thermodynamically stable and the proposed autoreduction process to be thermodynamically feasible at temperatures normally encountered in the pretreatment of as-exchanged CuZSM-5. In addition, we have investigated the interactions of Cu2+ cations with both 6-T site and 5-T site ring structures containing two Al atoms. We have found that Cu2+ in a 6-T site ring structure is thermodynamically unstable, while that in a 5-T site ring structure is thermodynamically stable.

1. Introduction Copper ion-exchanged ZSM-5 (CuZSM-5) has been found to be exceptionally active for the direct decomposition of NO to N2 and O2.1-9 Comparison of the activity of this catalyst with that of Cu exchanged into other zeolites and other metals exchanged into ZSM-5 indicates that the high activity of CuZSM-5 results from the combined properties of the metal cation and the zeolite.10,11 EPR and XANES investigations have shown that all of the Cu in CuZSM-5 prepared by ion exchange from aqueous solution is present as Cu2+.5,12-15 It is believed that the Cu2+ cations are associated with isolated anionic tAl-O--Sit sites, and that the Cu2+ is present as Cu2+OH-. Infrared observations support this interpretation.16 Protons also charge compensate these anionic sites,15,17 and the extent of Cu exchange is always less than the stoichiometric amount needed for a one-to-one correspondence between Cu2+OH- species and anionic sites. Upon heating, as-exchanged CuZSM-5 undergoes autoreduction, a process in which a part of the Cu2+ is reduced to Cu+. The presence of Cu+ cations in autoreduced CuZSM-5 has been observed directly by both XANES14 and fluorescence12 and indirectly by IR spectroscopy.7,18-24 Recently, Larsen et al.25 have reported a detailed EPR investigation of the autoreduction process. They observed that for CuZSM-5, with a Si/Al ratio of 18, the EPR signal intensity attributable to paramagnetic Cu2+ species decreased by ∼50% upon heating the catalyst to temperatures up to 500 °C, independent of the extent of Cu exchange. This change in EPR signal intensity could be fully reversed by exposing the catalyst to water vapor at room temperature. The following steps were proposed to explain these observations:

[Cu2+OH-]+Z- h Cu+Z- + ‚OH [Cu2+OH-]+Z- + ‚OH h [Cu2+O-]+Z- + H2O 2[Cu2+OH-]+Z- h Cu+Z- + [Cu2+O-]+Z- + H2O

(1)

The symbol Z- represents an Al-substituted T site in the ZSM-5 zeolite, which is associated with a net negative charge, i.e., tAl-O--Sit. Note that in the above equations and in those * Author to whom all correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, February 1, 1996.

0022-3654/96/20100-4173$12.00/0

to follow, formal charges are used as labels only for the sake of convenience. Partioning the electron density distribution to assign formal charges can be done only in an arbitrary manner, and so has no firm physical meaning. In the first step, the [Cu2+OH-]+Z- (EPR detectable) decomposes to form Cu+Z(EPR silent) and an ‚OH radical. The ‚OH radical reacts with another [Cu2+OH-]+Z- (EPR detectable) to form [Cu2+O-]+Z(hypothesized to be EPR silent because of the presence of the paramagnetic O- anion) and H2O. Thus, two EPR detectable copper sites form two EPR silent copper sites and H2O. Larsen et al. proposed that the Cu2+ cations that do not undergo autoreduction are associated with two Z- sites in close proximity. The objective of this study is to determine the structural and electronic properties of the copper species which play a role in the mechanism of the autoreduction of copper in ZSM-5, to evaluate the thermodynamic stability of these species, and to calculate the thermodynamics for the interconversion of species. We also report results for Cu systems which do not undergo autoreduction. We have chosen to use LSDFT because it is the least costly, tractable first-principles approach in which electron correlation effects can be included. We discuss the techniques that we have developed in order to implement LSDFT calculations for this ZSM-5 system. The results of our calculations show that the mechanism proposed above is plausible and each of the copper species in the mechanism is thermodynamically stable. 2. Theoretical Methods 2.1. Density Functional Theory Methods. Density functional theory (DFT) is a well-established technique for performing first-principles studies of bulk solid state materials and surfaces. Only recently has DFT been used to study the structure and bonding of molecules, and primarily closed shell, low molecular weight molecules26-29 have been examined. In the past several years DFT has been used to investigate the properties of progressively larger closed-shell structures, including zeolites30-32 and open-shell (spin unpaired) transition metal compounds.33-36 Transition metal systems are much more complicated than closed-shell organic molecules because (1) they often have net nonzero electronic spin, (2) they can have more elaborate bonding structures, (3) they have potentially © 1996 American Chemical Society

4174 J. Phys. Chem., Vol. 100, No. 10, 1996 multiple oxidation states and coordination numbers, and (4) their valence electrons are in d-orbitals, which are diffuse and tend to overlap with core electron orbitals.37 The LSD code that we have used for this study is based on a local density approximation (LDA) code used previously in our group,31,32 but it has been rewritten. We use the PerdewZunger form of the exchange-correlation functional38 and recursive Gaussian integration methods39,40 for all integral calculations, enabling the code to be highly vectorizable. In addition, to perform the geometry relaxation, we have implemented analytical gradients, similar to those in DGAUSS.29 We use Gaussian basis sets and the direct self-consistent field (SCF) method.29 In order to reduce the computational cost from increasing as n4, where n is approximately the number of basis functions, we use Gaussian fitting functions both for the electron density and for the exchange-correlation potential and energy, as proposed by Dunlap et al.41 Application of these methods causes the computational cost to increase as n3. To perform the geometry relaxation, we use the minimization method developed by Davidon.42 All of our calculations are performed using a mixed basis set, i.e., minimal basis set for the terminating protons which substituted for silicon atoms and fuller basis sets for the rest of the atoms, including all other protons in the system. We use orbital basis sets optimized for Hartree-Fock calculations. For the protons, they were chosen from Pople, and for the other atoms, from Huzinaga as follows:43,44 Hterminating, STO-3G; Hcluster, STO-5 G**; O, (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. Note that in order to achieve convergence for the 2S1/2 ground state electronic configuration for the Cu atom, Huzinaga’s largest basis set was needed. All atoms except for H and Cu have a single d polarization function in their basis set. All of the basis functions are uncontracted in order to allow full variational flexibility. Our code uses an even-tempered expansion for the basis sets employed for fitting the electron density and the exchangecorrelation potential. We developed these basis sets separately using small clusters which closely mimic the bonding environment to be studied. For example, the oxygen fitting basis sets were optimized for the three atom SiOSi cluster. In all cases, the local fit quality, defined as ∫(|Ψ|2 - F) dr, where Ψ is the wave function and F is the fitted electron density, decreased when the fitting procedure was implemented on the larger structure. This improvement in the fit is to be expected because of the combined effect of many fitting sites and fewer tails in the larger cluster. The fitting basis functions for Cu+ cations were optimized for the CuO molecule. Fitting functions positioned only at the atom centers resulted in an unacceptable fit quality. Three dimensional plots revealed the form of the error, which was greatest along the CuO bond. We removed this error by adding four extra sites placed 0.1 Å around the Cu atom. The addition of these sites, however, increased the number of SCF iterations necessary for convergence. All electrons are treated explicitly in our calculations. We found that calculations using pseudopotentials of the form developed by Bachelet et al.45 with the implementation for 3d elements by Greenside and Schlu¨ter46 resulted in numerical instability. Our DFT calculations are carried out on clusters containing one Al-substituted T-site and 34-36 atoms (depending on which copper species is in the cluster) or two Al-substituted T-sites and 43-49 atoms (depending on the size of the structure). The small cluster is used to represent a O-Si-O shell around a central Al-substituted T-12 site. The negative charge of the

Trout et al.

Figure 1. Minimum energy structure of Cu+ in 1-fold, 2-fold, and 3-fold coordination sites in Al-substituted ZSM-5. Bond lengths are given in angstroms.

Figure 2. Minimum energy structure of [CuO]+ coordinated to two oxygen atoms in Al-substituted ZSM-5. Bond lengths are given in angstroms.

Figure 3. Minimum energy structure of [CuOH]+ coordinated to two oxygen atoms in Al-substituted ZSM-5. Bond lengths are given in angstroms.

Al-substituted T-site is compensated by H+, Cu+, Cu2+OH-, or Cu2+O-, as shown in Figures 1-3. The larger clusters are used to represent either five or six membered rings containing two negatively charged Al-substituted T-sites. The net 2- charge of the two Al-substituted T-sites is compensated by Cu2+, as shown in Figures 4 and 5. All clusters are terminated by H atoms. Electronic structure calculations must be performed on a finite sized cluster, but the true system is practically infinite. Since ZSM-5 is a dielectric, there will be a small energy contribution

LSDFT Study of Copper Ion-Exchanged ZSM-5

J. Phys. Chem., Vol. 100, No. 10, 1996 4175 TABLE 1: Comparision of LSDFT Model Calculations with Experiment quantity Cu ionization potential (eV) CuO bond length (Å) CuO bond strength (eV) CuO vibrational frequency (cm-1)

Figure 4. Minimum energy structure of Cu2+ coordinated to (a, top) four oxygen atoms and (b, bottom) two oxygen atoms in a six T-site ring with two Al-substituted T-sites ZSM-5. Structure 4b is 18 kcal/ mol lower in energy than structure 4a. Bond lengths are given in angstroms.

Figure 5. Minimum energy structure of Cu2+ coordinated to (a, top) oxygen atoms and (b, bottom) two oxygen atoms in a five T-site ring with two Al-substituted T-sites ZSM-5. Structure 5a is 70 kcal/mol lower in energy than structure 5b. Bond lengths are given in angstroms.

due to the long-range electrostatic interaction between the finite cluster and the infinite crystal; this contribution is call the Madelung energy. We have investigated calculating the Madelung energy using the method of Ewald sums.47 Kyrlidis et

theory 7.92 1.77 2.71 630

expt 53

7.73 1.72 49 2.79 49 64049

diff 2% 3% 3% 1%

al.32 have shown that this energy contribution can be treated using first order perturbation theory because it is small and it does not alter the geometry of the cluster. We used a technique that is very similar to theirs and found that in all cases this contribution is 0.09% of the energy of the Hamiltonian or less, justifying the use of perturbation theory. Sauer et al. in a recent review30 have noted that there have been no reported cases in which including the effects of the external crystal potential in a finite cluster calculation has increased the accuracy of the results compared both to experiment and to electronic structure calculations with periodic boundary conditions. This is because of the necessary element of arbitrariness in the calculation. For this reason, we report only the results without the external potential perturbation. We have tested our LSDFT method by comparing the calculated electronic and structural properties of Cu and CuO to experimental measurements. Our results are shown in Table 1. The ionization potential of the Cu atom is determined to within 2%, and the length, bond strength, and vibrational frequency of CuO are determined to within 3% or better relative to experimental measurements. Given the tendency of the LSD approximation to predict overbinding, the fact that the results of our calculations agree with experiment to within 5% may be fortuitous. 2.2. Thermodynamic Calculations. As part of this study, we are interested in determining the change in internal energy and the change in free energy for various chemical reactions. We define ∆Urxn as the change in internal energy of reaction and ∆G°rxn as the change in Gibbs free energy of reaction in the standard state. ∆Urxn at 0 K and 0 atm is calculated directly from the differences in energies obtained from the LSDFT calculations. At experimental temperatures, Ui, the internal energy of species i, increases ideally for monatomic gases as 3/ RT, for diatomic and liner polyatomic gaseous species as 2 5/ RT, and for nonlinear polyatomic gaseous species as 3RT, 2 where RT ) 1.5 kcal/mol at 500 °C. When calculating the heat capacity, we ignore vibrational contributions, which should be small. Thus, for all reactions reported which involve diatomic gaseous species, for example, ∆Urxn (500 °C) can be obtained approximately from ∆Urxn (0 K) by adding 4 kcal/mol to ∆Urxn (0 K) for each mole of diatomic gaseous product and subtracting 4 kcal/mol from ∆Urxn (0 K) for each mole of diatomic gaseous reactant. If we ignore the effect of intermolecular interactions in the gaseous species, ∆Urxn is not a function of pressure, and hence, ∆Urxn ) ∆U°rxn, where ∆U°rxn is the internal energy of reaction in the standard state. ∆G°rxn ) ∆U°rxn + ∆(PV) - T∆S°rxn. We have ∆U°rxn from the calculations described above. The PV term can be estimated by assuming that the gaseous species are ideal and that the equations of state of the zeolites are the same. Thus, ∆(PV) ) nRT for the gaseous species liberated, and ∆(PV) ) -nRT for the gaseous species consumed or adsorbed. ∆S°rxn is estimated after making the following assumptions: the entropies of the zeolite species, [Cu2+OH-]+Z-, [Cu2+O-]+Z-, and Cu+Z-, are equal; the entropic degrees of freedom of the gases, O, ‚OH, and H2O, are separable; and O, ‚OH, and H2O are ideal gases at 500 °C and 1 atm. Thus, we are taking into account the entropic contributions from only the gas phase species. The entropy of each of these species is evaluated from the partition

4176 J. Phys. Chem., Vol. 100, No. 10, 1996

Trout et al.

function, which is a product of individual partition functions (see, e.g., ref 48).

q(V,T) ) qt(V,T) qr(T) qv(T) qe(T)

(2)

where the terms on the right side of the equation are the individual partition functions in the following order: translational, rotational, vibrational, and electronic. For all of the species treated in this paper, qe(T) ) 1 for T < 1000 K. For the zeolite species, qt(V,T) and qr(T) depend on their masses, which are very large compared to the mass of the additional O in [Cu2+O-]+Z- or the additional OH in [Cu2+OH-]+Z-; thus, these terms can be considered equal for all of the zeolite species. There will be additional vibrational modes in [Cu2+OH-]+Zand [Cu2+O-]+Z- that are not present in Cu+Z-, but the entropic contribution from these modes will be small. Since O is monatomic, qr(T) and qv(T) do not contribute to the entropy of O, and qt(V,T) is the sole contribution. For ‚OH and H2O, we calculate qr(T) and qv(T) using spectroscopic data taken from Huber and Herzberg.49,50 3. Results and Discussion The cluster that we use to study single Al-substituted T-sites is shown in Figure 1, with several positions of a Cu+ charge balancing cation. The cluster was selected from part of the crystalline structure of the siliceous zeolite51 with a T-12 site in the center. An Al was substituted for the Si in the T-12 site, and a Cu atom was added in various places (Vide infra). All atoms were relaxed except the terminating OH groups. The Cu+ cation is expected to be coordinated to the highly electronegative oxygen atoms that are adjacent to the Alsubstituted T-12 site. There are three possibilities for bonding of Cu+ cations, corresponding to 1-fold, 2-fold, or 3-fold coordination. The results of the geometry optimization show that, in the minimum energy structure, the Cu+ is asymmetrically coordinated to two oxygen atoms, with bond lengths 0.1 and 0.2 Å longer than the experimental CuO gas phase molecular bond length of 1.7 Å. The two small spheres numbered “3” and “1” denote two local minima possible for Cu+, one for 3-fold coordination and one for 1-fold coordination. In none of the structures is the Cu+ symmetrically coordinated to oxygens, a result that is not surprising, since the zeolite does not possess local symmetry around a single T-site. The relative energies of the three structures are shown in Figure 1. The minimum energy location of the Cu+ species in the zeolite is a result of the subtle interplay of three factors: the favorable covalent bonding interactions between the Cu atom and the O atoms, the favorable ionic bonding interactions between the Cuδ+ atom and the Oδ- atoms, and the unfavorable Coulombic interaction between the Cuδ+ atom and the Alδ+ atom. The 2-fold coordination structure has the lowest energy primarily because the individual Cu-O bonds are stronger in this structure than in the 3-fold coordination structure and because there is only one Cu-O bond in the 1-fold coordination structure. The favorable ionic bonding interactions between the Cuδ+ atom and the Oδ- atoms are slightly different in each structure, depending on the partial charge of each atom. The unfavorable ionic interactions between the Cuδ+ atom and the Alδ+ atom are different in each structure, both because of slightly different partial charges and because of the differences in the geometry of the structures. In the 2-fold coordination site, Cuδ+ is 2.4 Å away from Alδ+, while, in the 3-fold coordination site, Cuδ+ and Alδ+ are separated by only 2.2 Å. The additional separation of 0.2 Å between the Cuδ+ and Alδ+ in the 2-fold site helps decrease its energy and add to its stability. In the 1-fold coordination site, the Cuδ+-Alδ+ separation is

large, but there is only one Cu-O bond. Thus, the 2-fold coordination has the lowest energy for a Cu+ cation interacting with a single Z- site. We also use our calculations for Cu+Z- to determine ∆Urxn(0 K) for the following reaction:

H+Z- + CuCl h Cu+Z- + HCl

(3)

∆Urxn(0 K) ) -15 kcal/mol This process has been used by Spoto et al.23,24 to prepare Cu+Zby the reaction of H+Z- with gas phase CuCl. The value of ∆Urxn(0 K) calculated for reaction 3 is consistent with the experimental observation that the reaction proceeds spontaneously at room temperature. Note that as explained in the theoretical methods section, ∆Urxn(room temperature) ≈ ∆Urxn(0 K) for this reaction. Figure 2 is a representation of the [Cu2+O-]+Z- structure, shown in a slightly different rotation from the structure in Figure 1. In the minimum energy structure for the [Cu2+O-]+Zcluster, the Cu is in a 2-fold coordination with the O atoms that are adjacent to the Al, similar to what was observed for Cu+Z-. The Cu-O bond lengths for the O atoms in this structure are slightly larger than those in Cu+Z-: 2.0 and 2.1 Å versus 1.9 and 2.0 Å, respectively. The Cu-O bond for the extra lattice oxygen (ELO) is 1.7 Å, the same as that for the Cu-O molecule. These results are consistent with the conclusions of the discussion of the Cu-O bonds in the Cu+Z- (Vide supra) and the fact that the ELO would tend to weaken the covalent nature of the Cu-Ozeolite bonds. Our calculations show that the electronic state of the ELO is more similar to that of the O atom in the CuO molecule than an O atom in the zeolite. We can determine the stability of [Cu2+O-]+Z- to loss of an ELO atom from the values of ∆Urxn and ∆G°rxn for the reaction

[Cu2+O-]+Z- h Cu+Z- + O

(4)

° ∆Urxn(0 K) ) +74 kcal/mol; ∆Urxn (500 °C) ) ° (500 °C) ) +47 kcal/mol +76 kcal/mol; ∆Grxn

It is evident that the ELO in [Cu2+O-]+Z- is tightly bound: at T ) 500 °C, POeq ) 2 × 10-14 atm, implying that exceedingly low pressures would be required to release O atoms from [Cu2+O-]+Z-. The strength of the [Cu2+O-]+ attachment to the zeolite lattice is comparable to that of Cu+, shown as follows:

Cu+ + Z- h Cu+Z-

(5)

∆Urxn(0 K) ) -227 kcal/mol [Cu2+O-]+ + Z- h [Cu2+O-]+Z-

(6)

∆Urxn(0 K) ) -224 kcal/mol Reactions 5 and 6 both have large, negative ∆Urxn as might be expected for the Coulombic interactions. Figure 3 shows the minimum energy structure for [Cu2+OH-]+Z-. Here again, the Cu2+ cation is coordinated to two of the lattice O atoms. The Cu-O bond lengths are 2.0 and 2.1 Å. The calculated O-H bond length, 0.95 Å, is within about 2% of the experimentally measured bond length of the •OH radical. The stability of [Cu2+OH-]+Z- is given by

LSDFT Study of Copper Ion-Exchanged ZSM-5

J. Phys. Chem., Vol. 100, No. 10, 1996 4177

TABLE 2: Mulliken Populations for Atoms in Different ZSM-5 Clusters species Cu+Z- (Figure 1)

[Cu2+O-]+Z- (Figure 2)

[Cu2+OH-]+Z- (Figure 3)

Cu2+Z22-(6) Cu2+ in center of ring (Figure 4a)

Cu2+ on left side of ring (Figure 4b)

Cu2+Z22-(5) Cu2+ in center of ring (Figure 5a)

Cu2+ on left side of ring (Figure 5b)

atom

spin up

spin down

total

Cu O (max adjacent to Al) O (min adjacent to Al) Al Si (max) Si (min) Cu O (in [Cu2+O-]+) O (max adjacent to Al) O (min adjacent to Al) Al Si (max) Si (min) Cu O (in [Cu2+OH-]+) H (in [Cu2+OH-]+) O (max adjacent to Al) O (min adjacent to Al) Al Si (max) Si (min)

14.116 4.302 4.255 6.312 6.632 6.577 14.064 4.205 4.294 4.207 6.349 6.594 6.573 14.288 4.458 0.398 4.327 4.241 6.334 6.579 6.559

14.116 4.302 4.255 6.312 6.632 6.577 14.073 4.110 4.286 4.278 6.357 6.593 6.571 13.824 4.051 0.422 4.259 4.267 6.322 6.567 6.559

28.231 8.604 8.510 12.624 13.264 13.154 28.137 8.315 8.579 8.485 12.707 13.187 13.144 28.112 8.509 0.820 8.586 8.508 13.656 13.146 13.119

Cu O (max adjacent to Al) O (min adjacent to Al) Al (left) Al (right) Si (max) Si (min) Cu O (max adjacent to Al) O (min adjacent to Al) Al (left) Al (right) Si (max) Si (min)

14.188 4.278 4.351 6.210 6.190 6.628 6.554 14.148 4.323 4.338 6.255 6.152 6.561 6.536

14.067 4.242 4.015 6.237 6.209 6.631 6.556 13.989 4.283 4.153 6.260 6.185 6.571 6.552

28.255 8.520 8.366 12.255 12.398 13.259 13.111 28.137 8.606 8.491 12.515 12.338 13.132 13.088

Cu O (max adjacent to Al) O (min adjacent to Al) Al (left) Al (right) Si (max) Si (min) Cu O (max adjacent to Al) O (min adjacent to Al) Al (left) Al (right) Si (max) Si (min)

14.225 4.307 4.299 6.146 6.131 6.578 6.539 14.073 4.361 4.323 6.218 6.091 6.544 6.501

14.026 4.285 4.215 6.174 6.145 6.580 6.541 14.106 4.368 4.185 6.224 6.107 6.566 6.495

28.251 8.592 8.497 12.320 12.276 13.158 13.080 28.179 8.729 8.508 12.442 12.198 13.110 12.996

∆Urxn(0 K) for the following reactions:

[Cu2+OH-]+Z- h H+Z- + CuO

(7)

∆Urxn(0 K) ) +116 kcal/mol [Cu2+OH-]+Z- h H+Z- + CuOads

(8)

∆Urxn(0 K) ) +111 kcal/mol For reaction 8, we estimate the physisorptive van der Waals interactions of CuOads with the rest of the cluster to be 5 kcal/ mol. From the value of ∆Urxn(0 K), it is evident that [Cu2+OH-]+Z- is quite stable. We also investigate the properties of Cu2+ coordinated to two Al-substituted T-sites. For these calculations, we use two ring clusters, each with two Al atoms substituted into T-12 sites. One of the clusters is a 6-T ring structure, and the other is a 5-T ring structure. Both of the ring structures occur at the channel intersections. We designate the Cu2+ in the 6-T ring structure as Cu2+Z2-(6) and that in the 5-T ring structure as 2

Cu2+Z2-(5) . In each of these clusters, all but the terminating 2 atoms and the atoms that are adjacent to the terminating atoms with are relaxed. Parts a and b of Figure 4 show Cu2+Z2-(6) 2 the Cu2+ in two different locations. In Figure 4a, the Cu2+ is in the center of the ring, coordinated to four O atoms, which are all adjacent to Al-substituted T-sites, and in Figure 4b, the Cu2+ is at the left side of the cluster, coordinated to two O atoms, associated with a single Al-substituted T-site. Comparing the total energies of the two clusters, E4b - E4a ) -18 kcal/ mol. In other words, the structure in Figure 4b is energetically preferred to the structure in Figure 4a by 18 kcal/mol. This is especially surprising, since the single negative charge associated with each Al-substituted T-site is fairly localized, and thus, in the structure in Figure 4b, there will be unfavorable charge separation. In fact, the calculated partial charges are +0.24 on the left side and -0.24 on the right side of the ring. Looking at Figure 4a, we can see why placement of the Cu2+ in the center of the ring is energetically unfavorable. The Cu-O distances are between 2.2 and 3.2 Å, 0.1-1.1 Å longer than the longest Cu-O bond length in the Cu+Z- structure. Because the Cu-O distances are very large, strong covalent or ionic

4178 J. Phys. Chem., Vol. 100, No. 10, 1996

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SCHEME 1

[Cu2+OH–]+Z– [Cu2+OH–]+Z– + •OH 2[Cu2+OH–]+Z–

∆Urxn (0 K), kcal/mol

∆U°rxn (500 °C), kcal/mol

∆G°rxn (500 °C), kcal/mol

Cu+Z– + •OH

+51

+55

+15

(9)

[Cu2+O–]+Z– + H2O

+8

+9

+3

(10)

+59

+64

+18

(11)

Cu+Z– + [Cu2+O–]+Z– + H2O

SCHEME 2 ∆Urxn (0 K), kcal/mol

∆U°rxn (500 °C), kcal/mol

∆G°rxn (500 °C), kcal/mol

[Cu2+OH–]+Z– + H+Z–

Cu2+Z22–(6) + H2O

+22

+27

–17

(12)

[Cu2+OH–]+Z– + H+Z–

Cu2+Z22–(5) + H2O

+2

+7

–37

(13)

bonds cannot be formed. Thus, Cu2+Z2-(6) with the Cu2+ in 2 the center of the six-membered ring is unstable. By contrast, Cu2+Z2-(5) with Cu2+ located in the center of 2 the five-membered ring is thermodynamically stable. The reason for the stability of this structure can be deduced from Figure 5a. Here, the Cu-O bonds are between only 1.9 and 2.6 Å, the longest bond in this structure being 0.6 Å shorter (center). In than the longest Cu-O distance in Cu2+Z2-(6) 2 addition, the Cu2+ cation is only 2.1 Å from the O atom that is not adjacent to an Al site and can presumably also interact favorably with that O atom. The counterpart of the minimum energy 6-T ring structure is the higher energy 5-T ring structure shown in Figure 5b. Because of the charge separation across the cluster, the structure in Figure 5a is 70 kcal/mol lower in energy than that in Figure 5b. In ZSM-5, there are a large number of 5-T site rings and 6-T site rings, both of which can accommodate Cu2+ compensating two Al-substituted T-sites in the rings. These structures may account for the copper that does not participate in autoreduction. Our calculation shows that the relative energy of interaction between the Cu2+ cation and the zeolite rings, ECu2+Z22-(6)(left) ECu2+Z22-(5)(center) ) +20 kcal/mol. In other words, the lowest

structure is favored over the lowest energy energy Cu2+Z2-(5) 2 Cu2+Z2-(6) structure by 20 kcal/mol. Nevertheless, because of 2 the large spatial separation between different rings in the zeolite, the kinetic barriers are most likely too large for the Cu2+ to move between rings. We can better analyze the detailed electronic structure of the clusters by looking at the Mulliken population of each atom in each cluster. The electron density distribution of any cluster is an unique function of the position and charges of the atoms in the cluster, but any division of this density distribution between atoms contains an element of arbitrariness. Mulliken populations split the electron density distribution by dividing the elements of the overlap matrix equally between the two atoms that correspond to the two Gaussians which make up the elements of the overlap matrix.52 Representative Mulliken populations for each spin direction and for the total electronic occupancies are shown in Table 2. The O atoms that are listed are those that are adjacent to the Al sites and have the maximum or minimum total electronic occupancy. The Si atoms that are listed are those that are not adjacent to the terminating atoms and that have the maximum or minimum total electronic occupancy. The net spin on each cluster is predetermined for each LSDFT calculation by setting the occupancy number of each orbital, given the fixed total number of electrons equal to the sum of all the nuclear charges. Thus, in our calculation, the Cu+Zcluster has a net spin 0, the [Cu2+O-]+Z- cluster has a net spin 0, and the [Cu2+OH-]+Z- cluster has a net spin 1/2. To evaluate

the accuracy of these spin settings compared to the minimum energy spin settings in nature, we can either perform additional, expensive calculations on each cluster with the spin changed by integer increments, and then choose the cluster with the lowest energy, or we can look at the net localized spin (spin unpairing) of the copper species in each cluster. If the local spin around the copper species is close to the net spin of the cluster, we accept the original choice of net spin as consistent. The individual spin populations for the net spin 0 Cu+Zcluster show that all electrons are paired, as expected. By contrast, the individual spin populations for the net spin 1/2 [Cu2+OH-]+Z- species are clearly unequal on each atom. The Cu atom has a spin unpairing of 0.46 and the O atom in [Cu2+OH-]+ has a spin unpairing of 0.42, resulting in a net spin unpairing of 0.85 with the inclusion of the spin unpairing of the H atom. Thus, the net spin of the cluster is localized around the Cu2+ cation, and our setting the net spin of the entire cluster to 1/2 is justified. For [Cu2+O-]+Z-, the Cu atom has a spin unpairing of 0.01 and the O atom in [Cu2+O-]+ has a spin unpairing of 0.09, resulting in a net spin unpairing of 0.10. Slight spin fluctuations about integer or half-integer values are normal in LSDFT calculations and indeed are one of the reasons why LSD (takes into account spin) is better able to describe complicated bonding structures than LDA (assumes all electrons perfectly paired).26 Thus, on the basis of Mulliken population analysis, we conclude that [Cu2+O-]+Z- has a net spin 0 and would be EPR slient as hypothesized by Larsen et al.25 Note that, in these three clusters and in the next four listed in Table 2, most of the spin fluctuation occurs on the Cu and O atoms, and the spin fluctuation on the Al and Si atoms is almost negligible. A measure of the partial charges on each atom can be determined by subtracting the Mulliken population from the nuclear charge. We are now in a position to determine ∆U°rxn and ∆G°rxn for the autoreduction process proposed by Larsen et al.25 The results are shown in Scheme 1. On the basis of ∆G°rxn(500 °C), the calculated equilibrium partial pressure of H2O for the net reaction is ∼1 × 10-5 atm. At 500 °C, when PHeq2O < 10-5 atm, reaction 11 will proceed in the forward direction. At 500 °C or cooler, water vapor will readily convert Cu+Z- and [Cu2+O-]+Z- back to [Cu2+OH-]+Z-. Both observations are consistent with the EPR observations reported by Larsen et al. The thermodynamic results show that the second step is more facile than the first. It is conceivable that the portion of [Cu2+OH-]+Z- in asexchanged CuZSM-5 that does not participate in the autoreduction process is converted to Cu2+ cations associated with Al-substituted T-sites located close to each other. This might occur via processes such as reactions 12 and 13 (Scheme 2), since not all of the tAl-O--Sit sites in Cu-exchanged

LSDFT Study of Copper Ion-Exchanged ZSM-5 ZSM-5 are charge balanced by Cu2+OH- and many sites are charge balanced by H+.17,25 The thermodynamic results presented above are for the minimum energy cluster of each ring structure, Cu2+Z2-(6) 2 and (center). Since both Cu2+Z2-(6) (left) and Cu2+Z2-(5) 2 2 2+ in both structures would be are paramagnetic, Cu Cu2+Z2-(5) 2 EPR detectable. The values of ∆G°rxn(500 °C) are both large and negative which means that reactions 12 and 13 will occur spontaneously at 500 °C. The energetics of the above reactions when the cations are hydrated would presumably be much different and may not be spontaneous. 4. Conclusions We have used LSDFT to determine the electronic and structural properties of various Cu species in CuZSM-5 and to calculate the thermodynamics for the following reaction, proposed to explain the autoreduction of Cu in CuZSM-5:

2[Cu2+OH-]+Z- h Cu+Z- + [Cu2+O-]+Z- + H2O The results of our calculations show that each of the species in the above reaction is stable and that the proposed autoreduction process is plausible. The Cu+ and Cu2+ cations are generally asymmetrically coordinated to two O atoms in the zeolite, and the Cu-O bond lengths are approximately 10-20% longer than the bond length of the CuO molecule. ∆G°rxn at 500 °C ) +18 kcal/mol. The corresponding equilibrium partial pressure of H2O is 1 × 10-5 atm, which means that the process is quite likely to occur at the conditions normally used to pretreat asexchanged CuZSM-5. We have also studied clusters with two Al-substituted T-sites, in order to evaluate the energetics and geometry of copper species that do not participate in autoreduction. For a 6-T site ring structure, we have found that Cu2+ is more stable when it is coordinated to O atoms adjacent to one Al atom, than when it is coordinated to O atoms adjacent to two Al atoms. The opposite situation is encountered for a 5-T site ring structure. We have also found that the change in Gibbs free energy is favorable for reactions in which Cu2+Z22 is formed (eqs 12 and 13). Acknowledgment. The authors would like to thank Dr. Tim Robinson for his help with visualization techniques. This work was supported by the Office of Industrial Technology, Advanced Industrial Concepts Division of the U.S. Department of Energy under Contract DE-AC03-76SF00098, and the San Diego Supercomputer Center. B.L.T. acknowledges support from a National Science Foundation Graduate Fellowship award, and A.K.C. acknowledges support from a National Science Foundation National Young Investigator Award. References and Notes (1) Iwamoto, M.; Yoko, S.; Sakai, K.; Kagawa, S. J. Chem. Soc., Faraday Trans. 1981, 77, 1629. (2) Iwamoto, M.; Furukawa, H.; Kagawa, S. In New DeVelopments in Zeolite Science and Technology; Murukama, Y., Ichijima, A., Ward, J. W., Eds.; Elsevier: Amsterdam, 1986; p 943. (3) Iwamoto, M.; Hamada, H. Catal. Today 1991, 10, 57. (4) Inui, T.; Kojo, S.; Shibata, M.; Yoshida; Iwamoto, M. Stud. Surf. Sci. Catal. 1991, 69, 335. (5) Iwamoto, M.; Yahiro, H.; Tanada, K.; Mozino, Y.; Mine, Y.; Kagawa, S. J. Phys. Chem. 1991, 95, 3727. (6) Teraoka, Y.; Ogawa, H.; Furukawa; Kagawa, S. Catal. Lett. 1992, 12, 361. (7) Iwamoto, M.; Yahiro, H.; Mizuno, N.; Zhang, W.; Mine, Y.; Furukawa, H.; Kagawa, S. J. Phys. Chem. 1992, 96, 9360. (8) Zhang, Y.; Flytzani-Stephanopoulos, M. In EnVironmental Catalysis; Armor, J. N., Ed.; ACS Symposium Series 552; American Chemical Society: Washington, DC, 1994; p 7.

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