J. Phys. Chem. 1995,99, 1505- 1515
1505
Electronic Structure Calculations of Ammonia Adsorption in H-ZSM-5 Zeolites Agathagelos Kyrlidis, Stephen J. Cook? Amp K. Chakraborty,* Alexis T. Bell, and Doros N. Theodorou Center for Advanced Materials, Lawrence Berkeley Laboratory, and Department of Chemical Engineering, University of Califomia, Berkeley, Califomia 94720 Received: July 13, 1994; In Final Form: October 17, 1994@
The structural and electronic properties of acid sites in zeolites are important in determining their catalytic behavior. Kohn-Sham density functional theory calculations are used to probe the local environment of the acid site in realistic zeolite clusters and to study its interaction with ammonia. The long-range electrostatic effects on the adsorption are incorporated self-consistently in the electronic structure calculations. We examine their effect on the acidity of the cluster and on both the structure and the energetics of adsorption. Systematic structural relaxations of the aluminum-substituted framework show that there are significant structural rearrangements from the entirely siliceous cluster, in the vicinity of the substitution site. In the case of ammonia adsorption, the energetics of adsorption are sensitive to the structural arrangement of the ammonia. Configurations where the adsorbed molecule interacts with three lattice bridging oxygen molecules are favored. The theoretical predictions are compared to recent solid state NMR and microcalorimetry experiments.
1. Introduction ZSMJ is a medium-pore zeolite which exhibits high Bransted acidity and is used as a catalyst with a wide range of applications, including the cracking of petroleum, the isomerization of xylenes, and the conversion of methanol to gasoline.'*2 The framework of ZSM-5 consists of tetrahedrally coordinated silicon atoms bound to one another by oxygen atoms. Framework substitution of a trivalent aluminum atom for a tetravalent silicon atom necessitates the introduction of a charge-compensating cation. When the charge-compensating ion is a proton, the solid becomes a solid acid referred to as H-ZSM-5. The protons in H-ZSMJ are associated with bridging oxygen atoms in Si-0-AI triads. The strength of the Br0nsted acidity is strongly dependent on the Si-0-AI bond angle. This angle is different for each of the 48 symmetrically different Si0-A1 triads possible in Z S M J and is influenced further by local structural rearrangements that occur when AI is substituted for Si. Most of what is known about the acidity of H-ZSM-5, and other zeolties, derives from experimental studies involving the adsorption and desorption of ammonia and other bases3 Temperature-programmed desorption (TPD)4-8and microcalor i m e t r ~ ~ 3 have ~ 3 ' ~ been used to characterize the energetics of base adsorption. IR4,8,11and NMR'1,'2spectroscopies provide information about the structural rearrangements in the zeolite accompanying the interactions of acid centers with the base. Since all of the experimental techniques integrate over all acid centers, the effects of local structure on acidity cannot be discemed. The effects of local structure on the properties of Bronsted acid centers in H-ZSM-5 and other zeolites can be explored through quantum mechanical calculations. Sauert3has recently reviewed the subject. Most of the studies done to date have been based on Hartree-Fock theory and have not included electron correlation effects. More recently, some studies have included correlations at the MP2 level, but most are restricted by small basis sets, small cluster sizes, and restrictive geometrical optimization methods.I4,l5 Brand et al. have recently started a systematic HF study incorporating the effects of cluster
(w
'
Current address: Air Products & Chemicals, Inc., Allentown, PA. @Abstractpublished in Advance ACS Abstracts, December 1, 1994.
0022-365419512099- 1505$09.00/0
size and basis sets on the properties of the acid site.l5%l6These issues are important in determining the local structure near the acid site and have been addressed recently by Teunissen et al.I7 Previous attempts to include the long-range electrostatic effects of the zeolite have been limited to embedding the quantum mechanical cluster in point ion clusters using either homolytic or heterolytic cuts, which have been shown to create large uncertainties in the predicted properties.I8 Allavena et al. developed a methodology for improving the embedding procedure, which still involved using point charges for the atoms in the quantum-mechanical c l u ~ t e r . ' ~This - ~ ~methodology was further improved by Cook et al., who explicitly incorporated the Madelung field in the Hamiltonian of the cluster.21 Previous quantum-mechanical studies of ammonia adsorption have also been restricted by the problems encountered in studies of the acid site. Brand et al.I5 studied the interaction of ammonia with the acid site in H-ZSMJ using clusters of increasing size but were restricted by the lack of geometry relaxation, the size of the basis set, and the neglect of correlation effects. Teunissen et aLZ2used extended basis sets, and included correlations at the MP2 level in their study of ammonia adsorption, but used monomeric or dimeric clusters that cannot capture the effects of framework relaxation on the energetics of adsorption. Kassab et aLZ3studied the energetics of proton transfer to ammonia in faujasites and found conflicting results with an earlier study, which included the effects of embedding.24 In this paper, we have improved the embedding technique of Cook et aLZ1leading to a more robust method. Using extended basis sets and our improved embedding methodology, we have performed a series of electronic structure calculations that characterize the Bronsted acid site in H-ZSM-5 and its interaction with ammonia. In section 2 the theoretical foundation of the method that we use and the refined embedding technique are discussed. The predictions for the electronic properties and the geometrical structure of the Bronsted acid site are presented in section 3.1, and the effects of the Madelung field are shown. Finally, results are presented for the adsorption of ammonia in H-ZSMJ in section 3.2. We predict that proton transfer is one of the steps involved in the adsorption of ammonia and find that our energetic and structural predictions agree relatively well with recent experimental results. 0 1995 American Chemical Society
Kyrlidis et al.
1506 J. Phys. Chem., Vol. 99, No. 5, 1995
2. Theoretical Principles. Application to H-ZSM-5 2.1. Density Functional Theory. Our calculations are carried out within the framework of Kohn-Sham density functional theory. The basic principles are reviewed before the specific details of our calculations are presented. Kohn-Sham density functional theory is based on the unique functional dependence of the ground state Hamiltonian on the electron density, e(r), of the system. This was first proved by Hohenberg and K ~ h n and , ~ the ~ proof is often referred to as the first HK theorem. The theorem states that the ground state electron density determines the Hamiltonian and hence all electronic properties of the system. The second HohenbergKohn theorem defines the energy variational principle, which requires that the ground state energy is a minimum of the energy functional and thereby that the correct ground state electron density minimizes the total energy. The total energy is
where Tis the kinetic energy of the electrons, V,, is the energy due to electron-electron interactions, and u(r) represents a potential interacting with the electrons. For molecular systems, u(r) includes electrostatic interactions with the nuclei and any extemal potential acting on the system. Given exact expressions for T and V,,, the ground state may be determined by direct minimization of the functional of eq 1.26 However, explicit expressions do not exist for inhomogeneous electron distributions that characterize molecules and solids, and thus, approximations are introduced. The Thomas-Fermi theory is an approximation to the functional of eq 1, which unfortunately is not accurate enough to predict molecular binding.26 Kohn and Sham (KS)27developed an ingenious method that trades some of the simplicity of a Thomas-Femi type theory for accuracy. However, the KS method is still tractable because it considers a noninteracting reference system for which the kinetic energy is computed exactly. The electron-electron interactions are computed using the classical mean-field approximation. All corrections, Le., nonclassical (correlation) effects in V,, and kinetic energy adjustments for interacting electrons, are incorporated in an additional term, known as the exchange-correlation energy. The electron density e(r) is found from N
i= 1
vi
where are the wave functions obtained by self-consistent solution of the N one-electron Kohn-Sham equations
(3) where the effective one body potential ueff is defined as
with unucthe nuclear electrostatic potential and uxcthe exchangecorrelation potential. A second level of approximation involves the nature of the exchange-correlation and nuclear potentials. In this work, uxc is computed by employing the local density approximation (LDA) in conjunction with the Perdew and Zunger28 parametrization. To reduce the size of the calculations, the Bachelet, Hamann, and Schliiter (BHS) ab initio pseudopotentials are used for all atoms except for some hydrogen atoms, and only valence electrons are c ~ n s i d e r e d . ~ ~
The wave functions are written as linear combinations of Gaussian-type orbitals (5)
where gj are uncontracted minimal basis sets used for variational flexibility. Polarization basis functions are included for all atoms, except for some hydrogen atoms.30 The variational principle is used to determine the coefficients of the expansion, which in turn determine the wave function and all ground-state properties of the system. For increased computational efficiency, the electron density and the exchange-correlation potential are also expanded in terms of Gaussian basis functions, whose coefficients are fit according to procedures described by Dunlap, Connolly, and Sabin3] and Cook et aL2’ Geometrical relaxations are performed using Hellman-Feynman forces and the Davidon optimization algorithm.32 The accuracy of the Hellman-Feynman forces is greatest when combined with the BHS pseudo potential^.^^ This is why some of the hydrogen nuclei have been modeled using pseudopotentials, even though this is a slightly more expensive calculation. The solution of the electronic structure problem was performed using a direct self-consistent-field method, which increases the efficiency of memory and disk management during the calculations and also vectorizes The model for the H-ZSM-5 cluster used in this work has been described in ref.21 We use a pentameric cluster centered on the aluminum-substituted T12 site, with the formula A10H03(SiO3H3)4. The T12 site was selected because it is located at the intersection of the straight and the sinusoidal channels which are characteristic of ZSM-5, thus being a favorable site for aluminum substitution and adsorption of small molecules.35The terminating oxygen atoms are placed at their positions in the ZSM-5 unit cell and are anchored there. The cluster terminating hydrogen atoms are placed at a distance of approximately 1 %, from the oxygen atoms along the bond direction connecting the oxygens to the neighboring silicon atoms, which are the first atoms not explicitly included in the quantum-mechanical calculation. The terminating hydrogen atoms are termed “boundary” hydrogen atoms and are treated minimally in terms of basis function description; also they are the only nuclei not modeled via pseudopotentials. This setup is both manageable in terms of the required computational resources and realistic because it captures the local geometry surrounding the acid site and thereby captures any steric effects that would otherwise be excluded from the studies of adsorption. Another advantage of this cluster is that it is large enough that the boundary hydrogens are sufficiently removed from the adsorption site and should not interfere with studies of adsorption. Previous studies which have used smaller clusters to model the zeolite-base interactions cannot capture these effect^.^*-^^ 2.2. Embedding Method. Investigating the local properties of a site by modeling the entire zeolite unit cell using quantummechanical methods is unfortunately limited by the processing abilities of today’s computers. However, such studies are not necessarily more insightful, given that the nature of interactions in studies of adsorption is local, and the effect of atoms located far away from the chemically active site is expected to be purely electrostatic. Such atoms need not be included explicitly in the quantum-mechanical study but nevertheless should be allowed to interact with the atoms in the cluster. We include the effect of such long-range electrostatic interactions on the cluster geometry and the adsorption energetics in our study. Atoms that are not included in the quantum-mechanical cluster are included as point charges positioned on the crystal-
Ammonia Adsorption in H-ZSM-5 Zeolites
J. Phys. Chem., Vol. 99, No. 5, 1995 1507
h
2
0 Isolated Cluster
VI
E
n 0.5 0 3 k
Figure 1. Geometry of pentameric siliceous cluster used to model the local properties of the T12 site in zeolite ZSM-5. The terminating hydrogen atoms are not shown.
lographic lattice sites (geometry from Olson et ~ 1 . of~ the ~ ) purely siliceous ZSM-5 crystal. This is equivalent to a very large Si/Al ratio in the crystal. The electrostatic potential at each point in space is generated in the following way: (1) The infinite purely siliceous crystal potential is computed using the method of Ewald sums.37 This requires knowledge of the partial charges of the silicon and oxygen atoms in the crystal and the specification of the geometry in the unit cell. (2) The contributions due to atoms treated quantum mechanically is substracted from the long-range potential. (3) The boundary hydrogen contributions are compensated for by appropriately adjusting the charges of atoms immediately surrounding the quantummechanical cluster. This procedure was originally suggested by Allavena et al.19320and implemented by Cook et ~ 1 In. ~ this paper the procedure is further refined, and some of its limitations are exposed and circumvented. 2.2.1. Lattice Charges. The unterminated siliceous cluster is shown in Figure 1. The silicon atoms that are replaced with the hydrogen atoms for the termination of the cluster and the noncluster oxygen atoms that are directly bonded to them constitute the frontier atoms whose charges are adjusted to compensate for the presence of the boundary hydrogen atoms. In the work of Cook et al. only the 12 frontier silicon charges were adjusted, by a least-squares fit of the field in a 4 8, cube centered on the central T12 site.21 This resulted in a field which created negatively charged boundary hydrogen atoms when the field was included in the quantum-mechanical calculation. Figure 2 compares the electron density along a terminating 0-H bond, in the isolated cluster, and in an embedded cluster using the fitting procedure of Cook et al. An effective draining of the electron density in the embedded cluster is observed, because its immediate vicinity is occupied by the positively charged silicon frontier atoms. In order to avoid this artificial effect and generate an internally consistent electrostatic potential, the fitting region is expanded to include the 32 oxygen atoms immediately bonded to the 12 frontier silicon atoms.38 The silicon atoms are assigned zeropoint charges, and the individual oxygen charges are fit in a domain comprised of spheres with radius 2 8, surrounding a are fit subset of the nuclei in the cluster. The charges {q:}& to minimize the objective function
where qsi and qo are the bulk point charges of the silicon and oxygen atoms, respectively. Using the Mulliken charges computed for the boundary hydrogens in the siliceous cluster
0.0 0.0
0.5
1.o
1.5
2.0
Distance along terminating 0-H bond Figure 2. Electron density variation along a terminating 0-H bond in the cluster. Comparison between the isolated cluster and the embedded cluster using the Madelung field of Cook et d2'and the new field presented in this work. Distances are in A.
TABLE 1: Partial Charges of Boundary Hydrogens with No Madelung Field and with Madelung Field Generated with Adjusted Charges of Frontier Silicon and Frontier Silicon and Oxygen Atoms charges, le1
charges, le1 Madelung field with
Madelung field with
H field
no
frontier Si
frontier Si, 0
0.45 0.42 3 0.45 4 0.47 5 0.42 6 0.46
0.02 -0.11 0.01 0.10 -0.22 0.14
0.51 0.42 0.52
1
~2
0.53
0.41 0.52
H
7 8 9 10 11 12
no field
frontier Si
0.47 0.45 0.44 0.46
-0.05 -0.05
0.44
-0.05
0.43
0.10 0.17 0.00
frontier Si, 0
0.49 0.48 0.45 0.54 0.45 0.49
in the absence of the electrostatic potential, and spheres centered on the inner five atoms, leads to an average fit quality of 1 x and a maximum error of 3 x The partial charges for the silicon and oxygen atoms in the infinite zeolite lattice are determined from a Mulliken population analysis of the electronic structure computed in the presence of the Madelung field. The total field is constructed, and then a self-consistent calculation is performed to test the internal consistency of the field. The frontier charges are fit to the boundary hydrogen charges in the presence of the Madelung field and the new charges for the silicon and oxygen atoms. Only one repetition of this cyclical procedure is sufficient to obtain converged charges for the frontier atoms consistent with the boundary hydrogen charges in the presence of the field. The partial charges of the boundary hydrogen atoms in the isolated cluster and the embedded cluster using the old and the new fitting procedure are compared in Table 1. The consistency of the boundary hydrogen charges accomplished with the new fitting method is unattainable with the fitting procedure of Cook et al., because an attempt to generate an internally consistent field leads to an additional draining of electron density toward the boundaries of the cluster. The net converged charge of the central T12 silicon atom sets the charges of the bulk silicon and oxygen atoms to qsi = 1.42 and qo = -0.71. These results differ from the previously reported values of qsi = 2.18 and qo = -1.09.21This is due to the inclusion of polarization functions in the basis set and the implementation of a different fitting procedure for the electrostatic potential. These results are compared to other published values in Table 2. A decrease in the ionic character of the zeolite upon inclusion of polarization functions in the basis set
1508 J. Phys. Chem., Vol. 99, No. 5, 1995
Kyrlidis et al.
TABLE 2: Partial Charges of Silicon, Oxygen, and Hydrogen Charges in Quantum Mechanical Calculations of Zeolites, as a Function of the Basis Set Used basis set"
Si
0
H
1.3s3p 2.3s3pld 3.6-31G 4.6-31G" 5.6-31G
2.18 1.42 2.29 1.65 1.48
- 1.09
0.45 0.45 0.45 0.47
-0.7 1 -0.99 -0.88 -0.74
a (1,2) Bulk silicon and oxygen charges, based on the charge of the central T12 site computed from a KS-DFT calculation. (3,4) Average partial charges of atoms included in a Hartree-Fock calculation (from ref 39). (5) Partial charges obtained from a periodic Hartree-Fock calculation for ZSM-5 (from ref 40).
Ha3 acidic proton
Figure 3. Geometry of the relaxed aluminum-substituted H-ZSM-5 cluster.
was also reported by Kassab et ~ 1 as. a ~trend ~ in their calculations for siliceous clusters. Interestingly, the new charges are in good agreement with the periodic HF calculations of White and Hess, who reported values of qsi = 1.48 and qo = -0.74:O and the partial charges reported for quartz.18 The differences observed are most likely due to the differences between the methods used in the calculation of the electronic structure. Therefore, the siliceous cluster is more covalent compared to the predictions of Cook et al.?' and the effects of the Madelung field are expected to be small.
3. Results
3.1. The Acid Site. Structural and Electronic Properties. 3.1.1. Structural Results. The structure of the aluminumsubstituted cluster is relaxed in the absence of the Madelung field using Hellman-Feynman forces rather than gradients. The charge-compensating proton is placed initially on the Si-0Al plane in the direction of the pore intersection. Only the inner AlH(OSi)4 atoms participate in this relaxation, while the other atoms are anchored to their ZSM-5 positions. This allows the atoms in the vicinity of the acid site to relax, while the cluster retains its position in the zeolite lattice, which is a requirement of the embedding procedure used in this work. The added variational flexibility in the determination of the ground state by the incorporation of polarization basis functions in the basis set leads to results that are somewhat different from the results reported by Cook et aL21 The geometrical properties of the relaxed cluster, which is shown in Figure 3, are compared to the older results and to the siliceous cluster properties in Table 3. The proton-bridging oxygen distance is found to be 1.04 8, and is not influenced significantly by the choice of basis set. Brand et al. have reported that this distance is 0.95 and
TABLE 3: Results of Geometric Relaxation quantity
r(024-H) r(T12-024) r(T12-H) LT12-024-T 12 LT12-024-H
Si cluster
1.59 143.4
LOOP
(L(T-0-T))
151.5
A1 clusteP
A1 cluster
1.02 1.78 2.38 131.9 114.1 10 144.4
1.04 1.81 2.33 134.6 106.6 14 132.5
anion
1.72 136.6 134.2
"Correspond to results of Cook et All distances are in angstroms and all angles in degrees. OOP corresponds to the angle between the OH and the Si-0-A1 plane.
also is not very sensitive to the description of the wave function. Semiempirical calculations of a variety of substitution sites by Redondo and Hay also gave similar predictions:' in agreement with previously reported results by S a ~ e r .The ~ ~ aluminumoxygen bond length predicted here is slightly larger than that reported by Cook et al. and is larger than the adjacent siliconoxygen bond length. We find that the silicon-oxygen bond length is 1.71 8, when d-type orbitals are included in the calculation and 1.52 A when they are not. The aluminumproton distance is found to be 2.33 A, slightly smaller than predicted previously but still in good agreement with the value of 2.43 8, measured using NMR spectroscopy by Kenaston et ~ 1 The . proton ~ ~ is found not to reside on the AI-0-Si plane, and the out-of-plane angle is computed to be 14". This result is in qualitative agreement with the NMR data reported by Root et aLM If the proton is removed, and then the zeolite anion is relaxed, the AI-0-Si angle increases, and the aluminum-oxygen bond length is reduced to 1.72 A, while the adjacent silicon-oxygen bond length becomes 1.59 A. These results agree with those of Brand et al., who report aluminum-oxygen bond lengths for the anion between 1.78 and 1.75 8, and adjoining oxygensilicon bond lengths between 1.63 and 1.60 A depending on the size of the cluster they used.15 Our results are closer to the predictions of the larger cluster that Brand et al. used, which indicates that the pentameric cluster used in this work is big enough to give a realistic description of the acid site properties. In the neutral cluster the smaller T-0-T bond angles indicate that the bridging oxygens are screening the electrostatic repulsion between the proton and the aluminum atom. In the anionic cluster this interaction is not present, and the bridging oxygens relax back to a configuration with larger T-0-T bond angles. The main conclusion from this structural relaxation is that the zeolite framework is relatively flexible and readjusts by significant rearrangements to accommodate the substituted aluminum atom. The flexibility of the zeolite framework has also been observed e~perimentally.~~ Further evidence for the flexibility of the framework is provided by our finding of local minima in the minimization parameter space which includes the coordinates of the first shell of oxygen and silicon atoms surrounding the T12 site and the proton. The local minimum closest to the reported configuration in terms of energy (difference of 21 kJ/mol) is noticeably different in terms of the T-0-T bond angles. This configuration corresponds to a Al024-Si angle of 129" while the remaining A1-0-Si angles are closer to the values of the entirely siliceous cluster. The proton-hydrogen distance for this configuration is once again 1.04 A. We have also examined the effects of the embedding Madelung field on the structure of the cluster. The charges of the frontier oxygen atoms are fit to the boundary hydrogen charges of the isolated aluminum-substituted cluster. The bulk oxygen and silicon charges determined by the self-consistent
Ammonia Adsorption in H-ZSM-5 Zeolites
J. Phys. Chem., Vol. 99, No. 5, 1995 1509
TABLE 4: Effect of Embedding on the Deviations in the Madelung Field Potential from Its Expected Values Due to the Fitting Procedur@ atom first-order perturbation SCF A1
4.8 x 10-5
H
-5.1 x 10-4
O* 0
-6.4 x -3.6 x 3.4 x 1.7 x
0 0
10-5 10-5 10-4 10-4
-0.11 -9.4 x 10-2 -0.11 -0.11 -0.10 -0.10
x 4
1.o
7
.-
- Isolated
v)
Cluster
P 0 Embedded Cluster
0.5
a The atoms listed are the atoms around which the fitting grid is centered. The charges of the boundary hydrogens that were used for the perturbation column are those of the isolated cluster, while the analogous charges for the SCF column are those obtained from the SCF calculation for the embedded cluster. The charges of the frontier oxygens for both cases were fit to the isolated cluster boundary hydrogen charges.
procedure described in the previous section are used to calculate the bulk contributions to the electrostatic potential. It must be noted that changes in the boundary hydrogen partial charges are not significant enough to warrant a second cycle in the intemal consistency iterative process for the Madelung field. Yet, this procedure generates errors in the Madelung potential because the boundary hydrogen charges in the embedded cluster are not the exact charges for which the frontier oxygen atom charges were fit. The differences between the “ideal” and the actual Madelung fields for the isolated and embedded boundary hydrogen charges are shown in Table 4 for the atoms around which the fitting procedure described in the previous section is done. The structure of the cluster remains practically unchanged in the presence of the Madelung field after relaxation. This is an important result which demonstrates that the local environment of the acid site is captured well by the pentameric cluster representation that was used. Also, the Madelung field used in this work appears to be a small perturbation to the overall Hamiltonian judging from the relative values of the total energy of an isolated and an embedded cluster. The difference in the energies of the relaxed cluster of Table 3 without and with the embedding field was 0.1 1 hartree, which is 0.04% of the total energy of the cluster. Since we find that the effect of the Madelung field on structural properties is minimal, it is appropriate to test the accuracy of a first-order perturbation theory for the cluster in the presence of the Madelung Field. The Hamiltonian in the presence of the field is written as
(7) where is the Hamiltonian of the isolated cluster description and uMad(r) is the Madelung field. Treating the effect of the field as a perturbation on the Hamiltonian allows us to write the following expression for the ground-state energy of the embedded cluster in the presence of the Madelung field:
where YOis the wave function of the isolated cluster, and the last term in the equation corresponds to the nuclei-field interaction which is not a part of the electronic problem and is added after the wave function has been determined in the BomOppenheimer (BO) approximation. The perturbation theory estimate of the ground state energy of the embedded cluster is calculated to be -280.076 764 9 hartrees and differs from the SCF result by 0.007%.
0.0 0.0
0.5
1.0
1.5
2.0
Distance from Bridging Oxygen Figure 4. Comparison of the electron density along the bond between the bridging oxygen and the acidic proton as calculated for the isolated and the embedded cluster. Distances are in A. The proton affinity or the energy required to remove the acidic proton from the zeolite cluster, thereby creating an anionic cluster is calculated as
(9) and is a measure of the strength of the acid site. This quantity and its dependence on cluster size have been studied extensively by Brand et al.15316Our calculations indicate that the proton affinity calculated as a difference between the energies of relaxed anionic and neutral clusters is 1432 kJ/mol, calculated without any corrections for basis set superposition error. The effect of embedding the cluster in the Madelung field is to increase the proton affinity to 1654 kJ/mol. Both the perturbation and SCF approaches for the evaluation of the energies of the embedded anion and neutral cluster yield the same result. An increase in the proton affhity indicates that the proton is more strongly bound to the zeolite framework in the presence of the field and is thus less acidic in character, from this perspective. The value resported as most accurate by Brand et al. is 1237 kJ/mol, which is between the limits of the experimentally determined range of 1189- 1331 k . I / m ~ l .Our ~~ prediction compares well with these values. The differences may arise from several factors which have been demonstrated by Brand et al. to have a significant impact on the proton affinity: crystallographic structure used to anchor the terminating atoms in the cluster, basis set used, termination of dangling bonds, and size of cluster.16 The largest difference is probably due to the use of OH units to terminate the cluster instead of H and would explain why our prediction for the proton affinity is larger. 3.1.2. Electronic Structure. In order to further characterize the acid site in the H-ZSM-5 cluster studied in this work, we present results for the electronic structure of the site and the cluster. In Figure 4, the electron density is plotted along the bridging oxygen-acidic proton bond for both the isolated and the embedded cluster. The results are very similar, indicating that the effect of the Madelung field on the electronic density in the vicinity of the acid site is very small, which further justifies the use of frst-order perturbation theory for the energetics of the cluster. As reported by Cook et al., there is significant polarization of the electron density along the O-H bond?I The differences between the embedded and the isolated cluster profiles are much smaller when the new Madelung field is used. The changes in the partial charges of the atoms in the vicinity of the acid site when the Madenlung field is included
Kyrlidis et al.
1510 J. Phys. Chem., Vol. 99, No. 5, 1995 TABLE 5: Partial Charges of Atoms in le1 in the Isolated and Embedded H-ZSM-5 ClusteF atom
isolated
embedded
atom
isolated
embedded
A1 H O* 0
+0.98 10.34 -0.75 -0.79
+0.99 +0.38 -0.76 -0.79
0 0 Si*
-0.71 -0.76 1.40
-0.71 -0.76 1.35
where Q N + ~and QN are the electron densities for the anionic and the neutral H-ZSM-5 cluster. The Fukui function along the 0-H bond is plotted in Figure 5 for the isolated and the embedded clusters. We find that in both cases the function has positive values toward the pore of the zeolite; however, in the presence of the Madelung field the Fukui function is somewhat smaller in the vicinity of the proton. The values of the two
t
0.006
A
-
.rl
c,
isolated cluster
u
$
“Atoms marked by an asterisk are the atoms in the immediate vicinity of the acid site.
in the calculation are shown in Table 5. We notice that most of the changes involve the Si-OH-A1 tetrad of atoms, while the partial charges of oxygen atoms that are farther away from the acid site remain practially unchanged. In the isolated cluster the proton has a partial charge of +0.341el, while in the presence of the embedding field the charge is increased to f0.381el. Using the proton partial charge as a measure of the acidity of the site, we find that the embedding field tends to increase its positive charge, thereby making it more available to electronegative atoms in its vicinity, and consequently increases the acid character of the proton. A similar increase in the charge was observed in Cook et al., but we believe that the effect of the field is not as pronounced as was thought previously. Other electronic properties of the substituted cluster have been recalculated in this work using the extended basis set. The ionization potential, electron affinity, and absolute hardness of the H-ZSM-5 cluster have been computed for the isolated and embedded clusters and are compared in Table 6. We shall focus on two properties of the cluster: the electron affinity and the absolute hardness.47 We find that the embedded anionic cluster is less stable than the isolated anionic cluster, which is not surprising, because the nearest point charges in the embedding cluster are negatively charged oxygen atoms, making the additional electron density unfavorable. In contrast with the calculations of Cook et a1.,2i the ionization potential of both the isolated and embedded clusters was hard to converge. The results for the ionization potential presented in Table 6 have been converged to an integrated square of the difference of charge densities between cycles of low6and are not very accurate. The electron affinity results are fully converged for both cases. Using the available results, we find that the effect of embedding is small and leads to a decrease in the absolute hardness of the cluster. The absolute hardness of the embedded cluster is 5.35 eV, which is comparable to the absolute hardness of the SO;?molecule, which is a soft acid. For reference, the hardest acid is the proton H+, which has an absolute hardness of infinity, and acids with absolute hardness values exceeding 10 eV are considered hard.47 Corma et al. performed an analysis of the acidity in zeolite Y.48 They predict that the proton in an aluminum-substituted cluster is a relatively soft acid. Their quantitative predictions are slightly different from ours, but that is expected because of the structural differences between ZSM-5 and Y, which influence the relative acidity of the acid sites. The Fukui function is another measure of the acidic character.26s49The reactivity toward nucleophilic attack is measured as
8
O.OoB
-
Embedded cluster
0.004
c
0.000
2
1
3
5
4
Distance from Bridging Oxygen Figure 5. Comparison of the Fukui functionf+ along the bond between the bridging oxygen and the acidic proton for the isolated and the embedded cluster. Distances are in A. TABLE 6: Characterization of Electronic Properties of H - Z S M d Cluster (in eV) configuration
electron affinity (A)
ionization potential (0
absolute hardness (7)a
isolated cluster embedded cluster
-1.48 -4.18
10.21 6.52
5.84 5.35
a
The absolute hardness is defined as
= ( I - A)/2.
functions become indistinguishable toward the zeolite pore. The n condensed Fukui functionSo for the proton& = qi+i - qN, where &+, and q: are gross Mulliken charges, is 0.21e for the isolated cluster and 0.27e for the embedded cluster. The increased values of the proton condensed Fukui function indicate that it becomes more vulnerable to nucleophilic attack in the presence of the Madelung field. This result is not inconsistent with the Fukui function prediction, which is merely an indication of the reactivity along a specific direction. The values are close enough to indicate that the changes due to the Madelung field are small. The orbital energies of the Kohn-Sham wave function do not have any specific physical meaning,26unlike the eigenvalues of the Hartree-Fock equations, which are related to the ionization potentials in a Koopman’s sense.5i However, they may be used to demonstrate the effects of embedding. Looking at the orbital energies of a transition state such as the ground state of the N-electron cluster with a LUMO occupancy of 0.5 and a HOMO occupancy of 1.5, with and without the presence of the Madelung field, provides qualitative information about the electronic properties of the cluster.26 Bartolotti et used this transition state to evaluate directly the electronegativity of atoms as the average energy of the LUMO and the HOMO orbitals. We find that in the absence of the embedding field those energies are €HOMO = -0.2149 au and CLUMO = -0.0308 au and in the presence of the Madelung field they become €HOMO = -0.1056 au and ELUMO = +0.0771 au. The LUMO becomes higher in energy in the presence of the field, thereby increasing the gap with the HOMO of an approaching base, showing an increase in hardness. When the changes in the HOMO of the cluster are also taken into account, the small decrease in the absolute hardness of the cluster shown in Table 6 may be explained. The characterization of acidity is a balance of several factors which might indicate conflicting trends,53such as the importance of the electrostatic contributions (dominant in hard acids) and the electron-sharing affinity (dominant in soft acids). Our main conclusion is that the factors contributing to the acid character of the proton are influenced by the presence of the
Ammonia Adsorption in H-ZSM-5 Zeolites
J. Phys. Chem., Vol. 99, No. 5, I995 1511
is computed to be 877 kJ/mol, compared with the measured value of 858 kJ/moLM The energy of adsorption of ammonia in the zeolite is computed as the energy of the desorption reaction
Monodentate
(b) Bidentate
H
(a"e Figure 6. Possible bonding geometries for ammonia in zeolites: (a) monodentate, (b) bidentate, and (c) tridentate configurations.
bulk zeolite framework, incorporated in the Madelung field. Charge transfer, the determining characteristic of the relatively soft acid character of the proton, is enhanced by the presence of the field, because the changes in the electrostatic factors are not big enough to indicate that the site becomes any harder. The studies of the acidity described above are based on the pure zeolite cluster. In the presence of an adsorbate molecule, such as ammonia, the cluster rearranges itself, and the electronic properties of the acid site are also affected. Changes in the acidity caused by the geometrical rearrangements in the presence of an adsorbate are not included in the above study of electronic properties. 3.2. Interaction with Ammonia, The interactions between an ammonia molecule and the acid site in the aluminumsubstituted cluster described in the previous section are studied here. Ammonia is a small molecule which may easily permeate the pores of zeolite ZSM-5 and interact with the acid site and the surrounding atoms in a variety of configurations. Three of the possible coordination geometries of ammonia adsorbed in H-ZSM-5 are shown in Figure 6. When the only interaction is through a single hydrogen bond with the zeolite framework, the configuration is called monodentate. As the number of interactions of the hydrogen atoms in ammonia with the bridging oxygens in the zeolite cluster increases to two or three, the configurations are called bidentate and tridentate. Proton transfer is considered to occur when the acidic proton bonds preferentially to the ammonia molecule and thereby forms an ammonium ion bonded to the zeolite framework through one or more hydrogen bonds. The geometry and energetics of the ammonia molecule are described relatively well by the Kohn-Sham DET framework used in this work for the electronic structure calculations. The N-H bond length predicted is 1.03 A, and the H-N-H bond angle is 105.6". The experimental values are m - ~ = 1.012 A and the L(H-N-H) = 106.67°.s1 For the ammonium ion, the calculated N-H bond length is 1.05 A and the H-N-H bond angle is 109". The gas-phase proton affinity of the ammonia molecule
In the above equation, the species ZeOH -k N H 3 corresponds to ammonia adsorbed in the zeolite, either in the form of a neutral molecule or, after proton transfer, in the form of an ammonium ion. In order to compute the energy of adsorption we have performed geometry optimizations of 38 atom clusters, once again keeping the terminating OH atoms anchored to their lattice positions. There constrained energy minimizations help us understand how the local geometry of the acid site in the zeolite changes during the adsorption process. The goals of our theoretical investigation of ammonia adsorption in H-ZSMS are to probe the nature of the interactions between ammonia and the zeolite and to make links and comparisons to experimental results whenever possible. The issues that we want to address are both structural and energetic. Does proton transfer occur? If so, how is the local geometry of the cluster and the adsorbed ammonium ion affected? What is the predicted energy of adsorption, and how is it affected by proton transfer and the bonding configuration? These issues are discussed in detail in the following sections. 3.2.I . Structural and Electronic Predictions. First, an ammonia molecule is placed with its symmetry axis along the acid proton-oxygen bond and its hydrogen atoms pointing away from the zeolite and is relaxed, keeping the 0-N bond length fixed at 2.5 A. The resulting configuration resembles more a bidentate configuration than a monodentate. Next, the 0-N bond length is reduced to 2 A, and the structure is once again relaxed. Then the constraint of fixed 0-N bond length is removed, and another energy optimization is performed. The final relaxed configuration, shown in Figure 7, corresponds to a bidentate configuration wherein proton transfer has occurred. The structural characteristics of the bonded ammonia molecule and the zeolite cluster are collected in Table 7. The relaxed tridentate bonded configuration is generated in the following way: First, the ammonium ion is constructed conforming to the symmetry of the zeolite and placed toward the sinusoidal channel of ZSMJ. Then the cluster is relaxed with a fixed AI-N distance of 2.75 A. Finally, the constraint is removed, and the cluster is relaxed further to the configuration shown in Figure 8. The structural characteristics of this bonded cluster are also collected in Table 7. Both the minimization procedures are relatively sensitive to the initial configurations and the paths chosen for the relaxation. This was also observed in the relaxations of the bare zeolite cluster and is an indication of the ruggedness of the energy surface of the zeolite. We report here the configurations corresponding to the lowest energies for each of the two bonding alternatives. In both cases proton transfer is observed. This result agrees with the predictions of IR spectroscopy, which allows the direct observation of the hydroxyl groups in acidic ZSM-5 and how they change upon adsorption of ammonia. A typical spectrum of H-ZSM-5 shows peaks in the vicinity of 3600 cm-l depending on the aluminum content and the subsequent strength The peaks disappear upon adsorption of of the 0-H ammonia, while peaks corresponding to the NI&+ ion appear, thereby indicating that proton transfer o c c ~ r s . I~ ~ I
Kyrlidis et al.
1512 J. Phys. Chem., Vol. 99, No. 5, 1995
\
1.41
Figure 8. Relaxed geometry of the ammonium ion bound to the zeolite in the tridentate configuration. Figure 7. Relaxed geometry of the ammonium ion bound to the zeolite in the bidentate configuration. TABLE 7: Structural Properties of the Geometry-Optimized Ammonium Adsorbed in the Bidentate and Tridentate Configurations
.VI
i
I. Framework Structure
quantity r(Al-0 1)
(L(T-0-T))
bidentate 1.74 133.2
1/$\ I
tridentate 1.68 133.2
AI cluster
1.81 132.5
I
n
0
Bidentate Acid site ionic
---
Tridentate ionic
G 0 3 k
0 Q,
i3
11. Adsorption Structure
quantity
bidentate tridentate quantity 3.34 2.88 r(N-03) r(Ol-HI) 1.41 1.68 r(N-HI) r(02-H2) 1.85 1.66 r(N-H2) r(03-H3) 5.16 1.90 r(N-H3) r(N-01) 2.56 2.43 r(N-H4) r(N-02) 2.53 2.54 L(H-N-H) r(AI-N)
bidentate tridentate 4.84 2.81 1.16 1.07 1.11 1.06 1.07 1.08 1.08 1.05 101-121 100-120
There are two main characteristics of both the bidentate and the tridentate bonded configuration: the stretching of the N-H bonds in ammonia that interact with the bridging oxygens, and the distortion of the tetrahedral symmetry of the adsorbed ammonium ion to conform with the zeolite structure. The N-H bond changes are slightly smaller for the tridentate configuration, because the hydrogen atoms are farther away from the bridging oxygens. Both of these theoretical results agree with multinuclear NMR experiments, which probe the structural aspects of ammonia adsorption. The NMR experiments were not performed on zeolite H-ZSM-5, but the general trends are expected to apply to the type of zeolite studied in this work. Specifically, 15N NMR experiments done for adsorption of ammonia in zeolite Y by Earl et al." show peaks corresponding to the chemical shifts characteristic of ammonium ions, which once again confirm that proton transfer occurs. 29Si NMR exhibits shifts characteristic of the particular Si/AI content of the zeolite and also provides a measure of the distortion from tetrahedral symmetry that occurs upon adsorption of bases. 12s5 Our calculations show that the differences in the average T-0-T angles between the adsorbed structures and the bare framework are smaller than lo, but the changes in each bond angle demonstrate that the zeolite readjusts in the presence of the base. Vega and Luz12 studied NH4-rho and H-rho and found a dispersity in the 29Si chemical shifts which may be indicative of distortions in the T-0-T angles and of asymmetric localization of the N&+ ions on each of the AI sites. The predicted localization of the ions was confirmed by the calculated ratio of H:AI, which was equal to 4. IH NMR
0.0 0.0
0.5
1.o
1.5
2.0
Distance from Bridging Oxygen Figure 9. Comparison of the electron density along the bridging oxygen-proton bond in the isolated cluster and after proton transfer to ammonia occurs for the ?dentate and the tridentate configurations. Distances are measured in A. indicated that the ammonium ions are fairly localized about the acid site and do not move translationally, because anisotropic interactions are present.12 The ions are also distorted from their tetrahedral symmetry because of their binding to the zeolite lattice framework and rotate rapidly even at low temperatures, demonstrating that the barriers for local rearrangements of the ions are relatively low. The distortions from the tetrahedral symmetry predicted by our calculations are indeed significant. The H-N-H angles in the adsorbed ammonium ion show deviations of the order of 10' from the ideal tetrahedral symmetry angle of 109.47' of the gas-phase ammonium ion. Similar distortion from tetrahedral symmetry are predicted from 2H NMR in deuterium-substituted samplesI2 and also by neutron scattering experiments by Udovic et al.56 The electron density along the 0-H1 bond, Le., the bond between the bridging oxygen and the acid proton transferred to the ammonia molecule, is shown in Figure 9 for the bidentate and the tridentate configurations, in order to probe the changes in the electronic structure which occur upon proton transfer and ammonia adsorption. We notice that as the proton is moved further away from the bridging oxygen, there is a more diffuse electron density distribution. In the bidentate configuration, where the 0-H-N angle is 166O, this plot shows that the proton has a stronger bond with the nitrogen atom than with the oxygen atom. Removing the proton creates an excess of electron density in the vicinity of the oxygen atom as expected. The electron density distributions along the N-HI bond in the ammonium
Ammonia Adsorption in H-ZSM-5 Zeolites
J. Phys. Chem., Vol. 99, No. 5, 1995 1513
t n X 0.6
- Bidentate - - - Tridentate
dlA
8
n 0.4 4 L
0 Q,
i3
0.2
0.0
1.0
0.5
1.5
2.0
Distance from Nitrogen Figure 10. Comparison of the electron density profile along the nitrogen-acidic proton bond in the bideatate and the tridentate configurations. Distances are measured in A.
TABLE 8: Energy of Adsorption (kJ/mol) for Ammonia Adsorbed in the H-ZSMd ClusteP bidentate isolated cluster SCF embedded cluster first-order perturb. SCF
tridentate
ionic
neutral
ionic
neutral
126.5
116.5
150.0
138.4
162.0 224.0
149.5 205.6
151.9
104.0
Comparison of results for isolated and embedded, neutral and ionic, bidentate and tridentate configurations.
ion are compared in Figure 10 for the bidentate and the tridentate configurations. We note that in the bidentate configuration, where the proton is closer to the bridging oxygen, the electron density in the vicinity of the proton is lower than in the tridentate configuration where proton transfer is more complete. In both cases there is excess electron density in the ammonium ion because of the hydrogen bonds with the bridging oxygens which reduce the electrostatic nature of the bonding of the ammonium to the zeolite anion. 3.2.2. Energetics of Adsorption and Effects of Embedding. The energies of adsorption for the bidentate and tridentate configurations calculated from eq 12 are shown in Table 8. We find that in the isolated cluster the higher the coordination of the ammonium ion with the bridging oxygen atoms, Le., the larger the number of hydrogen bonds linking the ion to the framework, the larger the adsorption energy. The energy difference between the two adsorbed configurations is 23.5 kJ/ mol. This difference is larger than that predicted by Teunissen et al., who found the energies of the stable bidentate and tridentate configurations to be within 1 kJ/mol of each other.22 However, their calculations were performed on much smaller clusters, and the geometry optimizations were unrestricted. In our calculations the long-range geometry of the zeolite is unperturbed, but the first three shells of atoms surrounding the substitution site are allowed to relax. Differences in the deformation energy of the zeolite framework between the two approaches may account for the differences in the total energies of adsorption. Brand et al. calculated the energy of adsorption for a monodentate configuration and report that it is roughly 200 kJ/mol.16 However, these calculations did not include the effects of geometry relaxation and correlation and also used a small basis set without any polarization basis functions. In order to estimate the relative stability of the bonding configurations before and after proton transfer, the relaxed
structures of the bidentate and tridentate configurations were taken and the proton was moved along the 0-H axis and placed 1.03 A away from the bridging oxygen atom. These configurations are termed “neutral”, compared to the ones discussed previously, which are termed “ionic”. Using this starting configuration and performing a geometry optimization, we found stable neutral configurations that were 10 Wmol higher in energy than the ionic configurations for both bidentate and the tridentate systems. This indicates that proton transfer stabilizes the adsorption by 10 kJ/mol. In all cases the surrounding zeolite was allowed to relax; therefore, the differences in energy due to proton transfer are not exclusive to this event but also include the energetic difference due to the rearrangements of the framework. This value is comparable to other predictions. Kassab et al. found that for rigid clusters and monodentate bonding the ionic form was stabilized by 13 kJ/m01.~~ In more recent results, Kassab et al. reported that the ionic structure was stable only when correlation effects were included in a bidentate bonding configuration and found that the energy differences between the neutral and the ionic species was of the order of 13 kJ/m01.~~ Again for rigid clusters, Brand et al. report a value of 28.5 kJ/m0l,I5which is significantly larger than our prediction but is less reliable because of the effect of framework relaxations. The effects of embedding the quantum-mechanical cluster in the Madelung field on the energy of adsorption were also studied. The frontier oxygen charges were adjusted according to the partial charges of the boundary hydrogen atoms in the bidentate and tridentate configurations relaxed in the absence of the field. Both the SCF and the perturbation theory precictions are summarized in Table 8. We find that the Madelung field tends to stabilize both the ionic bidentate and the ionic tridentate configurations. It should be noted that it was impossible to converge the bonded tridentate configuration in the presence of the Madelung field. The reason for this is that the H4 atom in the ammonium ion lies approximately 2 %, away from one of the frontier oxygen atoms, which compromises the accuracy of the calculated field in that region of the cluster. The ammonium ion in the tridentate configuration is pointing toward the sinusoidal channel of the zeolite and thus is closer to atoms in the frontier region than the bidentate configuration, which is pointing toward a relatively more open region in the zeolite. This result shows that embedding effects should be considered, at least at a perturbation theory level, in order to identify configurations that may be feasible in isolated clusters, but which are strongly prohibited when the surrounding atoms in the zeolite are included. In this work, the tridentate configuration in the presence of the Madelung field is poorly described, even in the context of a first-order perturbation study. The quality of the fit of the adjusted charges in the region surrounding the ammonium and the central /do4 cluster of atoms is about an order of magnitude worse than that for the bidentate configuration, which is 2 x The maximum error in the field for the tridentate configuration in the fitted region is 0.75, while for the bidentate configuration it is 0.05. In both cases the partial charges of the boundary hydrogen atoms do not change significantly in the presence of the Madelung field. The differences observed between the energetic predictions of the first-order perturbation theory and the self-consistent results are explained as follows. In first-order perturbation theory the electron density of the bare cluster is used to calculate energies, and any inaccuracies due to the embedding procedure enter only in calculating the last two terms of eq 8. In the selfconsistent-field calculations any inaccuracies due to the embedding procedure are included in the calculation of the electron
1514 J. Phys. Chem., Vol. 99, No. 5, 1995 density and are thereby further amplified, because of the differences in the “ideal” and imposed Madelung fields, shown in Table 4. The embedding method used does not change the electron density of the inner part of the cluster, where the chemistry of the adsorption process occurs. This is why we believe that the perturbation theory predictions are more accurate. The sensitivity of the energy calculations to the nature of the embedding procedure and its internal consistency make the predictions of Kassab et al.24somewhat questionable. In their calculations the field effects are not included explicitly in the quantum-mechanical calculation but calculated as a postprocessing step based on the Mulliken charges of the cluster atoms. Their predicted stabilization of an ionic monodentate bonded configuration by 197 kJ/mol in the presence of the Madelung field appears to be exaggerated. We find that the embedding stabilizes the bidentate ionic configuration relative to the neutral by 12.5 kJ/mol when first-order perturbation theory is used and by 18.4 kJ/mol when the SCF energy predictions are used. In the case of the tridentate configuration, where the field is not computed as accurately, the stabilization of the ionic configuration is enhanced. This result, however, is not as reliable as that for the bidentate. Our calculations predict that the energy of adsorption of ammonia in H-ZSM-5 for a tridentate ionic configuration, which is the most stable configuration in an isolated cluster, is 150 kJ/mol and for a bidentate ionic configuration, which is the most stable configuration in an embedded cluster, is 162 kJ/mol. These predictions agree very well with recent microcalorimetry experiments, which yield accurate measurements of the energy of adsorption of small molecules in zeolites, as long as the acid sites are dilute and accessible and equilibrium is reached. Parillo et ai. recently reported the results of microcalorimetry experiments in high SUAI ratio ZSM-5 at conditions chosen to overcome these diffi~ulties.7,~ They found that the heat of adsorption of ammonia is roughly 140-150 kJ/mol. They also found that the heat of adsorption remains relatively constant until all acid sites have been saturated. These results were confirmed by TPD-TGA experiments, which showed that most of the ammonia desorbs below 475 K, while ammonia at concentrations roughly equal to the number of acid sites per unit cell remains strongly bonded and desorbs at higher temperatures. This means that there are two types of ammonia molecules in the zeolite: (a) chemisorbed ammonia proportional to the number of acid sites in the zeolite and (b) physisorbed ammonia which desorbs fast at relatively low temperatures. TPD experiments by Hidalgo et aL8 deduce a value of the heat of adsorption for the high-temperature stage approximately equal to 145 kJ/mol, using a formula developed by Cvetanovic and A m e n ~ m i y z awhich , ~ ~ links the temperatures of the peaks in desorption and the heating rate to the adsorption energy. Topsae et a1.4 also found that the heat of adsorption of the strongly bound ammonia is approximately 160 kJ/mol, in agreement with our predictions. Parillo et ai. suggest that the energy of adsorption depends largely on the differences in the gas phase proton affinities of the adsorbed bases.’ Our results agree with the general principle behind their simple model. Proton transfer alone, however, is not enough to energetically favor the adsorption of ammonia, because the proton affinity of the zeolite cluster is larger. The additional stabilization that leads to adsorption is the result of interactions of the ammonium ion with the zeolite framework in the form of the hydrogen bonds and is enhanced by the presence of the Madelung field. The proton in the substituted cluster is a soft acid, as was shown in the previous section.
Kyrlidis et al. Parillo et ai. present results for its interaction with a series of amines. The deviations seen in ref 9 from the results which account only for the proton affhities may be explained because of the differences in the interactions of the adsorbed bases with the zeolite. AI1 molecules that may form tridentate bonding configurations with the zeolite have expected behavior with the exception of n-butylamine whose heat of adsorption is higher, probably due to interactions with the channels in the zeolite. The two molecules which do not conform to this rule are dimethylamine and trimethylamine, which may only form bidentate and monodentate bonding configurations. The energies of adsorption of monodentate and bidentate configurations are reported to be 22 and 6 kJ/mol smaller than those of the tridentate configurations. We find that in the isolated cluster the bidentate configuration energy of adsorption is 23.5 kJ/mol smaller than that of the tridentate configuration, which is larger than the 6 kJ/mol difference measured experimentally. It is hard to isolate the contributions to the experimentally measured energies that are directly comparable to our study of adsorbed ammonia. Factors other than the coordination, such as interactions of the larger molecules with the zeolite, and the changes in the sharing ability of the basic electron pair due to the presence of the additional methyl groups may influence these reported energies. The important conclusion is that the molecules prefer to bind in a highly coordinated way. 4. Summary The structural and electronic properties of the acid site in zeolite H-ZSMJ and its interaction with ammonia have been studied using Kohn-Sham LDA density functional theory. Using geometrical relaxation and extended basis sets, we predict that the substitution of a silicon atom in the T12 site by an aluminum and a charge-compensating proton lead to significant geometrical rearrangements in the local environment of the T12 site. The acidity of the proton was examined using several measures of acidity such as the partial charge of the proton, the electron affinity, the HOMO-LUMO gap, and the condensed Fukui function, and all tests imply that the proton is a soft species. The study of the interaction of the Bransted acid site with ammonia indicates that proton transfer occurs and that the adsorbed ammonium ion is distorted from its tetrahedral symmetry. The zeolite also rearranges itself in the presence of the ammonium ion, in agreement with recent spectroscopy studies of zeolite structure. The ionic adsorbed species are favored over neutral adsorbed species by approximately 10 kJ/ mol. The energy of adsorption of ammonia in the zeolite cluster is computed to be 126.5 and 150 kJ/mol for bidentate and tridentate configurations. The higher the number of hydrogen bonds formed, the more stable the adsorbed species. We have also incorporated the zeolite Madelung field in the Kohn-Sham Hamiltonian to study long-range electrostatic effects on the properties of the acid site and on the adsorption of ammonia. The Madelung field does not change the structural properties of the zeolite but influences the energetic predictions and the electronic properties. Including the Madelung field leads to an increase in the softness of the acid site, as measured by an increase in the proton affinity of the cluster and a decrease in the absolute hardness. Incorporating the Madelung field as a first-order perturbation to the Kohn-Sham Hamiltonian provides relatively accurate energetic information that would otherwise not be available. The tridentate bonded configuration for ammonia, which is favored over the bidentate configuration in the isolated cluster, is affected the most by the inclusion of the Madelung field, because the molecule is located close to framework atoms not explicitly included in the quantum
Ammonia Adsorption in H-ZSM-5 Zeolites mechanical cluster. Embedding provides indications that particular configurations are probably not as stable as they appear to be from isolated cluster calculations. We find that the bidentate species for which it is possible to construct a relatively accurate Madelung field representation is stabilized by the longrange electrostatic potential of the zeolite. Acknowledgment. We are grateful to the Department of Energy, Advanced Industrial Concepts Division, for providing us with supercomputer time at NERSC. References and Notes (1) Introduction to Zeolite Science and Practice; van Bekkum, H., Flanigen, E. M., Jansen, J. C., Eds.; Studies in Surface Science and Catalysis 58; Elsevier; Amsterdam, 1991. (2) Perspectives in Molecular Sieve Science; Flank,W. H., Whyte, T. E., Eds.; ACS Symposium Series 368; American Chemical Society: Washington, DC, 1988. (3) Van Hooff, J. H. C.; Roelofson, J. W. In ref 1, Chapter 7. (4) Tops@e,N.-Y.; Pedersen, K.; Derouane, E. G. J. Catal. 1981, 70, 41. (5) Karge, H. G.; Dondur, V. J . Phys. Chem. 1990, 94, 765. (6) Karge, H. G.; Dondur, V.; Weitkamp, J. J. Phys. Chem. 1991,95, 283. (7) Parrillo, D. J.; Gorte, R. J. J. Phys. Chem. 1993, 97, 8786. (8) Hidalgo, C. V.; Itoh, H.; Hattori, T.; Niwa, M.; Murakami, Y. J. Catal. 1984, 85, 362. (9) Panillo, D. J.; Gorte, R. J.; Farneth, W. E. J . Am. Chem. SOC.1993, 115, 12441. (10) Vbdrine, J. C.; Auroux, A.; Bolis, V.; Dejaifve, P.; Naccache, C.; Wierzchowski, P.; Derouane, E. G.; Nagy, J. B.; Gilson, J.-P.; Van Hoff, J. H. C.; Van den Berg, J. P.; Wolthuizen, J. J. Catal. 1979, 59, 248. (1 1) Earl, W. L.; Fritz, P. 0.;Gibson, A. A. V.; Lunsford, J. H. J. Phys. Chem. 1987, 91, 2091. (12) Vega, A. J.; Luz, Z. J. Phys. Chem. 1987, 91, 365. (13) Sauer, J. Chem. Rev. 1989, 89, 199. (14) Teunissen, E. H.; van Duijneveldt, F. B.; van Santen, R. A. J . Phys. Chem. 1992, 96, 366. (15) Brand, H. V.; Curtiss, L. A.; Iton, L. E. J . Phys. Chem. 1992, 96, 7725. (16) Brand, H. V.; Curtiss, L. A.; Iton, L. E. J. Phys. Chem. 1993, 97, 12773. (17) Teunissen, E. H.; Roetti, C.; Pisani, C.; de Man, A. J. M.; Jansen, A. P. J.; Orlando, R.; van Santen, R. A.; Dovesi, R. Mod. Simul. Mater. Sei. Eng. 1994, 2, 921. (18) Sauer, J. In Modelling of Structure and Reactiviry in Zeolites; Catlow, C. R. A., Ed.; Academic Press: London, 1992; Chapter 8. (19) Allavena, M.; Seiti, K.; Kassab, E.; Ferenczy, G.; Angyan, J. G. Chem. Phys. Lett. 1990, 168, 461. (20) Allavena, M.; Kassab, E. Solid State lonics 1993, 61, 33. (21) Cook, S. J.; Chakraborty, A. K.; Bell, A. T.; Theodorou, D. N. J . Phys. Chem. 1993, 97, 6679. (22) Teunissen, E. H.; van Santen, R. A,; Jansen, A. P.; van Duijneveldt, F. B. J. Phys. Chem. 1993, 97, 203.
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