4020
Ind. Eng. Chem. Res. 1996, 35, 4020-4027
MATERIALS AND INTERFACES Ab Initio Molecular Orbital Study of Adsorption of Oxygen, Nitrogen, and Ethylene on Silver-Zeolite and Silver Halides N. Chen and R. T. Yang* Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109
An ab initio molecular orbital study is undertaken on the adsorption of N2, O2, and C2H4 (adsorbate) on Ag-zeolite and Ag halides (adsorbent). Geometry optimization is performed at the HF/3-21G level, while MP2/3-21G with natural bond orbital calculations are performed to obtain energies, atomic charges, orbital energies, and orbital populations (occupancies). The bonding of adsorbate to adsorbent is discussed in the context of σ-donation (i.e., overlap of the 2p orbitals of the adsorbate molecule with the 5s orbital of Ag) and d-π* backdonation (i.e., overlap of the 4dyz orbitals of Ag with the 2p* antibonding orbitals of the adsorbate). For all adsorbate-adsorbent pairs, the ratio of σ-donation to d-π* backdonation is approximately 3:1. Results on occupancy analysis indicate that a considerable electron redistribution from the 4dz2 orbitals to the 4dyz orbitals occurs in Ag during adsorption and that this redistribution has possibly enhanced the d-π* backdonation. Net charge and energy gap (∆) analyses indicate that it is slightly easier for N2 than O2 to adsorb, whereas a comparison of N2 and O2 adsorption from calculations of the energies of adsorption is inconclusive. However, a fair agreement is obtained in comparison of theory and experiment for energy of adsorption of N2 and C2H4 on Ag-zeolite. The dispersion energies of adsorption, based on the MP2 correlation energies, are nearly the same for all adsorption pairs, i.e., approximately 4-5 kcal/mol. Introduction Since the development of synthetic zeolites and pressure-swing adsorption (PSA) cycles, adsorption has been playing an increasingly important role in gas separations (Yang, 1987). In particular, adsorption has become important for air separation to produce N2 and O2 in the last decade. At the heart of any adsorption process is the adsorbent (or sorbent); new sorbents will lead to new separations. Rational design and synthesis of new sorbents require a fundamental understanding of adsorbateadsorbent interactions. Studies during the past 2 decades on molecular simulations using tools of statistical mechanics have significantly improved our understanding of adsorption (e.g., Glandt, 1980; Panagiotopoulos, 1987; Rasmus and Hall, 1991; Karavias and Myers, 1991; Balbuena and Gubbins, 1993; Van Tassel et al., 1993; Li and Talu, 1993; Snurr et al., 1994; Kaminsky and Monson, 1994). However, empirical intermolecular potential energy functions are required as the input in these simulations. Thus, these techniques remain empirical and are not capable of a priori predictions. On the other hand, rapid progress in molecular orbital theory calculations based on quantum mechanics has reached a point where it is now possible to make reliable predictions, based on first principles, of molecular structures, relative energies, potential surfaces, and vibrational properties. Molecular orbital calculations are well suited for studying adsorption, i.e., adsorbateadsorbent interactions (as well as adsorbate-adsorbate * To whom all correspondence should be addressed. Phone: (313) 936-0771. FAX: (313) 763-0459. E-mail: yang@ engin.umich.edu.
S0888-5885(96)00299-0 CCC: $12.00
interactions), although such studies are relatively few as compared to statistical mechanics simulations. We have recently employed a semiempirical molecular orbital technique to study adsorption of simple hydrocarbons on sorbents containing Ag+ and Cu+, for the application of olefin-paraffin separations by π-complexation (Chen and Yang, 1995). Unlike semiempirical molecular orbital theories, the ab initio molecular orbital methods evaluate all integrals without drastic approximations. Thus, the ab initio methods provide meaningful solutions to the electronic Schro¨dinger equations for all molecular orbitals in a molecule. A large number of ab initio calculations have been made in studies of catalysis, surface reactions, and adsorption on silica and zeolites (e.g., Sauer, 1989; Beran, 1990; Kobayashi et al., 1985; Kassab et al., 1988, 1993; Ahlrichs et al., 1989; Teunissen et al., 1992, 1993; Brand et al., 1993; Haase and Sauer, 1994, 1995; Suzuki et al., 1994; Hill and Sauer, 1995; Shah et al., 1996). Although the majority of the ab initio calculations on adsorption involved “chemisorption” or strong “physisorption”, ab initio molecular orbital methods do not make such a distinction and are well suited for physisorption. Adsorption systems that have been studied by using ab initio molecular orbital theories include O2/ C2H4/vanadia (Kobayashi et al., 1985) and the adsorption of H2O, NH3, CO, and various hydrocarbons on silica and zeolites (as referenced above). In the present work, we used an ab initio method to investigate the interactions of C2H4 with Ag+ and that of O2 and N2 with Ag-zeolite. The purpose of the work is 2-fold: (1) to obtain a fundamental understanding of the π-complexation bond that is applicable for olefinparaffin separations (Yang and Kikkinides, 1995); (2) to explore feasibility of studying the important N2/O2/ © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4021
Figure 1. Six-membered oxygen ring as the basic unit in zeolite types A and X. T denotes Si or Al.
zeolite system (for air separation) by ab initio molecular orbital theories. It is known that strong interactions exist between N2 and Ag+-exchanged zeolites (being strong relative to interactions of N2 with zeolites containing other cations). The isosteric heat of adsorption of N2 on AgX zeolite is approximately 8 kcal/mol, which we have described as “weak chemisorptionassisted” adsorption (Yang et al., 1996). We have, therefore, chosen the N2/O2/Ag-zeolite system as the first N2/O2/zeolite system for ab initio study. Model Selection and Computational Method The adsorption systems being considered are N2/O2/ C2H4 on Ag+-zeolite. In addition to Ag+-zeolite, halides (F, Cl, and I) of Ag are also included in order to see the effects of anions to which the Ag cation is bonded. The system C2H4-Ag+ is a classic π-complexation system (e.g., Chen and Yang, 1995), so it can be used as a standard for comparison for the systems involving N2 and O2. Model for Zeolite. Because of the infinite dimension of solids, it is important to select a finite structure that can adequately represent the infinite structure. A large number of ab initio molecular orbital studies have been devoted to model selection for zeolites, as reviewed by Sauer (1989). Cluster models as simple as Si(OH)4 (Gibbs, 1982) and as large as H49Si45AlO68 (Brand et al., 1993) have been employed. The most commonly used zeolites as sorbents are types A and X zeolites (Yang, 1987). The framework of these zeolites is composed of silica and alumina tetrahedra, represented by TO4 (where T ) Si or Al). Six tetrahedra are joined together through shared oxygen atoms to form a six-membered oxygen ring, as shown in Figure 1. Cages (e.g., sodalite cage and R-cage) are formed by connecting these six-membered rings through additional tetrahedra. These cages are the basic units that form types A and X zeolites. These zeolites also contain exchangeable cations that serve to offset the negative charge introduced by the AlO2- groups. The cations are not part of the framework but sit near the six-membered ring as indicated in Figure 1. Therefore, the six-membered ring represents the basic unit for A and X zeolites. For economy in computation, however, the cluster structures shown in Figure 2, rather than the six-membered ring, are selected for computation. These clusters have the formula (HO)3SiOAg-Al(OH)3. The cluster is truncated from the sixmembered ring; however, it contains the essential structural and chemical information of the zeolite, including the cation, the charge, and the Si/Al ratio. In addition, the Al and Si atoms are surrounded by oxygen, rather than being directly saturated by hydrogen; the latter is done in most of the previous studies. Addition
Figure 2. Geometry-optimized cluster models for Ag-zeolite.
of oxygen more accurately describes the chemical environment in the zeolite. The oxygen dangling bonds are saturated with hydrogen in order to terminate the model. The cluster model shown in Figure 2 reflects a compromise between adequate structural representation and computational economy. Consequently, cluster models of sizes similar to that shown in Figure 2 are the most frequently employed in the literature. Selection of Basis Sets. The linear combination of atomic orbitals (LCAO) self-consistent-field (SCF) methods are used as the starting points for all well-defined ab initio molecular orbital calculations. The most extensively used method involves the minimal basis set STO-3G (Hehre et al., 1969; Collins et al., 1976), created by replacing the Slater-type atomic orbital (STO) with three Gaussian functions. The split-valence basis sets are higher level basis sets with more basis functions used for each valence atomic orbital. The 3-21G basis set is the simplest one among the split-valence basis sets (Binkley et al., 1980; Gordon et al., 1982). The notation for the 3-21G basis set denotes an s-type innershelf function with 3 primitive Guassian functions, an inner set of valence s- and p-type functions with 2 primitive Gaussian functions, and another outer sp set function with 1 primitive Gaussian function. Silver has been seldom studied by ab initio calculations because it has 47 electrons; hence, it generates a large number of basis functions even with small basis sets such as STO-3G and 3-21G. Moreover, suitable basis sets for transition metals are very limited in ab initio programs. These are mostly restricted to STO3G and 3-21G basis sets. The higher split-valence basis set, 6-311G basis set, is not available to transition metals such as Ag. Therefore, only STO-3G and 3-21G basis sets are used in this study.
4022 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
Geometry Optimization and Electron Correlation. Geometry optimization is the first step in all calculations. Calculations for all other parameters such as charges, populations, and energies are all based on the geometrically optimized system. In geometry optimization, the geometry is adjusted until a stationary point on the potential surface is found. In the Gaussian 94 program that is used in this study, the Berny algorithm using redundant internal coordinates was the default algorithm for energy minimization (Frisch et al., 1995). Moreover, full optimization was carried out; i.e., all geometric parameters are optimized with no “frozen” variables. Electron correlation effects, which are neglected in the Hartree-Fock approximation, can be used to evaluate the dispersion energy (see, e.g., Sauer, 1989; Tsuzuki and Tanabe, 1992) and are, hence, included in this study. A second-order Møller-Plesset (MP2) perturbation method, available in the Gaussian program, is employed in this work. Although higher-order MP perturbation programs (i.e., MP3 and MP4) are available, correlation energies calculated at the MP2 level are only a few percent different from those at the MP4 level (for ethylene dimers) (Tsuzuki and Tanabe, 1992). Also, substantial portions of the dispersion energies can be obtained by the MP2 method (Sauer, 1989). The MP2 program in the Gaussian 94 program is used in this study. Natural Bond Orbital (NBO). Atomic charge, orbital energy, and population are important pieces of information for determining electronic configuration, net charge association, and, hence, the nature of the bond. However, their quantification is difficult. Among the numerous schemes that have been proposed, Mullikin population analysis (see, for example, Mullikin and Ermler, 1977) is a widely used method in most ab initio molecular orbital calculations. However, reports about Mullikin population analysis failing to yield reliable characterization of molecular systems have appeared (Mullikin and Ermler, 1977). A more accurate method for population analysis, the natural bond orbital (NBO) method, was introduced in 1983 (Reed and Weinhold, 1983; Reed et al., 1985; Glendening et al., 1995) and is used in this work. The NBO method transforms a given wave function for the whole molecular structure into localized forms corresponding to one-center and twocenter elements. The NBO method encompasses sequential calculations for natural atomic orbitals (NAO), natural hybrid orbitals (NHO), natural bond orbitals (NBO), and natural localized molecular orbitals (NLMO). It performs population analysis and energetic analysis that pertain to localized wave-function properties. It is very sensitive for calculating localized weak interactions, such as charge transfer, hydrogen bonding, and weak chemisorption. Therefore, NBO is the preferred method for population analysis for studying adsorption systems involving weak adsorbate-adsorbent interactions and is, hence, employed in this work.
set is good enough for geometry optimization (Brand et al., 1993) and that the 3-21G level optimization takes much more CPU time, optimization at the 3-21G level is performed in this study. The bond length calculated by the 3-21G basis set deviates by only 1.7% (i.e., by 0.016 Å for a 0.95 Å hydrogen bond), whereas that calculated by STO-3G deviates by 3.7% for the same bond (Binkley et al., 1980). Hence, 3-21G should yield higher accuracy. After geometry optimization, MP2/3-21G with NBO calculations are performed to obtain all the information such as energies, atomic charges, orbital energies, and orbital populations (occupancies), and all the calculated results are based on the same calculation level. The interaction energy, or the energy of adsorption (∆E), can be calculated from energy of adsorbateadsorbent (EAB), energy of free adsorbate (EA), and energy of free adsorbent (EB):
Calculations
Geometry-Optimized Zeolite Model. The cluster (HO)3Si-OAg-Al(OH)3, extracted from the six-membered ring (Figure 1), is used to represent the zeolite. The SiO4 and AlO4 tetrahedra can rotate along the SiO-Al axis (Kassab et al., 1993; Hill and Sauer, 1995), yielding three different types of structures, shown in Figure 2. Among the three structures, only structure A can fit in the six-membered ring. However, geometry optimization is performed for all three free structures, and the energies of the three optimized structures are
The calculations are performed using the Gaussian 94 program supplied by Gaussian, Inc. (Frisch et al., 1995; Glendening et al., 1995). An IBM RS/6000 workstation is used. All adsorbate-adsorbent systems being considered in this study are subjected to geometry optimization first at the STO-3G level and then at the 3-21G level. Although some reports claimed that the STO-3G basis
∆E ) EAB - EA - EB
(1)
Calculations using the 3-21G basis set have yielded accurate predictions for molecular structures and properties. For example, deviations in geometries from experimental data are only 1.7% (for H-bonds) as discussed. Deviations in molecular vibrational frequencies are within 13%, and that in dipole moments are within 0.50 D (Binkley et al., 1980; Gordon et al., 1982). Deviations in energies are, however, considerably larger. In the Hartree-Fock (HF) self-consistent-field (SCF) equations, the SCF energy is a sum of one-electron energies, Coulomb interactions, and exchange terms. The more the electrons are involved in a molecular system, the larger is the SCF energy. Because Ag contains 47 electrons, the SCF energies calculated for our systems are considerably larger than most of the molecular systems that have been studied (Sauer, 1989; Beran, 1990; Teunissen et al., 1992, 1993; Kassab et al., 1993; Brand et al., 1993; Haase and Sauer, 1994, 1995; Hill and Sauer, 1995; Suzuki et al., 1994; Shah et al., 1996). For example, the SCF energies for the Ag systems can be as high as 12 200 hartrees (or 7 600 000 kcal/mol) for N2-AgI. Meanwhile, the adsorption energies between the adsorbates and the model adsorbents are on the order of 10 kcal/mol, which are 6 orders of magnitude smaller than the total SCF energies of the adsorbed systems. In addition, it is expected that the deviations in energies calculated by the 3-21G basis set from experimental values are around 10 kcal/mol (Pietro et al., 1982). In our calculations, since the same basis set is used for adsorbate, adsorbent, and the bonded adsorbate-adsorbent, it is expected that the adsorption energy calculated by eq 1 is meaningful. However, results on atomic charges and orbital occupancies calculated in this work are expected to be more accurate than those on energies. Results and Discussion
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4023
Figure 3. Schematic of the C2H4-Ag interactions by π-complexation, showing (A) donation of π-electrons of ethylene to the 5s orbital of Ag, (B) backdonation of electrons from the 4dyz orbitals of Ag to the antibonding p* orbitals of ethylene, and (C) redistribution. B also depicts the possible electron redistribution from the 4dz2 orbitals (the dumbbell and doughnut-shaped orbitals) to the 4dyz orbitals. Table 1. Energy of Zeolite Cluster Models, (HO)3Si-OAg-Al(OH)3, in hartrees (see Figure 2 for Structures) calculation level
HF/3-21G
MP2/3-21G
structure A structure B structure C
-6226.9936 -6226.6044 -6226.3351
-6227.9750 -6227.6773 -6227.3805
given in Table 1. Comparison of the results shows clearly that structure A is the most stable. The SCF/ 3-21G energies for structure A are lower than those for structure B by 244 kcal/mol and lower than those for structure C by 413 kcal/mol; the MP2/3-21G energies for A are lower than those for B by 187 kcal/mol and lower than those for C by 373 kcal/mol. The optimized structure A also shows a tilt of the Ag atom toward the Al atom, as would be expected. Structure A shown in Figure 2 is the zeolite model for further calculations. π-Complexation and Orbital Energies. The highest molecular orbitals in the adsorbate molecules (N2, O2, and C2H4) are the 2p orbitals (or π-bond orbitals), whereas those in the transition metals are the dorbitals, such as 4d orbitals for Ag. The bonding between these two types of molecules is know as π-complexation, illustrated in Figure 3. In π-complexation, electrons transfer from the 2p orbitals (of the adsorbate) to the 5s orbital of Ag (that is not filled), i.e., σ-donation. This is followed by the d-π* backdonation; i.e., electrons transfer from the fully occupied 4d orbitals of Ag to the 2p* (antibonding p) orbitals of the adsorbate molecule. Interactions by π-complexation between N2/ O2 and transition metals (or ions) have not been studied, partly because their interactions are weak. The strong adsorption of N2 on Ag-zeolites (Huang, 1974, 1980; Yang et al., 1996) indicates that such interactions are possible. The electronic configurations of N2 and O2 are (Gray, 1964)
N2[KK(σ2s)2(σ2s*)2(σ2px)2(π2py)2(π2pz)2(π2py*)0(π2pz*)0] (2) O2[KK(σ2s)2(σ2s*)2(σ2px)2(π2py)2(π2pz)2(π2py*)1(π2pz*)1] (3) Obviously, it is easier for N2 than O2 to have π-complexation interactions with Ag (or Ag+) since the two π*-antibonding orbitals of N2 are empty while those of O2 are occupied by one electron each. It is meaningful to compare the differences in energy levels between the highest occupied molecular orbital
Figure 4. Energy gap (∆) for adsorbate-adsorbent pairs. ∆ ) LUMO (adsorbent) - HOMO (adsorbate).
(HOMO) of the adsorbate and the lowest unoccupied molecular orbital (LUMO) of the adsorbent, since a smaller energy gap (∆), where
∆ ) LUMO (adsorbent) - HOMO (adsorbate)
(4)
will facilitate electron transfer, by both σ-donation and d-π* backdonation. By definition the energy level for the HOMO of the adsorbate pertains to the 2p orbitals and that for the LUMO of the adsorbent to 5s. Calculations using MP2/3-21G with NBO are performed for the HOMO energies of N2, O2, and C2H4 and the LUMO energies of AgX (halides) and Ag-zeolite (AgZ). The energy gaps (∆) for all the adsorbate-adsorbent systems are shown in Figure 4. It is clear that the ∆ for adsorbate-adsorbent pairs follow the order:
O2-AgX/AgZ > N2-AgX/AgZ > C2H4-AgX/AgZ (5) This rank order indicates that it is most difficult for O2 to form the π-complexation bonds with the Ag+ sorbents, due to the largest orbital energy gap, while it is the easiest for C2H4 to form such bonds. For the same adsorbate molecules interacting with different adsorbents, ∆ follows the order:
Ag-zeolite > AgF > AgCl > AgI
(6)
This rank order indicates that the formation of π-complexation bonds would be most difficult for Ag-zeolite and easiest for AgI. For Ag-zeolite, the result may be different by using a larger cluster zeolite model such as the entire six-membered ring, which is a focus of our further study. Comparing the three Ag+ halides, it seems to be most difficult to form π-complexation bonds with AgF and
4024 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 Table 2. Atomic Charges Calculated by MP2/3-21G with NBO Methods (AgZ Denotes Ag-Zeolite) N N2 O2 C2H4 AgF AgCl AgI AgZ N2-AgF O2-AgF C2H4-AgF N2-AgCl O2-AgCl C2H4-AgCl N2-AgI O2-AgI C2H4-AgI N2-AgZ O2-AgZ C2H4-AgZ
O
C
Ag
0.0000 0.0000 0.0000
0.0465 0.0377 0.0552 0.0492 0.0401 0.0608 0.0504 0.0409 0.0602 0.0536 0.0416 0.0408
0.5798 0.6571 0.4866 0.5419 0.4831 0.5030 0.4640 0.5557 0.5774 0.5421 0.3841 0.4094 0.3867 0.4174 0.4519 0.4499
least difficult with AgI. A careful examination of the ∆ shows that the rank order shown above is caused by the large differences in the 5s (LUMO) orbital energies of Ag. The 5s orbital energies of Ag in AgF, AgCI, and AgI are respectively 0.0903, 0.0181, and -0.0106 hartrees. This rank order may be counterintuitive based on the argument of electronegativity of the halide anion. However, it reveals that polarization plays a role here. With increasing radii of the halide anions from F- and I-, the polarizability of the halide anion increases in the same order. Consequently, the nature of the bond between Ag and the halide changes from being ionic (in AgF) to partly covalent (in AgI). This polarization effect can influence the 5s (LUMO) orbital energies of Ag. Net Charges. Net charges are calculated for N, O, C, and Ag in free molecules and the adsorbateadsorbent systems. The results are given in Table 2. As expected, upon adsorption the net charges of the adsorbate increase, while those of the adsorbent decrease. This result indicates that there is a net transfer of electrons from the adsorbate molecule to the Ag atom of the adsorbent. This result also indicates that the σ-donation is greater than the d-π* backdonation for all adsorption systems considered in this study. Moreover, the changes in net charge upon adsorption are the smallest for O2 as compared to other adsorbate molecules. This result indicates that the interactions are the weakest between O2 and the adsorbents. This result is consistent with the result on ∆ as discussed above. There has been much discussion in the literature on the Brønsted acidity based on results of ab initio calculations (Sauer, 1994; O’Malley, 1994). The net charge of the H atom in the OH group has been correlated with the Brønsted acidity. As mentioned, the H atoms are used to terminate the structure (see Figure 2). However, it is of interest to see the net charges of these H atoms. The net charges of the H atoms of structure A in Figure 2 are 0.4066 (H7), 0.4029 (H8 and H9), 0.4529 (H14), and 0.4215 (H15, H16). Numbers 7-9 are H atoms bonded to Al. It is seen that these actually have weaker Brønsted acidities than those bonded to Si. The tilting of Ag toward H numbers 7-9 may have contributed to their lower charges. Moreover, since it is known (O’Malley, 1994) that the terminal hydroxyls have lower Brønsted acidities than the bridging hydroxyls, i.e, Al-(OH)-Si and that the Brønsted
acidity of zeolite derives from bridging hydroxyls, no conclusion can be drawn on Brønsted acidities from this study. Population (Electron Occupancy) Analysis. Unlike semiempirical molecular orbital calculation methods such as the extended Hu¨ckel method, ab initio methods reevaluate iteratively all integrals, electron densities, and force fields. Hence, ab initio molecular orbital methods are capable of evaluating electron redistribution among different molecular orbitals during the formation of the adsorption bond. Moreover, ab initio methods combined with the NBO method enable the statistical analysis of the core, valence, and Rydburg orbitals (Reed and Weinhold, 1983; Reed et al., 1985). Using the NBO method, the results on electron occupancy (Oc) from population analysis of NAO are listed in Table 3, for O, N, and C atoms in the adsorbate molecules and for Ag in the adsorbents. Occupancies for both before and after adsorption are given. The changes in occupancy (∆Oc) upon adsorption are also given, in Table 4. It is obvious from Tables 3 and 4 that upon adsorption the electron occupancy of the 5s orbital of Ag always increases, whereas the total occupancy of its 4d orbitals (4dxy,4dxz,4dyz,4dx2-y2, and 4dz2) always decreases. This result is caused by the σ-donation from the π-bond (i.e., 2Px, 2Py, and 2Pz, orbitals) of the adsorbate molecule to the 5s orbital of Ag and the d-π* backdonation from the 4d orbitals of Ag to the π*-bond (2Px*, 2Py*, and 2Pz* orbitals, also shown in the 2P orbitals) of the adsorbate. The total change in occupancies over all valence orbitals of Ag, i.e., ∑[5s + 4d], is also shown in Figure 4 for all adsorption pairs. The total change in occupancies is positive for all pairs and follows the order:
C2H4-AgX (or AgZ) > N2-AgX (or AgZ) > O2-AgX (or AgZ) (7) The net increase in occupancy indicates a net electron transfer from the adsorbate to the Ag-containing adsorbent. The net increase in the occupancy in the 5s orbital of Ag indicates the strength of the forward σ-donation bond; see also Figure 3. The net decrease in the occupancies of the 4d orbitals of Ag indicates the strength of the d-π* backdonation bond. The ratios of ∆Oc of 5s over the ∆Oc of 4d are approximately 3:1, indicating the relative contributions of the σ-donation over the d-π* backdonation to the overall bond. It follows, then, that relation (7) indicates that the C2H4Ag bond is the strongest while O2-Ag is slightly weaker than N2-Ag. A careful examination of the occupancy changes in the 4d orbitals of Ag reveals an interesting pattern. The occupancy changes for 4dxy, 4dxz, and 4dx2-y2 are small, while the major changes occur in the 4dyz and 4dy2 orbitals. The overlap between the 4dyz orbital of Ag with the 2p* orbitals of the adsorbate molecule follows the classic picture of π-complexation, shown in Figure 3. However, the large occupancy decreases of the 4dy2 orbitals are unexpected. The three other 4d orbitals (4dxy, 4dxz, and 4dx2-y2) are pointing in perpendicular directions with that of 4dyz; hence, there is no possibility for them to overlap with 4dyz. The 4dz2 orbitals, or the dumbbell-doughnut orbitals, also shown in Figure 3, are in the vicinity of the spatial direction of the 4dyz orbitals. As a result, the 4dz2 orbitals are the only ones that can overlap with the 4dyz orbitals. This result indicates that there is considerable redistribution of
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4025 Table 3. NAO (Natural Atomic Orbital) Electron Occupancies O, N, or C
Ag
atom
2s
2Px
2Py
2Pz
∑2P
O2 N2 C2H4 AgF AgCl AgI AgZ O2-AgF N2-gF C2H4-AgF O2-AgCl N2-AgCl C2H4-AgCl O2-AgI N2-AgI C2H4-AgI O2-AgZ N2-AgZ C2H4-AgZ
1.8399 1.6023 1.0376
1.9996 0.9993 0.9977
0.9989 0.9993 1.2216
1.1575 1.3788 1.1578
4.1560 3.3774 3.3771
1.8429 1.6042 1.0597 1.8420 1.6033 1.0602 1.8407 1.6020 1.0591 1.8403 1.6018 1.0579
1.9953 0.9993 0.9824 1.9937 0.9992 0.9747 1.9931 0.9992 0.9735 1.5640 0.9982 0.9829
0.9985 0.9978 1.2573 0.9984 0.9956 1.2576 0.9984 0.9948 1.2567 1.1499 0.9979 1.2530
1.1497 1.3667 1.1587 1.1493 1.3659 1.1590 1.1492 1.3656 1.1591 1.4291 1.3656 1.1605
4.1435 3.3638 3.3984 4.1414 3.3607 3.3913 4.1407 3.3596 3.3893 4.1430 3.3617 3.3964
5s
4dxy
4dxz
4dyz
4dx2-y2
4dz2
∑4d
0.1551 0.1223 0.1947 0.0670 0.1877 0.1943 0.2820 0.1559 0.1641 0.2427 0.2283 0.2395 0.3038 0.0901 0.0989 0.1266
2.0000 2.0000 2.0000 1.9936 1.9998 1.9999 1.9999 1.9999 1.9999 1.9999 1.9999 1.9999 1.9999 1.9927 1.9928 1.9920
1.9966 1.9986 1.9991 1.9928 1.9966 1.9965 1.9963 1.9986 1.9984 1.9982 1.9991 1.9990 1.9987 1.9955 1.9926 1.9839
1.9966 1.9986 1.9991 1.9999 1.9976 1.9910 1.9675 1.9991 1.9949 1.9781 1.9994 1.9957 1.9808 1.9983 1.9965 1.9967
2.0000 2.0000 2.0000 1.9915 2.0000 2.0000 1.9996 2.0000 2.0000 1.9997 2.0000 2.0000 1.9997 1.9920 1.9918 1.9904
1.9615 1.9817 1.9846 1.9966 1.9505 1.9512 1.9194 1.9757 1.9765 1.9559 1.9795 1.9801 1.9627 1.9962 1.9962 1.9937
9.9547 9.9789 9.9828 9.9744 9.9445 9.9386 9.8827 9.9733 9.9697 9.9318 9.9779 9.9747 9.9418 9.9747 9.9699 9.9567
Table 4. Changes in NAO Electron Occupancies (∆Oc) upon Adsorption O, N, or C atom
2s
2Px
Ag 2Pz
∑2P
5s
4dxy
4dxz
4dyz
4dx2-y2
4dz2
∑4d
∑(5s + 4d)
-0.0078 -0.0121 0.0009 -0.0082 -0.0129 0.0012 -0.0083 -0.0132 0.0013 0.2716 -0.0132 0.0027
-0.0125 -0.0136 0.0213 -0.0146 -0.0167 0.0142 -0.0153 -0.0178 0.0122 -0.0130 -0.0157 0.0193
0.0326 0.0392 0.1269 0.0336 0.0418 0.1204 0.0336 0.0448 0.1091 0.0231 0.0319 0.0596
-0.0002 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 -0.0009 -0.0008 -0.0016
0.0000 -0.0001 -0.0003 0.0000 -0.0002 -0.0004 0.0000 -0.0001 -0.0004 0.0027 -0.0002 -0.0089
0.0010 -0.0056 -0.0291 0.0005 -0.0037 -0.0205 0.0003 -0.0034 -0.0183 -0.0016 -0.0034 -0.0032
0.0000 0.0000 -0.0004 0.0000 0.0000 -0.0003 0.0000 0.0000 -0.0003 0.0005 0.0003 -0.0011
-0.0110 -0.0103 -0.0421 -0.0060 -0.0052 -0.0258 -0.0051 -0.0045 -0.0219 -0.0004 -0.0004 -0.0029
-0.0102 -0.0161 0.0450 -0.0056 -0.0092 -0.0470 -0.0055 -0.0081 -0.0410 0.0003 -0.0045 -0.0177
0.0224 0.0231 0.0819 0.0280 0.0326 0.0734 0.0281 0.0366 0.0681 0.0234 0.0274 0.0419
2Py
0.0030 -0.0043 -0.0004 O2-AgF 0.0019 0.0000 -0.0015 N2-AgF 0.0221 -0.0153 0.0357 C2H4-AgF 0.0021 -0.0059 -0.0005 O2-AgCl 0.0010 -0.0001 -0.0037 N2-AgCl 0.0226 -0.0230 0.0360 C2H4-AgCl 0.0008 -0.0065 -0.0005 O2-AgI -0.0003 -0.0001 -0.0045 N2-AgI 0.0215 -0.0242 0.0351 C2H4-AgI 0.0004 -0.4356 0.1510 O2-AgZ -0.0005 -0.0011 -0.0014 N2-AgZ 0.0203 -0.0148 0.0314 C2H4-AgZ
Table 5. Total SCF Energies (E, in hartrees) and Adsorption Energies (∆E, in kcal/mol), by HF/3-21G and MP2/3-21G Calculations HF/3-21G E N2 O2 C2H4 AgF AgCl AgI AgZ N2-AgF O2-AgF C2H4-AgF N2-AgCl O2-AgCl C2H4-AgCl N2-AgI O2-AgI C2H4-AgI N2-AgZ O2-AgZ C2H4-AgZ
-108.3010 -148.6872 -77.6010 -5272.7045 -5631.1794 -12061.7249 -6226.99.3 -5381.0150 -5421.4044 -5350.3329 -5739.4898 -5779.8801 -5708.8059 -12170.0355 -12210.4258 -12139.3502 -6335.3059 -6375.6948 -6304.6191
MP2/3-21G ∆E
E
∆E
5.96 7.97 17.19 5.90 8.47 16.00 6.02 8.60 15.25 6.97 8.79 15.37
-108.5295 -148.9641 -77.7801 -5272.9205 -5631.3110 -12061.8378 -6227.9750 -5381.4666 -5421.9068 -5350.7371 -5739.8566 -5780.2980 -5709-1235 -12170.3838 -12210.8251 -12139.6488 -6336.5227 -6376.9613 -6305.7867
10.42 13.93 22.90 10.10 14.37 20.33 10.35 14.56 19.39 11.42 13.93 19.83
exptl ∆E
8.2a and 8.4b 18.1c
a Heat of adsorption of N on AgX zeolite (Huang, 1974). b Heat of adsorption of N on AgX zeolite (Yang et al., 1996). c Heat of adsorption 2 2 of C2H4 on AgX zeolite (Huang, 1980).
electrons between the two 4d orbitals during the d-π* backdonation. Taking the argument one step further, it seems that the electron redistribution (from the 4dz2 to the 4dyz orbitals) enhances the d-π* backdonation (from the 4dyz orbital of Ag to the 2p* orbitals of the adsorbate). The electron redistribution is also illustrated in Figure 3. In most of the adsorption pairs, as seen in Table 4, the net occupancy decreases are larger in the 4dz2 orbitals than those of the 4dyz orbitals. Since
only one Ag atom is used in the model, the electron redistribution is intraatomic rather than interatomic in nature. Adsorption Energies and Adsorbate Bond Length. The interaction energies calculated by eq 1 are taken as adsorption energy at zero amount adsorbed. The results obtained from the RHF/3-21G level and those from the same level with MP2 correction are both listed in Table 5. Also listed are the available
4026 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
Figure 5. Geometry-optimized structures for O2, N2, and C2H4 adsorbed on Ag-zeolite.
experimental data for N2 adsorption on Ag-type X zeolite and C2H4 on Ag-type X zeolite. Within the accuracy range of the employed calculation levels, the comparison between theory (MP2/3-21G) and experiment is quite satisfactory. Comparing the three adsorbates, the interactions of C2H4 with all adsorbents are considerably stronger than those of N2 and O2. However, it would be meaningless to compare the calculated adsorption energies between N2 and O2 at the calculation levels used in this work, as discussed in detail in the foregoing, namely, (1) the small basis set (that is available for Ag); (2) the large total SCF energies involving Ag as compared to the small ∆E, and (3) the small zeolite cluster and the small models for AgX. Nonetheless, the ∆E for O2-adsorbent seems to be consistently higher than that for N2adsorbent. This is certainly not the case for experimental values with Ag-zeolite. The experimental isotherm data show only weak adsorption of O2 on Ag-zeolite (Yang et al., 1996). The reason for the disagreement lies in the kinetics. Predictions from molecular orbital theories are for bonded structures that are at chemical equilibrium. In experimental measurements of adsorption isotherms at room temperature, chemical equilibrium is obviously not reached for the O2-AgX and O2-
AgZ systems. For the N2 and C2H4 adsorption, however, chemical equilibrium is likely reached in the experiment. Monte Carlo simulations (based on statistical mechanics) have been used to simulate the “stronger” adsorption of N2 over O2 on zeolites. However, these simulations require empirically fitted potential energy functions, based on experimental adsorption data measured at room temperature. The results of our ab initio molecular orbital calculation seem to indicate that the origin of the N2/O2 selectivity on zeolites could be in the kinetics; i.e., the chemical equilibrium between O2 and the cation in zeolite is not reached at room temperature in the experimental measurements. This important question is under further investigation in our laboratory. The MP2 electron correlation energy approximates the dispersion energy (Sauer, 1989; Tsuzuki and Tanabe, 1992). The difference between the ∆E by MP2/3-21G and that by HF/3-21G, shown in Table 5, is approximately the dispersion portion of the adsorption energy. Accordingly, the dispersion energies for the adsorption from Table 5 are in the range 4-5 kcal/mol. These are reasonable values for dispersion energies. The adsorption energy will increase if we choose a large model for the sorbent, i.e., (AgX)n, particularly for O2 and N2. Further work on larger models of different crystalline faces is in progress. For all adsorption systems, the bond lengths of O2, N2, and CdC have increased upon adsorption. The HF/ 3-21G-optimized geometries for O2, N2, and C2H4 on Ag-zeolite are shown in Figure 5. In all optimized structures, the Ag atom tilts toward the Al tetrahedral, whereas the adsorbate molecule, normal to the plane shown in Figure 5, tilts toward the other direction. The detailed data on the bond lengths and bond angles are not included here (but are available upon request). Upon adsorption, the increases in bond lengths are the largest for CdC, which increases from 1.3151 to 1.32831.3307 Å (on the four adsorbents), or by 1.00-1.19%. The increases for O2 are in the range 0.1-0.2%, from 1.2419 Å in free O2. The increases for N2 are also in the range 0.1-0.2%, from 1.0828 Å. The increases in bond lengths reflect the weakening of these bonds upon adsorption, and the CdC bond is weakened the most. Acknowledgment This work was supported by the National Science Foundation (CTS-9520328) and The BOC Group, Inc. Nomenclature AgZ ) silver zeolite E ) energy HF ) Hartree-Fock HOMO ) highest occupied molecular orbital LUMO ) lowest unoccupied molecular orbital MP2 ) second-order Møller-Plesset perturbation for electron correlation NAO ) natural atomic orbital NBO ) natural bond orbital Oc ) electron occupancy SCF ) self-consistent field STO ) Slater-type atomic orbital Greek Letters ∆E ) adsorption energy ∆ ) orbital energy gap
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4027
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Received for review May 28, 1996 Revised manuscript received August 28, 1996 Accepted August 30, 1996X IE960299N
Abstract published in Advance ACS Abstracts, October 15, 1996. X
