11754
J. Phys. Chem. 1993,97, 11754-1 1761
Quantum Chemical Studies of Acid Sites in Zeolite ZSM-5 Antonio Redondo' and P. Jeffrey Hay' Los Alamos National Laboratory. Los Alamos, New Mexico 87545 Received: March 31, 1993; In Final Form: August 30, 1993' Semiempirical quantum chemical calculations have been performed using cluster models for the acid sides of zeolite ZSM-5. The effects of lattice relaxation and oxygen protonation at T sites where AI has been substituted for Si have been treated using 12 clusters containing about 100 atoms to represent the 12 distinct T sites. The calculations show a wide range (1.2 eV) in the (Al,H)/Si substitution energies, but nearly every site gives rise to a t least one acid site whose energy is less than 0.2 eV from that of the lowest-energy T9 site. The calculations also show that there exists a direct correlation between the substitution energy and the proton affinity of a given s i t e t h o s e sites that exhibit the largest proton affinity are the ones for which the aluminum is most stable, From comparing the most favorable location for a proton at each of the 12 T sites in ZSM-5, the proton affinities are found to vary by 0.3 eV (29/kJ/mol). In addition, both the (Al,H)/Si substitution energy and the proton affinity depend on the geometric parameters, such as bond lengths and angles, of the optimum configurations for the acid sites. The most stable sites for protons correspond to "pore" sites where the proton is oriented into the major pores of the zeolite lattice. The most important conclusion from this study is that there is a direct relationship between the experimental T-0-T angle and the proton affinity. This suggests that the T-0-T angle can be used as a measure of the acidity of the site. This conclusion, although obtained for the 48 sites of zeolite ZSM-5, would be expected to be transferable to other zeolites.
Introduction The catalytic activity of zeolites is fundamentally determined by the characteristics and properties of their acid sites. For this reason, recent years have seen a significant number of experimental'" and theoreticald-I0studies of the acidity of zeolites. However, the prediction of acid properties has been elusive, and to date, our understanding of what makes strong or weak acid sites in zeolites is far from complete. In an earlier study,lOweexamined theenergetics ofsubstituting aluminum for silicon at the 12 distinct sites in zeolite ZSM-5. The study employed ab initio wave functions on clusterscontaining a single silicon or aluminum atom. This work also examined the dependence of the results on the quality of the basis set used in the calculations. This study did not include the effects of (1) lattice relaxation when the larger aluminum atom is inserted into the position otherwise occupied by a silicon atom and (2) protonation of the neighboring oxygen atoms upon A1 substitution. The current study deals with both of these effects by using much more realistic cluster sizes to model the acid site regions of the zeolite. Details of tbe Calculation Because of the much larger sizes (on the order of 100 atoms per cluster), the calculations reported herein were performed using the semiempirical MNDO" quantum chemistry approach. To test the reliability of this approach, we performed extensive comparisons of the MNDO technique to equivalent ab initio calculations. We repeated the previous study of substituting AI for Si in the "frozen- lattice with MNDO and compared it to ab initio calculations. The relative energies for the 12 different sites generally agreed to within 1 kcal/mol. In addition, we performed the same set of calculations for the PM3 and AMI parametrizations" of the MNDO approach. The PM3 results are somewhat less satisfactory than those of the MNDO parametrization, whereas the AMI scheme led to considerably less satisfactory agreement with ab initio values than either the MNDO or PM3 approaches. As a result of these comparisons and a number of monomer and dimer models of zeolites, the MNDO parametrization in the MOPAC codek1was chosen to carry out these studies. Abstract published in Aduance ACS Abstracts, October 1, 1993.
0022-3654/93/2097-11754$04.00/0
Zeolite ZSM-5 has 12 distinct sites, labeled TI through TI^, in which an aluminum atom can substitute a silicon atom. We chose to model each one of these sites with finite clusters (one cluster for each site) constructed according to the following procedure. We started with a silicon atom at the Ti center. We then placed around its position, using the experimental crystallographic coordinates of the lattice,12 the first shell of oxygen atoms followed by the first shell of silicon nearest neighbors. Next, we included the second shell of oxygen atoms and the second shell of silicon atoms (second-nearest-neighborsilicons) around the original Ti center. An additional shell of oxygen atoms was attached, and each was terminated by a hydrogen atom. The hydrogen atoms were located at a normal 0-H distance of 0.95 A from the corresponding oxygen, oriented along the bond direction to what would otherwise have been the next silicon atom. In all cases, some additional silicons and oxygens (corresponding to the third shell of silicons and the fourth shell of oxygens) had to be included to eliminatethe possibility of having two hydrogens that represented the same silicon. This process was repeated in all 12 sites in ZSM-5 using a computer code that generated the clusters. The resultant size of the clusters varied from 96 to 125 atoms, including the hydrogens. Having thus constructed a cluster corresponding to a central Si atom at site Ti, which we will label as Co(Ti), successiveclusters, CI(Ti) to C4(Ti), were made by replacing the central silicon with an aluminum and attaching a hydrogen atom to one of the four oxygens adjacent to the aluminum. All of these clusters were electrically neutral (zero net charge). Finally, a negatively charged cluster, CS(Ti), corresponding to the unprotonated form, was obtained by replacing the central silicon atom by an aluminum, without adding the proton. The geometries of the atoms in the central region of each of the clusters were then optimized at the MNDO level while fixing the outer atoms at their lattice positions. The atoms that were allowed to relax included the central silicon or aluminum, the first shell of oxygens, the first shell of silicons, and the proton (if present). Calculated substitution energies were determined by comparing the energies of the relaxed Si cluster to that of the corresponding relaxed (A1,H) cluster. For example, E[Cl(T,)] - E[Co(T4)] would represent the calculated (A1,H) substitution energy for site T4 with the proton at the first oxygen position Q 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No.45, 1993 11755
Acid Sites in Zeolite ZSM-5 (AI, H)/Si Substitution Energy 1.2
1
TABLE I: Effect of Relaxation on the Total Energy for the TS Site in Zeolite ZSM-5(All Energies in eV) relaxed atoms
1.o
nl
0.8
5 Y
0.6 C a
W
0.4
Cluster C0(T9)C -22 992.425 -22 992.484 -22 992.564 -22 992.701 -22 992.900 Cluster C3(T9)d proton (H)C -22 964.133 H+O -22 965.089 H+A1+40 . -22 965.471 H + A1 + 4 0 + 4 Si -22 965.625‘ H + A1 4 0 + 4 Si + 12 0 -22 965.968 none (X-ray structure) cental Si Si+40 Si + 4 0 + 4 Si Si+40+4Si+120
+
0.2
0
Tl
T2
T3
Figure 1. Calculated substitution energy required to replace a silicon atom with an aluminum-proton pair for the 48 inequivalentsites of zeolite ZSM-5. The ordering of the sites is the same as in Tables I1 and 111. Solid bars indicate “pore” sites; open bars correspond to “framework” and “pocket” sites.
adjacent to the T4 site. The lowest substitution energy for all 48 cases was taken as the zero of energy, and all other energies are reported relative to this value. To calculate proton affinities, again the relative energies of the relaxedunprotonated and relaxed protonated clusters (e.g., E[C5(T4)] - E[Ci(Ts)]) were used for each of the four oxygen atoms (i = 1-4) for each of the 12 sites.
Result!?
(Al,H) Substitution Energies. The calculated substitution energies for replacement of a silicon atom by an aluminumproton pair at each of the 12 inequivalent sites in ZSM-5 are shown in Figure 1 (and also in Table 111). As described above, each energy includes the relaxation of the lattice (up to the first shell of silicon neighbors) and the presence of counterions (in this case protons). For each T site there are four energies, corresponding to the four different oxygen atoms to which the proton can be bound, leading to 48 cases overall. As shown in the figure, there is a wide variation of about 1.2 eV (1 16 kJ/mol) between the largest and the smallest substitution energies. This is in marked contrast with the much narrower variation (about 0.2 eV, or 19 kJ/mol overall) from our earlier studies. This difference emphasizes the importance of including the lattice relaxation and protonation effects. The magnitude of the relaxation effects is illustrated in Table I for the representative Tg site. Starting from the unrelaxed structure, corresponding to the experimental X-ray geometry12 for a silicon atom at the Tg site, the top portion of the table shows the successive lowerings in energy as the consecutive shells of atoms about the T site are allowed to relax. The bottom portion of Table I shows the same information about successiverelaxation of shells for the same cluster but containing an aluminum instead of the central silicon and a proton associated with one of the oxygens (018) adjacent to the aluminum. For the comparable cases of allowingthe central 9 atoms to relax for the Si-containing cluster and the central 10 atoms (including H) for the Alcontaining cluster, relaxation energies of 0.28 and 1.49 eV are obtained for Si and Al, respectively. The larger energy lowering for A1 is expected for substituting the larger A13+ ion into the zeolite lattice. As more shells of atoms about the T site are allowed to relax, as shown in the table, the energy lowerings per atom become more comparable. For the remainder of the paper, the calculations are reported for the cases above where 9 (or 10) atoms are optimized for each cluster containing Si (or Al). One issue that merits further comment concerns the procedure of relaxing the Si-containing clusters as well as the ones with A1
total energy
energy per atomb
0.06 0.02 0.03 0.02
0.96 0.10 0.04 0.03
* Each successive row corresponds to the total energy of the cluster when an additional shell of atoms (around the silicon for the top part of the table and around the aluminum for the bottom) is allowed to relax freely. Energy increment (current row minus previous row) per additionally relaxed atom. Cluster containing a silicon atom at the central (T9) site (total of 114 atoms). Same cluster as that of footnote a but containing an AI atom at the T9 site and a proton associated with oxygen 0 1 8 (total of 115 atoms). In this cluster, only the proton is allowed to move; all other atoms remain at the crystallographic positions. f This is the lowest total energy of the 48 cases reported in column 5 of Table 111. in order to calculate the (A1,H) substitution energies. For our initial guesses, the atoms in the cluster were positioned at the experimental geometry obtained from X-ray diffraction. For the results reported in this paper, we chose to use an identical procedure on both types of clusters in order to obtain the most consistent theoretical results for clusters containing either A1 or Si. On the other hand, one could argue that it might be equally plausible to use unrelaxed energies for the Si clusters since the initial geometry was taken from experiment on highly siliceous ZSM-5. However, there are sources of uncertainty in the experimental data including (1) the fact that the measured positions represent an average over obth A1 and Si occupancies of the T sites, (2) possible influence of the tetrapropylammonium counterions and other defects in the lattice, and (3) the overall precision in the refinement itself which led to a standard deviation of 0.004A in the reported positions. Another source of deviations between calculated and experimental results is the inherent errors in computed Si-0 bond lengths in the MNDO parametrization. In any event, the effect of relaxation in the Si clusters is quite small in absolute terms and even less for relative substitution energies. The relaxation energies of the Si-containing clusters (in electronvolts)are as follows for thevarious T sites: Tl(0.28 l), TZ(0.279), T3 (0.299), T4 (0.190), T5 (0.291), T6 (0.299), T7 (0.145), T8 (0.237), Tg (0.275), Ti0 (0.250), Ti1 (0.217), Ti2 (0.268). The effect of using unrelaxed versus relaxed Si clusters on the results in Figure 1 would be to alter the relative energies by the difference in relaxation energies between the T9 cluster and the other T sites. The biggest difference occurs for T7 where the relative difference is 0.130 eV, and this would lead to substitution energies for the T7 sites that would be 0.130 eV higher than shown. This makes the already unfavorable T7 site energetically even higher relative to Tg. For most other sites besides T4 and T7 the effect would be less than 0.04 eV. An important point that should be emphasized is that in the calculations reported here the positions of all atoms in the outer coordination shells (secondshell and beyond, relativeto the central T site) were fixed at their crystallographic locations. It is crucial that at least one shell of oxygen atoms (together with their “capping” hydrogens) on the outside of the cluster be kept at fixed positions. The reason for this is that when the outer atoms are allowed to move there is no longer a constraint to conform, at least at some level, with the experimental geometries. This leads to optimized structures that are much more similar to those observed in small molecules (typically with longer S i 4 bond lengths and smaller T-0-T angles) than to what X-ray diffraction shows for the crystalline materials. We believe the compromise
11756 The Journal of Physical Chemistry, Vol. 97, No.’45, I993
Figme 2. Structure of the cluster corresponding to substitution of A1for Si at the T9 site with the proton bound to 0 1 8 .
we have employed in the present workstrikes a reasonable balance between the inclusion of relaxation effects around the T sites and consistency with the experimental X-ray geometries. The oxygen atom to which the proton is bound plays an important role in the relative stabilities of aluminum. For a given T site, both low substitution energies ( 0 4 . 4 eV) and high substitution energies (0.6-1.2 eV) are found, depending on which oxygen atom is protonated. To analyze thesevariations in greater detail, we have characterized the proton positions as either “pore” or “framework” sites. The “pore” sites correspond to protons located in the large pores characteristic of all zeolites, while the “framework”sites correspond to protons located inside the zeolitic frameworkin positionsthat are generallyinaccessibleto molecules or other species. In addition, four of the 48 sites appear to have the proton located in pockets near the intersection of the straight and zigzag channels in zeolite ZSM-5; we will refer to these sites as “pocket” sites. A comparison of the substitution energies for all the sites (Figure 2) with those of only the pore sites (solid bars) shows that all of the sites with the low (Al/H)/Si substitution energies correspond to pore sites. This correlation suggests that placing the protons in the small framework regions of the zeolite lattice is energetically unfavorable compared to having the proton oriented into the large pore regions. The structure of a typical “pore” site with favorable energy is shown in Figure 2 and is discussed in greater detail in the next section. The (Al,H)/Si substitution energies for the “pore” sites range between 0 and 0.7 eV above the most stable site, with seven of the 32 pore sites above 0.4 eV. This clearly indicates that the driving force behind high replacement energies is also determined by factors other than the location of the counterions in pore or framework sites. We will return to this issue below. Structures. The structure of an acid site corresponding to (A1,H) substitution for Si at a representative site (T9 with the proton bound to 018) in ZSM-5 is shown by the cluster model in Figure 2. This cluster yielded the lowest substitution energy of all 48 proton sites in ZSM-5 for the MNDO level of calculation (Table I). A summary for the structural information for all 12 sites is presented in Table 11. For comparison, the table also shows (in column 2) the experimental values for the T-O bond lengths. Because these distances are obtained from X-ray diffraction patterns, where it is not possible to discriminate between Si and Al, the experimental values should represent an average over the actual S i 4 and A1-O distances weighted by the aluminum distribution over the lattice sites. Column 3 reports the correspondingcalculated T-O distanceswhen no aluminumsor protons are present in the cluster. In column 4, we show the distance
Redondo and Hay between the aluminum atoms and the protonated oxygens. Columns 5 and 6 present the calculated M i bond lengths corresponding to the internuclear separation between the first oxygen and first silicon shells for thedealuminated and aluminated clusters. The next column shows that the proton-oxygen distance is uniformly constant irrespective of the binding site. The last two columns report the H-0-A1 and proton twist angles. A consistencycheck of the calculated geometries is offered by a comparison of the internuclear distances between the central Si atom and the first shell of oxygens and those distances between the first shell of oxygens and the next shell of silicons. Under ideal circumstances, one should obtain identical T& distances when calculated from the central atom to the first shell of oxygens in one cluster and between the first shell of oxygens and the first shell of silicons in a different cluster. However, because of the finite size of the clusters, a given O r T i bond (between the first oxygen and first silicon shells) might be sufficiently close to the “outside”of the cluster to provide a sightly different environment than the same bond in the cluster that has the Ti atom at its center. As a consequence, the calculated bond distance, for the same type of bond, from the two clusters might be different. Thus, significantdifferencesbetween these two sets of bond lengths should constitute a very clear indication that the geometries are suspect and that the clusters are not sufficiently large. In our case, the calculated rsi(Si-0) and rSi(0-S) values (columns 3 and 5 in Table 11) exhibit only minor differences of 0.01 A in 17 of the 48 entries and of 0.02 A in only one case [corresponding to a distance of 1.59 A for the OlSi2 bond length in cluster Co(T1) and a value of 1.57 A for the S i d l distance in cluster Co(T2)]. This excellent agreement indicates that all of our calculated bond lengths are internally consistent and that the clusters are sufficiently large for inclusion of the appropriate relaxation and protonation effects. (It should be kept in mind that long-rangeelectrostatic interactions from atoms in the lattice that lie outside the cluster are consistentlyneglected in the current study.) A much more stringent consistency test is afforded by comparingof the calculatedT-0-T angles in thedifferent clusters. The reason is that the potential energy surfaces for angle bending normally have flattened minima when compared to those of bond stretches (Le., relatively large angle deviations from the equilibrium value only produce small changes in the energy). As a result, small changes in the environment can lead to large discrepancies in the equilibrium angles. In Table I11 we show that comparison of the calculated values of the same T-0-T angle in different clusters leads to excellent agreement. Indeed, from column 3 we can see that the difference between corresponding angles is less than 2.5O for all cases except for the following four angles: Sil-O2lSi~,Si7-07Si8, Si1-01Si2, and Si4-04Sis with respective discrepanciesof 4.8,4.2,3.4,and 3.4O. The key features about the geometry of the protonated sites are a long A1-O bond (1.77-1.89 A, see column 4 in Table 11) and a somewhatlonger S i 4 bond (1.67-1.72 A, Table 11,column 6) compared to the Si-O distances typically encountered in the ZSM-5 lattice without A1 present (1.57-1.62 A, column 3, Table 11). The Al-OSi bond anglesvary from 121 to 143O (see column 4 in Table 111), whereas the corresponding Si-oSi linkages had much larger bond angles (141-172O, column 3, Table 111). The main conclusion from these results is that the Briinsted acid sites have an equilibrium conformation that resembles that of predominantly tricoordinated aluminum atoms (i.e., the A1-0 bond lengths correspondingto the oxygens not associatedwith the proton are considerably shorter than those of the protonated oxygen atoms). On the other hand, there must be a significantinteraction between the aluminum and the protonated oxygen because the A1-O distances are consistent with those found in the molecules AlOH and A102H13(but are considerably longer than those found in aluminum oxides that do not contain hydrogen). Proton Affities. The proton affinities for the 48 distinct 0 sites in ZSM-5, calculated by comparing the energies of the Al-
The Journal of Physical Chemistry, Vol. 97, No. 45, 1993 11757
Acid Sites in Zeolite ZSM-5
TABLE II: Summary of Calculated Geometric Qurntitiea for tbe 12 T Sites of Zeolite ZSM-5 (All Bond Lengths in A and AU Annlesindeld 1.580 1.591 1.583 1.598 1.568 1.582 1.591 1.601 1.575 1.586 1.601 1.606 1.571 1.580 1.583 1.586 1.586 1S68 1.594 1.598 1.571 1.582 1.589 1.597 1.586 1.585 1.589 1.594 1.568 1.574 1.580 1.578 1.588 1.590 1.594 1.598 1.58 1 1.591 1.591 1.605 1.583 1.573 1.586 1.591 1.583 1.592 1.595 1.591
1.61 1.58 1.59 1.58 1.60 1.59 1.57 1.58 1.60 1.59 1.58 1.58 1.59 1.61 1.58 1.59 1.60 1.60 1.57 1.58 1.59 1.60 1.58 1.58 1.59 1.58 1.59 1.59 1.60 1.60 1.58 1.58 1.59 1.62 1.58 1.57 1.60 1.58 1.61 1.59 1.60 1.60 1.58 1.59 1.61 1.59 1.58 1.57
1.89 1.79 1.80 1.77 1.84 1.81 1.78 1.78 1.84 1.81 1.77 1.78 1.82 1.84 1.78 1.80 1.82 1.84 1.77 1.78 1.83 1.84 1.77 1.78 1.80 1.78 1.80 1.80 1.79 1.83 1.79 1.79 1.81 1.87 1.77 1.78 1.82 1.79 1.85 1.80 1.82 1.83 1.79 1.79 1.87 1.80 1.77 1.78
1.61 1.58 1.59 1.59 1.59 1.60 1.57 1.58 1.59 1.59 1.57 1.58 1.60 1.61 1.59 1.59 1.59 1.60 1.58 1.58 1.59 1.60 1.58 1.58 1.58 1.58 1.58 1.58 1.60 1.61 1.58 1.58 1.58 1.62 1.58 1.58 1.60 1.58 1.62 1.59 1.60 1.60 1.58 1.59 1.60 1.58 1.58 1.57
1.71 1.69 1.69 1.68 1.71 1.71 1.67 1.67 1.70 1.70 1.67 1.68 1.71 1.72 1.69 1.69 1.69 1.71 1.68 1.67 1.70 1.70 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.71 1.68 1.68 1.68 1.72 1.68 1.68 1.70 1.68 1.72 1.68 1.71 1.69 1.69 1.69 1.70 1.69 1.68 1.68
0.94 0.95 0.94 0.94 0.94 0.95 0.95 0.94 0.94 0.95 0.94 0.94 0.94 0.94 0.95 0.95 0.95 0.94 0.94 0.95 0.95 0.95 0.94 0.94 0.95 0.95 0.95 0.94 0.95 0.94 0.95 0.95 0.95 0.94 0.94 0.95 0.95 0.95 0.94 0.94 0.94 0.95 0.95 0.95 0.94 0.95 0.94 0.95
104.4 112.4 116.2 116.9 108.7 112.7 114.8 116.6 109.2 110.0 115.9 116.6 107.8 107.4 113.6 114.0 112.0 110.8 117.3 116.4 105.7 108.4 116.2 118.0 112.4 120.2 114.6 116.7 107.9 107.8 111.9 118.2 111.4 112.4 116.8 113.8 107.8 114.4 110.7 115.3 109.7 109.4 114.9 119.5 104.4 111.6 116.5 114.3
0.3 8.6 11.6 10.8 1.6 14.5 2.3 1.9 0.4 4.0 1.1 6.3 6.2 1.o 1.6 2.4 0.6 3.8 3.9 7.5 15.5 12.3 6.7 5.4 8.7 3.9 3.4 5.0 1.3 7.5 0.3 1.9 2.5 8.1 3.0 10.8 16.6 8.1 12.5 10.0 3.8 5.5 1.3 1.3 11.2 9.2 11.1 0.2
Experimental T-O distance, from ref 12. Distance from Si atom at T site to first shell oxygens, calculated from cluster Co(Tt). Distance from Al atom to protonated oxygen, calculated from the corresponding cluster CI(T,)-C~(T~).Distance from first shell oxygens to first shell silicons, calculatedfromcluster C!IJ(T,).e Distancefromprotonatedoxygen toadjacent silicon,calculated from thecorrespondingcluster Cl(Ti)-C4(T,). /Protonoxygen bond length, calculated from the corresponding cluster CI(TI)-C~(T,).Proton-oxygen-aluminum angle, calculated from the corresponding cluster Cl(T,)44(T,). Twist angle of the proton with respect to the plane of the Al-O-Si triangle, calculated from the corresponding cluster Cl(T,)CdTi).
substituted clusters with the energy of the corresponding unprotonated cluster, are shown in Figure 3 and tabulated in column 6 of Table 111. As in the case of the substitution energies, we find a variation of about 1.2 eV (1 16 kJ/mol) between the sites with the lowest and highest proton affinities. As one would expect from simple chemical arguments, the sites with the most stable aluminum-proton substitution energies (Figure 1) closely correspond to those sites with the highest proton affinities (Figure 3). We find that the protons located at the 'pore" sites (open bars in Figure 3) correspond to thesites with high proton affinities, a trend similar to that found for the substitution energies. In the actual zeolite H-ZSM-5one would expect the proton for a given T site to be located on the oxygen with the greatest proton affinity. To compare the relative proton affinities among different sites, one can single out those proton affinities of the maet stable proton in each T site. If one assumes for the moment that (Al,H) substution occurs with equal probability at all T sites in ZSM-5and takes the largest proton affinity of each site from Table 111, the resulting proton affinities vary over 0.3 eV (or 29
kJ/mol) as a function of T site. Within the limitations of the cluster model, the highest proton affinity is associated with site T6 with nearly as stable sites occurring for Ts, T7, Tg, and T12. The reason that the two quantities in these calculations-the (A1.H) substitution energy and the proton affinity-are related to each other is as follows. The substitutionenergiesare obtained from the energies of the A1 clusters [e.g., Cl(Ti)] relative to the corresponding cluster with a silicon atom at the T site [e.g., CO(Ti)]; the proton affinities, on the other hand, are determined from the energies of the A1 clusters [e.g., C1(T,)] relative to the negatively charged (unprotonated) cluster with A1 at the T site [e.g., Cs(Tt)]. The correlation between the two quantities is established because the difference between the energy of the unprotonated cluster and that of the corresponding cluster with asiliconatomat theTsite, (e.g.,E[Co(T,] -E[C5(TJ]) isroughly constant from site to site. A number of trends between the proton affinity (or the A1 stability) and the geometrical parameters can be established. For example, from Figure 4 we find that the least acidic sites (largest
11758 The Journal of Physical Chemistry, Vol. 97, No. 45, 1993
Redondo and Hay
TABLE III: Calculated T-0-T An les, SubstitutionalEnergies, and Proton Affinities for the 12 T Sites of Zeolite ZSM-5(All Angles in deg and All Energies in e"$ T site (angle)
(T-O-T)expa 164.7 148.2 152.6 145.4 175.9 158.2 152.6 149.7 175.8 162.8 149.7 147.7 175.8 164.7 156.0 149.4 156.0 169.1 147.9 145.4 162.8 158.2 147.9 145.0 156.3 153.3 149.4 150.3 175.9 164.6 156.3 154.5 154.5 154.6 145.0 148.0 164.4 148.2 154.6 144.9 169.1 164.4 153.4 150.3 164.6 153.4 146.3 147.7
(Si-OSi)b 165.0 145.9 158.4 141.0 171.7 159.1 161.8 146.1 168.6 167.1 147.9 150.2 168.6 163.8 156.8 151.4 153.4 159.2 146.1 145.8 169.4 159.6 144.4 143.6 157.3 147.6 153.0 148.0 171.9 164.6 161.5 154.6 154.4 149.8 141.3 154.5 160.8 148.4 150.9 144.7 161.5 161.4 154.4 150.0 164.5 156.0 141.8 152.2
(Al-O-Si)c 143.2 128.6 123.4 121.2 137.9 130.0 127.2 122.9 137.0 135.2 123.4 123.9 138.2 139.4 128.7 126.8 130.3 134.2 122.0 122.9 139.3 135.5 122.4 120.6 123.4 128.8 126.0 122.9 130.0 138.3 131.0 127.1 130.5 131.0 121.7 126.7 137.2 125.6 131.8 123.9 134.9 138.1 127.0 126.6 142.3 129.8 121.9 125.6
(AIH)/B energyd 1.06 0.27 0.22 0.04 1.14 0.45 0.28 0.22 1.11 0.55 0.25 0.15 1.04 0.96 0.25 0.19 0.53 0.98 0.06 0.16 0.72 0.66 0.10 0.10 0.63 0.26 0.45 0.33 1.06 0.97 0.43 0.28 0.43 0.86 0.00 0.22 0.74 0.17 0.76 0.16 0.92 0.91 0.26 0.31 1.16 0.36 0.09 0.20
proton affinity 12.33 13.12 13.17 13.35 12.33 13.02 13.19 13.26 12.30 12.86 13.16 13.26 12.45 12.54 13.24 13.30 12.96 12.51 13.43 13.33 12.90 12.97 13.52 13.52 13.04 13.40 13.21 13.34 12.46 12.56 13.09 13.24 12.96 12.53 13.39 13.17 12.65 13.22 12.63 13.22 12.69 12.70 13.35 13.30 12.30 13.10 13.37 13.26
typee
F P P P F P P P F P P P F F P P P F P P C C
P P P
P P P F F P P P F P P C
P F P F C
P P F
P P P
0 Experimental T-0-T angle, from ref 12. Calculated from the Co(Ti) cluster. Calculated from the correspondingCI(TI)-C~(T,) clusters. d Aluminum substitutional energy, calculated from the equation E[C,(Ti)] - E[Co(Ti)]; relative to the value at the site T9 (with the proton bound to Ole). e Type of site: P = pore site; F = framework site; C = pocket site at intersection of channels (see text).
proton affinity, using proton affinity as a measure of acidity) are associated with shorter equilibrium A1-0 bond lengths (1.771.8 1 A), shorter Si-0 calculated distances (1.67-1.70 A), large AI-O-H angle (1 13-1 20°), and small equilibriumAl-O-Si angle (120-130O). This picture is consistent with a view of the acid site as a tricoordinated Al-(OSi)3 species forming a dative bond with the H-OSi-(OSi)3 adjacent unit (Figure sa), rather than the ionic picture of an (Si0)p-Al- stabilized with a (Si0)j-S0-H+unit (Figure 5b). The shorter the equilibrium Al-0 bond length, according to this picture, the more stable the dative bond with the OH species. These relationships hold even better (solid squares in Figure 4) if we consider only those sites corresponding to protons located in the large pores of the zeolite. Proton Site Occupancies. Using the calculated substitution energies and proton affinities discussed above, we have calculated the occupancies of protons at the various oxygen sites in ZSM-5. To date, these occupancies have not been measured in ZSM-5, although this information has been obtained by X-ray and neutron diffraction studies in other zeolites. The occupancies have been calculated in two different regimes: (1) assuming the A1 atoms are substituted with equal probability at all T sites in ZSM-5 and
(2) assuming the A1 atoms are substituted thermodynamically according to their relative substitutional energies. In the first model, where it is assumed that the A1 atoms are equally probable to occupy all T sites, the relative population pri of a proton on 0 atom j associated with a particular site TI is given by the Boltzmann factor at 300 K pij = Pij/PY
Pij = exp(-AEi,/kT) where AEij = PA0 - PA/ and PA0 and PAJ represent the proton affinities of the most stable 0 atom site and 0 atom j for the particular site Tr, respectively. Ptot is the sum of the four Boltzmann factors for the particular T site so that the occupancies are normalized to unity for each T site. Figure 6a shows the probabilities of finding protons at each of the oxygens associated with the different T sites according to these assumptions. However, it is not clear whether A1 is actually substituted at all T sites. On thermodynamic grounds the wide range of substitution energies from Figure 1 indicates not all sites would
The Journal of Physical Chemistry, Vol. 97, No. 45, 1993 11759
Acid Sites in Zeolite ZSM-5 Proton Affinities
-%
..
-
13.4
1
> 13.0 -
13.5
13.2
-
Y
.-C
2 12.8 -
c
2
12.6
n
12.2 -
e
0
0 O
0
12.4
T4
T5
T6
T7
T8
T9
TIO
T12
Figure 3. Calculated proton affinities for the 48 inequivalent sites of zeolite ZSM-5.The ordering of the sites is the same as in Tables I1 and 111. Solid barsindicate “pore”sites;open bars correspondto “framework” and “pocket” sites.
be populated. If one assumes that the probabilities of (A1,H) substitution for Si at particular T sites are weighted by the Boltzmann factors corresponding to their relative substitution energies A&,$ub in Table 111, the site occupancies po would be given by
:= 13.2
.-
13.0
E a
12.8
0
0
(4
1
T3
0
R
0
E I
Tl T2
0
D.
I
I
. . . =.. I
. B
B
1
1
I
.
.
0
D 0
0
0
0
0
12.4
12.2
0
I
‘1
fn
O
I
0
1
(b)
12.0 1.67
pjj = P u p ‘ *
0
I
I
I
1.68
1.69 1.70 r(0-Si) [A]
1.71
1.72
Proton Affinity vs AI-0-H Angle 13.6
In this case, Potis the sum of all Boltzmann factors over all 48 combinations of 0 atoms and all T sites. In this regime the probability of finding protons at 300 K is shown in Figure 6b. As shown in the figure, acid sites would occur at only T9 and a few other sites in this limit. Relationship between Proton Affinity and Experimental Structure. A desideratum in zeolite catalysis is the formulation of simple relationships between experimentallymeasured quantities and the chemical properties of the zeolites. For example, for many reactions catalyzed by zeolites there exist empirical rules associating the efficiency of the catalyst for the particular reaction with its acidity. Although these correlations are far from being universal for all catalysts and all reactions, they constituteguiding principles that are used in the development of new catalysts. Because zeolite ZSM-5 has 48 distinct sites where protons can bind, it lends itself to analyses that can yield important relationships between the geometry and the chemical properties of the sites. In addition, if the relationships are presented in sufficiently general terms, they would be expected to be transferable to other zeolites without major modifications. We have found one such correlation that, we believe, can be profitable to the experimentalist. Namely, there exists an important relationship between site acidity, as measured by proton affinity, and the T-0-T angles obtained from X-ray diffraction studies. This relationshipcan be glimpsed already in Figure 4d. However, that plot corresponds to the calculated A I - M i angle, which cannot be measured directly because of the very similar X-ray scattering factors of silicon and aluminum. On the other hand, if one plots (as shown in Figure 7) the corresponding quantities for the experimentally measured T-0-T angles from Table 111, it is evident that there still exists a correlation between the proton affinity and the measured angle, in spite of the fact that these angles really correspond to a weighted average over the silicon and aluminum sites. Because the relationship is approximately linear (with a slopeof 0.034 eV/deg), it is legitimate to assume that the proton affinity (or the acid strength of the site) can be measured by the T-0-T angles. By the argument
-%
I
13.4
-
13.2
-
I
0
5 12.8 -
0
?
13.0
0
0
-
O O
(a I
e.-
1
I.
.
I
-
I
I
1
I
..
=
.
E
P
0 0
0
-
12.2 -
0 0
0 0
0
0
0
0
0
12.4
o o
0 0
(4 12.0 1 120
~
r
I
12.6
I
I
2 12.8 C
I
I
c
2
.
0
00
6
.-.-
,
m
-
12.4. r 12.2
I
.
. ....
0
12.6
I
m
.-5c 13.0 c
I
B
Y
2 e n
I
1
1
1
1
125 130 135 140 Equilibrium AI-0-Si Angle [deg]
1 145
Figure 4. Relationships between the calculatedproton affinitiesand the optimum structural parameters for the 48 inequivalent sites of zeolite ZSM-5.Solid squares indicate “pore”sites; open squares correspondto “framework”and “pocket”sites. (a) Proton affinity vs aluminum-first shell oxygen bond length. (b) Proton affinity vs first shell oxygen-first shell silicon bond length. (c) Proton affinity vs A1-O-H equilibrium angle. (d) Proton affinity vs AI-OSi equilibrium angle.
of the previous paragraph, one would hope that this relationship is transferable to a series of other zeolites, so that the X-ray
Redondo and Hay
11760 The Journal of Physical Chemistry, Vol. 97, No. 45, 1993
Proton Affinity vs Exp. T-0-T Angle 13.6
1
m
H
1
I
a
2, 13.0
.-b
.-
I
I
I
I
.
..
. 0 0
C
a
12.8 0
C
2 n
0
12.6
0 0
12.4
B
8
12.2 12.0 140
145
150
155
160
165
170
175
180
Experimental T-0-T Angle [deg]
Figure 7. Calculated proton affinity vs crystallographic T-0-T angles (after ref 12). Solid squaresindicate "pore"sites;open squarescorrtspond to "framework"and "pocket"sites.
(OSi)
I
(SiO)
Figure 5. (a) Schematic of a "tricoordinated" aluminum site. (b) Schematic of a "tetracoordinated"ionic aluminum site. Proton Populations for Uniform AI Distribution 1.o
3 0.9
.-
c)
0.8
c 0.7 0.6
3
0.5
; 5 0.4 C
v
.-.--b n 2 2
n
0.3
0.2 0.1 u
0 Tl T2
T3
J T4
L
L
T5
T6
T7
T8
T9
TIO
T12
AI, H Thermodynamic Populations at 300 K 0.8 0.7 0.6
.-
0.5
5 m
0.4
L.
n
2 n
0.3 0.2
0.1 0
Figure 6. (a) Predicted populations of protons at 0 sites in ZSM-5 assuming equal distribution of A1 at all T sites at a temperature of 300 K. (b) Predicted populations of protons at 0 sites in ZSM-5 assuming thermodynamicdistribution of A1 substitution for Si at T sites (see text) at a temperature of 300 K.
structures can be used to predict their acidity. We are currently investigatingthis issue, and the results will be published elsewhere. The relationship between the T-0-T angle and the proton affinity can be analyzed with simple chemical arguments as follows. When the proton is bonded to the oxygen, one expects the three pairs of electrons in the H-O, A1-0, and S i 4 bonds, all of which are roughly in the same plane (Table I1 shows that the twist angles are consistent with this picture, particularly for the pore sites), to stay out of each other's way as much as possible.
In the absence of constraints, this would produce H-O-AI, H-OSi, and Al-OSi angles close to 120O. Thus, the tendency for the protonated oxygen is to have an equilibrium Al-OSi angle slightly larger than 120° (see column 4 in Table 111), subject to the constraints of the lattice. On the other hand, in the absence of the proton, the T-0-T angle should be strongly determined by the lattice constraints. Because the experimental X-ray12 diffraction patterns have been taken on a sample with a relatively low concentration of aluminum, the measured T-0-T angles are more heavily weighted by the sites that do not contain aluminum (compare columns 2 and 3 in Table 111) and, hence, to the unprotonated angles, which are large. Then, one would expect a large amount of strain to be introduced as a result of the 0-H bond. Consequently,one expectsthe proton affinity to be smaller (stronger acidity) when the starting angle is large than when the unprotonated T-0-T angle is closer to 120O.
Discussion The results of the present calculationsshow important relations between the energeticsof acid sites and their geometricstructures. Consideration of all 48 possibilities arising from the 12 T sites of ZSM-5 (each site having four distinctoxygen nearest neighbors) shows that there is a wide range of 1.2 eV in the aluminumproton substitution energies (Figure 2). However, at least half of these cases lie within 0.4 eV of the lowest energy, corresponding to the T9 site with a proton bound to 0 1 8 . In fact, every site, except T7 and T8, gives rise to at least one acid site whose energy is less than 0.2 eV from that of the T9 site. These results are quite different from our earlier ab initio studylo and from previous ab initio studies by Fripiat et al.,' neither of which allowed for lattice relaxation or protonation effects. In the former study, we found the T6, T9, and T12 sites to be the most stable, while Fripiat et al. found the Tl2 site to be most stable. The present results can be compared with a recent cluster study of ZSM-5 also employing the semiempirical quantum chemical MNDO method by Lonsinger et a1.14 They found Tl2 to be the favored site based on the computed (A1,H) substitution energies. The relative energies of the most stable (A1,H) configuration at the other T sites varied over a range of 26 kcal/mol. In the present study a narrower range of 6 kcal/mol (0.28 eV) of substitutional energies was found when comparing the most favorable proton locations for the 12 T sites, and T9 was the overall favored site. One significant difference between the two approaches involves the overall cluster sizes: in the present work typically 100-120 atoms were included in the cluster while clusters containing 34 atoms were used in the survey of 48 sites in ref 14. (A larger cluster was constructed to represent the T12 acid site.) Positions of fixed atoms in the clusters examined by Lonsinger et al. were based on the X-ray refinement of the crystal structure
Acid Sites in Zeolite ZSM-5 by Olsen et a1.19 whereas the present study used the more recent refinementby van Koningsveld et ~ 1 . As ’ ~discussed in our earlier paper,lOthelatterexperimentalworkprovidesa significantly more accurate atom positions; for example, Olsen et al. obtained T-O bond lengths ranging from 1S O to 1.67 A compared to a narrower range of 1.567-1.605 A obtained by van Koningsveld et al. Finally, we note that the imposition of lattice constraints needs to be done with considerablecare (see the section on the calculationaldetails); the procedure by which this is done could be another possible source of discrepancy between the two studies. A recent classical simulation of A1 substitution and 0 protonation has been carried out on ZSM-5 by ShrMer e? al.15 using classical force fields. Their study is based on the more recent monoclinic (low temperature) structureof ZMS-5 reported by van Koningsveld et a1.,16while our study is based on the earlier orthorhombic (high temperature) structure reported by the same group.1z For the 96 different structures they obtain a narrower range of substitution energies (less than 0.35 eV) compared to our larger range of 1.2 eV for the 48 different structures. If one examines the most stable form for (Al,H) substitution at each T site, however, both papers are in basic agreement in predicting very small energy differencesfor the lowest nine sites-less than 0.2 eV in our study and less than 0.05 eV in the study by ShrMer et al. The analysis of the semiempirical quantum chemistry calculations showed that sites with high proton affinities corresponded to structures with strongly bent Al-OSi linkages. In addition, a similar correlation of high proton affinity with smaller T-O-T angles taken from the experimental crystal structure of ZSM-5 was observed. The experimental T-O-T angles essentially correspond to unprotonated Si-OSi linkages in the zeolite because of the low AI/Si ratio. It has been shown that computed Al-OSi bond angles are considerably smaller than the unprotonated Si-OSi bond angles from ab initio9quantum chemistry calculationson dimer models for acid sites in zeolites by Nicholas et aL9 as well as in semiempirical studies.I7 It has also been pointed out that other geometric and compositional factors, such as the presence of nearby aluminum atoms, can affect the acidity of the sites.18 The resultant conclusion that acidity (lower proton affinity) is correlated with larger T-O-T angles has been similarly noted in these st~dies.~J’The present study represents the most extensive analysis of the correlation of acidity with computed T-O-T angles using realistic models for ZSM-5. Similarly, the correlation of acidity with experimental T-O-T angles appears not to have been emphasized before. The recent series of calculations by Brand e? aLBanalyzed acidity in clusters representing the ZSM-5 framework using ab initio approaches. They examined the effect of cluster size on the calculated proton affinities for two representativeT sites and also noted the greater tendency for protonation at smallerT-O-T angles. They also found considerable variation (20 kcal/mol) with cluster size in computed proton affinities. Most of this variation can be attributed to the fact that some clusters were terminated by Si-H groups and other clusters were terminated by Al-OH groups. The variation with cluster size is only a few kcal/mol if one compares the latter clusters terminated by AlOH groupswhich are analogousto the clusters used in the present study. Experimental studies of acidity in ZSM-5 using calorimetry3 generally obtain a single binding energy for adsorption of a base such as ammonia or methanol at the acid site. The present results indicate that one would expect a distribution of binding energies corresponding to variations in the proton affinities at different T sites (at least 29 kJ/mol if one takes only the largest proton affinity for each T site). Whether one should describethe acidity in ZSM-5 in terms of a single site or in terms of a distribution of sites remains an interesting, but unresolved, issue for future study.
The Journal of Physical Chemistry, Vol. 97, No. 45, 1993 11761 COOChSiOM Our semiempirical quantum chemical calculations on 12 clusters modeling the acid sites of zeolite ZSM-5 show that there is a wide range of 1.2 eV (1 16 kJ/mol) in the aluminum-proton substitution energies. However, every site, except T7 and Te, gives rise to at least one acid site whose energy is less than 0.2 eV from that of the lowest energy (T9) site. Thecalculations also show that there exists a direct correlationbetween the aluminumproton substitution energy and the proton affinity of a given site-those sites that exhibit the largest proton affinity are the ones for which the aluminum is most stable. The proton affinities corresponding to the most favorable oxygen for a given T site vary by 0.3 eV (29 kJ/mol) for the 12 acid sites in ZSM-5. We find that the sites with the most favorable (A1,H)Si substitution energies and concomitant highest proton affinities are the ones where the proton is located at Ypore”sites where the proton is protruding into the large zeolite pores. The unfavorable sites correspond to “framework” locations where the proton lies within the smaller regions of the zeolite framework. In addition, both the (Al,H)/Si substitution energy and the proton affinity depend on the geometric parameters, such as bond lengths and angles, of the optimum configurations for the acid sites. In particular, overall acid site stability is correlated with smaller Al-OSi bond angles, larger A1-O-H bond angles, and short A I 4 and Si-O bond lengths. Perhaps the most important conclusion from this study is that there is a direct relationship between the experimental T-0-T angle and the proton affinity. This suggests that the T-0-T angle can be used as a measure of the acidity of the site. This conclusion, although obtained for the 48 sites of zeolite ZSM-5, would be expected to be transferable to other zeolites. Ackoowsledgment. The authors have benefited from a critical reading of the manuscript by Dr. P. J. MacDougall and Prof. A. K. Cheetham and from fruitful discussions with Drs. A. E. Alvarado-Swaisgood and M. K. Barr. We also thank Profs. R. J. Gorte and J. Sauer for providing helpful comments and copies of manuscripts prior to publication. This work was performed under the auspices of the US.Department of Energy, Advanced Industrial Concepts Division.
References and Notes (1) Dwyer, J.; OMalley, P. J. Srud. Surf.Sci. Carol. 1988, 35, 5. (2) Rabo, J. A,; Gajda, G. J. Cur. Rev.-%. Eng. 1989, 4, 385. (3) (a) Gricus Kofke, T. J.; Gorte, R. J.; Fameth, W. E.J. CUtUl. 1988, 114, 34. (b) Panillo, D. J.; Gortc, R. J. Curul. I r r r . 1992, 16, 17. (4) Beyerlein, R. A,; McVicker, G. B.; Yacullo, L. N.; Ziemiak, J. J. J . Phys. Chem. 1988,92, 1967. (5) Carvajal, R.; Chu, P.-.J.; Lunsford, J. H. J. Carol. 1990, 125, 123. Sun, Y.;Chu, P.-J.; Lunsford, J. H. Lungmuir 1991, 7, 3027. (6) Sauer, J. Chem. Rev.1989,89, 199 and references therein. (7) Fripiat, J. G.; Berger-Andre,F.;Andrt, J. M.;Derouane,E. G. Zeolires 1983, 3, 306. Derouane, E. G.; Fripiat. J. G. Zeolites 1985, 5, 165. (8) Brand, H. V.; Curtiss, L. A.; Iton, L. E. J. Phys. Chem. 1992,96, 7725. (9) Nicholas, J. B.; Winans, R. E.;Harrison R. J.; Iton, L. E.; Curtiss, L. A.; Hopfinger, A. J. J. Phys. Chem. 1992.96, 10247. (10) Alvarado-Swaisgood,A. E.; Barr, M. K.; Hay, P. J.; Redondo, A. J. Phys. Chem. 1991, 95, 10031. (1 1) Dewar.M. J. S.;Thiel, W.J. Am. Chem.Soc. 1977,99,4899. Stewart, J. J. P. J. Compur. Chem. 1989, 10, 209, 221. (12) vanKoningsveld,H.;vanBekkum,H. J.; Jansen, J.D.AcruC~srullog. 1987, 843, 127. (13) JANAFThcrmochemiculTubles,2nded.;Nat. Bur.Stand.Documsnt NSRDS-NBS 37; US.Government Printing Office:Washington, DC,1971. (14) Lonsinger, S.R.; Chakraborty, A. K.; Theodorou, D. N.; Bell, A. T. Curul. I r t r . 1991, 11, 209. (15) ShrBder, K.-P.; Sauer, J.; Leslie, M.; Catlow, C. R. A. Zeolires 1992. 12, 20. (16) van Koningsveld, H.; Jansen, J. D.; van Bekkum, H.J. Zeolires 1990, 10, 236. (17) Senchenya, I. N.; Kazansky, V. B.; Beran, S.J . Phys. Chem. 1986, 90,4857. See also: Gibbs, G. V. Am. Minerul. 1982,67,421 and referencca
therein.
(18) Barthomeuf, D. Murer. Chem. Phys. 1987, 17,49. (19) Olson, D. H.; Kokotailo, G. T.; Lawton, S.L.; Meier, W. M. J . Phys. Chem. 1981,85, 2238.
