Symposium on Molecular Modeling of Petroleum Processes
Presented before the Division of Petroleum Chemistry, Inc.
American Chemical Society
San Francisco Meeting, April 5-10, 1992
Reprinted from PREPRINTS
Division of Petroleum Chemistry, Inc.
American Chemical Society, San Francisco Meeting
Volume 37, No. 2, March, 1992
Modeling Acid Sites in MFI Zeolites with Realistic Geometric Constraints
Amoco Chemical Company
PO Box 3011
Naperville, Illinois 60566
The Brønsted acid generated by substitution of B or Al for Si in an MFI zeolite has been modeled with the semi-empirical, MNDO method. A 70 heavy atom fragment based on the silicalite X-ray crystal structure was used, and only the atoms closest to the acid site were allowed to relax. This compromise between whole crystal and small molecule modeling allows the use of a molecular orbital method to model active sites within a zeolite catalyst, with a realistic representation of the geometric constraints imposed by the surrounding crystal lattice. Consistent bond orders and charges can be calculated by relaxing those atoms within 2 bonds of the site, but consistent geometries and energies require relaxation of atoms up to 4 bonds away. This method is able to reproduce the change from planer to tetrahedral B upon deprotonation of a borosilicate, and shows electronic differences between a borosilicate and an aluminosilicate site.
A large volume of the catalyst used in petroleum processing has been based on zeolites, specifically aluminosilicates and borosilicates with the MFI crystal structure. Modeling the acid sites of these catalysts as the acid and as ion exchanged forms as well as the acid sites in other zeolite crystal structures will help to understand and predict catalytic activity. To model the geometry, energy (acidity), electronics, and bonding, a molecular orbital method is desirable.
The acid site is not an isolated hydroxyl, but is part of a well defined crystal lattice. This introduces two issues for modeling. First, even a single unit cell of a zeolite crystal has more atoms than is practical to model with ab initio methods: an MFI unit cell, for instance, contains 288 atoms. The second issue is to reproduce the localized flexibility of the framework to accommodate substitution of B or Al for Si, while retaining the geometric constraints imposed by the surrounding crystal lattice.
Without the correct geometry, a meaningful energy cannot be calculated. Attempts to reproduce the observed acidity difference (MFI aluminosilicate is known to be a stronger acid than the borosilicate) by modeling small molecules, have shown wide variance. The literature reports values for the relative deprotonation enthalpy of 0.0, 7.4, 14.0, 1.0, and 15.6 kcal/mole based on a 9 heavy atom metallosilicate partially optimized with the STO-3G basis set,1 a 3 heavy atom metallosilicate hydride fully optimized with the 3-21G basis set,2 a 9 heavy atom metallosilicate optimized with restricted symmetry with the 6-31G basis set,3 an MNDO calculation on the same geometry, and a 3 heavy atom metallosilicate hydride-ammonia complex optimized with the 3-21G basis set,4 respectively.
Approach to Incorporate Geometric Constraints
One reason modeling borosilicate acidity is so sensitive to how realistically the geometry constraints are reproduced, is the shorter B-O bond length relative to Si-O or Al-O bonds. Modeling the simplest tetracoordinate aluminum and boron acids (M(OH)3H2O) with the MNDO approximation and imposing no geometric constraints, calculates the boron acid to be more acidic than the aluminum acid by 4.7 kcal/mole. Incorporating the metal atom center into a polycyclic (MSi3O10H5, adamantane-like metallosilicate) structure, and relying on the connectivity of the ring system to constrain the geometry around the metal center also fails to reproduce the known relative acidity: the boron acid is still calculated to be more acidic than the aluminosilicate by 4.8 kcal/mole.
The approach that has been developed to model these systems with realistic geometric constraints is to use a large fragment with localized geometry optimization. This is a compromise between modeling a whole crystal and modeling a small molecule. The semi-empirical MNDO approximation with an expanded version of Mopac 5.1 (to handle 70 heavy atoms) on a Tektronix CAChe WorkSystem was chosen to match the level of sophistication of the calculation to the size of the problem. A 70 heavy atom fragment was constructed, based on the reported MFI crystal structure,5 and the terminal oxygen atoms were capped with hydrogens to maintain the MFI bond angles. Boron or aluminum was substituted for the silicon at the T3 site, and the appropriate oxygen was converted to a hydroxyl and to a hydroxide to generate the corresponding acid and conjugate base sites as shown for boron:
The positions of the outer shell of atoms were held fixed, and those atoms within 0 bonds, 2 bonds, or 4 bonds of the acidic O-H were allowed to relax and the entire metallosilicate was also allowed to relax. The results of these calculations were used to determine the minimum relaxation required to reproduce observed geometry and acidity differences, and to calculate consistent geometries and electronics.
Results and Discussion
One geometry difference that has been observed is that boron prefers to be more planer in the acid form of an MFI borosilicate, while only tetrahedral aluminum has been observed. The large molecule with localized minimization approach requires relaxation of those atoms within 2 bonds (1st sphere) of the acidic O-H to reproduce the boron preference for a planer geometry, but relaxing atoms 4 bonds away (2nd sphere) makes little additional difference, so relaxation of the 1st sphere seems sufficient. Boron in the conjugate base form stays essentially tetrahedral.
Relaxation of the geometries of atoms within 2 bonds of the acidic O-H is necessary to achieve a consistent bond order for the borosilicate. It also seems sufficient, because there is little additional change upon relaxing atoms further away. The aluminosilicate bond order is consistent, even with relaxation of the O-H only.
Modeling aluminosilicate and borosilicate acidity (the change upon loss of a proton to form the conjugate base) shows a similar requirement for relaxation: most of the change in geometry, bond order, and partial charge can be modeled by relaxing the 1st sphere of atoms. One exception is the energy of the aluminosilicate, which continues to change as more of the molecule is relaxed. The energy of the borosilicate changes substantially with relaxation of the first sphere, then returns to the initial value as more of the molecule is allowed to relax. The change in the B-O-Si angle also continues to change, so that relaxation of the 2nd sphere of atoms may be necessary to model that geometry variable.
Finally, determining the extent of relaxation necessary to reproduce the difference in acidity (the relative change upon deprotonation of the aluminosilicate and the borosilicate) was examined. One of the geometry variables, the relative change in the M-O-Si bond angle, does continue to change with relaxation of the 2nd sphere of atoms. Most of the relative change in the M-O bond order is accounted for by relaxing the 1st sphere. The difference in deprotonation energy shows an interesting crossover: with relaxation of only the O-H, the boron acid is more acidic than the aluminum acid, but with relaxation of the 1st sphere (of 9 atoms) the borosilicate is calculated to be the weaker acid by 8.7 kcal/mole. Relaxation of the 2nd sphere (17 atoms) gives a slightly smaller value, but relaxing the entire fragment is clearly unrealistic, because the relative difference in deprotonation energy climbs and the borosilicate becomes the stronger acid again.
The semi-empirical MNDO method can be used to model a zeolite acidic site by using a large fragment with localized optimization to realistically reflect the geometric constraints of the crystal lattice. Relaxation of atoms within 2 bonds of the acidic site is necessary for consistent charges and bond orders and to reproduce acidity differences. Relaxation of atoms 2-4 bonds away may be necessary to model certain geometry variables. This method reproduces the experimental observations that: the MFI borosilicate is a weaker acid than the aluminosilicate; in the acid form boron prefers to be more planer; and both boron and aluminum become tetrahedral in the conjugate base form. It predicts that the charge is delocalized rather than simply transferred to the T3 metal atom, and that there is increased M-O bonding in the conjugate base.
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