J. Phys. Chem. 1993,97,8703-8706
8703
An Examination of the Electrostatic Potential of Silicalite Using Periodic Hartree-Fock Theory Julia C. White and Anthony C. Hess’ Pacifc Northwest Laboratory, P.O. Box 999,MS Kl-95,Richland, Washington 99352 Received: April 29, 1993; In Final Form: June 23, 1993”
ZSM-5 is a widely used industrial catalyst. Its siliceous analog, silicalite, is a molecular sieve with unique hydrophobic properties. To begin to understand the properties of this zeolite and to provide a base line for the study of aluminated forms, we have carried out a periodic Hartree-Fock (PHF) calculation on silicalite. The position of molecules in the lattice has been speculated for many years. From three-dimensional plots of the PHF electrostatic potential, we postulate that the most favorable position of intercalated species is near the intersection of the 10-ring channels. Introduction
Zeolites are open-framework structures composed of TO4 tetrahedra (T = Si, Al) that interconnect by sharing corners to form multidimensional channels throughout the crystal.’ This system of channels allows zeolites to function as molecular sieves, the width of the channel determining which molecules can diffuse through the material. The crystals also contain charge-compensating cations and can act as ion exchangers, adsorbents, and catalysts. Silicalite is the siliceous analog of ZSM-5, with the same topology as that member of the pentasil group but not the catalytic activity associated with an aluminated lattice.* This analog has unique hydrophobic and organophilic properties that are absent in its aluminosilicate relative.233 Silicalite has a two-dimensional pore system, with 10-ring channels in the [OlO] and [loo] directions (“10”-ring refers to the number of TO4 tetrahedra comprising the covalently bonded ring). The straight [OlO] channel (Figure 1) has an effective cross section of approximately 5.6 X 5.3 A.4 Because of its pore size and the hydrophobic and organophilic nature of the lattice, silicalite is an important adsorbent of small to medium sized nonpolar molecules. However, the location and orientation of molecules within the crystal is the subject of some debate. A theoretical study of the electronic structure of silicalite not only provides a base line for future studies involving the selective alumination of the lattice but also quantifies the characteristics of the siliceous lattice. There are numerous theoretical studies of silicalite and ZSM-5 using classical me~hanicss-~ and ab initio cluster models;8v9however, both methods have well-known inherent limitations. For example, classical mechanics studies commonly use Lennard-Jones and Coulomb functions to describe the interaction between the molecule and zeolite, but these functions must be parametrized to existing experimental or theoretical data. Previous ab initio calculations on zeolites used small fragments to model the crystal. This is potentially problematic since many of the calculated properties of zeolites are dependent upon the size of the fragment used, converging only when the fragment is large. For example, it has been shown9 that in order to determine the proton affinity in ZSM-5 it is necessary to consider a 50atom cluster. The PHF-method employed in this study avoids the problems described above. The ab initio calculations require no semiempirical functions, and the use of cyclic boundary conditions eliminates terminal cluster effects. This first-of-its-kind quantum a Abstract
published in Advance ACS Abstracts, August 15, 1993.
0022-365419312097-8703$04.00/0
mechanical study of silicalite also represents one of the largest self-consistent-field (SCF) calculations on zeolites to date. In this study, we present the results of an examination of the electrostatic potential in the zeolite lattice. Using classical arguments, we postulate that the most favorable region for intercalated molecules is near the intersection of the 10-ring channels. These results are in agreement with NMRlO and classicalll studies and contrast with other simulations that find the molecules to reside preferentially in the straight or sinusoidal channels.7J2J3 Method
The ab initio calculations were performed using the SCF linear combination of atomic orbitals periodic Hartree-Fock (PHF) method, which is implemented in the program CRYSTAL.14 A detailed explanation of the operation of CRYSTAL has been provided by Pisani et al.ls and Hess and Saunders.16 The S C F energy was converged to 1 P hartrees, with the tolerances for the infinite Coulomb and exchange series set at s, = M t = 4 and sex = pgeX= 4 andpl,, = 8.15 The physical properties of the system were calculated using the ground-state wave function. The structure chosen for silicalite was orthorhombic with Pnma symmetry. The ZSM-5 structure of Olson et al.17 was dealuminated by placing silicon atoms on all the T sites. This structure was chosen because of its high silicon-to-aluminum ratio (Si/Al = 86). The unit cell has 288 atoms, and the calculation was done using a standard Pople STO-3G b a ~ i s , ~producing *J~ 1824 basis functions. The S C F evaluation of the ground-state energy and wave function required 18 h of CPU on a Cray-2S and 40 megawords of memory. Results and Discussion
The total PHF-SCF energy of the siliceous ZSM-5 lattice is -41 610.519 08 hartrees. TheaverageMullikenchargesonsilicon and oxygen are 1.48 le1 and -0.74 lei, respectively. Electrostatic potentials were evaluated from the PHF charge density for points in the unit cell uniformly spaced about 0.25 8,apart. The resulting data were analyzed using both two-dimensional contour plots and three-dimensional isopotential surfaces, as discussed below. The multidimensional 1O-ring channel system is the only region of the crystal that is accessible to intercalated species. The electrostatic potential in the [OlO] 10-ring channel has been plotted
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0 1993 American Chemical Society
8704 The Journal of Physical Chemistry, Vol. 97, No. 34, 1993
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Figure 1. Top: schematic representation of pores in silicalite. Bottom left: 2 X 2 unit cell of silicalite in the uc plane. Bottom right: Wring of the sinusoidal channel, in the bc plane.
as a two-dimensional contour map in a plane that bisects the channel along the 6 axis (Figure 2). Asterisks indicate the intersectionof the plane and lattice. For a point of reference, the electrostaticpotential has been shiftedby the additionof a constant so that the value in the center of the channel is zero. Contour spacingsare 0.02 hartree, and dashed lines are negativenumbers. The magnitude of the electric field (defined as the modulus of the negative gradient of the electrostaticpotential) is small in the center of the channel. The plane bisects oxygen atoms of the [OlO] 10-ring channelonly, and thenegativelobe-shaped contours are directed from these atoms toward the center of the channel. This slice of the unit cell of silicalite supports our intuitive understanding of the siliceous lattice. Namely, the potential clearly decays with increasing distance from the atoms of the lattice, and the minimum of the electrostatic potential (dashed contours)is associatedwith the negatively charged oxygen atoms. A three-dimensional map, or isosurface, of the electrostatic potential is more informative. An isosurface is a plot of the interpolationbetween points with the same value. The isosurface in Figure 3 correspondsto the value of the electrostaticpotential near its minimum, relative to values near the nuclei. Classical electrostaticspredicts this negativeregion of space to be the most energeticallyfavorablelocation for a positive test charge present
in the lattice. The negative contours of Figure 2 are now seen as relatively small features (L1 and L2) compared to large hemispherical-shapedpotentials labeled H 1to H4. From Figure 2 it can be seen that the minimum in the potential is associated with the oxygen atoms as lobe-shaped contours. We suggest that, in terms of size and orientation, these lobes correspond to lone pair electrons on oxygen atoms. To determine why the lobe shapes coalesce into the large hemispherical object mentioned above, it is useful to first examine the 10-rings associated with the [ 1001 sinusoidal channel. The top illustration in Figure 1 is a schematic representation of the pores in silicalite. Roman numerals I and I1 indicate the straight and sinusoidal channels, respectively. The intersection of these two channels is denoted by numeral 111. The bottom-left diagram of Figure 1 shows an edge-on view of the [OlO]channel. The siliconatomsof one of the 1O-ringsthat composethe sinusoidal channel, connecting two straight [OlO] pores, are labeled 1 to 5. The other half of this 10-ring is produced by a mirror plane, as seen in the bottom-right diagram of Figure 1. The hemispherical isosurface is associated with the five oxygen atoms labeled a,@, y, 6, and u. The dihedral angle formed by a,@,r, 6 and by @, y, 6, u does not exceed 7 O . Except where generated by symmetry, there are no other Occurrences of an extended planar-
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The Journal of Physical Chemistry, Vol. 97, No. 34, 1993 8705
Figure 2. Top: two-dimensional contour plot of the electrostatic potential down the [OlO] 10-ring channel. Value at the center of the plot has been set to zero. Bottom left: unit cell of silicalite in the bc plane. Bottom right: unit cell of silicalite in the uc plane. Astericks indicate intersection of lattice with contour map.
type sequence of oxygen atoms in the unit cell. We postulatethat the nonbonding electronsof the five oxygen atoms, coplanar and directed toward the same point in space, act in concert upon a positive test charge to produce the continuous hemispherical surface. While the size of the calculation precludes any attempt to determinethe optimum position of an intercalated species in the lattice using CRYSTAL,14this three-dimensionalplot allows us to postulate that the most energetically favorable position of a positively charged species is near the regions marked Hl-H4. The electric field is also greatest in this region, indicating that a molecule with a dipole would interact most strongly with this part of the lattice. Lastly, it is important to comment upon the basis set used in this study. The STO-3G basis functionsare very contracted and produce large average errors in molecular properties.20 Preliminary studies of silica sodalite show that the lattice is more contracted when optimized with the STO-3G basis (8.815 A) than with a split-valence plus polarization basis (8.895 A). However, increasing the quality of the basis set to 3-21G* (dtype functions on silicon and oxygen) would require over 200 Megawords of memory and diagonalization of a 4416 X 4416 matrix. This calculation is beyond the current capabilities of most supercomputers. For this reason, and because the hemispherical surface we are interested in correlates with the atoms in a single 10-ringsystem, molecular calculations based on this unit were performed to assess the effect of basis set size on the
electrostatic potential. The positions of atoms in the 10-ringare identicalto thecrystal coordinates, with terminaloxygens replaced by hydrogens. The geometry of the molecular structure was not optimized. Ground-statewave functionsfor the Si10010H20ring were determinedusing STO-3Gand 6-21G*21f2 basis sets. Threedimensionalplots of the electrostaticpotential near its minimum (Figure 4) show that adding d-type polarization functions and relaxing the sp Gaussians has little effect on the shape of the minimum potentialisosurface, although thevalueof the isosurface decreased from about -19 to -47 kcal/mol for the STO-3G and 6-21G* basis sets, respectively. It is also interesting to note the degree of similarity between the topology of the isosurface generated from the cluster and the periodic calculations.
Conclusion By performing periodic Hartree-Fock calculationson silicalite, we are able to obtain information about the electronic structure of the lattice without truncating long-range interaction terms. Classicalelectrostaticspredicts the regions of spacenear the PHF potential minimum to be the most energeticallyfavorablelocation for positively charged species present in the lattice. This region occurs near the intersection of the 10-ring channels. Although it may be argued that charged or strongly dipolar species would not enter a completely siliceouslattice, large portions of ZSM-5 may be devoid of aluminum (and the correspondingcations), and so an understanding of the electrostatic potential in this area is necessary. With a more accurate description of the molecule-
8706 The Journal of Physical Chemistry, Vol. 97, No. 34, 1993
Letters studies will focus on the changes in the electronic properties of the lattice as it is aluminated. Acknowledgment. We acknowledge V. R. Saunders, R. Dovesi, and C. Roetti for allowing the use of prereleased versions of CRYSTAL.I4 The authors thank the Advanced Industrial Concepts Division of the DOE Office of Conservation and Renewable Energies (Contract No. 16697) for their support of this study. This work was undertaken at Pacific Northwest Laboratory, which is operated for the U.S.Department of Energy (DOE) by Battelle Memorial Institute under Contract DE-AC0676RLO 1830. We also thank the Scientific Computing Staff, Office of Energy Research, U.S. Department of Energy, for a grant of computing time at the National Energy Research SupercomputerCenter. The illustration in Figure 4 was generated using the Space Module-Version 3.0by Erin Thornton, Chance Younkin, Anthony Hess, John Nicholas, Michael Thompson, and Donald Jones, Integrated Computational Chemistry Environment, Pacific Northwest Laboratory, Richland, WA 99352.
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H1
H3 References and Notes
H4
i L
H2 -
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Figure 3. Top: isosurface of electrostatic potential minimum value, superimposed with the unit cell lattice, in the ac plane. Bottom: same as above, rotated 90°.
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Isosurface of theelectrostatic potential minimum for SiloOl&I~o, using a 6-21G* basis set. Key: white balls, hydrogen; yellow balls, silicon; red balls, oxygen.
Figure4.
lattice interaction, molecular dynamics simulations may find the intersection region to be more energetically favorable. Future
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