6398
J. Phys. Chem. 1993,97, 63984404
Periodic Hartree-Fock Study of Siliceous Mordenite Julia C. White and Anthony C. Has* Molecular Sciences Research Center, Pacific Northwest Laboratory, P.O. Box 999, MS KI -95, Richland, Washington 99352 Received: February 2, I993
We report results of an all-electron ab initio periodic Hartree-Fock LCAO calculation on a completely dealuminated form of mordenite, Si48096, possessing Cmcm symmetry. The reported physical properties were computed using a modified 6-21G" basis. The resulting calculation is one of the largest ab initio studies carried out to date and demonstrates the feasibility of using ab initio methods to investigate large, complex systems. The sensitivity of the total crystal energy to small changes in geometry is explored by comparing the relative stabilities of seven reported experimental mordenite structures. The total energies of the structures are found to vary by as much as 186 kcals/mol. We note that the larger the standard deviation in S i 4 bond distances and 04-0 angles the less energetically favorable the lattice will be. Crystal charge density and deformation density maps have been computed in the cylindrical channel of one of the reported crystal Structures. Those calculations indicate the absence of charge density in the center of the channel ( 10-6 e/bohr3) and a polarization of charge density localized near the oxygen atoms. Ab initio electrostatic potentials and electric fields in chemically important regions of the material have been computed from the Hartree-Fock ground state density. Comparisons of the ab initio electrostatic potential to those resulting from model charge distributions (Mulliken point charges and formal point charges) are made. The point charge models investigated did not provide a quantitatively correct description of the electrostatics of these lattices. The average Mulliken charges are +2.091el and -1.041el for silicon and oxygen, respectively. The total valence density of states and projected density of states condensed to all silicon and all oxygen atoms as well as projections into oxygen 2s and 2p orbitals have been evaluated. N
Introduction Zeolitesare open-framework structures composed of Si04 and A104tetrahedra in conjunctionwith charge compensatingcations. The TO4 tetrahedra (T = Si, Al) in these porous materials interconnect by sharing corners to form 1-, 2-, or 3-dimensional channelsthroughout thecrystal. The resulting systemof channels allowsthese compoundsto efficientlyfunction as molecular sieves.' In addition,they have been demonstrated to act as ion exchangers, adsorbents and catalysts.' Zeolites have applications in a wide variety of fields, including bulk separation proces~es,~-~ gasoline refinement: and long-term storage of nuclear waste product^.^*^ The composition of mordenite is more silicon rich than most naturally occurring zeolites, with a typical Si/Al ratio of approximately five. It has a 2-dimensional pore system, with 12and 8-ring interconnectingchannels (1 2 and 8 refer to the number of TO4 tetrahedra in the ring). The larger channel, which is approximately cylindrical in shape, lies parallel to the [OOI] direction and has an effectivediameter' of about 6.5-7.0 A. This allows molecules as large as neopentane' to diffuse through the material. Our motivation for studying siliceous zeolites stems from the observation that by selectivelydealuminating such materials, their catalytic properties can be manipulated and an increase in the stabilityof the lattice in acidicand high temperatureenvironments can be a c h i e ~ e d . In ~ . addition, ~ coking is decreased in mordenites partially dealuminated by either acid-leaching techniques or the initial synthetic conditions. As a result, catalytic activity (e.g., cracking n-hexanelOJland cumene12or converting methanol to gasoline4) is increased. Siliceous zeolites are also hydrophobic and can be used to selectively sorborganic molecules from aqueous solution^.'^ Since mordenite can be dealuminated without loss of crystallinity,' structures with Si/Al ratios ranging from 5 to several hundred have been synthesized and the adsorption and catalytic activity of these compounds have been exami ~ i e d . ~ J & - ' In ~ -addition, * ~ ' ~ such studies provide a well-char0022-3654/93/2097-6398$04.00/0
acterized initial state to study the controlled introduction of aluminum into the lattice. The chemistry and reactivity of zeolites are ultimately dependent on atomic-scale properties such as proton affinities, ion-exchange capacities, and the location and chemical identity of the framework atoms and charge-compensatingions. Quantifying the individual effect that each of these atomic features ultimately has on the properties of a zeolite is a difficult experimental task. Traditional theoretical studies of zeolite chemistry have relied on the use of either molecular dynamics simulations of the or ab initio calculations on 'molecular zeolite fragment^".^^-^^ The classical dynamics simulations are limited by the quality of the potential energy function used in the solution of Newton's equations of motion. Difficulty in identifying suitable molecular "clustersmconstrains molecular cluster methods. In addition,thecluster approximation necessarily introduces unphysical effects into the problem. The need to achieve charge neutrality often involves the addition of hydrogen atoms that results in a stoichiometrydifferent from the parent compound and the neglect or approximate treatment of long-range forces. Hence, the representativeSchrodinger equation is ultimately solved subject to boundary conditions that are inconsistent with theoretical and empirical definitions of a crystalline material. The method used in this study exploits the long-range order present in crystalline systems by solving the Hartree-Fock-Roothaan equations subject to periodic boundary conditions. The formal incorporation of translational and rotational symmetries into the theoretical method provides an efficient mean to study crystalline systems without the approximations inherent to the cluster approach described above. We begin the following sections with a brief statement of the approach and a discussion of the computational details. We will then present the results of a geometric analysis and total energy calculationscarried out on the T-O framework of seven reported experimental mordenite structures. This is followed by a discussion of the physical propertiesof siliceousmordenite. These Q 1993 American Chemical Society
Siliceous Mordenite include aspects of the charge density distribution, electrostatics, and density of states. We close with a summary of the results of this study and an outline of the feasibility of applying periodic Hartree-Fock theory to compounds such as mordenite. Computational Details The calculations reported here were carried out using the ab initio self-consistent-fieldlinear combinations of atomic orbitals periodic Hartree-Fock (LCAO-PHF) method. This method is fully implemented in the program and a detailed discussion of the mathematical formulism and computational implementation of the method has been presented by Pisani et al.30 Briefly, the multistep process begins by evaluating all oneand two-electron integrals necessary to construct the direct space Fock matrix. The direct space Fock matrix and the associated overlap matrix are then Fourier transformed to reciprocal space where they became block diagonal. The subsequent solution of the corresponding matrix equations yields a set of eigenvalues and eigenvectors at points in reciprocal space. A new density matrix can then be defined in reciprocal space, back Fourier transformed to direct space, and used to redefinethe Fock matrix. This “cyclen continues until convergence of the total energy is achieved. All physical properties reported here have been evaluated from the fully converged ground-state wave function. For a more detailed overview the reader is referred to Hess and S a ~ n d e r sI . ~ The basis set used in this study was based on Pople’s 6-21G32333 with the outer valence functions reoptimized in an earlier study on ilmenite.34 In that study, the exponentof siliconwas contracted from 0.093 339 2 to 0.13 and oxygen went from 0.373 684 to 0.35. Polarization functions (d-type) were added to silicon and oxygen with exponentsof0.45 and 0.8, respectively. The structure of mordenite used to compute the physical properties was the dehydrated cesium structure reported by Schlenker et al.35 The T = (Si, Al) atom positions in the reported crystal structure were fully occupied by silicon atoms. Consequently, the calculations included no cesium ions. The lattice parameters and atomic positions were not optimized due to the high cost of the calculations. The self-consistent-fieldcalculation of the groundstate energy and wave function of mordenite using the 6-21G* basis set required 20 h of CPU time on a Cray-2S, 4.5 Gigabytes of space and 19 Megawords of memory. The tolerances for the infinite Coulomb and exchange series in the calculations were so = t ~ = 5 a n d s , , = ~ ~ ~ = 5 a n d p ’ ,ll.’O ,= Readts and Discussion Analysis of Mordenite Framework. To carry out the quantum mechanical calculations described above, it is necessary to first choose an appropriate framework geometry for the study of mordenite. The selection process is complicated by the fact that siliconand aluminum atoms (the “T” atoms) are indistinguishable in X-ray diffraction Since X-ray diffraction measurements are the primary source of structural information for these materials, it is possible to state the average T atom positions in the framework but not the specific locations of silicon and aluminum atoms on the available sites. Reported experimental space groups, therefore, represent the maximal topological symmetry that the framework can possess rather than the actual symmetry of the material. The actual symmetry of the crystal is often much lower and would correctlyaccommodatethereported chemical composition of the material. There is no reported experimental structure for purely siliceous mordenite (although Si/Al ratios of up to several hundred have been observed), and full optimization of the over 30 structural variables in the material is not computationally practical at this time. Alternatively, we have investigated the sensitivity of the total H F energy resulting from a limited set of variations in the geometric parameters defining the framework geometry. The different sets of geometric parameters were derived from seven
The Journal of Physical Chemistry, Vol. 97, No. 24, 1993 6399
TABLE I: Mean and Standard Deviation of the Mean ( 0 ) of the S i 4 Bonds (angstroms)and 043-0 Bond Angles (degrees) in Siliceous Mordenite Structures Derived from Experimental Crystal Structures Reported in the LiternturGS-”’ * angles mean 108.97 109.62 109.61 109.58
bonds
mean 1.603
1961 1985 1978b
1978a
1.618 1.613 1.617 1.615 1.603 1.606
’
1976 1975 1979
U
0.037 0.025 0.019 0.017 0.016 0.020 0.013
109.60
U
6.16 2.50
EPHP 0
2.64
-140 -154
2.14 2.11 2.42 1.28
-155 -163 -172 -186
109.60 109.54 PHFenergies (kcals/mole, per Si48096unit cell) are reported relative to the “1961” structure and were calculated with the STO-3Gbasis.
‘I
1961
I
1985
I
0
a
1 m
’ i
1976
1975
I, I 154
1979 1
156
158
159
160
162
164
168
Bin Dimensions (angstroms)
Figure 1. Histogram of the S i 4 bond lengths occurring in each of the siliceousmordenite lattices. The possible values in each structure range from 1.54 to 1.68angstroms. From top to bottom, the structuresreported are“1961”,”1985”,‘1978b”. “1978a”,“1976”, “1975”,and “1979”.3M1
reported experimentalmordenitestructures, all of which belonged to the space group Cmcm. The crystal structures investigated include three hydrated and four dehydrated compounds. The hydrated set contains a 1961 study of Na m ~ r d e n i t e a, ~1976 ~ study of a rehydrated Caexchanged sample,4O and a 1985 investigation of a sample containing both Na and Ca.41 The dehydrated materials came from a series of studies carried out by Smith and co-workers. These include a 1975study of Ca m~rdenite?~ studies of the Cs3s and Rb36forms, and finallyan acid-treated hydrogen m~rdenite.~’ Reported in Table I are the mean T-O bond lengths and 0-T-0 angles present in these compounds, and their associated standard deviations from those means (not to be confused with reported experimental errors). Histograms of the actual distribution of the distances and angles are depicted in Figures 1 and 2, respectively, and are labeled by the year in which the study was carried out. Several general commentscan be made concerningthese data. From Table I it can be seen that the crystal structures are distributed into two group, one characterized by mean T-O bond lengths near 1.60 A and the other with mean values nearer 1.62 A. The reported experimental error in the mean T-O distances
White and Htss
6400 The Journal of Physical Chemistry, Vol. 97, No. 24,1993 75
1961 Total
0
I
1985
0
a
h
Oxygen
3
'g
P
0
n
,
I
v
Silicon x 10
2 I
1
1976
30
,
0
Oxygen2s
I J ,
1979 Oxygen 2p I
96
1
I
l
100
l
1
1
I
l
105
l
I
110
I
I
I
115
I
I
I
120
A
Bin Dimensions (degrees) Figure 2. Histogram of the 043-0 bond angles occurring in each of
the siliceous mordenite lattices. The possible values in each structure range from 96.00 to 120.0O0. From top to bottom, the Structuresreported are '1961", '1985", '1978b", '1978an, '1976", "1975", and '1979".
Figare 3. Total and projected density of states (DOS)of silica mordenite
is approximately 0.003 A, as computed by Schlenker et a1.35 from an analysis of errors in the fractional coordinates of the atomic positions. A Student t test (assuming either equal or unequal variances) supports the partitioning of the structures according to their means. It shows negligible probability that the means are the same between the two groups but a high probability that the means are the same within a given group. The 1961 Na structure3*possesses the largest standard deviation from the mean T-O bond length, as is evident in Figure 1. The Student t test shows that the mean and u values ( u is the standard deviation from the mean) of the 0-T-O angles in the reported crystal structures are very similar, with the largest deviations again occurring in the 1961 structure. Notwithstanding the larger deviations of the 1961 crystal structure, the statistical analysis of these data indicates that the remaining structures are qualitatively similar. To the eye, a superposition of any two of the reported structures is essentially identical. As mentioned above, the exact position of the aluminum atoms is not known in these materials (or may even be disordered).The following calculations have been carried out with all T atom positions in the reported framework geometries completely occupied by silicon atoms. Since this portion of the study was meant only as a qualitative survey, all calculationswere carried out using a standard STO-3G basis.42 Relative energy differences (per S i 4 8 0 9 6 unit cell) are shown in Table I. The total energy is scaled to zero for the highest energy structure (EPHF= -10 402.630 93 hartrees for the 1961material). From this table it is apparent that the 1961 crystal structure is at least 140 kcal/ mol higher in energy than the other structures and the remaining materials are grouped within 46 kcal/mol of each other. In general, we find that a correlation exists between the magnitude of the standard deviation in the observed T-O bond lengths (and to a lesser extent the 0-T-O angles) and the total energy (see Table I). More specifically, it was noted above that the T-O bond distances occurred in two statistically distinct sets, one with a mean near 1.60 A and the other with a mean closer to 1.62 A. Within in a given set, it was observed that the larger the standard deviation found for the T-O bond lengths the higher the total crystal energy. Reducing the spread in the bond distances and
angles apparently favors crystal stabilization. This is supported by empiricalobservations made by Gibb~.4~ A similarconclusion was reached in an experimental study by Petrovicand Navrotsky44 in which they compared the structures and thermal stabilities of various siliceouszeolites. The reader is reminded that thisanalysis does not predict the accuracy of the experimental crystal structures, since the set we chose contained both hydrated and dehydrated crystals with different chemical compositions (e.g., cations). It does, however, provide one of the fmt measures of the sensitivity of the relative ob initio PHF energies to small changes in complex structures of this size. We have carried out the following calculations using the framework geometry of the '1978a" structure of Schlenker et al.35 The physical propertiesdescribed in the following sections were computed using the modified 6-21G' basis. The choice of silica lattice geometry had no qualitative effect on the properties ofinterest (electrostaticpotential, charge density, densityof states, etc.). Deasity of States. Information about the chemical bonding in siliceous mordenite can be obtained from an investigation of the total and projected valence density of states (DOS). In the following paragraphs we will discuss the total valence DOS and its associated decomposition into projections from silicon and oxygen atoms. Additionally, we will discuss projections into the 2sp space of oxygen to establishthe origin of peaks in the spectra. This information can be compared with experimental X-ray emission spectra. However, to our knowledge, the spectrum for silica mordenite is not available. The total valence DOS and projections onto oxygen and silicon atoms and oxygen 2s and 2p orbitals are illustrated in Figure 3. Energies were normalized so that the highest value corresponds to 0, the fermi level. The total DOS has two distinct seta of peaks, ranging from 0 to -12 eV and from -23 to -26 eV relative to the fermi energy. The sharp peak observed at about -1 eV is indicativeof a nonoverlapping state, probably due to the oxygen lone-pair electrons. Contributions from states originatingon the oxygen atoms dominate the total valence DOS. The orbitals on silicon overlap slightly with oxygen but provide a much smaller contribution to the total valence DOS than oxygen.
9978a".
Siliceous Mordenite
The Journal of Physical Chemistry, Vol. 97, No. 24, 1993 6401
b Figure 4. Total charge density isosurface (1 .S X 1O-I e/bohr3) of silica mordenite “1978a” calculated with the 6-21G* basis.
Because the total valence DOS is mainly composed of states originatingfrom the oxygen orbitals, projections onto oxygen 2s and 2p orbitals were calculatedto analyze the sourceof the peaks. The orbital projections are distinct for the 10 symmetryinequivalent oxygen atoms in mordenite. However, each is composed of sets of peaks between 0 and -1 2 eV and between -23 and -26 eV. The orbital projection for one oxygen site is shown in Figure 3. We can now readily assign the set of peaks in the total valence DOS with energies ranging from 0 to -1 2 eV to the oxygen 2p orbital and the set from -23 to -26 eV to the oxygen 2s orbital. There is little mixing between the oxygen 2s and 2p states. The overlap of these states with the silicon 3s and 3p orbitals dominates the total valence DOS. Charge Density a d Mulliken Analysis. We investigated the spatial characteristicsof the charge distribution by sampling the calculated charge density on a grid of points spanning the entire volume of the unit cell, computed using the 6-21G*basis described above. One aspect of the total energy charge density is its rapid decay in magnitude from the atom centers composing the framework to points in space located in ring and cavity centers. For example, the charge density in the center of the large cylindrical channels formed by the 12-rings is found to be about 10-6 e/bohr3. This is illustrated in Figure 4, which depicts a surface of constant chargedensity, at a value of 1.5 X 1V e/bohr3, superimposed on a drawing of the mordenite structure projected onto the (ab) plane of the crystal. Because of the porous nature of the zeolite, there are regions of space far from the nuclear centers where the charge density has decayed to negligiblevalues. For reference, the isosurface depicted in Figure 4 delineates a volume that can be essentially reproduced by a superposition of atomic radii4s placed at the framework atom positions. The diameter of space in the channel, outlined by the charge density isosurface,could be taken as an estimateof the effective pore size in this material. From such a definition, the effective diameter of the pore is approximately7 A, which is in reasonableagreement with empirical estimate^.^.^.^^ Figure 5 shows the deformation density map (the difference between the total crystal charge density and the superposition of atomic charge densities placed on their appropriate lattice sites) sampled in a plane parallel to the (ab) plane of the crystal at a value of I/~c. The solid lines in the figure represent positive values (regions of the structure where charge increased relative to the atomic reference state), the dashed lines are negative
L
a
Figure 5. Deformation density map (crystal density - atomic density) in a slice parallel to the (ab) plane, at I/$. Values range from -0.5 to 0.07,withcontourspacingsof0.01. Negativedifferencesappearasdashed lines.
numbers which are regions where the chargewas depleted. Figure 5 indicates that charge transfer is localized on the framework and involvestransfer of electron density from silicon atoms to the oxygen atoms. As noted in an earlier study of kaolinitePl the charge density in mordenite is also depleted from the face of the Si04 tetrahedron. This presumablyreflects the general tendency for atomdensitiestocontract upon crystal formation. Onepossible estimate of the amount of charge transferred from the silicon centers to the oxygens is evident from the Mulliken analysis that shows the total charges to be +2.091e( and -1.04lel on silicon and oxygen, respectively. Electrostatic Properties. An analysis of the electrostatic properties of a clean lattice can be usedto help identify chemically importantregions of a material. In zeolites, electrostaticpotential maps can be used to predict the behavior of extraframework species present in the lattice. The electrostaticscomputed from the ab initio charge density can also provide constraintson model charge distributions commonly used in semiempirical and empirical studies. The potential energy functions commonly implemented in classical dynamics simulations frequently incorporate infinitesimal point charges of some magnitude placed in coincidencewith the nuclear positions. The resulting collection of point charges then defines the magnitude and spatial characteristics of the electrostatic potential and its derivatives. A comparison of the electrostatic potential resulting from the 46 initio charge distribution to that resulting from a point charge model allows the accuracy of the latter to be readily assessed. In the following section we will first discuss the behavior of the electrostatic potential in the large cylindrical channels of mordenite. Comparisonswill be made between the electrostatic potential resulting from either formal point charges or Mulliken point charges with the ab initio potential obtained from the Hartree-Fockground-statedensityfor this region of the structure. A brief discussion of the 3-dimensional minimum in the potential will then be presented. For an excellentdiscussion of electrostatics in 3dimensional lattices and specific implementations in CRYSTAL29the reader is referred to S a ~ n d e r s . ~ ~ The large cylindrical channels parallel to the [Ool] direction of mordenite are of chemical and physical importancesince they
White and Hess
6402 The Journal of Physical Chemistry, Vol. 97, No. 24, 1993 2.8 -
2.8
_I_
b c-
-+
18.2 Figure 6. Electrostatic potential maps of a slice parallel to the crystal (uc) plane. Values are scaled so that the potential in the center of the plane is zero. Dashed lines indicate negative values, relative to the center of the plane. The potentialswerecalculated from (a) theub inirioground state charge density, (b) Mulliken point charge model, (c) formal point charge model. Contour spacings are 0.005 au.
provide the most unhindered path for sorbatemolecules to diffuse through the crystal.' Figure 6a depicts a portion of the electrostatic potential, computed from the ground state charge density, sampled in a plane parallel to the (ac)plane of the crystal, "traveling down" the channel. Figure 7 illustratesthe orientation of this plane and a depiction of the channel. For the purposes of comparison, the electrostatic potentials in Figures 6a-c have been scaled so that the value of the potential in the center of the plane (coincident with the center of the channel) is zero. Dashed lines in the figure indicate negative values of the potential and solid lines denote positive values. The spacing between contours is 0.005 hartrees, or -3 kcal/mol. From Figure 6a it is evident that the electrostatic potential near the center of the channel is essentiallyconstant. Consequently,the magnitudeof the electric field in this region is small (the magnitude of the electric field is defined as the modulus of the negative gradient of the electrostaticpotential). In addition,the figure indicatesthat the most negative portion of the potential occurs in regions of space near the oxygen atoms and is directed in an oblate shape toward the center of the channel. Classical electrostaticspredicts these negative regions of space to be the most energetically favorable locations for positively charged species present in the lattice. We have also evaluated the electrostaticpotential in the plane depicted in Figure7,using the two model point chargedistributions mentioned above. The potential map shown in Figure 6b results from replacing the Hartree-Fock charge density with point charges located on the silicon and oxygen sites whose magnitudes were derived from a Mulliken population analysisof theconverged PHF wave function. The results of the second model, shown in Figure 6c,were obtained from a charge distribution containing formal point charges, equal to +4(ei and-2(el for silicon and oxygen, respectively. One of the most significant differences is that the two point charge models overestimatethe magnitudeof theelectric field relative to the ab initio model. Additionally, the positive contoursextend much furtherinto thecenter of the 12-ring channel in Figures 6b and 6c. Before discussing these two results, it is valid to ask if they are likely to occur in chemically
Figure7. Unit cell of siliceousmordenite. Horizontalline denotesposition of the electrostatic potential map of Figure 6 in the (uc) plane.
accessible regions of the crystal. Thus, vertical arrowshave been drawn at the top of Figure 6 to indicate the position of oxygens in the planes. Horizontal arrows indicate the width of an 02anion (2.8 The contours extend beyond the radius of the oxygen anions, and will be considered to be accessible to intercalated molecules. From these results we conclude that, due to increasing repulsive interactions,the chemicallyfavorable area for positively charged species encapsulated in lattices characterized by the formal point charge model is much smaller than in a lattice modeled using the ab initio ground state charge density. We note, however, the qualitative similarity between the potentials depicted in Figure 6a-c. This similarity might be anticipated given the large diameter of the cylindrical channel. Overall, the potential derived from the Mulliken point charge model is in better qualitative agreement with the ab initio results than that derived from the formal charge model. A particularly interesting component of the complete 34% mensional electrostaticpotental is the spatialdistribution of points whose magnitudes are near that found at the global minimum. This collection of points can be conveniently represented in 3 dimensions as an isopotential surface (the analog of a contour plot in 2 dimensions). Classical theorems indicate that such regions of space represent the most energetically favorable locations for positively charged species. We will refer to this bounding surface as the "spatial minimum". Figure 8 illustrates the isosurface that surrounds the minimum value found for the electrostatic potential. The data required for this plot were obtained by evaluating the potential on a 3-dimensional grid of points that span a unit cell of the Hartr-Fock ground-state density. From Figure 8 it can be seen that the most attractive regions in the potential exist at the "edges" of the cylindrical cavity and in portions of the sinusoidal channels. These results indicate that it is energetically more favorable for cations to be distributed near the "edge" of the large channels than in the center of the channel. Short-range repulsions will, in reality, keep the cations some distance from the framework atoms.
Conclusiom An understanding of the atomic scale properties of siliceous zeolites is necessary to promote thedevelopmentof new structures with increased stabilizationand sorption capacities. In this study we report the results of ab initio all-electron calculationscarried outonasiliceousmordenitewhichcontains 144siliconandoxygen
Siliceous Mordenite
The Journal of Physical Chemistry, Vol. 97, No. 24, 1993 6403 would be near the “walls”of thecylindricalchannels, in thevicinity of oxygen atoms. Analogous calculationshave been c a m 4 out for silicaliteand siliceous zeolite-A and will be reported in the future. Further studieswill include investigations of the changes in the structural and electronic properties of mordenite resulting from the systematicaluminationof the lattice. Calculationsare also being done to determine the optimal set of point charges that will reproduce the ab initio electrostatic potential?’
-a Figure 8. Minimum electrostatic potential isosurface (most attractive to a positive test charge) for silica mordenite ‘1978a”. calculated with the 6-2 1G* basis.
atoms in the conventionally centered unit cell. The calculations effectively demonstrate the feasibility of studying a system of this size using the latest generation of periodic ab initio HartreeFock theory. It is shown that this approach yields extensive informationabout properties of the systemswithout invoking the approximationspreviously thought to be required in the study of large complex materials. In addition, this study provides a valuable description of the physical properties of mordenite. These results can be used to characterize the behavior of nonperiodic methods and approaches that employ more approximate Hamiltonians. In the preceding sections we discussed the sensitivity of the total crystal energy to small variations in the frameworkgeometry. We observed that large fluctuations about the mean S i 4 bond distances (and to a lesser extent the O S i - 0 angles) increased the total energy of the system. These observations imply that crystal stabilizationis favored by a reduction in the spread of the bond distances and angles in the siliceous compounds. The electronic structure of mordenite was discussed based upon the total and projected valence density of states. It was shown that the dominant characterof the upper valence statesis from oxygen 2s and 2p orbitals, with small contributions from silicon 3s and 3p orbitals. We also noted that framework bonding results from the presence of significant overlap between the silicon 3s and 3p orbitals and the 2p orbitals of oxygen. The total charge density and density deformation maps were evaluated in the large cylindrical channels parallel to the [Ool] direction of the crystal. We noted that there was little total charge density in the center of the channel ( 10-6 e/bohr3).The deformation density analysis shows that the oxygen density has been polarized toward the channel center in an oblate shape relative to spherical atomic reference densities. As expected, the Mulliken analysis indicated that charge had been transferred from the silicon atoms to the oxygens, resulting in formal charges of +2.09(e( and -1.04(e( on silicon and oxygen, respectively. Evaluations of the electrostatic potential in the same region of the structure indicated that points near the oxygens are at a negative potential relative to the channel center. We also noted the presence of “lobes” of negative potential about the oxygens directed towards the center of the channel. These presumably arise from nonbonding oxygen p-type orbitals. We surmise that the most energetically favorable region for cations in the lattice N
Acbwledgmeat. The authors gratefullyacknowledge Dr. M. I. McCarthy for her advice regarding the statistical analysis and for editorialcomments during the preparation of the manuscript. We would also like to acknowledge V. R. Saunders, R. Dovesi, and C. Roetti for allowing the use of prereleased versions of CRYSTAL.29 J. Nicholas is thanked for helpful suggestions and discussions during the course of the study. The authors wish to 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-AC06-76RLO 1830. We also wish to thank the ScientificComputingStaff, Office of Energy Research, U.S. Department of Energy for a grant of computing time at the National Energy Research Supercomputer Center.
References a d Note (1) Breck, D. W. ZeoliteMolecularSieves; Robert E.Krieger Publishing Co.: Malabar, 1974. (2) Jasra, R. V.; Bhat, S. G. T. Sep. Sci. Technol. 1988,23,945-989. (3) Zamzow, M. J.; Eichbaum, B. R.; Sandgren, K. R.; Shanks, D.E. Sep. Sci. Technol. 1990.25, 1555-1569. (4) Sawa, M.; Kato, K.; Hirota, K.; Niwa, M.; Murakami, Y. Appl. C a r d 1990.64, 297-308. ( 5 ) Carl, D. E.; Rykken, L.E.;Stimmel, J. R.; Marlow, J. H.;Bray, L. A.; Wise, B. M. Adv. Ceram. 1986,20,383-389. (6) Ketola, W. S. Nuclear Waste Management 1991, 4, 11-14. (7) Meier, W.M.; Olson, D. H. Atlas of Zeolite Structure Types; 3rd ed.; Butterworth-Heinemann: London, 1992. (8) Kornatowski, J.; Baur, W. H.; Gerhard, P.; Rozwadowski, M.; Schmitz, W.; Cichowlas, A. J. Chem. Soc., Faraday Trans. 1992.88.13391343. (9) Ooms, G.; van Santen, R. A.; den Ouden, C. J. J.; Jackson, R. A.; Catlow, C. R. A. J. Phys. Chem. 1988,92,44624465. (10) Goovaerts, F.;F., V. E.; Philippaerts, J.; De Hulsters, P.; Gelan, J. J. Chem. Soc., Faraday Trans. I 1989.85.3675-3685. (1 1) Kim, G. J.; Ahn, W. S. Zeolites 1991, 11, 745-750. (12) Eberly, Jr., P. E.; Kimberlin, Jr., C. N. I d . Eng. Chem., Prod. Res. Devel. 1970, 9, 335-340. (1 3) Flanigen, E. M.;Bennett, J. M.; Grose, R. W.; Cohen, J. P.; Patton, R. L.; Kirchner, R. M.; Smith, J. V. Nature 1978, 271, 512-516. (14) Remy, M. J.; Genet, M. J.; Poncelet, G.; Lardinois, P. F.;Notte, P. P. J. Phys. Chem. 1992, 96,2614-2617. (15) Sawa, M.; Niwa, M.;Murakami, Y. Zeolites 1990, IO, 532-538. (16) Olsson, R. W.; Rollmann, L. D. Inorg. Chem. 1977,16,651-654. (17) Santikary, P.; Yashonath, S. J . Chem. Soc., Faraday Trans. 1992, 88, 1063-1066. (18) Titiloye, J. 0.;Parker, S.C.; Stone, F.S.;Catlow, C. R. A. J. Phys. Chem. 1991, 95,4038-4044. (19) Yashonath,S.;Thomas, J. M.;Nowak,A. K.;Cheetham,A. K.Narure 1988,331,601-604. (20) Barreto, M. C.; Ciambelli, P.; Del Re, G.; Peluso, A. J. Phys. Chem. Solids 1987, 48, 1-12. (21) den Ouden, C. J. J.; Jackson, R. A.; Catlow, C. R. A.; Post, M.F. M. J. Phys. Chem. 1990,94, 5286-5290. (22) Pickett, S. D.; Nowak, A. K.; Thomas, J. M.; Peterson, B. K.; Swift,
J. F. P.; Cheetham, A. K.; den Ouden, C. J. J.; Smit, B.; Post, M. F. M. J. Phys. Chem. 1990, 94, 1233-1236. (23) Preuss, E.; Linden, G.; Peuckert, M. J. Phys. Chem. 1985.89.2955296 1. (24) Goursot, A.; Fajula, F.; Dual, C.; Weber, J. J. Phys. Chem. 1988, 92,4456-4461. (25) Beran, S. Chem. Phys. Lett. 1982, 91.86-90. (26) Alvarado-Swaisgood, A. E.; Barr, M. K.; Hay, P. J.; Ruiondo, A. J. Phys. Chem. 1991.95, 10031-10036. (27) Sauer, J. Chem. Rev. 1989.89, 199-255. (28) Catlow, C. R. A.; Price, G. D.Nature 1990,347,243-248. (29) Dovesi, R.; Pisani, C.; Roetti, C.; Causa, M.;Saunders, V. R. In Quantum Chemistry Programs Exchange, Publication 577: University of Indiana, 1988.
6404 The Journal of Physical Chemistry, Vol. 97, No. 24, 1993 (30) Pisani, C.; Dovesi, R.; Roetti, C. Wartree-FockAb Initio Treatment of Crysralline Systems; Springer-Verlag: New York, 1988. (31) H.m, A. C.; Saundem, V. R. J. Phys. Chem. 1992,96,43674374. (32) Bmkley, J. S.;Pople, J. A.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102,939-947. (33) Gordon, M. S.;BinLley, J. S.;Pople, J. A.; Pietro, W. J.; Hehre, W. J. J. Am. Chem. Soc. 1982,104,2797-2803. (34) Nada,R.;Catlow,C. R.A.;Dovesi,R.;Saunders, V.R. Proc.R.Soc. London, A 1992,436,499-509. (35) Schlenker, J. L.;Pluth, J. J.; Smith, J. V.Mater Res. Bull. 1!V8,13, 901-905. (36) Schlenker, J. L.;Pluth, J. J.; Smith, J. V.Mater Res. Bull. 1978,13, 77-82. (37) Schlenker,J. L.;Pluth, J. J.;Smith, J. V.MaterRes. Bull. 1!V9,14, 849-856. (38) Meier, W. M. 2.Krisr. 1961,115,439-450.
White and Heas (39) Mortier, W. J.; Pluth, J. J.; Smith, J. V. Mater Res. Bull. 1975,IO, 1037-1046. (40)Mortier, W. J.; Pluth. J. J.; Smith, J. V.Marer. Res. Bull. 1976,II, 15-22. (41) Ito, M.; Saito, Y . BUN. Chem. Soc. Jpn. 1985,58,3035-3036. (42) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1%9,51, 2647-2664. (43) Gibbs, G. V. Am. Mineral. 1982,67,421450. (44)Petrovic, I.;Navrotaky, A. Thermochemistryof Zeolites: Structure and Energetics of Cages in High Silica Zeolites. (45) Cornelius, S.;Hurlbut, J.; Klein, C. Manual of Mineralogy, 19th ed.; John Wiley & Sons: New York, 1977. (46) Saunders, V. Mol. Phys., in press. (47) Nicholas, J. B.; White, J. C.; Hess, A. C. Electrostatic Potential Derived Charges in Zcolitcs From Periodic Hartree-Fock Calculations, manuscript in preparation.
