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Approximations of the Mulliken Charges for the Oxygen and Silicon Atoms of Zeolite Frameworks Calculated with a Periodic Hartree Fock Scheme
A. V. LARIN,* D. P. VERCAUTEREN
Institute for Studies in Interface Sciences, Laboratoire de Physico-Chimie Informatique, Facultes ґ Universitaires Notre Dame de la Paix, Rue de Bruxelles 61, B-5000 Namur, Belgium Received 21 February 1998; accepted 8 June 1998

ABSTRACT: Distributed multipole analysis ZDMA. on the basis of periodic
Hartree Fock ZPHF. calculations, using the CRYSTAL code, is applied to five different all-siliceous zeolite models: chabazite, gmelinite, merlinoite, montesommaite, and RHO. Mulliken charges of the framework atoms were calculated with a pseudopotential ps-21G* basis set for silicon and a 6-21G* basis for oxygen. The charge values of the silicon atoms were approximated by a simple one-dimensional function with respect to the average Si -- O distance within the respective SiO4 tetrahedra, whereas a twodimensional function with respect to the average Si -- O distance and the Si -- O -- Si angle was used for the oxygen atoms. Both dependences were then utilized to evaluate the Mulliken atomic charges of 10 other frameworks with a larger number of atoms per unit cell. The validity of such application is confirmed by comparison with results obtained 1998 John Wiley & Sons, Inc. through direct PHF calculation for all-siliceous mordenite.
Int J Quant Chem 70: 993 1001, 1998

Key words: Mulliken charges; zeolite; periodic Hartree Fock

*Permanent address: Laboratory of Molecular Beams, Department of Chemistry, Moscow State University, Vorob'evu Gory, Moscow, B-234, 119899, Russia. Correspondence to: D. P. Vercauteren. Contract grant sponsor: FNRS-FRFC. Contract grant number: 9.4595.96. Contract grant sponsor: Russian Foundation of Basic Researches. Contract grant number: 96-03-33771. International Journal of Quantum Chemistry, Vol. 70, 993 1001 (1998) 1998 John Wiley & Sons, Inc.

CCC 0020-7608 / 98 / 040993-09


LARIN AND VERCAUTEREN applied to other zeolites with a higher number of AOs per UC, those latter constituting most of the materials effectively used in various types of chemical catalytic processes. In our previous works, the Mulliken charges Zmoments of zeroth order. were calculated with the ab initio Hartree Fock linear combination of atomic orbital ZLCAO. code CRYSTAL92 w 6x for two types of periodic systems w 4, 5x . One-dimensional expressions with respect to the average T -- O distance ZT s Al, P, Si. were then fitted to represent the Mulliken charges of the silicon atoms within all-siliceous structures w 4x and of both the aluminum and phosphorus atoms within aluminophosphates ZAlrP s 1. w 5x . It has also been shown that various distortions of the TO4 tetrahedra do not influence strongly the charge value of the T atoms. A two-dimensional type dependence was obtained for the Mulliken oxygen charges within all-siliceous analogs and a three-dimensional one for the Mulliken charges and dipolar atomic moments of oxygens within the aluminophosphate ZALPO. frameworks w 5x . In order to verify our method of estimating the multipole moment dependences for any arbitrary siliceous zeolite or ALPO based on the approximate results obtained for structures with a relatively small number of AOs per UC, the behavior of both types of dependence of each multipole moment and their convergence need to be confirmed with different basis sets. To our knowledge, this has so far been discussed only for the Mulliken charges w 7 9x , but not for their dependences with the internal geometric characteristics of the respective atom. In our previous study treating a series of all-siliceous zeolites w 4x , we confirmed the use of a same type of two-dimensional analytical dependence for the Mulliken oxygen charges and of a one-dimensional expression for the silicon charges with two basis sets, i.e., the STO-3G and a 6-21G type quality basis. In this study, we analyze the evaluation of their dependences with higher quality basis sets, including a split valence pseudopotential ps21G* ZDurant Barthelat. on Si and 6-21G* on O, for 5 all-siliceous zeolites, i.e., chabazite ZCHA., gmelinite ZGME., merlinoite ZMER., montesommaite ZMON., and RHO. In total, this amounts of 6 different types of silicon atoms and 19 types of oxygens. In the next section, we briefly discuss the basis sets together with the characteristics of the frameworks. In the third section, we present the fitting

Introduction
luminosilicate zeolite frameworks with a high SirAl ratio, such as MCM-22 ZSirAl s 10 14., ZSM-5 ZSirAl s 20 50., Beta ZSirAl s 5 15., etc. constitute an important class of adsorbent and catalyst materials. The necessity to consider accurate electrostatic interactions to locate the preferential positions of an adsorbed species is now confirmed by direct ab initio Hartree Fock calculations on systems such as the all-siliceous form of ZSM-5, i.e., silicalite w 1x . All-siliceous forms are the simplest models which can be considered by three-dimensional Z3D. periodic ab initio Hartree Fock ZPHF. computations and whose study could provide a deeper knowledge to simulate electrostatic interaction effects. The modeling of the behavior of an adsorbed molecule then requires the most accurate estimation of the field which is created only by the silicon and oxygen atoms of the all-siliceous frameworks Zor mainly by these atoms within zeolites with high SirAl ratio.. Therefore, the largely used cluster embedded models require to consider the long-range interactions between the adsorbed molecule and the inert rest of the zeolite structure. In the case of embedded cluster models, which include a molecule near a cation or near a bridged hydroxyl group linked to the closest aluminum atom w 2x , the electrostatic long-range interactions have often been estimated as created by these last two types of framework atoms only. A conventional way to evaluate the electrostatic field is through the derivation of the atomic multipole moments for the total host guest system for which we can calculate the wave function. The distributed multipole analysis ZDMA. scheme related to the atomic positions developed by Saunders et al. w 3x allows to express these moments in terms of internal geometric coordinates. For the case of zeolite frameworks, the application of the DMA scheme was proposed first through ab initio computations of some zeolite models with a relatively small number of atomic orbitals ZAO. per elementary unit cell ZUC. considering basis sets of a relatively advanced level w 4, 5x . More particularly, it allowed to derive simple analytical approximations of the calculated multipole moments with respect to some internal geometric characteristics of each atom, which interestingly can be

A

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ZEOLITE FRAMEWORKS of the atomic Si and O charges with respect to the internal geometric parameters using the dependences obtained previously w 4, 5x . In the last section, the approximations using the herein computed parameters are applied to predict the Mulliken charges of 10 siliceous zeolites with a larger number of AOs per UC, for which the direct solution can hardly be achieved with the most modern available computing platforms and electronic structure codes. The validity of such an application is confirmed by comparison with available results obtained by direct PHF calculation for all-siliceous mordenite with a basis set of 6-21G* quality w 10x . oxygens w 27x with conventional exponents for the d-polarization functions, i.e., 0.5 and 0.92 a.u.y2 for Si and O, respectively, was applied to all zeolites considered in Table I. An exponent value of 0.35 a.u.y2 for the oxygen d-polarization function was optimized in the case of the MON zeolite, but we held the value of 0.92 a.u.y2 providing acceptable computation limits for all 5 frameworks. No convergence could be reached for DAC and MON, whereas the other zeolites could not be treated with the ps-21G*ZSi.r6-21G*ZO. basis set because the number of atomic orbitals in their UC was too large. Computations with the CRYSTAL92 code were carried out partly on an IBM RISC 6000 model 560 workstation Zwith 256 Mb of memory. and partly on an IBM 15-node Z120 MHz. Scalable POWERparallel platform Zwith 1 Gb of memoryrCPU.. For all cases, the thresholds for the calculations were fixed to 10y5 for the overlap Coulomb, the penetration Coulomb, and overlap exchange, to 10y6 and 10y11 for the pseudo-overlap exchange, and to 10y5 for the pseudopotential series.

Theoretical Aspects
The theoretical bases for the solution of the Schrodinger electronic problem in three dimenЁ sions considering periodic boundary conditions have already largely been described in the literature w 3, 6, 11, 12x . The choice of the siliceous structures was done on the basis of a relatively small number of atoms per UC, hence a reasonable number of two-electronic Coulomb and exchange integrals to evaluate. The characteristics of the 5 all-siliceous frameworks, which were treated with the CRYSTAL92 code, have been taken from the MSI database w 13x ZTable I.. The characteristics of the other 10 all-siliceous forms whose charge values were predicted on the basis of the herein derived approximations are presented in Table II. The pseudopotential Durant Barthelat ps-21G* basis set on silicon atoms w 26x and 6-21G* on

Approximation of the Mulliken Charges of the Si and O Atoms in Small Size Type Zeolites
Omitting d-polarization functions on the oxygen atom, we first wished to compare the quality of the basis sets chosen with available results of Apra et al. for the ``Opt3'' model of silico-chabazite w 8x . The Mulliken total silicon charge 12.230 < e < calculated with the CRYSTAL92 code and ps-21G*

TABLE I
Symbol, number of different silicon and oxygen types, of total atoms, and of atomic orbitals (AO) per unit cell (UC) using the ps-21G*(Si) / 6-21G*(O) basis set, and symmetry group of the considered zeolite frameworks.a Name Montesommaite Chabazitec Merlinoite Gmelinite RHO
a b c d

Symbolb MON CHA MER GME RHO

n Si / n 1 1 2 1 1 / / / / / 3 4 6 4 2

O

Atoms / UC 24 36 48 72 72

AO / UC 328 492 656 984 984
d

Symmetry group I41 / amd R3c Immm P6 3 / mmc Im3m

All coordinates are from Ref. [13] if no other reference is given. Ref. [14]. Ref. [6, 8]. 368 for basis set 6-21G* on both atoms.

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LARIN AND VERCAUTEREN TABLE II
Symbol, number of different silicon and oxygen types, of total atoms, and of atomic orbitals (AO) per unit cell (UC) using the STO-3G basis set, and symmetry group of the zeolite frameworks whose charge distributions were predicted on the basis of the estimations with functions (1) and (2).
a

Name Ferrierite ZSM-57 Mordenite ZSM-12 Mazzite VPI-5 ZSM-11 Beta NU-87 MCM-22 Silicalite
a b

Symbol FER MFS MOR MTW MAZ VFI MEL BEA NES MCT b MFI

n Si / n

O

Ref. 15 16 17 18 19 20 21 22 23 24 25

Atoms / UC 54 54 72 84 108 108 144 192 204 216 288

AO / UC (STO-3G) 342 342 456 532 684 684 912 1216 1292 1368 1824

Symmetry group Immm Imm2 Cmc21 C2 / c P6 3 / mcm P6 3 / mcm I4m2 P4122 P2 1 / c P6 3 / mmm Pnma

4/8 8 / 14 4/9 7 / 14 2/6 2/6 7 / 15 9 / 17 17 / 34 8 / 12 12 / 26

Ref. [14]. Symbol from Ref. [13].

basis coincides exactly with the value given in w 8x Zbelow for simplicity, we consider the difference between the number of electrons of the neutral atom, i.e., 14 < e < for Si and 8 < e < for O, and the Mulliken charge.. The PHF computation of the 5 all-siliceous frameworks allowed us to obtain the Mulliken charges with the ps-21G* basis set for 6 different types of silicon atoms and 19 types of oxygens ZTable I.. Then, a fitting of the Si charges Z < e <. was made using a simple 1D expression with respect to ° the average Si -- O distance R s Zщ4s 1 R SiO k .r4 ZA. k of each Si atom within its respective SiO4 tetrahedron w 4x :
0 Q0 Z R . s a1 e a 2 Z Ry a 3 .

Z1.

with a1 s 2.019, a 2 sy0.771, and a 3 s 1.517 being obtained by fitting. For the oxygen charges Z < e <., we fitted the calculated values with a 2D function depending on the average Si -- O distance ° of each O atom R s Z R OS i2 q R O Si1 .r2 ZA. and Si Z , radian. w 5x : -- O -- Si angle
0 Q0 Z R ,

. s b1 e

nR

q b2 e

mZ R yR 0 .

cos Z y

0

. Z2.

with b 1 sy1.373, n sy0.277, b 2 s 0.198, m s y0.595, R 0 sy0.139, and 0 s 0.091 being obtained by fitting. The root mean square deviation ZRMSD. values for the approximate Mulliken charges obtained with the ps-21G* basis for the Si and O atoms are 0.40 and 1.23%, respectively. Function Z2. leads to a better RMSD for the two

STO-3G and 8-31GZSi.r6-21GZO. basis sets, i.e., 1.57 and 0.77%, respectively, as compared to 2.0 and 1.2% presented earlier w 4x . The positions of the calculated Si charge values Zopen circles. relative to the approximate function Z1. is presented in Figure 1 together with the other results obtained with STO-3G Zdiamonds. and with a basis of 6-21G quality Ztriangles. w 4x . One can remark a very slight variation of the slope of the new dependence Z1. obtained for the different basis sets. But the principal conclusion is that the conservation of the same type of approximate functions with all three basis sets for both the Si and O atomic charges is clearly verified. The quality of function Z1. obtained here with only 6 silicon charge values needed to be tested. For this, we compared our results with those calculated with the 6-21G* basis w 10x for siliceous mordenite. The closeness between the 6-21G* and ps-21G* basis sets suggests that dependence Z1. corresponding to 6-21G* could be estimated using a simple shift by a constant value Zvertical arrow in Fig. 1. from the charge values obtained with ps-21G* ZTable III.. Namely, a value of 0.223 < e < obtained as the difference between the Si charge values 2.102 Ztriangles in Fig. 1. and 1.879 < e < obtained for MON with the 6-21G* and ps-21G* basis, respectively. The average Si charge value 1.872 < e < evaluated with dependence Z1. for the MOR framework was corrected accordingly to 2.095 < e < Zcorresponding to the average value over the 4 charges depicted by ). which nearly coin-

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ZEOLITE FRAMEWORKS TABLE IV
Mulliken oxygen charges ( < e <) for the MOR zeolite approximated via function (2) including the average Si O distance R = ( ROSi1 + ROSi 2 ) / 2 and Si -- O -- Si angle ( ) using the parameters fitted over the Mulliken charges calculated with ps-21G* basis sets for five smaller size type zeolites. Type 7 2 3 4 5 6 1 9 8
a

° R ,A
1.5872 1.6060 1.6115 1.6116 1.6243 1.6295 1.6313 1.6373 1.6408 Average Correctionb Corrected Calculated with 6-21G* basis set [10]

, degree 180.00 158.00 168.45 144.37 150.52 137.26 145.81 146.80 147.17

yQ

0 0

FIGURE 1. Mulliken Si charge values (in < e <) of various
zeolite models calculated with: STO-3G (diamonds, Ref. [4]), 8-31G (Si) / 6-21G (O) (triangles, Ref. [4]), ps-21G* (empty circles), and 6-21G* (filled circles, MON zeolite) compared to the approximate dependence [eq. (1)] (solid lines) versus the average Si -- O distance R = 4 ° ( k =1 R S iO k ) / 4 (in A). The dashed line corresponds to (1) corrected for the 6-21G* level charges (stars) function in the case of MOR. The vertical arrow depicts the difference between the charges of MON estimated with ps-21G* and 6-21G* basis sets.

0.955 0.942 0.945 0.931 0.932 0.920 0.927 0.926 0.925 0.935 0.112 1.047 1.04

a b

Numbering from Ref. [10]. From the calculation with the MON zeolite (see text).

cides with 2.09 < e < w 10x . An analogous correction of the average O charge y0.935 < e < for the same framework in the opposite direction by half of the upper estimated correction Zy0.112 < e <. led to y1.047 < e < also in agreement with the direct PHF calculated value y1.04 < e < w 10x ZTable IV.. TABLE III

Mulliken silicon charges ( < e <) for the MOR zeolite approximated via function (1) including the average 4 Si -- O distance R = ( k =1 RS i O k ) / 4 using the parameters fitted over the Mulliken charges calculated with ps-21G* for five smaller size type zeolites. Type 2 1 4 3 Average Correctiona Corrected Calculated with 6-21G* basis set [10
a

These results suggest that function Z1. is precise enough despite the small number of charge values. It also proves the validity of a similar behavior of dependence Z1. obtained with the ps-21G* and 6-21G* basis sets here applied. We hence conclude that functions wZ 1. and Z2.x for the Si and O charges conserve their types with all three basis sets. However, on the other hand, this coincidence could be due to the relative short differences between the Si -- O distances within the mordenite framework Zstars in Fig. 1.. Further studies would thus be useful to clearly ascertain the extrapolation of one dependence versus another corresponding to a different basis set.

° R, A
1 1 1 1 .6047 .6189 .6214 .6352

Q

0 0

1.893 1.874 1.870 1.851 1.872 0.223 2.095 2.09

Evaluation of the Mulliken Charges of the Si and O Atoms in Larger Size Zeolites
The good agreement obtained above between the calculated and approximate w functions Z1. and Z2.x charge values for the mordenite framework permits us to evaluate the charge distributions of some other all-siliceous zeolites. Moreover, this work is very useful considering the absence, to our

]

From the calculation with the MON zeolite (see text).

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LARIN AND VERCAUTEREN knowledge, of any data about the electrostatic field for most of the herein studied zeolite forms. Thus, we chose some zeolite forms whose UC sizes make the direct calculation with a periodic Hartree Fock approach and an advanced basis set Zlike ps-21G*. either rather ``expensive'' or even nonrealistic. The simple charge evaluations with formulas Z1. and Z2. for the chosen zeolites can indeed be easily performed knowing the geometric parameters of all types of silicon Zi.e., R . and oxygen Zi.e., R and . within the frameworks ZTable V and VI.. TABLE V
0 Mulliken oxygen charges Q 0 ( < e <) approximated with function (2) including the average Si -- O distance ° R = ( ROSi1 + ROSi 2 ) / 2 (in A) and Si -- O -- Si angle (in degree).

TABLE V
(Continued) Atom numb. 10 3 5 4 2 12 8 7 14 9 3 7 13 2 12 15 6 1 8 4 11 10 5 8 3 2 6 4 13 10 11 7 12 9 14 1 5 6 8 2 13 3 14 10 12 5 7 4 1 11 9
a

Type

R 1.5952 1.6093 1.6225 1.6323 1.6409 1.6458 1.6482 1.6502 1.5578 1.5619 1.5800 1.5855 1.5871 1.5895 1.5983 1.6006 1.6049 1.6148 1.6155 1.6171 1.6291 1.6326 1.7452 1.5814 1.5818 1.5842 1.5851 1.5854 1.5855 1.5898 1.5916 1.5938 1.5944 1.5955 1.5961 1.5981 1.6043 1.5641 1.5673 1.5685 1.5777 1.5877 1.5891 1.5926 1.5936 1.6014 1.6042 1.6228 1.6236 1.6292 1.6340 143.22 136.21 180.00 145.83 142.13 145.82 151.18 159.31 165.13 158.57 150.96 151.92 165.27 146.59 145.64 160.43 147.55 149.77 144.07 161.00 145.37 159.10 120.59 162.19 162.32 158.00 157.17 158.00 158.95 154.93 149.55 148.56 147.58 147.69 146.67 145.40 145.13 144.77 155.57 156.21 146.09 146.37 145.86 152.09 144.86 148.05 156.91 157.94 158.59 152.79 134.39

yQ

0 0

MEL

Type BEA

Atom numb. 16 4 2 9 8 15 12 5 17 6 13 1 10 3 14 7 11 6 5 4 8 7 2 1 3 6 2 3 4 5 1 1 11 6 9

a

R 1.6155 1.6158 1.6158 1.6159 1.6159 1.6160 1.6160 1.6160 1.6160 1.6161 1.6161 1.6161 1.6161 1.6161 1.6162 1.6162 1.6163 1.5910 1.5916 1.5974 1.6029 1.6108 1.6148 1.6179 1.6251 1.6403 1.6407 1.6414 1.6429 1.6488 1.6558 1.4457 1.5194 1.5632 1.5874 154.80 153.27 148.29 137.46 162.35 149.23 144.86 148.28 150.62 157.91 154.81 163.02 143.84 156.45 165.58 154.53 137.45 153.26 180.00 157.95 147.35 152.85 152.67 169.27 153.52 136.64 171.19 146.54 144.74 137.34 149.24 180.00 157.04 164.50 159.45

yQ

0 0

FER

MAZ

MCT

0.938 0.937 0.933 0.924 0.942 0.934 0.930 0.933 0.935 0.939 0.937 0.942 0.930 0.938 0.943 0.937 0.924 0.944 0.954 0.945 0.936 0.938 0.936 0.944 0.934 0.917 0.938 0.925 0.923 0.915 0.923 0.997 0.966 0.958 0.948

MFS

MTW

0.935 0.925 0.945 0.927 0.921 0.923 0.926 0.931 0.959 0.955 0.945 0.944 0.951 0.939 0.936 0.945 0.936 0.934 0.930 0.941 0.927 0.935 0.874 0.951 0.951 0.948 0.948 0.948 0.948 0.945 0.941 0.939 0.939 0.938 0.937 0.936 0.934 0.945 0.952 0.952 0.942 0.940 0.939 0.943 0.937 0.937 0.942 0.938 0.938 0.933 0.917

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ZEOLITE FRAMEWORKS TABLE V
(Continued) Atom numb. 4 1 3 6 2 5 3 17 18 19 16 2 20 7 22 27 10 8 5 23 14 9 29 33 34 28 4 6 31 21 12 30 26 32 15 13 11 1 24 25 17 19 13 15 10 3 6 22 4 7
a

TABLE V
(Continued) R 1.4339 1.5766 1.6074 1.6250 1.6551 1.7025 1.5713 1.5714 1.5749 1.5764 1.5787 1.5847 1.5875 1.5876 1.5880 1.5883 1.5890 1.5898 1.5905 1.5906 1.5910 1.5922 1.5925 1.5939 1.5942 1.5948 1.5949 1.5953 1.5956 1.5963 1.5982 1.5995 1.6016 1.6020 1.6101 1.6107 1.6191 1.6287 1.6301 1.6358 1.5378 1.5538 1.5608 1.5620 1.5704 1.5724 1.5736 1.5788 1.5808 1.5811 164.41 180.00 131.02 156.52 174.48 167.59 136.21 156.91 151.91 153.04 166.49 168.10 145.64 170.98 145.19 150.87 141.46 164.28 143.54 148.84 157.54 148.73 145.98 143.91 156.27 143.37 154.64 160.26 137.72 140.07 149.76 140.75 146.65 164.84 145.91 158.69 146.81 167.36 157.03 150.57 149.61 171.81 175.00 157.40 159.94 174.01 162.62 149.49 162.14 156.40 yQ
0 0

Type VFI

Type

Atom numb. 12 2 11 14 21 24 25 9 5 26 18 8 20 1 23 16

a

R 1.5819 1.5839 1.5839 1.5852 1.5859 1.5910 1.5930 1.5947 1.5982 1.6049 1.6148 1.6156 1.6165 1.6223 1.6375 1.6554 155.59 145.18 158.93 166.54 150.86 142.85 152.73 153.39 146.12 145.84 139.89 155.37 148.21 142.61 156.04 151.94

yQ

0 0

NES

MFI

0.995 0.958 0.920 0.936 0.935 0.920 0.935 0.951 0.947 0.947 0.954 0.953 0.939 0.953 0.938 0.943 0.935 0.950 0.936 0.941 0.946 0.940 0.938 0.936 0.944 0.935 0.943 0.946 0.930 0.932 0.939 0.932 0.936 0.947 0.933 0.941 0.931 0.940 0.935 0.929 0.956 0.963 0.962 0.954 0.953 0.958 0.954 0.944 0.951 0.948

0.948 0.940 0.949 0.952 0.943 0.936 0.943 0.943 0.936 0.934 0.927 0.938 0.933 0.927 0.932 0.925

a

Numbering of the atoms from references given in Table II.

0 Mulliken silicon charges Q 0 ( < e <) approximated with function (1) including the average Si -- O distance 4 ° R = Z k =1 RS i O k ) / 4 (in A).

TABLE VI

Type BEA

Atom numb. 8 5 1 9 4 3 6 2 7 4 3 1 2 2 1 7 6 5 2 4 3 8 1

a

R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 .6159 .6159 .6159 .6159 .6160 .6160 .6161 .6161 .6163 .5964 .5984 .6140 .6263 .6405 .6513 .5485 .5801 .5861 .5914 .5932 .6071 .6268 .6604

Q

0 0

FER

MAZ MCT

1.878 1.878 1.878 1.878 1.878 1.878 1.877 1.877 1.877 1.905 1.902 1.880 1.864 1.844 1.830 1.972 1.927 1.919 1.912 1.909 1.890 1.863 1.818

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LARIN AND VERCAUTEREN TABLE VI
(Continued) Atom numb. 2 6 3 7 5 1 4 2 1 4 2 7 1 3 6 5 8 1 3 2 7 5 6 4 8 2 14 15 1 3 16 7 6 17 9 11 12 10 13 4 5
a 0 0

TABLE VI
(Continued) R 1.5617 1.5783 1.6048 1.6050 1.6170 1.6290 1.6596 1.5948 1.6064 1.5878 1.5879 1.5881 1.5886 1.5912 1.5915 1.5917 1.5933 1.5677 1.5901 1.5971 1.5984 1.6007 1.6094 1.6146 1.5814 1.5841 1.5849 1.5852 1.5867 1.5868 1.5877 1.5904 1.5910 1.5940 1.5958 1.6023 1.6057 1.6079 1.6082 1.6095 1.6211 Q Atom numb. 8 6 10 11 4 5 3 9 7 1 2 12
a 0 0

Type MEL

Type MFI

R 1.5610 1.5734 1.5756 1.5768 1.5769 1.5831 1.5874 1.5935 1.5941 1.6007 1.6137 1.6257

Q

VFI MFS

MTW

NES

1.954 1.930 1.893 1.893 1.876 1.860 1.819 1.907 1.891 1.917 1.917 1.916 1.916 1.912 1.911 1.911 1.909 1.945 1.913 1.904 1.902 1.859 1.887 1.880 1.926 1.922 1.921 1.920 1.918 1.918 1.917 1.913 1.912 1.908 1.905 1.896 1.892 1.889 1.888 1.887 1.871

1.955 1.937 1.934 1.932 1.932 1.923 1.917 1.909 1.908 1.899 1.881 1.864

a

Numbering of atoms from references given in Table II.

spatial optimization using empirical type potentials could lead to reasonable results if the dependences wZ 1. and Z2.x are also taken into account. Second, the charge distribution obtained herein with the ps-21G* basis set can be corrected to the level corresponding to 6-21G* considering the simple shift by a constant value of 0.223 < e < for the Si charges and by y0.112 < e < for the O charges. Caution should, however, be taken if the zeolite system under study has very large Si -- O bond lengths. The boundaries for the hopeful estimates applying the charge distribution shift may be evaluated from the extremal values of the Si -- O distances for the 4 types of Si charges of mordenite, ° i.e., 1.605 to 1.635 A.

Conclusions
The Mulliken charges for 5 all-siliceous zeolites, i.e., chabazite, gmelinite, merlinoite, montesommaite, and RHO, were calculated using the CRYSTAL92 code with a pseudopotential ps-21G* ZDurant Barthelat. basis set on the silicon and 6-21G* on the oxygen atoms. The Si charge values were approximated by a simple one-dimensional function with respect to the average Si -- O distance within the respective SiO4 tetrahedra. A two-dimensional function with respect to the average Si -- O distance and Si -- O -- Si angle was con-

Two evident features of the charge estimations can be emphasized. First, all the charge values are strictly related to the spatial models referenced in Table II. Any optimization of these initial coordinate sets would alter the internal geometry and hence the charge distribution. But evidently, a

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ZEOLITE FRAMEWORKS sidered for the O atomic charges. Both types of approximate functions were found to be appropriate to fit the charge values computed with this presently proposed basis set in the same way as it was shown previously for charges obtained with STO-3G and 6-21G sets w 4, 5x . The comparison between the atomic charges computed directly with the CRYSTAL92 code for mordenite showed a good agreement with our estimations based on the two simple proposed analytical functions. This also allowed to evaluate the charge distribution for some zeolites with a larger number of atoms per elementary unit cell without the necessity to pass thru the direct solution of the electronic problem. The knowledge of the Mulliken charges only provides a rather qualitative level for the evaluation of the electrostatic field w 3, 9x ; however, it is useful to estimate an order of magnitude for the electrostatic field of the considered host system and hence to propose preferential positions of any adsorbed molecule. We hope that the approximate charge Zmultipole moments of zeroth order. dependences for both the silicon and oxygen atoms could be completed later by similar types of approximate dependences for the hydrogen and aluminum atoms obtained on the basis of analogous fitting of the charges and higher order multipole moments for a series of H-form zeolite models with a small number of atomic orbitals per UC. The direct calculations of these moments with the CRYSTAL code are presently in progress. ACKNOWLEDGMENTS All authors wish to thank the FUNDP for the use of the Namur Scientific Computing Facility ZSCF. Centre. They acknowledge financial support of the FNRS-FRFC, the `` Loterie Nationale'' for the convention no. 9.4595.96, IBM Belgium for the Academic Joint Study on ``Cooperative Processing for Theoretical Physics and Chemistry,'' and MSI for the use of their software in the framework of the ``Catalysis and Sorption'' consortium. One of us ZA.V.L.. acknowledges the PAI 3-49, ``Science of Interfacial and M esoscopic Stru ctu res,'' the ``Services du Premier Ministre des Affaires Scientifiques, Techniques et Culturelles'' of Belgium for his Postdoctoral stage and the Russian Foundation of Basic Researchers for financial support ZGrant No 96-03-33771..

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