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Quadrupole Coupling Constants CQQ for 2H, 27Al, and 17O Atoms Calculated at the Periodic Hartree­Fock Level for Understanding the Geometr y of H-Form Aluminosilicates
A. V. LARIN,1 D. P. VERCAUTEREN
1

2

Laboratory of Molecular Beams, Department of Chemistry, Moscow State University, Vorob'evu Gory, Moscow, B-234, 119899, Russia 2 Institute for Studies in Interface Sciences, Laboratoire de Physico-Chimie Informatique, FacultÈs Universitaires Notre Dame de la Paix, Rue de Bruxelles 61, B-5000 Namur, Belgium Received 6 November 2000; revised 26 January 2001; accepted 5 February 2001

ABSTRACT: The coordinates of crystallographically different atomic types of
Si­O(H)­Al BrÆnsted centers within five H-form aluminosilicate frameworks--ABW, CAN, CHA, EDI, and NAT--were optimized using a full periodic ab initio Hartree­Fock scheme at the STO-3G level. Single-point calculations were then carried out at the ps-21G (Al, Si)/6-21G (O, H) and 6-21G (Al, Si)/6-21G (O, H) levels to obtain the 2 H, 27 Al, and 17 O respective nuclear quadrupole coupling constants and electrostatic field gradient anisotropies. The latter are discussed and compared to the experimental values measured for different zeolites. c 2001 John Wiley & Sons, Inc. Int J Quantum Chem 82: 182­192, 2001

Key words: quadrupole coupling constants; H-forms; aluminosilicates;
Hartree­Fock theory

Correspondence to: D. P. Vercauteren; e-mail: vercau@scf.fundp. ac.be. Contract grant sponsor: Interuniversity Research Program. Contract grant number: PAI/IUAP 4/10.

International Journal of Quantum Chemistry, Vol. 82, 182­192 (2001) c 2001 John Wiley & Sons, Inc.


QUADRUPOLE COUPLING CONSTANTS C

QQ

Introduction
etailed analyses of the spatial characteristics of the most efficient known zeolite precursors surely can help the synthesis of perspective new catalyst materials. More particularly in the special case of H-form aluminosilicates, applied in important industrial methanol to gasoline (MTG) and catalytic cracking processes [1], the structure of the active bridged Si­O(H)­Al moiety can be studied by combining nuclear magnetic resonance (NMR) and theoretical methods [2]. The direct relation between the quadrupole coupling constant (CQQ ) of the atoms constituting the framework and the electrostatic field gradient, indeed, makes the CQQ constant a valuable source of data on the field gradient, which is directly related to the respective atomic environment. The interest for such theoretical studies is, moreover, increased owing to the problematic determination of the electrostatic field gradient (EFG) values from X-ray data [3] as compared, for example, to the electrostatic potential (EP) evaluation [4]. The experimental EFG data at the framework atoms are preferable for the assertion of the derivatives of the EP as compared to any other source of experimental data, i.e., the infrared (IR) estimation of the electrostatic field at the positions of small adsorbed probes. The field should be assigned to the positions of the probes that require the determination of the adsorbate­adsorbent potential and adsorbate location [5, 6], while the positions of the framework nuclei are usually well known. As a result, considering periodic Hartree­Fock (PHF) methods for the calculation of the electrostatic field presents some advantages as compared to IR estimations. Various ways to evaluate the EP have been proposed since the 1970s. One of them, proposed by Stewart [4], is based on the calculation of multipole moments (MM) of high orders on the basis of X-ray data. Within this method, the fitting parameters are the atomic MM values. Recently, Larin et al. [7] showed that correlations between the MMs, including the neighbor atoms, and without addressing the experimental electron density from X-ray data, is also very useful for the calculation of the MM of high orders. The particular interest for such MM relations is that they are particularly suitable to tackle frameworks that cannot be treated with PHF schemes owing to a large number of atoms per unit cell (UC). These relations could also be considered for systems possessing some unordered cations or hydrogen atoms. In these frameworks, fitting the

D

positions and MMs for the constituting atoms from X-ray experiment is indeed a problem often encountered. The method to calculate MMs for "large" zeolites is indirectly based on the proposition that the TO4 units in "small" or "large" frameworks are embedded in essentially the same media and their characteristics could, hence, be discussed within a common approach of MM analysis, i.e., MM dependences on both the geometry and low-order MMs can be described by common functions [7]. However, a comparison between all measured characteristics of the possible different frameworks is desirable to confirm the identity or closeness of the electrostatic field values. Also, the basis sets applied to obtain the MM dependences should be tested to provide a sufficiently precise correlation with available relevant experimental data. In this study, we first will shortly present the adopted computational strategy. The main geometrical features of the optimized models are discussed below. The discussion is devoted to the results of the calculations of the nuclear quadrupole coupling constants (CQQ ) and the EFG anisotropy of the quadrupolar nuclei, 2 H, 27 Al, and 17 O, respectively, for five H-form zeolites (ABW, CAN, CHA, EDI, and NAT) as well as to the comparison with experimental data available for zeolites possessing "large" unit cells (ZSM-5 and Y zeolite).

Computational Strategy
The theoretical bases for the solution of the SchrÆdinger electronic problem in three dimensions considering periodic boundary conditions have already largely been described in the literature [8, 9]. In this work, we optimized the fractional coordinates of the different BrÆnsted centers, i.e., the Si­ O(H)­Al moieties, for a series of five cationic forms of aluminosilicate, with a relatively small number of atoms per unit cell, i.e., ABW [10], CAN [11], CHA [12], EDI [13], and NAT [14] (Table I), using a full periodic Hartree­Fock CO-LCAO-SCF scheme. Respective low symmetry groups were held for the optimization because they allow to consider nonequivalent Al and Si positions. Starting from initial cationic forms, one could avoid appreciable variations of the cell volume when replacing a cation by a bridged hydrogen atom. The cell parameters could, hence, be kept fixed. For all five frameworks, we allowed the variation of the coordinates of the four (O, H, Si, Al) framework atoms involved in each

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LARIN AND VERCAUTEREN TABLE I
Symbol, number of atoms, of different Al, Si, and O types (nH = nAl ), of atomic orbitals (AO) per unit cell (UC), and symmetry group of the H-form aluminosilicates.a AO/UC (6-21G ) 388 582 517a 480 480 Symmetry group Pna21 P63 R3 P21 21 2 Fdd2

Name ABW Cancrinite Chabazite Edingtonite Natrolite
a

Symbol HABW HCAN HCHA HEDI HNAT

Atoms (UC) 28 42 39 34 34

nAl /nSi /nO 1/1/4 1/1/4 1/3/8 1/2/5 1/2/5

With the ps-21G basis set.

type of bridged BrÆnsted center (12 variables) [15]. In the case of HEDI, the optimization of the same fractional coordinates allowing the additional variation of the cell parameters was also considered for comparison. [Note: In this article, we will show that their influence on the final geometry is of lower significance.] The optimizations were carried out, with CRYSTAL95 [16] in which we implemented the Polak­Ribiere algorithm [17], with energy convergences of 10-3 kcal/mol. The minimal STO-3G basis set was chosen to handle a reasonable number of atomic orbitals (AO) per UC, hence leading to moderate computing times. Using the optimized geometry, single-point calculations were then considered with the ps-21G (Al, Si)/6-21G (O, H) and 6-21G(Al, Si)/6-21G (O, H) basis sets (named hereafter as ps-21G and 6-21G , respectively) to obtain the atomic nuclear quadrupole coupling constants (CQQ ) of 2 H, 27 Al, and 17 O, as well as the EFG tensor elements at their respective locations, as implemented in the CRYSTAL code. With the ps-21G basis, the SCF part converged properly for each of the four different TO4 moieties in all the five H-forms, i.e., 20 cases in total. The exponents used for the 3sp orbitals of Si and Al were 0.12339 and 0.17 a.u.-2 , respectively, and that for the 2sp orbital of O was 0.3737 a.u.-2 .The exponents for the d polarization functions of Al, Si, and O were optimized as 0.45, 0.5, and 0.6 a.u.-2 , respectively. The sp/d exponents used for the 6-21G basis are 0.9, 0.15/0.35, 0.15/0.4, and 0.42/0.72 a.u.-2 for the H, Al, Si, and O atoms, respectively. With the 6-21G basis, the SCF convergence was achieved in 9 among all 20 optimized Si­O(H)­Al moieties. All computations with the CRYSTAL95 code were carried out on an IBM 15-node (120 MHz)

Scalable POWERparallel platform (with 1 Gb of memory/CPU). In all cases, the thresholds for the calculations were fixed to 10-5 for the overlap coulomb, the penetration coulomb, and overlap exchange, to 10-6 and 10-11 for the pseudo-overlap exchange, and to 10-5 for the pseudopotential series for all levels of basis sets. A typical total geometry optimization of one bridged BrÆnsted center (12 variables) with the STO-3G basis set took 2­3 days on the above-cited CPU. Single-point computations with the split-valence bases were executed directly without keeping the bielectronic integrals. The respective shortest SCF convergence (7­8 cycles) took around 1.5­2 h in the case of the BrÆnsted centers of the HABW zeolite. The nuclear CQQ characterizes the quadrupole interactions of an asymmetric nucleus. The CQQ values (in MHz) for all atoms within the five H-forms were obtained using the EFG values at their respective positions [16]: CQQ = 2.3496 â 102 Q Ezz , (1 )

where the coefficient on the right hand-side corresponds to Ezz expressed in e â a.u.-3 , and the nuclear quadrupole moments Q are 0.1402 [18], -0.026 [19], and 0.00286 [20, 21] barn (1 barn = 10-28 m2 ) for 27 Al, 17 O, and 2 H, respectively. Another parameter that influences the spectra of a nucleus having a quadrupolar nuclear moment is the EFG anisotropy: = ( Exx - Eyy )/ Ezz , (2 )

wherein all EFG elements are related to the EFG tensor principal axes.

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QUADRUPOLE COUPLING CONSTANTS C

QQ

Results
GEOMETRY OPTIMIZATIONS The variations of the structural characteristics of the bridged moieties while optimizing the fractional coordinates of each crystallographically different atomic type of BrÆnsted center were already discussed earlier [15]. The variety of the models considered covers a wide range of Al­O and Si­O distances, Si­O­Al angles, and H deflection angles from the Si­O­Al plane. Here, for conciseness, we TABLE II

only discuss the more recent geometries obtained considering the additional variation of the cell parameters for the HEDI case by comparison with the previous optimization based on the fractional coordinates of the bridged atoms only (Table II). The first observation is that even if the relative energies obtained, varying both the fractional coordinates and cell parameters, qualitatively repeat the ratio obtained earlier, varying the fractional coordinates only [15], the spatial characteristics of the Si­O(H)­Al moieties between the O(1) and O(4) types become closer. Second, the simultaneous increase of both the Si­O­Al angle and the H de-

Geometry of the BrÆnsted sites (distances in å, angles in degrees), for HEDI optimized with the STO-3G basis set varying either the fractional coordinates (FC) of the H, O, Si, and Al atoms only (upper part) or the FC together with the cell parameters (lower part, with cell parameters a, b, c, in å, and change of volume V of unit cell, in %).a Fractional coordinates (FC) Parameters Si­O­Al initial Si­O­Al opt. O­H Si­O Al­O Al­H O(3) 134.76 135.41 0.970 1.775 1.845 2.396 3.7 111.6 112.9 0.0/0.0 O(4) 138.27 129.10 0.983 1.827 1.906 2.493 0.3 115.3 115.6 15.4/14.1 O(2) 132.47 142.00 0.971 1.746 1.829 2.353 1.2 107.5 110.5 16.1/34.2 O(1) 143.38 139.26 0.983 1.676 1.913 2.463 0.4 108.2 112.5 62.4/59.3



b

Si­O­H Al­O­H USTO-3G / Up

s-21G

FC + cell parameters Parameters Si­O­Al initial Si­O­Al opt. O­H Si­O Al­O Al­H O(3) 135.41 137.76 0.976 1.740 1.830 2.377 6.8 109.7 112.2 9.490 9.455 6.363 7.92 0.0 O(4) 129.10 137.51 0.975 1.748 1.827 2.343 6.0 112.6 109.7 9.448 9.555 6.430 3.59 9.4 O(2) 142.00 142.84 0.974 1.715 1.796 2.287 14.9 108.3 107.6 9.320 9.585 6.503 3.51 27.5 O(1) 139.26 141.27 0.978 1.680 1.865 2.377 6.4 109.0 109.5 9.429 9.662 6.376 3.52 68.9



b

Si­O­H Al­O­H ac b c -V USTO-3
a

G

Relative energies (in kcal/mol) are also given for the ps-21G (Al, Si)/6-21G (O, H) basis set. Angle (in degrees) of the H deflection form the Si­O­Al plane. c Initial values of a, b, and c are 9.55, 9.665, and 6.523 å, respectively [13].
b

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LARIN AND VERCAUTEREN flection angle from the Si­O­Al plane for all centers together with the cell parameters decrease was not predictable. One could indeed expect a smaller Si­O­Al angle while decreasing the cell parameters. The Al­H distance, considered as one of the most reliable geometric parameters of the Si­O(H)­Al moiety from the experimental point of view, also shortens as compared to the lower experimental estimate 2.37 ± 0.04 [22] observed for the bridged groups in the 6-membered rings of zeolite HY or to even a smaller value for O(2) in HEDI. The decrease of the cell volume does not exceed 8% while adding H to the Si­O(3)­Al moiety as compared to the initial cationic EDI form, and it is smaller than 4% for the other Si­O(H)­Al groups (Table II). This is appreciably smaller and opposite to the increase by 14% noted by Ugliengo et al. [23] while optimizing the replacement of Si by (Al + H) starting from an initial all-siliceous EDI structure using the GULP code [24] based on B3LYP parameterization. Total optimizations, i.e., coordinates of all atoms and cell parameters, for the other HABW, HNAT, and HCAN frameworks were not completed, but we can confirm that the decrease of their cell volume starting from their cationic form is even smaller than for the HEDI case. Cationic models are thus more appropriate initial structures as compared to their all-siliceous analogs for the optimization of the H-forms because they require a smaller variation of the cell parameters. This tendency should, however, be evidently tested with a higher quality basis set level. QUADRUPOLE COUPLING CONSTANTS OF THE DEUTERIUM ATOMS For 2 H, while the EFG anisotropies at the positions of the different crystallographically independent types of H are in agreement with the measured value 0.1 ± 0.05 [25], the calculated CQQ (2 H) values (circles in Fig. 1) are usually overestimated by 25­30% as compared to the experimental ones for HY and HZSM-5 forms [2, 25, 26] (dashed lines in Fig. 1). The reason for the relatively large difference between experiment and calculation can come either from overestimated nuclear quadrupole moments Q, or from a wronggeometryaccepted for the interpretation. Allowing the high computation accuracy of the nuclear quadrupole 2 Hmoment Q, i.e., ±0.7% [20], one hence can only discuss the problem from the point of view of geometry.

FIGURE 1. C

2 QQ ( H) (in MHz) calculated with the ps-21G (filled circles) and 6-21G (open circles for all models and triangles for the Si­O1 (H)­Al moiety with elongated O1 ­H bond within HEDI) basis sets for the five H-form aluminosilicates with respect to O­2 H bond length (å). Interval of experimental data [2, 25, 26] is limited by dashed lines.

The CQQ (2 H) values, which decrease with the O­2 H bond length with both ps-21G and 621G basis sets, are relatively close for all different 2 H atoms, which thus indicates that the replacement of the core electrons of the remoted Si and Al by pseudopotentials has no influence. We also extrapolated the CQQ (2 H) values for longer O­2 H bond lengths (lines in Fig. 1) as compared to that optimized, with cluster or periodic calculations, in the O­H case. To verify such extrapolation, we calculated the CQQ (2 H) values with 6-21G for the Si­O1 (H)­Al moiety of HEDI. This moiety was chosen as it corresponded closely to the cluster geometry case: |O­H| = 0.983, |O­Si| = 1.676, |O­Al| = 1.913 å, and = 0.4 . The interval for the O­H bond length variation was chosen between 0.9933 and 1.0333 å (triangles in Fig. 1), while all other structural parameters (the |O­Si| and |O­Al| distances, as well as the H­O­Si, H­O­Al, and Al­O­Si angles) were kept fixed. A satisfactory agreement with the measured CQQ (2 H) values, between 208 and 264 kHz [2, 25, 26], was obtained for the shortest O­2 H bond lengths, between 0.9933 and 1.025 å, as compared to what could be predicted from the extrapolated values, between 1.005 and 1.043 å (621G level). The CQQ (2 H) and (2 H) variations with the H deflection angle from the Si­O1 (H)­Al plane were also tested, but they are negligible. So, a longer O­2 H bond length can explain the difference between the theoretical and experimental CQQ (2 H)

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QUADRUPOLE COUPLING CONSTANTS C values. This difference could be explained taking into account that the experimental CQQ (2 H) and O­2 H bond values are measured at the averaged ground state value R0 as compared to the equilibrium value Re usually obtained via ab initio computations. This larger value is confirmed by the experimental value of 1.051 å for the O­H bond in zeolite Y obtained from inelastic neutron scattering experiment [27]. Hence, we decided to check the possible anharmonic increase of the O­H bond length of a bridged moiety in the v-vibrational state as [28]: Rv = Re - (3aBe Re /e ) v +
1 2

QQ

,

(3 )

where the anharmonicity coefficient a is -2.210/ -2.466, the rotational constant Be is 18.825/10.028, and the harmonic frequency e is 3727/2721.2 cm-1 for the O­H/O­2 H bond lengths, respectively, [29]. Using these values, one could evaluate the increase at the ground vibrational state, R0 = R0 - Re , as around 0.0162/0.0273 å. The larger anharmonicity correction for the O­2 H bond is in agreement with the known longer O­2 H bond lengths [30]. So, if an equilibrium O­2 H value Re of 0.97­0.98 å is obtained via any optimization scheme, then the resulting ground-state distance provides, owing to the O­2 H anharmonicity, a decrease of CQQ (2 H) to 208­264 kHz, which is in the usual range of the experimental estimates for the H-forms [2, 25, 26]. The reason for a smaller length R0 obtained via Eq. (3) as compared to the average experimental value 1.051 å [27] could be discussed knowing the respective experimental error values, but no values were presented in Ref. [27]. Another important question is the influence between the local characteristics such as the O­H frequency [31 ­ 34] or the O­H bond length [23, 33] and the geometry of the bridged moiety. So far, to our knowledge, the influence of the local geometry was usually limited to the Si­O­Al angle ( ) omitting the other local characteristics. Particularly, several authors showed that the O­H frequency [32, 34] badly correlates with the angle in a series of H-forms of SAPO (based on the ALPO-5 and ALPO-34 sieves [32]) as well as in aluminosilicates (SSZ-13, SSZ-24 [32], MCM-22 [34]) empirically optimized with GULP [24] considering both empirical and ab initio based force fields. These results were supposed to be sufficient to conclude to a domination of the long-range effects on the O­H frequency. An opposite conclusion about the existence of the dependence on the O­H frequency, although not very precise, was observed in HSAPO-34 using a

plane wave approach [31]. A last example of the importance of the local characteristics was demonstrated via a quadratic dependence of the O­H bond length on the angle for HEDI optimized with GULP applying a parameterization based on B3LYP calculations [23]. The influence of the electron correlation on the EFG values can be estimated as rather small by comparison with the corresponding values recently published for the HEDI structure [35]. From our calculated CQQ (2 H) values (Fig. 1), one estimated, using expression (1), that the respective EFG value ranges are 43.4­49.2 å-2 and 41.9­47.7 å-2 for the H-forms studied herein with Si/Al ratio between 1 and 2 at the ps-21G and 6-21G basis set levels, respectively. This is in good agreement with the approximate interval 42.5­43.5 å-2 calculated with B3LYP for HEDI structures with Si/Al ratio between 1 and 3 [23]. One could thus suggest that a more precise coordinate dependence should be proposed to reveal the real influence of the local moiety on the O­H characteristics. For a complete conclusion, the influence of all other local characteristics, like the angle of the proton deflection from the Si­O­Al plane, should also be checked. As soon as the electrostatic field at the proton position correlates with the O­H frequency [32, 33], the field value should, indeed, also depend on the local coordinates. We thus verified this dependence avoiding the problem of the O­H frequency calculation with the usual wave functions as applied in CRYSTAL. The field vector was calculated at the H position while the latter was allowed to "move" along the angle with respect to the Si­O(1)­Al plane within the HEDI framework. The most favored H position in this grid is 6.0 with the 6-21G basis set, which coincides to 6.24 fitted with STO-3G while varying the cell parameters (lower part of Table II). The barrier of the vibration (Fig. 2) is lower than 70 K = 2.2 â 10-4 a.u. for a motion between 6 and -2 and lower than 163 K = 5.2 â 10-4 a.u. between 6 and 20 , so that the motion relative to the plane is not strongly hindered within a wide temperature interval. The absolute value of the electrostatic field |F| = 0.00575 a.u. (or 29.57 V/å) at = 6 varies up to 30% ( = -2 ) and 31.5% ( = 20 ). For comparison, the difference between the field values for the H atoms of all the bridged groups does not overhead ±8% relative to the average value [32, 34]. One should remark that the electrostatic field evaluation at the "cross" positions within the H-form of the MCM-22 zeolite, with ab initio based force fields [34], is close to our field

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LARIN AND VERCAUTEREN

FIGURE 2. Absolute value of the electrostatic field |F|
(â10, a.u., solid line) at the proton position and total energy U - 4201.35 (â10, a.u., circles) with respect to the angle (degrees) of the proton deflection from the Si­O(1)­Al plane within HEDI.

FIGURE 3. Approximation "a1 sin( - 0 ) + a2 Rn + a3 " (solid line) of the

estimation within HEDI, both being twice as large as the value obtained with empirical force fields. Evidently, the optimization of the O­H bond length at different angle values seems to decrease the field value as well as the barrier of the vibration. But even after optimization (not performed here), the range of the field variation with would remain appreciable with respect to the differences between its value at the different adsorption centers. QUADRUPOLE COUPLING CONSTANTS OF THE ALUMINUM ATOMS The same question of the choice of correct local coordinates discussed above for deuterium holds for aluminum. Both the deformational and stretching distortions lead to a symmetry lowering of the AlO4 tetrahedra, which could lead to a variation of the CQQ values. To our knowledge, only the deformational distortions were used so far to construct a local shear strain coordinate connecting any arbitrary AlO4 distortion with the respective CQQ (27 Al) value [36]. This coordinate is, however, only appropriate for cationic forms as studied in Ref. [36], wherein no particularly long O­Al bond appeared owing to the bridged O neighbor. We performed a two-dimensional fitting with respect to the difference between the absolute values of the rows of both the deformational and stretching vibrational coordinates of the F2 type. The valence and deformational types correspond to the rows of the irreducible representation of the F2 type within the Td point-symmetry group, that is, the stretching (valence) distortions R = maxi,j (ai - aj ), i, j = 1­3,

CQQ (27 Al) (in MHz) calculated with 6-21G (circles) for the four H-form aluminosilicates (excluding HCHA) with respect to the maximum deviation R (in å) of the O­Al bond length from the average AlO4 value (å) and to the maximal difference (in degrees) of the rows of the F2 -type deformational vibration of the AlO4 s. Interval of experimental data for HZSM-5 and HY zeolites [2, 25, 26] is limited by dashed lines.

where a1 = r1 + r2 - r3 - r4 , a2 = - r1 + r2 + r3 - r4 ,and a3 = r1 - r2 + r3 - r4 ,in which rk = (rk - R) is the displacement length of the k atom from the average value R = ( rm )/4, and the angular (deformational) distortions = maxi,j (bi - bj ), i, j = 1­3, where b1 = 12 - 34 , b2 = 23 - 14 , and b3 = 13 - 24 , in which kl is the Ok ­T­Ol angle between the bonds with k- and l-oxygen neighbors of each T atom (k, l = 1­4) and kl = kl - 109 47. The fitting with respect to the R and parameters was, however, not successful; R was then replaced by the largest deviation from the average AlO4 value of the longest O­Al bond, so that R = maxi (ri - R). Doing so, with a simple analytical form as "a1 sin( - 0 ) + a2 Rn + a3 ," where ai , n, and 0 are fitted parameters (note; this nearly arbitrary form was chosen to become zero for and R approaching zero), led to a more reasonable agreement (Fig. 3). Most of the calculated points (circles in Fig. 3) are, indeed, within the range of the experimental evaluations from 11 to 18 MHz [2, 25, 26]. Let us add that applying the ps-21G basis set on Al atoms was unsuccessful as it led to strongly underestimated CQQ (27 Al) values. We did not find a simple ratio between the EFG anisotropy and the AlO4 distortion and, hence, the results regarding are not discussed herein.

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QUADRUPOLE COUPLING CONSTANTS C TABLE III
EFG anisotropies and CQQ (27 Al) values of the Al atoms interval of experimental quadrupole coupling values with i, j = 1­3, where bi (in degrees) is a row of the irreducible type within the Td point-symmetry group, and to the bond over ri = |Al­Oi | (all in å) for the AlO4 tetrahedra. Nearest O(H) type O O O
4 1 1

QQ

whose calculated values do not coincide with the respect to the angular distortion = maxij (bi - bj ), representation for the deformational vibration of the F2 distortion R = maxi (ri - R), i = 1, 4, R being averaged R (å) 1.692 1.727 1.741

H-form HNAT HNAT HEDI

|Al­O(H)| (å) 1.836 1.884 1.913

R (å) 0.143 0.157 0.171


(deg) 7.53 21.41 16.85

C

QQ


0.601 0.248 0.184

(27 Al) (MHz) 20.2 22.6 23.9

So far, to our knowledge, CQQ (27 Al) values were measured for two Y and ZSM-5 zeolites only. Considering other zeolites could evidently shift the bounds of the experimental estimates of CQQ (27 Al). A relation between the AlO4 distortion (as described by the structural and R parameters) and the CQQ values can, however, be preliminary discussed. Three CQQ values are higher than 18 MHz and do not correspond to the measured values between 11 and 18 MHz [2, 25, 26]. Two of the three 27 Al atoms with the highest CQQ values (22.6 and 23.9 MHz) in HEDI and HNAT frameworks are connected to the bridged moieties, which possess structural parameters that are close to the "cluster " model with an |O­Al| bond length of 1.90 å (Table III). The smaller value of 20.2 MHz outside of the experimental limits corresponds to the typical Si­O(H)­Al moiety obtained with CRYSTAL at the STO-3G basis set level [12, 15] for an |O­Al| bond between 1.80 and 1.90 å. So we can suggest that this long |O­Al| bond is responsible for the CQQ (27 Al) deviation out of the experimental range. Simultaneous verifications of the CQQ (27 Al) values with higher quality basis sets and further measurements of the CQQ (27 Al) range for other H-forms are thus necessary in order to discriminate between the different Al environments. One should mention that if we use the higher value Q = 0.1466 barn [37] recently obtained, CQQ (27 Al) values increase by 4.6% as compared to the value calculated with Q = 0.1402 barn [18]. It yields to 21.1, 23.6, and 25.0 instead 20.2, 22.6, and 23.9 MHz, respectively, in Table III. Considering all possible H locations in the five frameworks, we obtained a wide variety of models of the bridged groups [15] as compared to the results of Teunissen, which optimized the HCHA framework at the same STO-3G level [12]. Together

with the models with shorter Al­O distances usually obtained at this basis set level, a close cluster geometry was also obtained for several H positions in the HEDI, HCHA, and HNAT zeolites [15]. This shows the importance of the long-range contributions for the resulting geometries. In accordance with the CQQ estimation [38] for the cluster geometry (respective model with |H­O| = 0.971, |Si­O| = 1.680, |Al­O| = 1.943 å) at the 3-21G level, we should have a correct CQQ value (as compared to experiment) of about 14 MHz or less using Q(27 Al) = 0.1402 barn [18], because our H-form presents a lower |Al­O| distance (last line in Table III, |H­O| = 0.983, |Si­O| = 1.676, |Al­O| = 1.913 å). But we obtained an overestimated CQQ (27 Al) value of 23.2 MHz with the 6-21G basis. The overestimation of the CQQ (27 Al) values calculated for the H-forms obtained via the isolated cluster approach as compared to the experimental ones was already discussed in the literature [38] allowing electronic correlation methods [secondorder MÜller­Plesset (MP2) or density functional theory (DFT)] and higher quality of basis sets. That is why we propose that more correct CQQ (27 Al) estimations owing to the long-range EFG contributions calculated within the PHF scheme could provide higher precision. We believe that the critics of the potential derived charge (PDC) model in [38] is not justified. The replacement of all electronic contributions to the EP by corresponding PDCs could be induced only for the remote electronic parts for which a presentation by a multipole series is appropriate as developed for example in [9]. Unfortunately, the limits of our available computational facilities did not allow us to test such possibilities of the PHF scheme with a higher quality basis.

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LARIN AND VERCAUTEREN QUADRUPOLE COUPLING CONSTANTS OF THE OXYGEN ATOMS Results of the calculations of the CQQ and Ezz values with respect to the T­O­T angle are reciprocally inverted [Eq. (1)], so that analogous trends can be demonstrated either in terms of zeolite type (Fig. 4) or in terms of the T­O­T moiety (Fig. 5). Simple linear approximations " Ezz = a â ( ) + b," where a = 7.5 â 10-4 , 1.47 â 10-3 , and -4.18 â 10-3 e â a.u.-3 â degree-1 and b = 0.877, 0.4873, and -0.7703 e â a.u.-3 for the Si­O­Si, Si­O­Al, and Si­O(H)­Al types of oxygen, respectively, as given in Figure 5 (by dashed, dotted, and solid lines, respectively) can be converted to obtain the CQQ values in Figure 4. However, the error of the respective fitting of the slope makes the Ezz approximation to be only qualitative. The CQQ values calculated herein for the Si­O­Si, Si­O­Al, and Si­O(H)­Al types of oxygen are partitioned from -5 to -6, -3.5 to -5, and 7.5 to 9 MHz, respectively. Absolute values of the Si­O­Si moiety are close to the experimental data obtained for all-siliceous faujasite [39], 5.1 to 5.39 MHz, or ferrierite [40], 5.22 to 5.64 MHz, while the experimental data for SiO2 is near 5.8 MHz [41]. Other CQQ data between 2.7 and 5.1 MHz were fitted from double rotation NMR spectra for a series of silicates [42]. The CQQ values for the Si­O­Al moiety are relatively larger as compared to the ones fitted for the NaA and NaLSX zeolites [43], for which most of the estimates were around 3 MHz. Having no experimental data on the bridged 17 O atom connected to a proton, we then concluded that the respective CQQ for the Si­O(H)­Al oxygens should be larger than those for the Si­O­Al moiety and hence would lead to a broadening of the respective lines in the NMR spectra. The EFG anisotropy did not reveal any difference between the Si­O­Al and Si­O­Si types of oxygen. Most of the obtained values for the Si­O­Si and Si­O­Al moieties are below 0.4. Only the O atoms of the Si­O(H)­Al type are characterized by higher values around 0.9. The variation of CQQ (17 O) with the elongation of the O­H bond for the Si­O(H)­Al moiety, as could be observed, for example, when the H is coordinatedtoan adsorbedparticle, has toour knowledge never been discussed in the literature. However, it has been shown that the CQQ (27 Al) values of a loaded sample decrease by 2­3 orders of magnitude as compared to the value for the nonloaded case [26] owing to the simultaneous increase of the O­H bond length as well as to the decrease of

(17 O) (in MHz) with respect to T­O­T angle (in degrees) in the Si­O­Si, Si­O­Al, and Si­O(H)­Al moieties, calculated with ps-21G for the five H-form aluminosilicates. Intervals of experimental data [39 ­ 43] for the Si­O­Si and Si­O­Al moieties are limited by dashed lines.

FIGURE 4. C

QQ

the O­Al bond upon H coordination. The H atom is very close to the oxygen and its influence is thus important. Hence, the theoretical evaluation of CQQ (17 O) with respect to the O­H bond length becomes very useful. We found that both the CQQ (17 O) and (17 O) variations are less than a few percent under elongation from 0.9833 to 1.0333 å, which is usually smaller than the experimental error. This slight dependence demonstrates the importance of

FIGURE 5. EFG Ezz (17 O) (in e â a.u.-3 ) with respect
to T­O­T angle (in degrees) in the Si­O­Si, Si­O­Al, and Si­O(H)­Al moieties calculated with ps-21G for the five H-form aluminosilicates. Intervals of experimental data for the Si­O­Si and Si­O­Al moieties, recalculated from the known CQQ (17 O) values [39 ­ 43], are limited by dashed lines.

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QUADRUPOLE COUPLING CONSTANTS C the contributions of the Si and Al neighbors, which possess higher atomic charges than the hydrogen, to the total EFG value at the O position. The small CQQ (17 O) change with the O­H stretching cannot be measured; however, it should be verified allowing an additional charge transfer of the electronic density to the H-bonded molecule, which was not considered in our calculations.

QQ

Conclusions
Quadrupole coupling constants CQQ of the crystallographically different 2 H, different 27 Al, and different 17 O atoms were obtained for a series of "small" size H-form aluminosilicate models (ABW, CAN, CHA, EDI, NAT) optimized with periodic Hartree­Fock calculations at the STO-3G level using the CRYSTAL code. Single-point calculations were then carried out at the ps-21G (Al, Si)/6-21G (O, H) and 6-21G (Al, Si)/6-21G(O, H) levels. Resulting CQQ (27 Al) values depend on both deformational (O­Al­O) and valence (O­Al) distortions of the AlO4 tetrahedra in the H-forms. Long-range contributions to the EFG Ezz (27 Al) calculated with a periodic Hartree­Fock scheme provide more precise estimations to the CQQ (27 Al) than a cluster approach at the same basis set level. The CQQ (17 O) values for the Si­O­Si and Si­O­Al moieties coincide with the respective data measured for the X and Y cationic forms and silicates. It thus confirms the correct representation of the derivatives of the electrostatic potential on the 17 O nuclei using the ps-21G (Al, Si)/6-21G (O, H) basis set. Correlations of the CQQ (17 O) values with the respective T­O­T angle were too weak and hence did not allow any quantitative reasoning in accordance with the recent results presented in [40]. For all variety of Si­O(H)­Al moieties (including the case corresponding to a cluster geometry), CQQ (2 H) coincided with the experimental data for the HY and HZSM-5 forms if the anharmonicity effects of the O­2 H bond are taken into account. We also showed that a precise angle value of the H deflection from the Si­O­Al plane should be considered to connect the absolute value of the electrostatic field/OH frequency with the local geometry of the bridged group. The agreement between the CQQ values of all considered atoms for the small size H-form aluminosilicates (ABW, CAN, CHA, EDI, NAT) with the values measured for "large" size forms (ZSM-5, Y) suggests a similar electrostatic "media" in which the

framework atoms are embedded. This confirms the possibility to describe their properties (like atomic moments) within a similar approach, i.e., a common dependence on geometry and low-order multipole moments for the atoms of small and large size zeolites as proposed in [7]. Cationic forms were shown to be more appropriate initial structures than their siliceous analogs for optimization of the geometry because they require a smaller perturbation of the cell parameters. The cationic forms are thus useful when one does not require a comparison of the H-form characteristics with respect to the basic siliceous structures. ACKNOWLEDGMENTS The authors wish to thank the FUNDP for the use of the Namur Scientific Computing Facility (SCF) Centre, a common project between the FNRS, IBMBelgium, and FUNDP as well as MSI for the use of their data in the framework of the "Catalysis and Sorption" consortium. We are grateful for the partial support of the Interuniversity Research Program on "Reduced Dimensionality Systems" (PAI/IUAP 4/10) initiated by the Belgian Government. The authors are grateful to Prof. J. Sauer and Dr. F. Jousse for useful discussions.

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