J. Phys. Chem. 1994, 98, 10735-10741
10735
Structural Distortions in Si8012 Fragments and D4R Units: A Comparison between Silasesquioxane Molecules and LTA Zeolites Anna M. Bieniokt and Hans-Beat Bur@* Laboratorium f i r Chemische und Mineralogische Kristallographie, Universitat Bern, Freiestrasse 3, CH-3012 Bern, Switzerland Received: May 23, 1994; In Final Form: July 29, 1994@
The structures of 62 TgO12 units from zeolite A crystal structures and of 16 molecular analogs from RgSig012 crystal structures have been analyzed for deformations from mgm (Oh)symmetry using principal component analysis. Overall, about 95% of the deformations correspond to those expected from a model of rigid tetrahedra joined flexibly across comer-sharing oxygen atoms. The six symmetry deformation coordinates found to be important in the analysis of static distortions are the same as the coordinates associated with the six lowest vibrational frequencies of HgSig012.
Introduction Silasesquioxanemolecules with the general formula RgSisOl2 show a cube-shaped Si8012 unit (Figure l), surrounded by different residues R, which can be organic groups or oxygen or hydrogen atoms. The interest in these materials arises from their unusual properties: they may be sublimed in vacuum without dissociation; some of them show relatively high thermal stability;'S2 and they are suitable as simple starting materials for the synthesis of ceramic^.^,^ The RgSig012 molecules can also be considered as molecular models of the secondary building unit Tg012 occumng in several zeolites (LTA, AFY, AST, and CLO).5 In zeolite language the fragment Tg012 is called a (4-4) or D4R unit, and the tetrahedrally coordinated atom T may be Al, Si, P, Ga, or Ge. In the case of the silasesquioxanes only one type of tetrahedral atoms (Si) is present, whereas in zeolites different chemical compositions of the framework are possible. We have therefore restricted our analysis to those LTA zeolite structures (Linde type A) which show statistical occupation of the tetrahedral position by Si and A1 in a 1:l ratio and which have been described in the crystallographic space group Pm3m. Relationships between some of the molecular silasesquioxanes and zeolite structures have been discussed in the literature for Na[N(CH3)4]7(OgSig012).54H20,6a which crystallizes with a topology corresponding to zeolite structure type AST. Water molecules and silicate anions (08Si8012)8- connected by hydrogen bonds form a three-dimensional network. In contrast to zeolite structures, it is a mixed framework with strong covalent-ionic and weak hydrogen bonds, which has been termed "heterogeneous tetrahedral network".6b Another structural link is provided by [N(C4H9)4]H.1(OgSig012).5.33H20, tetrabutylammonium silicate hydrate,s a framework structure of hydrogenbonded silicate D4R units arranged as in the structure of zeolite A. Here the D4R units are connected by Si-O-H-O-Si hydrogen bonds rather than by T-0-T bonds. The structure is another example of a heterogeneous network. Here we compare the distortions, i.e. the flexibility of the D4R fragment in molecular crystals with that in zeolite framework structures. In the former the shapes of the Si8012 units are determined by the form and the size of the substituents t Present address: Institut fiir Kristallographie und Mineralogie, Universitat Frankfurt, Senckenberganlage 30, D-60054Frankfurt/Main, Germany. Abstract published in Advance ACS Abstracts, September 15, 1994. @
0022-365419412098-10735$04.50/0
R, as well as by the crystalline environment; in the latter the TgOl2 units are part of and constrained by an infinite zeolite framework which may be loaded to varying degrees. Some interesting molecular species with mixed D4R units have also been characterized structurally, e.g. [(OH)~Si4A40121* [N(CH3)4]4,'a [Ph7Si7(Ph3PO)A1012]*(CH3)2C07b with Ph = W 5 , [(C6H11)7Sig01210[(C6H11)7Si7A10121'[Sb(CH3)4l~3CH3CN,'C and [(Me3C)4Si4(Mecp)4Ti4012]~~ with Me = CH3 and Mecp = C5bCH3. Conversely, the clathrasil phase [Si2004]* [HC(CH2CH2)3NH]2*2F'e contains D4R units in a pure Si02 framework structure. All of these compounds have been excluded from our analysis, not that these structures were uninteresting, but rather because we aimed at maximizing the degree of chemical homogeneity in our selection of RgSig012 molecules and of Tg012 units.
Preliminary Considerations Data Retrieval. The structural data used in this investigation were obtained with the help of crystallographic databases. A search in the Cambridge Structural Database (CSD)9 revealed structural information on 12 different RgSisO12 compounds (Table 1). One of these (VAWXUM) shows two crystallographically different Si8012 units; for another (FUSWAR) the structure was determined at two different temperatures. The simplest member in this class of compounds, HgSig012,10is also included in the analysis. A further isolated D4R fragment occurs in the mineral steacyite (originally misnamed ekanitel1J2), a dicyclosilicate with chemical composition ThKNaCa(OsSig012); among the compounds studied here it is the only naturally occurring one. In columns 1 and 2 of Table 1 the 16 structures or structural fragments are identified by literature references, CSD reference codes, sum formula, or name. In columns 3-9 some chemical and crystallographic characteristics are listed. Data for zeolite A structures were obtained from the Inorganic Crystallographic Database (ICSD).21 Apart from LTA frameworks there is no other zeolite structure type containing doublefour rings with silicon and aluminium tetrahedra. Zeolite A structures were included in the analysis if their refinement residue, the R-value, is less than 10%. Only refinements in space group Pmjm with complete SUA1 disorder on the tetrahedral position were considered for reasons of comparability to the molecular fragments which show only one type of tetrahedral atom. This led to a selection of 62 zeolite structures with different cation loadings. Tables with chemical and 0 1994 American Chemical Society
Bieniok and Biirgi
10736 J. Phys. Chem., Vol. 98, No. 42, 1994
Figure 1. The RBTRO,~ fragment. The labels of the I2 0-0 distances are those used in the principal component analyses. TABLE 1: List of the 16 &Si8012 Molecules: Literature Reference Number, CSD Name, Chemical Environment, R-value of Structure Determination as Listed in CSD, Data Collection Temperature, Crystallographic Space Group, Site Symmetry of the Fragment, Approximate Molecular Symmetry, and Mean Si-0-Si Angles CSD entry space site approx mean ref no. or formula substituent R-value T (K) group symm mol symm Si-0-Si (deg) 11.12 steacyite 8 x -O-(TH4+, Caz+, Na+, K+) 0,058 293 P4/mcc !/m 4/mmm 149.3 2 VAWXUM 8 x -CH&Hr 0.082 203 PI I mmm 149.0 13 ENCUSI 8x -00.089 pi 1 mmm 151.0 4x -(C~HMCUN~)".38 H>O/uc h x -0-
0.071
RT"
PZdn
0.102
RT
P63
I
m"
149.8
3
3
148.7
m3 mjmm mmm 4/mmm mmm mmm
147.6 149.2 148.2 149.2
3
R2
1
m3 3 3
PI
1
m"
149.3 150.1 151.0 149.3
CsHs. 3 x (CHilCN)
IO 15 2 16 3 1 6 17
20 I9 18
HaSi801* OCPSIX VAWXUM
OPSlOY DIRXAD BEGGEZ FUSWAROI OCMSIOOI VINSIO FUSWAR
ZZZVUOOI
.
8 x -H 8 x -CsHr. 0.5(Cdl6) 8 x -CH,C~HI 8 x -CsH5,C1HsO
8x-0-CHI 8 x -CHz-CH=CH* 8x 8x 8x 8x 8x
-0--Na+. 7 x -(N(CH,)#.
.
54 HzO/uc
-CHr
-CH=CH2 -0--Na+, 7 x -(N(CH33+, 54 H2O/uc -CzHr
0.030 0.065 0.082
100
Rj
2
203
0.062
RT
P! PI P4/n
5
0.038
293
0.078 0.03 I 0.110 0.060 0.120
I90 291 153
Pi pi R? RZ R3
I
1 2
m1
148.2 150.7 150.5
RT = mom temperature crystallographic data and literature references are available as supplementary material. Data Preparation, Symmetry Analysis, and Principal Component Analysis. A general analysis of the distortions of the Si8012fragment would have to take into account 3 x 20 6 = 54 degrees of freedom. However, inspection of the bond distances and angles1-4,6,10-20-especially those from very accurate determinationslOJ-shows that Si-0 distances and 0-Si-0 angles vary over a small range compared to Si-0-Si angles. We therefore assume, tentatively, that the Si8012 fragments, and also the TsOlz ones. may he considered as built from rigid C3,-symmeuic RSi03 or OTO3 tetrahedra connected through flexible hinges, the oxygen atoms. This implies that the 24 Si-0 distances and the 24 0-Si-0 angles within the cage are essentially constant. For such a model the number of degrees of freedom necessary to describe distortions of the D4R unit is reduced from 54 to 6. The six degrees of freedom may he chosen in different ways. e.g. as linear combinations of the torsion angles about the bonds and of the Si-0-Si bond angles.
Alternatively. they may he expressed as linear combinations of the 12 nonhonded 0-0 distances across the faces of the cuheshaped Si8012 unit. Whichever we choose, there are only six independent combinations. Figure 1 shows the labeling of the twelve 0-0 distances: they are designated X1 to X4,Y 1 to Y4, and Z1 to 24 depending on whether they intersect the X, Y,or Z axis of a Cartesian coordinate system positioned in the center of the D4R unit. X1 is parallel to X3,X2 to X4,etc. In order to test the assumption of rigid tetrahedra, we have included 16 additional variables in the analysis of the Si8012 fragments, namely, the average 0-Si-0 angles and average Si-0 distances of each Si03 unit. This led to a total of 28 variables. A table of these quantities is given as supplementary material. The maximal symmetry of the D4R unit is m2m (Oh). -The observed crystallographic symmetries are always lower: 1, 3, 3, or 4 for the molecular species, 4/m for the dicyclosilicate (Table l), and 4immm for the- zeolites. Since all observed symmetries are subgroups of m3m, it is convenient to consider
Silasesquioxane Molecules and LTA Zeolites
J. Phys. Chem., Vol. 98, No. 42, 1994 10737
any D4R unit as a more or less distorted version of an mgmsymmetric reference structure. Deformation of a particular D4R unit can occur in several different but equivalent ways. For example, the fragment may be elongated by the same amount along each of the three 4-fold directions in tum, leading to three different but isometric and 4/mmm-symmetric distorted fragments. To account for this in a systematic way, the 28 geometric parameters of the Si8012 fragment have been permuEd using each of the 48 symmetry operations of point group m3m. The permuted data are also included in the analysis. This adds no new information to the data but produces an explicit representation of their symmetry properties. Another, alternative, way of looking at this symmetry expansion of the data is to recall that the labeling of pairs of cube faces as 3 3 , k Y , or &Z is completely arbitrary. To avoid this arbitrariness, we must include all possible labelings; this is equivalent to the permutation of the data.22 As pointed out above, a D4R model of edge-sharing, flexibly joined but rigid tetrahedra admits only six different types of deformation. These may be expressed as symmetry-adapted linear combinations of the 0-0distances and classified in terms of the irreducible representations of the point group mgm. A straightforward but somewhat tedious calculation leads to an A2g, a doubly degenerate E,, and a triply degenerate Tzu deformation coordinate, six in all. They are
+ X4 - Y 1 + Y2 - Y3 + Y4 + z1 - 2 2 + 23 - Z4)/12’” S,,(E,) = (-X1 + X2 - X3 + X4 + 2(Y1) - 2(Y2) + 2(Y3) - 2(Y4) + Z1 - 2 2 + 23 - 24)/24l” Slb(Eg)= (-X1 + X2 - X3 + X4 - Z 1 + 2 2 - 2 3 +
S(A,,) = (-X1+ X2 - X3
Z4)/8112
+ X2 + X3 - X4)/2 Sb(T,,) = (-Y1 + Y2 + Y3 - Y4)/2 S,(T,) = (Z1 - 2 2 - 23 + 24)/2 S,(T2,) = (-X1
A schematic representation of these deformations is given in Figure 3. There are also six other linear combinations of the 0-0distances, of type A,,, E,, and TI,. The f i s t three of these are S(Alg)= ( X 1 + X2 + X 3 + X 4
S2,(E,)=(X1+ X2
+ Y 1 + Y2 + Y3 + Y 4 + z 1 + 2 2 + 23 + Z4)/121”
+ X3 + X4 - Z1 - 2 2 - 2 3 Z4)/8lI2
S2b(Eg)= (-X1 - X2 - X3 - X4 2(Y3)
+ 2(Y1) + 2(Y2) +
+ 2(Y4) - Z1 - 2 2 - 23 - Z4)/24lI2
Their contributions to the observed deformations of the D4R units are expected to be small, however, provided the assumption of rigid tetrahedra holds. This hypothesis may be tested by principal component analysis (PCA).23,24 PCA is a statistical method to detect linear relationships among a large number of varibles by finding the eigenvalues and eigenvectors of their variance-covariance matrix, i.e. by finding an orthogonal transformation of the original variables to a new set of uncorrelated variables, called the principal components (PC). The PCs give the directions of uncorrelated
variance in parameter space, and their components or loadings indicate the relative importance of the original variables in each PC. If symmetry is included explicitly in the data as described above, the PCs can be classified in terms of the irreducible representations of the reference point group. The importance of each PC is measured by the magnitude of its eigenvalue. The number of significant eigenvalues is often smaller than the number of original variables. PCA thus provides an indication of the number of variables necessary to describe most or all of the variance in the original data and is an ideal tool to test the validity of our hypothesis conceming the number and nature of deformation modes of a D4R unit. Note that there is a close analogy between symmetry-adapted PCA and normal coordinate analysis.25 PCAs were performed on the variance-covariance matrices of the geometric parameters with the program system SAS 6.07.26 Degenerate PCs were rotated such that as many new principal components as possible correspond to deformations of the Si8012 unit, maintaining cokemel symmetry. This mathematical procedure does not change the physical meaning of the principal components.22
Results Deformation Analysis for Silasesquioxanes and Steacyite. In the preceding section we have hypothesized that there should be only six important types of deformation of an mjm-symmetric Si8012 fragment and we have derived corresponding distortion coordinates from a symmetry analysis. We concluded that PCA of the 0-0 distances, properly processed to account for symmetry, provides a test for the hypotheses. The results of the PCA are shown in Table 2 in order of decreasing importance of the PCs. The first three of them account for 92.6% and the first seven for 97.7% of the total variance. They belong to irreducible representations A2,. E,, AI,, and Tzu. With the exception of AI,, this is what is expected. The loadings of pC1, P5, P6, and PC7 correspond exactly to those of S(A2,) and S(Tzu) given above, those of PC2 and PC3 are close to but not identical with those of S1(Eg). Thus, on the whole, the results of the PCA are as expected, but there are also some discrepancies to be discussed below. The most prominent distortion in silasesquioxanes can be described as a cooperative rotation of all tetrahedra about the body-diagonals of the Si8 cube and is called “torsion” in Table 2. Considering only the cuboctahedron of oxygen atoms, the same deformation can also be visualized as a deformation from a cuboctahedron toward an icosahedron. Figure 2 shows this. Eight of the 20 faces of the icosahedron, shown in the right part of the figure, are the 03-triangles of the rigid tetrahedra (shaded), and the other 12 triangular faces originate from the six deformed 0 4 - squares. This deformation, _transformingas the irreducible representation A2,, retains m3 symmetry. It explains 36.4% of all distortions. The PC loadings are as expected, 12-lI2 = 0.289. PC2 can be regarded as a combination of a compression and an elongation along two different 4-fold axes, here X and Z. It retains mmm (kernel) symmetry. PC3 corresponds to a compression along the third 4-fold axis, here Y,and preserves 4 l m ” (cokernel) symmetry.22 Each of the two accounts for 28.1% of the total variance. The PC loadings are close to but not exactly equal to the coefficients of Sl(E,): 0.407 instead of 2 x 24-‘j2 = 0.408 and 0.231 or 0.176 instead of 24-l” = 0.204 for PC2; similarly 0.032 instead of 0 and 0.337 or 0.368 instead of 8-lI2 = 0.354 for PC3. This means that some deformation other than S1(E,) is also involved in PC2 and PC3. The only possibility is &(E,), a deformation belonging to the same irreducible
Bieniok and Burgi
10738 J. Phys. Chem.. Vol. 98,No. 42, 1994
TABLE 2
Results of Principal Component Analysis I R ~eigenvalue' (A')
pnncipal compnenP
+
+
PCI =0.289(-Xl + X 2 - X3 X4 - YI Y2 - Y3 + Y 4 + ZI -zz + z 3 - 24) PC2 = 0.407(Y1 - Y2 Y3 - Y4) - 0.231(XI X3 - Z1 - 23) 0.176(-X2 - X4 2 2 + 24) PC3 = 0.032(-YI - Y2 - Y3 - Y4) - 0.337(Xl+ X3 ZI 23) 0.368(X2 + X4 + 2 2 24) PC4 = 0.265(XI XZ X3 X4 Yl Y2 Y3 Y4 Zl 22 + 2 3 +24)+ 6' PC5 = OS-XI X2 X3 - X4) PC6=0.5(-Yl+Y2+Y3-Y4) PC7 = OS(Z1 - 2 2 - 2 3 +a) PC1 = 0.408(Y1 - YZ Y3 - Y4) - 0.218(X1 X3 - Z1 - 23) 0.190(-X2 - X4 2 2 24) PC2 = O:Ol6(-YI - Y2 - Y3 Y4) - 0.345(Xl + X3 + ZI 23) 0.36l(X2 X4 2 2 Z4) PC3 = 0.289(Xl+ X2 X3 X4 Y1 Y2 Y3 Y4 Zl 2 2 2 3 + 24) PC4 = 0.408(Y1 Y2 Y3 Y4) - O.I28(Xl X3 Z1+ 23) 0.190(X2 + X4 + 2 2 24) PC5 = O.O16(YI - Y2 Y3 - Y4) 0.345(X1+ X3 - Zl - 23) 0.361(-X2 - X4 22 24)
+
+
+
+ + + + + + + + + + + + + +
+
+
+ + + + +
+
+
+
A,.-a
0.0655
36.4
torsion
E,
0.0505
28. I
compression
E,
0.0505
28.1
compression II 4-fold axis
AI,
0.0042
2.4
expansionlcontraction'
T2"
0.001 68
T2"
0.001 68 0.001 68 0.2427
0.9 0.9 0.9 47.8
tetrahedral distortion tetrahedral distortion tetrahedral distortion compression
0.2421
47.8
compression II4-fold axis
A,,
0.0128
2.5
expansionlcontraction
E,
0.0049
1.0
tetrahedral distortion
E,
0.0049
1.0
tetrahedral distortion
T2"
E,
+
+ + + + + + + + + + + + + + + + + +
coordinate
% va+
Definitions XI to X4, YI to Y4, and Z1 to 24 see Figure - I . *Irreducible representation of the deformation. 'Importance of each component. dPercentage variance explained by PC. 6' = 0.14Z?==lAa-(O-Sii-O) positive loadings on all 28 variables, large ones for 0-0 distances and 0-Si-0 angles and negligibly small ones for the Si-0 bonds. The term 6' in Table 2 refers to deformations in the 0 - S i 4 angles; it is approximately 0 . 1 4 ~ i % ( 0 - S i j 4 ) . This coordinate reflects not only intrinsic differences of the 0-Si-0 angles due to the nature of R in the different R8SisOtz molecules but also systematic errors in the interpretation of the diffraction data such as the neglect of corrections arising from atomic vibrations. PC5-PC7, irreducible representation T2" and expected to be present. are of lesser importance in this data set, accounting for only 3 times 0.9% of the total variance. They may be described as tetrahedral distortions in which two opposite faces of the fragment are antisymmetrically deformed, preserving overall 42m symmetry (Figure 3, bottom). The following two PCs are the second pair of E, distortions, complementary to PC2, PC3: PC8, PC9 = 0.078 Sl(E,) f 0.997 S,(E,)
Figure 2. Deformation of a cubmahedron to an icosahedron representation. Projection of PC2 and PC3 on SI and S2 yields PC2, PC3 = 0.997 Sl(E,) - 0.078 S2(E,) The contributions in SZ are a measure for the nonrigidity of the Si03 groups, since they would have to equal 0 for a molecular model built from rigid tetrahedra. They contribute only 2 times 0.2% to the total variance, to be compared with twice 27.9% for the SI components. Note that the mixing of SI and S2 in PCA is analogous to the mixing of symmetry coordinates in normal coordinate analysis.25 PC4, irreducible representation AI,, is a totally symmetric expansionlcontraction or breathing coordinate. It is expected 10 vanish for the rigid-tetrahedra model, but can clearly not be neglected; it accounts for 2.4% of the variance. PC4 shows
The large coefficient in S2 indicates that this pair of coordinates is another expression of deviations from the rigid-tetrahedra model. It is quite unimponant in absolute terms, accounting for only 0.9% of the total variance. PC10-PC28 have eigenvalues smaller than 0.001 A2; each of them explains less than 0.5% of the total variance, and they will not be discussed funher. The above discussion may be summarized as follows: In an average statistical sense 94.9% of the deformations of the 16 Sis0,z fragments studied here are those expected from a rigidtetrahedra model (36.4% 2 x 27.9% 3 x 0.9%). Expressed in angstroms, the combined S(A2,), SI(E,). and S(T2.) deformations amount to 0.41 8, on average. the 22 remaining ones to less than 0.1 8,. Table 3 shows results of the deformation analysis for each S i g o , ~fragment separately. The entries are given in order of decreasing total deformation, which is measured as the sum of the squared deviations from the mean 0-0 distances or, equivalently, as the sum of the squared component scores. A PC score is simply the coordinate in angstroms of a data point along one of the PC axes. Scores for the first seven PCs and for the largest remaining one are also given in Table 3.
+
+
J. Phys. Chem., Vol. 98, No. 42, 1994 10739
Silasesquioxane Molecules and LTA Zeolites
TABLE 3: Some Results of the Deformation Analysis for Individual R&3&012 Molecules CSD entry
refno.
11.12 2 13 14 4 10 15 2 16 3 1 6
17 20 19 18
total def (A2) 0:603 0.447 0.405 0.359 0.347 0.290 0.155 0.099 0.088 0.085 BEGGEZ 0.064 FUSWAROl 0.024 OCMSIOOl 0.018 VINSIO 0.014 FUSWAR 0.006 zzzvuoo1 0.005
PC1 ( A d
orformula steacvite VAWXUM ENCUSI COENSI VIBVAD H8Si801z OCPSIX VAWXUM OPSIOY DIRXAD
%
42.7 8.5 71.3 73.2 98.0 1.6 0.9 43.4 13.2 92.5 96.8 ‘0.01 20.4 52.0
(A, 0.44 0.19 0.51
PC2 (E& %
0.6 87.1 26.1
PC3 (Eg)
0 0.05
0.59 0.31
%
98.6 56.2 1.8 0.4
0.05
0.53 0.05 97.1 0.39 ‘0.1 0.03 ‘0.1 ‘0.01 95.2 99.5 0.19 51.9 0.21 1.5 0.09 1.8 0.03 52.3 0.15 0.13 ‘0.01 0.03 0.05 3.9 0.01 0.2
(A)
PC4 (Alg) %
(A)
0.77 1.6 0.10 0.50 cO.01 ‘0.01 0.08 0.9 0.06 1.1 0.06 0.04 ‘0.01 0.01 2.0 0.08 ‘0.01 0.2 0.02 0.06 0.31 3.6 0.01 0.30 1.9 0.01 0.04 0.1 0.5 0.02 0.18 1.8 0.02 4.4 0.03 0.10 78.9 13.1 0.03 0.02 ‘0.01 6.5
PC5,6, 7 (Tzu)
largest remaining PC, % PC9 (Eg),1.3 PC9 (E;); 2.7 PC9 (Eg),1.3 PC9 (Eg),0.4 3 x 7.9 3 x 0.17 PC14 (TI,,),0.7 PClO (Aig), ‘0.01 PC8 (Eg).1.0 PC8 (Eg),0.3 PC9 (Eg),0.7 PC9 (Eg),0.2 PC9 (Eg),9.2 PClO (Aig),5.7 PC17 (Tzg). ‘0.01 PClO (Aig),20.1 3 x 13.1 3 x 0.03 PClO (Aig),6.0 PClO (Aig),12.5 %
(A)
structures was performed with the 12 nonbonding 0-0distances across the six faces of the cube-shaped units. Results of a PCA for 62 zeolite A structures are given in Table 2 (bottom). Overall, the eigenvalues for Tg012 are about 3-4 times bigger than those for Sig012; that is, the deformations are generally larger in the zeolites than in the molecular species. Here, five PCs are sufficient to explain all of the variance, the first two accounting for 95.6%. There are two pairs of E, coordinates and one AI, coordinate. PC1 and PC2 are combinations of Sl(Eg) and WE,): PC1, PC2 = 0.999 S,(E,) = 0.040 S2(E,)
z
J$$f ,
,,... ......i’... ... .. g’f
-
Figure 3. Schematic representation of some symmetry distortion coordinates of a D4R fragment. Thin lines across the faces of the cubes represent the 0-0 distances used as variables in the PCA. Arrows at the end of a line imply elongation of the corresponding distance (positive coefficient in symmetry coordinate); arrows in the middle of the line imply contraction (negative coefficient in symmetry coordinate). Top: S(Azg). Middle: &,(E,) and Slb(Eg). Bottom: &(Tzu),Sb(Tz,,), and Sc(T2u). The total distortions of individual molecules vary widely from 0.60 Az for the ionic compound steacyite with R = 0- to 0.005 A2 for the octaethyl compound with R = C2H5. Given the high R-value of 0.12 for the latter compound, the distortion is probably not statistically significant. There is no obvious relationship between the magnitude of the distortion and the nature of the exocyclic substituent. Individual scores for a given PC are also quite variable and not correlated to the total distortion. PC scores given as horizontal bars in Table 3 equal 0 and are forbidden by the crystallographic site symmetry of the fragment. Scores along PC1, PC2, PC3, PC5, PC6, and PC7 account for more than 98% of the distortion for most molecules. Exceptions are VIBVAD, BEGGEZ, ZZZUOOl, FUSWAR, and VINSIO, which show a large R-value or small total distortions or both. Deformation Analysis for Zeolite A Structures. The deformation analysis for the Tg012 fragments from zeolite A
As above, the contribution in S2 is a consequence of the nonrigidity of the tetrahedra; it is of the same order of magnitude as for the SigOlz fragments and absorbs 0.2% of the variance. The second E, pair may be written as PC4, PC5 = 0.040 S,(E,)
+ 0.999 S,(E,)
and is almost entirely due to distortion of TO3 groups. Its contribution to the overall distortion is much smaller than that of the first E, pair. As before, the AI, coordinate cannot be neglected, its relative importance being about the same as for the SigO12 fragment. The loadings correspond to those of S(A1,). The AI, coordinate is another indication of deformations within the TO3 units. For zeolite A structures A2, and Tzu deformations are not found. This is due to the site symmetry of the Tg012 fragments, which is 4lmmm. As mentioned earlier, the Azg deformation leads to an m?-symmetric fragment lacking 4-fold symmetry, whereas the T2u deformations destroy the center of inversion. Both deformations are incompatible with 4/mmm site symmetry and are therefore not observed. Total deformations of individual structures are in the range between 0.006 and 2.093 A2. A total distortion larger than 1.0 A2 occurs in nearly one-third of all structures. The highest distortion is observed in Li-LTA27 (2.09 This structure also shows one of the two extreme forms of d e f ~ r m a t i o nof~ ~ the single-eight-ring opening (S8R) of the a-cage (T-01-T = 171.6”, T-02-T = 140.4”, where T-01-T belongs to the D4R fragment and T-02-T connects D4R fragments to a S8R opening). The other extreme deformation of the S8R is found in K-LTAZ8(T-01-T = 128.5”, T-02-T = 178.4”), which also shows a high distortion of the D4R unit (1.19 A2). The lattice constant of Li-LTA is the smallest observed for zeolites A, with space group Pm3m (11.956 A) and that of K-LTA is among the largest (12.317 A). In most of the zeolite A
Az).
10740 .I. Phys. Chem., Vol. 98, No. 42, 1994
Bieniok and Biirgi
structures more than 90% of all deformation is explained by the compressions PC1 and PC2. In two forms of zeolite A distortion occurs primarily (more than 80%) along PC4 and PC5, indicating strong deformation of the 0-T-0 angles in the TO3 groups. These two forms are C S - L T A , with ~ ~ a total deformation of 0.228 Az,and fully hydrated Tl-LTA,30with 0.042 A2; both are highly loaded structures. In both cases the total deformation is at the low end of the observed range. A detailed table of results is given as supplementary material. In each individual structure the E,-type distortions are found exclusively along PC1 or along f(d3/2)PC2 - (1/2)PC1, depending on whether the T8012 fragment is distorted along the Y, X,or Z axis. This is a consequence of the site symmetry 4/mmm, which is only conserved along the above directions but not in between.22 Discussion Our analysis has shown that distortions of Si8012 and TsO12 fragments may, to a large extent, be explained by invoking only three types of coordinates: the “torsion” S(Az,), the elongation/ compressions S(E,), and tetrahedral deformations S(Tzu)of the cage as a whole (not of individual RSi03 and OT03 tetrahedra). These follow naturally from a molecular model built of rigid tetrahedra which are joined flexibly across the edge-sharing oxygen atoms. This finding implies that the D4R units react quite flexibly to forces imposed on them by the substituents R, by the constraints resulting from the three-dimensional crystal structure, and by the chemical entities contained in the zeolite cavities. Thus, the force constants F(Azg), F(E,), and F(T2,) are expected to be quite low. This is indeed the case. A normal coordinate analysis based on IR and Raman spectra of HsSi8012 and DsSi8012 yields F(A2g) = 0.0040 mdyn 8, and F(E,) = F ( T d = 0.091 mdyn A, to be compared with F(OSi0) 1.1 mdyn Corresponding calculated frequencies are 57, 84, and 68 cm-’. The same force constants were also derived from the atomic displacement parameters (temperature factor parameters) of HgSi801233obtained from an accurate single-crystal diffraction experiment at 100 K.’O They are F(A2,) = 0.0034(15) mdyn 8, and F(E,) = F(T2”) = 0.077(2) mdyn A; the calculated frequencies are 49, 75, and 62 cm-’. The two determinations from two completely independent experiments agree and provide further confirmation of the simplified molecular model used here. Deformations of the D5R unit from D5h symmetry in RloSi10015 molecules,34of R12Si12018 m0lecules3~from D2d symmetry, and of the D8R unit T16024 in zeolite RHO, merlinoite, and p a ~ l i n g i t efrom ~ ~ D8h symmetry have been analyzed in analogous ways. In all cases it was found that the same kind of molecular model accounts for most of the observed distortions. The model presented here is thus quite general for both molecular spherosiloxanes and zeolite building blocks. It may be generalized to integral zeolite frameworks, as will be discussed briefly for zeolite A. There are only four crystallographically independent framework atoms in the pseudo cell description with space group Pmgm (a 12.3 8,). The atoms, their coordinates, and site symmetries are
-
A.31332
-
T:
01:
xl, 112, 0 (“2)
03: x39 x33 23 (m) Thus, the entire framework structure is specified by seven
variables, the six positional parameters, and the cubic cell constant a. There are three independent T-0 distances d and three independent 0-T-0 angles in the structure. If they are known, six equations of constraint among the seven parameters are obtained, e.g. d(T-01) = a h 2 (1/2 Z O ~ ] etc. ”~, This leaves one degree of freedom undetermined. In terms of the above analysis it is the Sl,(E,) elongatiodcompression coordinate. On the basis of empirical computer simulation, has described this deformation qualitatively as the motion of “antirotating hinges”. In a detailed geometrical analysis,38 Depmeier has given the equations of constraint, primarily in terms of tilting rigid tetrahedra relative to the cubic coordinate axis, but also in terms of T-0 distance and 0-T-0 angle changes. The analogy between preferred modes of static deformation and low-frequency, soft vibrations may also be extended;39it may well help in analyzing soft phonon modes and associated structural phase transitions in framework structures consisting of rigid polyhedral units linked flexibly across comer-sharing atoms.
+
+
Acknowledgment. We thank U. Brendel and V. Malogajski for preparing some of the figures. This work was supported by the Schweizerischer Nationalfonds. Supplementary Material Available: Tables of Si-0 distances, 0-Si-0 angles, and 0-0 distances and a table of results for zeolites (4 pages). Ordering information is given on any current masthead page. References and Notes (1) Podberezskaya, N. V.; Baidina, I. A.; Alexeev, V. I.; Borisov, S. V.; Martynova, T. N. Zh. Strukt. Khim. 1981, 22, 116. (2) Feher, F. J.; Budzichowski, T. A. J . Organomet. Chem. 1989,373, 153. (3) Day, V. W.; Klemperer, W. G.; Mainz, V. V.; Millar, D. M. J . Am. Chem. Soc. 1985, 107, 8262. (4) Feher, F. J.; Weller, K. J. Organometallics 1990, 9, 2638. ( 5 ) Meier, W. M.; Olson, D. H. Atlas of Zeolite Structure Types; Butterworth Heinemann: London, 1992. (6) (a) Wiebcke, M.; Koller, H. Acta Crystallogr. 1992, B48, 449. (b) Wiebcke, M. J . Chem. SOC., Chem. Commun. 1991, 1507. (7) (a) Smolin, Yu. I.; Shepelev, Yu. F.; Ershov, A. S.;Hoebbel, D. Sov. Phys. Dokl. 1987, 32, 943. (b) Feher, F. J.; Budzichowski, T. A,; Weller, K. J. J . Am. Chem. SOC.1989, I l l , 7288. (c) Feher, F. J.; Weller, K. J. Organometallics 1990, 9, 2638. (d) Winkhofer, N.; Voigt, A.; Dom, H.; Roesky, H. W.; Seiner, A.; Stake, D.; Reller, A. Angew. Chem. 1994, 106, 1414. (e) Caullet, P.; Guth, J. L.; Hazm, J.; Lamblin, J. M.; Gies, H. Eur. J. Solid State Inorg. Chem. 1991, 28, 345. (8) Bissert, G.; Liebau, F. Z. Kristallogr. 1987, 179, 357. (9) Allen, F. H.; Davis, J. E.; Galloy, J. J.; Johnson, 0.; Kennard, 0.; Macrae, C. F.; Mitchell, E. M.; Mitchell, G. F.; Smith, J. M.; Watson, D. G. J . Chem. Inf. Comput. Sci. 1991, 31, 187. (10) Auf der Heyde, T. P. E.; Biirgi, H. B.; Burgy, H.; Tomroos, K. W. Chimia 1991, 45, 38. (11) Richard, P.; Perrault, G. Acta Crystallogr. 1972, 828, 1994. (12) Szymanski, J. T.; Owens, D. R.; Roberts, A. C . ; Ansell, H. G.; Chao, G. Y. Can. Miner. 1982, 20, 65. (13) Smolin, Yu. I.; Shepelev, Yu. F.; Butikova, I. K. Kristallografiya 1972, 17, 15. (14) Smolin, Yu. I.; Shepelev, Yu. F.; Pomes, R.; Khobbel, D.; Viker, V. Sov. Phys. Crystallogr. 1976, 20, 567. (15) Shklover, V. E.; Struchkov, Yu. T.; Makarova, N. N.; Andrianov, K. A. Zh. Strukt. Khim. 1978, 19, 1107. (16) Hossain, M. A,; Hursthouse, M. B.; Malik, K. M. A. Acfa Crystallogr. 1979, 835, 2258. (17) Koellner, G.; Muller, U. Acta Crystallogr. 1989, C45, 1106. (18) Podberezskaya, N. V.; Magerill, S.A,; Baidina, I. A,; Borisov, S. V.; Gorsh, L. E.; Kanev, A. N.; Martynova, T. N. Zh. Struk. Khim. 1982, 23, 120. (19) Shepelev, Yu. F.; Smolin, Yu. I.; Ershov, A. S.;Rademacher, 0.; Scheler, H. Sov. Phys. Crystallogr. 1987, 32, 822. (20) Baidina, I. A.; Podberezskaya, N. V.; Alexeev, V. I.; Martynova, T. N.; Borisov, S. V.; Kanev, A. N. Zh. Stmk. Khim. 1979, 20, 648.
Silasesquioxane Molecules and LTA Zeolites (21) Bergerhoff, G.; Hundt, R.; Sievers, R.; Brown, I. D. J. Chem. Znf. Comput. Sci. 1983, 23, 66. (22) Murray-Rust, P.; Biirgi, H. B.; Dunitz, J. D. Acta Crystallogr. 1979, A35, 703. Dunitz, J. D.; Burgi, H. B. In Structure Correlation; Biirgi, H. B., Dunitz, J. D., Eds.; Verlag Chemie: Weinheim, 1994; Chapter 2, p 23. (23) Murray-Rust, P.; Mothenvell, S. Acta Crystallogr. 1978,834, 2518. (24) For a concise summary. see for examde: Auf der Hevde. - . T. P. E. J . Chem. Educ. 1990, 67, 461: (25) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1955. (26) SAS 6.07, SAS Institute Inc.: Cary, NC, 1989. (27) Jirak, Z.; Bosacek, V.; Vratislav, S.; Herden, H.; Schollner, R.; Mortier, W. J.; Gellens, L.; Uytterhoeven, J. B. Zeolites 1983, 3, 255. (28) Pluth, J. J.; Smith, J. V. J . Phys. Chem. 1979, 83, 741. (29) Heo, N. H.; Seff, J. J . Am. Chem. SOC. 1987, 109, 7986. (30) Thoeni, W. 2.Kristallogr. 1975, 142, 142. (311 Btirtsch. M.: Bornhauser. P.: Calzafem. G.: Imhof. R. J . Phvs. Chem.' 1994, 98, 2817. '
J. Phys. Chem., Vol. 98, No. 42, 1994 10741 (32) These force constants have been derived31on the basis of internal coordinates. Transfomtion on the basis of 0-0 distances used here does not change the general conclusions. (33) Raselli, A. Ph.D. Thesis, Universitat Bern, 1991. (34) Biirgi, H. B.; Tijmoos, K. W.; Calzafem, G.; Biirgy, H. Inorg. Chem. 1993, 32, 4914. (35) Tomroos, K. W.; Biirgi, H. B.; Calzafem, G.; Biirgy, H. Submitted. (36) Bieniok, A.; Burgi, H. B. In Studies in Surface Science and Catalysis. Part A: Zeolites and Related Microporous Materials; Weitkamp, J., Karge, H. G., Pfeifer, H., Holderich, W., Eds.; Elsevier: Amsterdam, The Netherlands, 1994; Vol. 84, p 567-574. (37) Baur, W. H. J . Solid State Chem. 1992, 97, 243. (38) Depmeier, W. Acta Crystallogr. 1985, 841, 101. (39) For a detailed discussion of these ideas, see: Giddy, A. P. Ph.D. Thesis, University of Cambridge, 1991.
