Vibrational Modes of Double Six-Member Rings of Oxygen-Bridged

The vibrational modes of double six-member ring (D6R) clusters with general composition (Mn+)x/nH12Si12-xAlxO18 (where x = 0, 2; M = H+, Li+, Na+, K+,...
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J. Phys. Chem. B 2004, 108, 13200-13207

Vibrational Modes of Double Six-Member Rings of Oxygen-Bridged Silicon and Aluminum Atoms in Zeolites: A DFT Study Hans Mikosch,*,† Ellie L. Uzunova,‡ and Georgi St. Nikolov*,‡ Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria, and Institute of Chemical Technologies and Analytics, Vienna UniVersity of Technology, Vienna 1060, Austria ReceiVed: March 30, 2004; In Final Form: June 23, 2004

The vibrational modes of double six-member ring (D6R) clusters with general composition (Mn+)x/nH12Si12-xAlxO18 (where x ) 0, 2; M ) H+, Li+, Na+, K+, Ca2+) are studied by DFT with the B3LYP method. The point group symmetry of the fragments with Si,Al substitution descends from C2h with AlO(SiO)3Al linkages, via C2V with AlO(SiO)2Al linkages in one T6O6 ring of a D6R, to Cs, where the Al atoms are closely spaced in an AlOSiOAl sequence. The C2h symmetry fragments represent centrosymmetric structures with maximum separation of Al atoms. The lower symmetry fragments C2V and Cs describe the band broadening, which arises from specific Si,Al distributions. The ring-opening vibrations, defined as in-phase radial displacement of tetrahedral and oxygen atoms parallel to the ring plane, are correlated to the framework vibrations of the zeolite structures, which contain D6R as secondary building units. The oxygen atom displacements are part of the ring-opening vibrations in the 200-600 cm-1 frequency range. The vibration assigned to the D6R in zeolites, based on previous empirical studies, is calculated at 570-600 cm-1 for cluster models with Si/Al ) 5 ratio and Al atoms at different positions. Both the shape and frequency of this vibration are sensitive to the specific Si,Al ordering and also to the type and position of the extraframework cations.

Introduction Zeolites have found widespread industrial applications as ion exchangers, selective adsorbents, and catalysts of various reactions in organic chemistry and petrochemistry.1 The framework density of zeolites is much lower compared to other tectoaluminosilicates, because the highly regular network of intracrystalline cavities and channels is an intrinsic property of the zeolite framework. The various types of zeolites are classified according to the distinct topology of the 3D framework and the overall Si/Al ratio. Pure silica molecular sieves are neutral, and it is the substitution of trivalent aluminum for tetravalent silicon that produces negatively charged frameworks. The general formula of zeolites is Mn+x/n[SiyAlxO2(x+y)]‚zH2O; Mn+ are extraframework cations, which balance the negatively charged framework, most of them being easily exchangeable.2 A common way to describe zeolite frameworks is to segregate their highly symmetric structure into smaller units, known as secondary building units (SBU).3 The D6R are highly symmetric SBU, and they are able to connect other larger high-symmetry units such as the β-cages. Depending on the scheme of connection a large number of frameworks emerge: FAU, EMT, or FAU/EMT structural intermediates. In FAU zeolites, the sodalite cages are linked by TOT bridges forming a D6R connection.3,17 Lo¨wenstein’s rule requires strict alternation of Si and Al atoms at a Si/Al ) 1 ratio.18a This is achieved in LSX zeolites (Si/Al ) 1), which belong to the space group Fd3h; ) Th4.19 Different ordering patterns may occur for Si/Al > 1 ratios, and they have been subjected to both experimental and theoretical studies.20-22 According to a systematic empirical study of Flanigen et al.,4 certain IR and Raman bands were assigned to local topological features of zeolite frameworks.4a,5 IR spectroscopy has thereafter † ‡

Vienna University of Technology. Bulgarian Academy of Sciences.

been largely used to recognize structural units in zeolites prior to X-ray diffraction analysis. The vibrational spectra are also sensitive to the Si/Al ratio and the type of extraframework cations.4b A number of theoretical studies have been devoted to the analysis of vibrational modes in polysiloxanes and zeolites.6-11 Local mode analysis of sodalite frameworks and LTA zeolites revealed that both frequencies and intensities of the IR and Raman bands are related to specific structural subunits.7 Analysis of the shape and energy of vibrations related to SBU in zeolites was however restricted to either entirely siliceous fragments6 or to fragments with indistinguishable T atoms,7d,e and in this way the frequency shift dependence on the average Si/Al ratio was examined only. Correlation schemes for the vibrations of rings and double-rings have been established,6 and vibrational frequencies have been assigned to displacements in specific structural subunits of LTA frameworks by local mode analysis,6,7 the pseudolattice approach,8 and DFT methods.9 The effect of Si,Al ordering and extraframework cation distribution was addressed for D4R in LTA zeolites.9a Generally, all methods reproduce well the trends in frequency changes with varying Si/Al ratio; it has been pointed out, however, that the ab initio treatment of fragments with unbalanced negative charges produces results that are in large discrepancy with experimental frequencies.11 Structural fragments with general composition (Mn+)x/nH12Si12-xAlxO18, where x ) 0, 2; M ) H+, Li+, Na+, K+, Ca2+, are the subject of the present study. They represent double sixmember rings (D6R), which are part of a number of zeolite frameworks: CHA, ERI, FAU, EMT, GME, LEV, OFF, EAB, KFI, LTL, LTN.2 D6R cluster models with different Si,Al orderings and cation site occupancy were constructed to examine their relative stability and vibrational frequencies. The point group symmetry of the examined fragments descends from D3d, which refers to entirely siliceous D6R in FAU zeolites with

10.1021/jp0486189 CCC: $27.50 © 2004 American Chemical Society Published on Web 08/10/2004

Vibrational Modes of D6R

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discernible oxygen atoms, to Cs, which allows the appearance of Al-O-Si-O-Al linkages, stabilized by appropriate extraframework cation ordering. The calculated vibrational modes of the different structural fragments were correlated to the framework vibrations of FAU zeolites. Further, the ring-opening vibrations were analyzed by introducing external symmetry coordinates, which define the radial synchronous atomic displacements in a direction parallel to the ring planes. Ring-openings and pore-size fluctuations are important because they control the access to active sites and are responsible for the permeability of zeolite frameworks to different reactants.6b,12 The frequency shifts that arise from specific Si,Al orderings and extraframework cation positions have been calculated. The IR and Raman band regions 200-600 cm-1 can be used as fingerprints for the detection of specific SBUs. Methods Geometry optimizations were performed in Cartesian coordinates by the B3LYP method, which includes local and nonlocal terms as implemented in the Gaussian 98 package.13-16 Hydrogen atoms were used to terminate the clusters via Si-H and Al-H bonds. The optimized geometries and the calculated vibrational frequencies are known to be relatively basis-set independent in DFT.7f Previous studies on D4R have shown that the error in calculating vibrational frequencies at the B3LYP level did not exceed 8 cm-1 in the lowest frequency range and was within 3 cm-1 in the medium- and high-frequency range, when substituting 6-31G(d) with the 6-311G(d) basis set.9a The standard 6-31G(d) basis set was employed for all atoms involved, with the exception of Ca2+ and K+, for which the basis was extended to 6-311G(d). For the OH-containing fragments, polarization functions at the hydrogen atoms were included via the 6-31G(d,p) basis. Harmonic frequency calculations were performed for all geometry-optimized clusters. The stationary points, resulting from the optimizations, which correspond to minima on the potential energy surface, were identified by the absence of negative eigenvalues in the diagonalized Hessian matrix; these eigenvalues give rise to imaginary vibrational modes. For the clusters containing Na+ with a coordination number lower than four and for extraframework cations positioned at S4R edges, the imaginary frequencies of absolute values lower than 40 cm-1 due to extraframework cation displacements were neglected.

Figure 1. Schematic representations of the D6R cluster models. Extraframework positions in the proximity of the D6R are denoted. Si,Al orderings examined are illustrated with protons as compensating charges. Atoms in decreasing size are O, M+ (Li+, Na+, K+), and M2+ (Ca2+), tetrahedral Si and Al. Oxygen atoms are large light gray circles; Si, black circles; extraframework cations, gray circles; Al atoms, white circles; and protons, small gray circles. The sequence of T atom linking is denoted below each model.

Structure and Stability of D6R Fragments (Mn+)2/nH12Si12-xAlxO18 Depending on the Si,Al Distribution and Ordering of Extraframework Cations

Figure 2. Relative stabilization energy of [H12Si10Al2O12]2- with variable Si,Al ordering according to the extraframework cation positions.

The H12Si12O18 cluster with D3d symmetry was selected to represent a D6R in entirely siliceous FAU framework with distinguishable O1, O2, and O3 atom types; see Figure 1. Cluster fragments of general composition (Mn+)2/nH12Si10Al2O18, where M ) H+, Li+, Na+, K+, Ca2+, describe a cation balanced structure with Si/Al ) 5 ratio. This ratio was selected because Si,Al ordering occurs in the high-silica region of FAU zeolites and the largest deviations from Dempsey’s rule (Si is favored at T-sites in the sequence T-O-Si-O-Al)18b were observed. The Si,Al distributions, while obeying Lo¨wenstein’s rule,18 range from maximum separation of negative charges in C2h fragments, to the appearance of Al-O-(Si-O)2-Al linkages in C2V fragments, and further to the allowance of Al-O-Si-O-Al linkages in Cs fragments. The extraframework cations are positioned as found in FAU zeolites. 17,19,23,24 The site SI lies in the center of the D6R, SI′ lies above the T6O6 plane and points to a sodalite cage, and SIII′ lies near the four-ring edges being

close to Al atoms. The stabilization of particular Si,Al orderings in D6R is strongly dependent on the type and location of extraframework cations; see Figure 2. All cations, except Na+, favor maximum negative charge separation, in agreement with Dempsey’s rule; the relative energy of different clusters increases with decreasing Al-Al distance. The calculated Si-O and Al-O bond lengths, as well as the ∠TOT bond angles and the distances between extraframework cations and the nearest oxygen atoms agree with experimental data for FAU zeolites; see Tables 1 and 2. Ca2+ and Li+ cations cause the largest bond angle deformations. The small-size Li+ cations create a higher positive electrostatic potential, and they can approach the negative framework charges, but they are unlikely to occupy either SI or SI′ sites when Al-O-(Si-O)n-Al linkages (n ) 1, 2) exist in the D6R; see Table 2. The Na+ cations at SI′ sites stabilize Al-O-(Si-O)2-Al linkages rather than Al-O-(SiO)3-Al and Al-O-Si-O-Al linkages. The variation in energy

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TABLE 1: Average Bond Lengths and Angles for D6R Fragments Calculated by B3LYP prism model

a

RSi-O (Å)

RAl-O (Å)

∠Al-O-Si (deg)

H12Si12O18: D3d M2H12Si10Al2O18:a C2h M2H12Si10Al2O18:a C2V M2H12Si10Al2O18:a Cs

1.639 1.635 1.630 1.636

1.763 1.755 1.766

145.9 148.1 145.9

LiLSX27 NaX(exp)17a CaLSX(exp)19 CaY(exp)26

1.649-1.651 1.631-1.651 1.596-1.649 1.633-1.671

1.695-1.755 1.701-1.714 130.4-141.4 129.0-161.0

126.6-144.5

∠Si-O-Si (deg) 150.3 149.7 149.4 150.8

M ) Li+, Na+, K+, Ca2+ as extraframework charge compensating cations.

TABLE 2: Internuclear Distances between Extraframework Cations and Nearest Oxygen Atoms in D6R Fragments with Composition M2H12Si10Al2O18 (M ) Li+, Na+, K+, Ca2+ as extraframework charge compensating cations), Calculated by B3LYP cluster symmetry/ cation site occupation

a

RM-O (Å)

C2h 2 Li+ at SI′ 2 Li+ at SIII′ 2 Na+ at SI′ 2 Na+ at SIII′ 2 K+ at SI′

1.985 1.798 2.420 2.162 2.691

2 K+ at SIII′

2.499

cluster symmetry/ cation site occupation

RM-O (Å)

C2V 2 Li+ at SIII′ 2 Na+ at SI′ 2 Na+ at SIII′ 2 K+ at SI′ K+ at SI and SI′ 2 K+ at SIII′ Ca2+ at SI Ca2+ at SI′

cluster symmetry/ cation site occupation

RM-O (Å)

RM-O,exp (Å)

Cs 1.801 2.323 2.166 2.709 2.734 2.500 2.392 2.289

1.902a

2 Li+ at SIII′ 2 Na+ at SI′

1.798 2.299

2.267b

2 K+ at SI′

2.719

2.644c 2.482d

Ref 27. b Ref 17a. c Ref 24. d Ref 19.

between clusters with C2V and C2h symmetry is small when the charge-compensating cations are at SIII′ sites. The smallest energy difference between the fragments with C2h and Cs symmetry, which represent the two limits in Si,Al distribution schemes, was found for Na+ at SI′ sites.

SCHEME 1: Numbering of the Atoms in D6Ra

Vibrational Analysis The lack of strict long-range ordering for FAU zeolites with Si/Al > 1 ratios defines their space group as Fd3hm; ) Oh7. The number of IR- and Raman-active vibrations predicted by factor group analysis for a unit cell with undistinguishable atoms at T-sites is as follows: 10A1g(R) + 18Eg(R) + 28T2g(R) + 28T1u(IR).10 The large number of vibrational modes predicted by group theory disagrees with the small number of bands observed in the experimental spectra. At a fixed Si/Al ratio, the Si,Al distribution and variable cation site occupancy are the main reason for shifts and broadening of bands, which complicate the proper assignment. D6R with D3d Symmetry, H12Si10Al2O18. A D3d symmetry cluster model with distinct O1, O2, and O3 sites was selected to represent the entirely siliceous D6R. The atomic displacements span the following irreducible representations (IR ) infraredactive, R ) Raman-active, in ) inactive vibrations):

a The arrows depict the vectors representing O(1), O(2), O(3), and Si atom displacements for one atom of each type, chosen to illustrate the composite vibrations.

ΓSi-O ) 3A1g(R) + 3A2g(in) + 6Eg(R) + 3A1u(in) + 3A2u(IR) + 6Eu(IR)

The vibrations of large structural subunits such as the rings and double-rings are of special interest: the ring-opening (RO) vibrations in zeolites control the access to cation sites and active centers, and they have been subjected to a number of studies.6-9 In all cage-shaped polysiloxanes the atomic displacements are mixed to a large extent and the assignment of frequencies to separate TO4 units is impossible. Synchronized vibrations of the rings are observed when all T-O-T bending and T-O stretching modes are effected in-phase. The displacement vectors of each T and O atom that represent the ring-opening motion were used to generate an appropriate set of symmetry coordinates for studying the D6R collective vibrations. The vectors are denoted as follows: p for T atoms; s for O(1) atoms which connect T6O6 rings to form a D6R; q for O(2); and r for O(3) in the D6R fragment of zeolite FAU. Indexes display the atom number in the prism as denoted in Scheme 1. The O(1) type atoms bear the numbers 25-30, and the two TO6 rings, which contain O(2) and O(3) atoms, are above and below the plane of the O(1) atoms, respectively. The irreducible representations for the D3d symmetry group, spanned by the atom displacements in the planes of the rings, are

Γ∠TOT ) 3A1g(R) + 3Eg(R) + A1u(in) + 2A2u(IR) + 3Eu(IR)

Γin-plane ) 4A1g(R) + A2g(in) + 5Eg(R) + 2A1u(in) + 3A2u(IR) + 5Eu(IR)

H12Si12O18 (D3d) Γ ) 11A1g(R) + 9A2g(in) + 20Eg(R) + 9A1u(in) + 11A2u(IR) + 20Eu(IR) The following irreducible representations are valid for the Si-O stretching and TOT bending modes:

Vibrational Modes of D6R

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TABLE 3: External Symmetry Coordinatesa for the Ring-Opening Vibrationsb of D6R with D3d Symmetry symmetry mode

sum of displacement vectors

P (a1g) P (a2u) P (a2g) P (a1u) Q (a1g) Q (a2u) Q (a2g) Q (a1u) R (a1g) R (a2u) R (a2g) R (a1u) S (a1g) S (a2u) S (a2g) S (a1u)

(1/x12)(p1+p2+p3+p4+p5+p6+p19+p20+p21+p22+p23+p24) (1/x12)(p1+p2+p3+p4+p5+p6-p19-p20-p21-p22-p23-p24) (1/x12)(p1-p2+p3-p4+p5-p6-p19+p20-p21+p22-p23+p24) (1/x12)(p1-p2+p3-p4+p5-p6+p19-p20+p21-p22+p23-p24) (1/x6)(q7+q9+q11+q14+q16+q18) (1/x6)(q7+q9+q11-q14-q16-q18) 0 0 (1/x6)(r8+r10+r12+r13+r15+r17) (1/x6)(r8+r10+r12-r13-r15-r17) 0 0 (1/x6)(s25+s26+s27+s28+s29+s30) 0 0 (1/x6)(s25-s26+s27-s28+s29-s30)

a For the construction of symmetry coordinates, see, for example, ref 25. b The doubly degenerate vibrations eu and eg contribute to ring deformations only and are not included.

The external symmetry coordinates of the in-plane ringopening motions were constructed by projection techniques in terms of the vector-displacement coordinates. Collective vibrations, leading to in-phase ring-opening vibrations, have A1g, A2g, A1u, and A2u symmetry, as seen from the sum of displacement vectors; see Table 3. The A1g RO vibration of tetrahedral atoms is totally symmetric with respect to the two T6O6 rings, being a breathing mode of the D6R, while the A2u RO vibration opens the front T6O6 ring and closes the back T6O6 ring. The O(1) atoms contribute only to the A1g RO mode. A change in the free aperture dimension of the T6O6 windows can be achieved by vibrations with A1g and A2u symmetry, provided that the displacements of O(2) and O(3) atoms are in the same direction. The calculated ring-opening vibrations of D3d cluster H12Si12O18 are represented in Figure 3. The low-frequency A1g vibration at 68 cm-1 involves T atoms and O(1) atoms in a synchronous displacement in the same direction. In the 274 cm-1 vibration both O(2) and O(3) atoms participate in ring-opening. The 449 cm-1 A1g vibration is dominated by O(2) and O(3) atom ringopening and O(1) atom ring-closure. In all three A2u modes, T atoms participate in opening the front ring and closing the back ring. While T atoms and O(3) atoms keep the same direction of displacement in the 404 cm-1 vibration, the O(2) atoms shift in alternation with the O(3) atoms, and this vibration causes a minor change in the D6R free aperture dimension. The displacement of oxygen atoms from the T6O6 rings contributes to opening the front ring and closing the back ring, effected by the 586 cm-1 mode; both O(2) and O(3) atoms are displaced in the reverse direction to the T atoms’ motion. The RO vibrations of clusters with C2V, C2h, and Cs symmetry can be correlated to the framework vibrations of zeolites via the higher symmetry groups: D3d f Oh for FAU zeolites and D3d f D6h for EMT and D3d for FAU/EMT structural intermediates (ZSM-3, CSZ-1, ECR-30); see Figure 4. The A1g RO vibrations of clusters with D3d symmetry and the Ag RO vibrations of clusters with C2h symmetry contribute to the A1g and T2g Raman-active modes of the FAU framework. The A2u RO vibrations in D3d symmetry clusters and Bu RO vibrations of C2h clusters contribute to the T1u and A2u IR-active modes of FAU, and respectively, EMT. The A′ and A1 symmetry RO vibrations of clusters with lower symmetry, Cs and C2V, respectively, contribute to both the IR and Raman spectra of the zeolite frameworks. The cluster models with different extraframework cation distribution reproduce correctly the IR

and Raman spectrum of FAU zeolites, the lower symmetry ones (C2V and Cs) being able to describe band broadening in the spectra; see Tables 4 and 5. D6R with C2h Symmetry, (MI)2H12Si10Al2O18. The Si,Al substitution lowers the symmetry of the D6R, and C2h symmetry is attained when the two Al atoms in a cluster with Si/Al ) 5 ratio are positioned at maximum distance. The C2h irreducible representations of the vibrational modes are

(M+)xH12Si12-xAlxO18; M ) Li+, Na+, K+, at either SI′ or SIII′ sites (C2h) Γ ) 35Ag(R) + 28Bg(R) + 29Au(IR) + 34Bu(IR) ΓSi-O ) 8Ag(R) + 7Bg(R) + 7Au(IR) + 8Bu(IR) ΓAl-O ) 2Ag(R) + Bg(R) + Au(IR) + 2Bu(IR) Γ∠SiOSi ) 3Ag(R) + 3Bg(R) + 3Au(IR) + 3Bu(IR) The Ag and Bu vibrations were found to contribute to the ring-opening displacements; see Tables 4 and 5. The shape and frequency of ring-opening vibrations are strongly affected by the type of the extraframework cations and their location with respect to the D6R. The M-O internuclear distance increases in the order Li+ < Ca2+ < Na+ < K+. The Li+ cations form the shortest Li+-O distances (see Table 1), and when they occupy the SI′ sites, they are very close to the plane of the six T atoms. Minor changes in the frequency and shape of RO vibrations were observed with 2Na+ as charge-compensating cations at SI′ sites when compared to the H12Si12O18 (D3d) fragment. The 301 cm-1 Bu vibration is formed by alternating displacements of O(2), O(3), and T atoms; it is correlated to the 277 cm-1 A2u vibration of the D3d symmetry cluster; see Figure 3. The 453 cm-1 Ag vibration is dominated by synchronous displacements of O(2) and O(3) atoms from both rings and corresponds to the 449 cm-1 A1g mode. The 583 cm-1 Ag vibration displaces T and O atoms from the rings in alternate directions; it correlates in shape to the 579 cm-1 A1g mode. The shape of vibrations is altered and the frequencies are shifted for clusters with Li+ and K+ cations; see Tables 4 and 5. In

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Mikosch et al. vibration, T and O atoms move in alternation, the displacement of T atoms in the two T6O6 rings being also in opposite directions as in the A2u vibration with the same frequency of the D3d cluster. D6R with C2W Symmetry, (Mn)2/nH12Si10Al2O18. The C2V symmetry clusters are less stable than the C2h symmetry ones when charge-compensating cations are Li+ and K+ at SI′ sites or Li+, Na+, and K+ at SIII′ sites. Despite this fact, a larger number of stable isomers were found (see Table 1). In clusters with C2V symmetry, an Al-O-(SiO)2-Al linkage is present in one of the T6O6 rings and the site SI in the D6R center becomes energetically more favorable: it is preferred by Ca2+ and can be occupied by K+ even when another K+ is positioned at the nearest SI′ site. 9b The vibrational modes span different irreducible representations depending on the position of the extraframework cations:

(Mn+)x/nH12Si12-xAlxO18 (C2W) M ) Ca2+ at either SI or SI′ Γ ) 35A1(IR,R) + 27A2(R) + 32B1(IR,R) + 29B2(IR,R) M ) Na+ at SI′; K+ at SI′; K+ at SI and SI′ Γ ) 36A1(IR,R) + 27A2(R) + 33B1(IR,R) + 30B2(IR,R) M ) Na+ or K+ at SIII′ Γ ) 36A1(IR,R) + 28A2(R) + 33B1(IR,R) + 29B2(IR,R) The individual TO stretching and TOT bending vibrations span the following symmetry modes:

ΓSi-O ) 8A1(IR,R) + 7A2(R) + 8B1(IR,R) + 7B2(IR,R) ΓAl-O ) 2A1(IR,R) + A2(R) + 2B1(IR,R) + B2(IR,R) Γ∠SiOSi ) 4A1(IR,R) + 2A2(R) + 2B1(IR,R) + 4B2(IR,R)

Figure 3. Approximate representation of the six-member ring-opening displacements involved in the 4A1g and 3A2u vibrations of D6R with D3d symmetry. Si atoms are small black circles; oxygen atoms are gray. Description of the vibrations in terms of external symmetry coordinates is included.

clusters with Li+ cations at SI′ sites, the 330 cm-1 Ag and the 450 cm-1 Bu vibrations consist of T atom displacements; the latter vibration corresponds to movement of front and back rings in reverse directions. The 582 cm-1 Ag vibration comprises outward displacement of O(2) and inward displacement of O(3) atoms from the T6O6 rings. When 2K+ occupy the SI′ sites above and below the T6O6 rings, respectively, the lowest frequency RO vibration is found at 417 cm-1; it has Ag symmetry and corresponds in shape to the 449 cm-1 A1g vibration (Figure 3). The 439 cm-1 Bu vibration involves mainly T atoms and is mixed with a TOT bending mode. The 575 cm-1 Ag vibration is dominated by oxygen atoms and corresponds to synchronous O(2), O(3) displacements in both rings; it is correlated to the 579 cm-1 A1g mode. In the 586 cm-1 Bu

Only the totally symmetric A1 modes contribute to the ringopening vibrations of C2V symmetry clusters; see Tables 4 and 5. These modes correlate to the A1g and A2u RO vibrations of the siliceous clusters with either D6h or D3d symmetry. In clusters with Na+ at SI′ sites, the 269 and 296 cm-1 A1 modes involve mainly oxygen atoms displacement. The 573 cm-1 vibration correlates to the 579 cm-1 A1g mode of the D3d symmetry fragment, while the 595 cm-1 RO vibration corresponds to the 586 cm-1 A2u mode; see Figure 3. The correct experimental trend in the shift of the (P-Q-R) A2u mode was also found for Ca2+ cations: it is shifted to 599 cm-1 when Ca2+ cations are located at SI′ sites and further to 608 cm-1 when the more stable arrangement with Ca2+ in the D6R center (SI site) is attained. Slight framework distortion contributes to the frequency shift in this case. The experimentally obtained frequency for Ca-exchanged FAU zeolite with Si/Al ) 2.5 ratio was 635 cm-1.4 Two different K+ cation distributions can be obtained in the C2V clusters: one with K+ at SI′ sites, above the Si4Al2O4 plane and below the Si6O6 plane, and another with K+ at SI and SI′ sites above and below the Si4Al2O6 plane; see Figure 1. When both the SI and SI′ sites in one D6R are occupied by K+, the cation at SI is displaced by 0.3 Å from the D6R center due to repulsive forces between the cations.9b The 572 cm-1 vibration

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Figure 4. Symmetry descent correlation diagram for the vibrations parallel to the T6O6-ring planes in D6R. M ) Li+, Na+, K+ (x ) 2); Ca2+ (x ) 1).

TABLE 4: IR-Active Vibrations of Hexagonal Prismsa (B3LYP-calculated frequencies (ν, cm-1) and symmetry modes (in parentheses) in the 250-610 cm-1 rangeb) H12Si12O18: D3d

Li2Z: C2h, Li+ at SI′

Na2Z: C2h, Na+ at SI′

Na2Z: C2V, Na+ at SI′

277 (A2u)RO

266 (Au) 313 (Au) 337 (Au) 346 (Bu) 358 (Au) 371 (Bu) 382 (Au)

264 (Bu) 279 (Bu) 301 (Bu) RO 315 (Au)

262 (B1) 279 (B2) 296 (A1)RO 299 (B2) 317 (B2)

313 (Eu)

333 (Bu) 349 (Au) 363 (Bu)

359 (Eu) 375 (Eu) 404 (A2u)RO

416 (Bu) 431 (Bu)

438 (A2u) 449 (Eu)

435 (Au) 450 (Bu) RO 464 (Au) 489 (Bu) 531 (Bu) 568 (Au) 579 (Au) 587 (Bu)

557 (Eu) 586 (A2u)RO

374 (Au) 394 (Bu) 417 (Au) 420 (Bu) 427 (Bu)

517 (Bu) 522 (Au) 539 (Bu) 568 (Au) 579 (Bu)

349 (B1) 350 (B2) 363 (A1) 368 (B2) 378 (B1) 419 (B1) 425 (A1) 425 (B1) 440 (A1) 441 (B1) 460 (A1) 519 (B2) 556 (B1) 562 (B2) 582 (B1) 586 (B2) 595 (A1)RO

K2Z: C2h, K+ at SI′

269 (Bu) 314 (Bu) 319 (Au) 334 (Bu) 345 (Bu) 354 (Au) 373 (Au) 384 (Bu) 415 (Au) 426 (Bu) 427 (Au) 439 (Bu)RO 516 (Bu) 546 (Au) 550 (Bu) 564 (Au) 586 (Bu)RO 605 (Bu)

K2Z: C2V, K+ at SI; SI′

K2Z: C2V, K+ at SI′

K2Z: Cs, K+ at SI′

Na2Z: Cs, Na+ at SI′

265 (A1) 267 (A1) 285 (B2) 291 (B1) 321 (B2) 343 (B1) 367 (B1) 369 (A1) 374 (B2) 378 (B1) 387 (A1) 408 (A1) 427 (B2) 448 (A1) 463 (B1) 475 (A1) 536 (B2) 550 (A1)RO 557 (B2) 563 (B1) 574 (B1) 577 (A1) 580 (A1)RO 592 (B2)

281 (A1)RO 281 (B2) 312 (B2) 313 (B1) 328 (B1) 330 (A1) 343 (B2) 344 (A1) 360 (B1) 390 (A1) 392 (B2) 417 (B1) 419 (A1)RO 431 (B1) 432 (B2) 445 (A1)RO 516 (B2) 524 (A1) 546 (B2) 551 (B1) 572 (B1) 572 (B2) 572 (A1)RO 578 (A1) 604 (A1) 605 (B1)

271 (A′′) 280 (A′) RO 285 (A′′) 303 (A′) 315 (A′′) 317 (A′) 322 (A′′) 323 (A′) 332 (A′′) 350 (A′) 352 (A′′) 362 (A′) 376 (A′) 401 (A′) 419 (A′) 421 (A′) 424 (A′′) 425 (A′) 440 (A′) 510 (A′′) 522 (A′) 538 (A′′) 538 (A′) 546 (A′) 552 (A′′) 566 (A′) 568 (A′′)

254 (A′) 257 (A′′) 278 (A′′) 315 (A′′) 319 (A′) 336 (A′′) 337 (A′) 352 (A′′) 353 (A′) 370 (A′) 386 (A′) 406 (A′) 418 (A′) 422 (A′) 432 (A′) 457 (A′) 510 (A′′) 526 (A′) 539 (A′) 546 (A′′) 555 (A′) 560 (A′′) 564 (A′) 581 (A′) 584 (A′) RO 596 (A′) RO

Y zeolitec

330 m

456 ms

504 wsh

575 m

a Vibrations, dominated by the displacement of hydrogen atoms forming T-H bonds (T ) Si, Al) and those with IR intensity lower than 0.1% of the most intense line are not listed. b All calculated vibrations and their IR intensities in the 0-1300 cm-1 range are listed in Tables 4S and 5S in the Supporting Information; w ) weak, s ) strong, b ) broad, sh ) shoulder, m ) medium; RO ) ring-opening vibrations; Z ) H12Si10Al2O18. c Si/Al ratio 2.82; ref 4.

of the cluster with SI′ site occupation represents T-opening coupled to O(2), O(3) closure in both the Si6O6 and Si4Al2O6 rings; it is correlated to the 579 cm-1 A1g vibration of the D3d cluster. In the configuration with both SI and SI′ sites occupied, the number of RO vibrations is reduced, because the atom displacements of the two T6O6 rings are not coupled. The 550 cm-1 vibration involves only RO of Si6O6, while the 580 cm-1 vibration is composed of RO of the T atoms in the Si4Al2O6 ring mixed with a TOT bending mode and T,

O(2), and O(3) RO of the Si6O6 ring. Taking into consideration the calculated IR intensities, this particular type of K+ cation ordering is responsible for the largest effect of band broadening in the 500-650 cm-1 frequency range of the IR spectrum. D6R with Cs Symmetry, (MI)2H12Si10Al2O18. In these clusters Al-O-Si-O-Al linkage is formed in one of the T6O6 rings, and these clusters are less stable than the clusters of C2h and C2V symmetry. The following irreducible

13206 J. Phys. Chem. B, Vol. 108, No. 35, 2004

Mikosch et al.

TABLE 5: Raman-Active Vibrations of Hexagonal Prismsa (B3LYP-calculated wavenumbers (in cm-1) and symmetry modes (in parentheses) in the 240-610 cm-1 range) H12Si12O18: D3d

Li2Z: C2h, Li+ at SI′

Na2Z: C2h, Na+ at SI′

262 (Ag) 274 (A1g)RO 305 (Eg) 310 (A1g)

276 (Bg) 277 (Ag) 297 (Bg) 308 (Ag)

268 (Bg) 278 (Ag) 297 (Ag) 300 (Bg)

330 (Ag)RO 345 (Bg)

389 (Eg)

364 (Bg) 367 (Ag)

321 (Bg) 329 (Ag)

370 (Ag) 393 (Bg)

405 (Eg)

392 (Bg) 397 (Ag)

399 (Bg) 404 (Ag)

422 (Bg) 446 (Eg) 421 (Ag) 443 (Bg) 445 (Ag)

434 (Bg)

449 (A1g)RO 463 (Ag) 576 (Eg)

453 (Ag)RO 514 (Bg)

488 (Ag) 520 (Ag)

579 (A1g)RO 592 (Eg)

549 (Ag) 561 (Bg)

534 (Ag)

582 (Ag)RO

583 (Ag)RO 586 (Bg)

Na2Z: C2V, Na+ at SI′ 242 (B2) 262 (B1) 269 (A1)RO 279 (B2) 280 (A2) 296 (A1)RO 299 (B2) 311 (B1) 317 (B2) 322 (A2) 330 (A1) 349 (B1) 350 (B2) 354 (A2) 363 (A1) 368 (B2) 378 (B1) 385 (A2) 401 (A1) 401 (B2) 419 (B1) 425 (A1) 425 (B1) 433 (A2) 440 (A1) 441 (B1) 455 (B2) 460 (A1) 519 (B2) 531 (A1) 546 (A2) 556 (B1) 562 (B2) 573 (A1)RO 579 (A2) 582 (B1) 586 (B2) 595 (A1)RO

K2Z: C2h, K+ at SI′

270 (Ag) 272 (Bg) 284 (Ag) 312 (Bg) 318 (Ag) 327 (Bg)

369 (Ag) 377 (Bg) 402 (Ag) 417 (Ag)RO 421 (Bg) 427 (Bg) 435 (Ag) 527 (Ag) 536 (Bg) 549 (Ag) 575 (Ag)RO 576 (Bg) 607 (Bg)

K2Z: C2V, K+ at SI; SI′

K2Z: C2V, K+ at SI′

K2Z: Cs, K+ at SI′

Na2Z: Cs, Na+ at SI′

240 (B1) 265 (A1) 267 (A1) 285 (B2) 291 (B1) 298 (A2) 313 (A1) 321 (B2) 325 (A2) 343 (B1) 348 (A2) 359 (B2) 367 (B1) 369 (A1) 374 (B2) 378 (B1) 387 (A1) 402 (A2) 408 (A1) 424 (B1) 427 (B2) 448 (A1) 452 (A2) 463 (B1) 465 (B2) 475 (A1) 536 (B2) 543 (A2) 550 (A1)RO 557 (B2) 563 (B1) 574 (B1) 577 (A1) 580 (A1)RO 587 (A2) 592 (B2) 612 (B1)

242 (B1) 260 (A1)RO 277 (A2) 281 (A1)RO 281 (B2) 312 (B2) 313 (B1) 323 (A2) 328 (B1) 330 (A1) 343 (B2) 344 (A1) 360 (B1) 362 (A2) 367 (B2) 381 (A2) 390 (A1) 392 (B2) 417 (B1) 419 (B1) 419 (A1)RO 420 (A1) 423 (A2) 431 (B1) 432 (B2) 445 (A1)RO 516 (B2) 524 (A1) 541 (A2) 546 (B2) 551 (B1) 572 (B1) 572 (B2) 572 (A1)RO 578 (A2) 578 (A1) 604 (A1) 605 (B1)

241 (A′) 262 (A′) 271 (A′′) 280 (A′)RO 285 (A′′) 303 (A′) 315 (A′′) 317 (A′) 322 (A′′) 323 (A′) 332 (A′′) 350 (A′) 352 (A′′) 362 (A′) 376 (A′) 382 (A′) 383 (A′′) 400 (A′′) 401 (A′) 419 (A′) 421 (A′) 422 (A′′) 424 (A′′) 425 (A′) 428 (A′′) 440 (A′) 510 (A′′) 522 (A′) 538 (A′′) 538 (A′) 546 (A′) 552 (A′′) 566 (A′) 568 (A′′) 575 (A′) 581 (A′) 591 (A′)RO

254 (A′) 257 (A′′) 270 (A′) 278 (A′′) 281 (A′′) 283 (A′)RO 315 (A′′) 319 (A′) 322 (A′′) 327 (A′) 336 (A′′) 337 (A′) 352 (A′′) 353 (A′) 370 (A′) 384 (A′′) 386 (A′) 393 (A′) 399 (A′′) 406 (A′) 418 (A′′) 418 (A′) 422 (A′) 432 (A′′) 432 (A′) 453 (A′′) 457 (A′) 510 (A′′) 526 (A′) 539 (A′) 546 (A′′) 555 (A′) 560 (A′′) 564 (A′) 576 (A′′) 581 (A′) 584 (A′)RO 596 (A′)RO

Y zeolitec

240

290

350

502

597 (Bg) 600 (Ag) a Vibrations dominated by the displacement of hydrogen atoms forming T-H bonds (T ) Si, Al) are not listed. RO ) ring-opening vibrations; Z ) H12Si10Al2O18. b Vibrations in the 0-1300 cm-1 range, all cation distributions included, are listed in Table 5S in the Supporting Information. c Si/Al ratio 2.7; ref 5c.

ΓAl-O ) 3A′(IR,R) + 3A′′(IR,R)

slightly altered when K+ cations take the SI′ sites; see Tables 4 and 5: the 280 cm-1 vibration involves synchronous displacements of T and O atoms in each T6O6 ring, and it is correlated to the 277 cm-1 A2u mode of the D3d group. The 591 cm-1 vibration is dominated by O atom displacement and correlates with the 586 cm-1 A2u vibration. Li+ cations stabilize Al-OSi-O-Al linkages in one T6O6 ring when they are closely positioned to the center, bearing the negative charge: the SIII′ site. The low-frequency RO vibrations are at 258 and 282 cm-1; the 573 cm-1 vibration is correlated to the 586 cm-1 A2u vibration of the D3d group. The largest effect of band broadening from Cs symmetry clusters in the 500-650 cm-1 frequency range of the IR spectra is produced by Li+ cations at SIII′ sites and bridging hydroxyl groups.

Γ∠SiOSi ) 7A′(IR,R) + 5A′′(IR,R)

Conclusions

In the cluster with Na+ cations at SI′ sites, the 283 cm-1 vibration is correlated to the 274 cm-1 A1g mode of D3d clusters; the shape of the 584 cm-1 vibration corresponds to the 579 cm-1 A1g mode. The 596 cm-1 vibration is described by the 586 cm-1 (P-Q-R) A2u mode; see Figure 3. The RO vibrations are

DFT studies of D6R structural fragments (Mn+)x/nH12Si12-xAlxO18 with x ) 0, 2, in which the negative charge, arising from Si,Al substitution, is compensated by Ca2+, Li+, Na+, K+, and H+, reveal that the shape and energy of the ring-opening vibrations depend on the type and positions of the extraframe-

representations of the normal vibrations are valid:

(M+)xH12Si12-xAlxO18 (Cs) M ) Na+, K+ at SI′ Γ ) 69A′(IR,R) + 57A′′(IR,R) M ) Li+ at SIII′ Γ ) 68A′(IR,R) + 58A′′(IR,R) ΓSi-O ) 17A′(IR,R) + 13A′′(IR,R)

Vibrational Modes of D6R work cations and the Si,Al distribution. The vibrational spectra of FAU zeolites were interpreted on the basis of D6R fragment models with descending symmetry (D6h f Cs). Maximum negative framework charge separation is attained in clusters with C2h symmetry and Al-O-(Si-O)3-Al sequence. With decreasing charge separation the symmetry of fragments is lowered to C2V, with Al-O-(Si-O)2-Al linkages, and further to Cs, with closely spaced Al atoms within one T6O6 ring. The ringopening vibrations of D6R with D3d, C2h, C2V, and Cs symmetry were identified in the 250-600 cm-1 range, and they were found to be correlated to the IR- and R-active FAU framework modes of the space group Oh7. The C2h symmetry model with maximum separation of the Al atoms reproduces well the vibrations of NaY, while the C2V model describes the vibrational band broadening. Though the frequency shifts arising from the specific Si,Al ordering in most of the examined clusters with Si/Al ) 5 ratio are within 20 cm-1, the symmetry of vibrations depends on the position of the cations with respect of the T6O6 rings, and larger shifts are observed when cations take the two nonequivalent positions SI and SI′. The lower symmetry clusters (Cs) display more significant band broadening in the IR and Raman spectra of zeolites. Oxygen atom displacements contribute to all ring-opening modes. Ring-opening modes in the 450-600 cm-1 range are found to be particularly sensitive to the type of T atoms and their ordering. The totally symmetric ring-opening modes of the D3d and C2h fragments can contribute only to the Raman spectra of FAU zeolites, while for the C2V and Cs fragments these modes should be active in both the IR and Raman spectra. Acknowledgment. The authors gratefully acknowledge CPU time at the Computer Center, Technical University, Vienna, where most of the Gaussian 98 calculations were performed. Supporting Information Available: Tables with the calculated IR and Raman frequencies and IR intensities of the cluster models in the 0-1300 cm-1 range. For centrosymmetric clusters containing Li cations or bridging hydroxyl groups, both IR and Raman active vibrations are listed. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Davis, M. E. Acc. Chem. Res. 1993, 26, 111. (b) Catalysis by Zeolites, Vol. 5; Imelik, B., Ed.; Elsevier: Amsterdam, 1980. (2) (a) Smith, J. V. Chem. ReV. 1988, 88, 149. (b) Newsam, J. M. In Solid State Chemistry: Compounds; Cheetham, A. K., Day, P., Eds.; Oxford University Press: Oxford, 1992; Vol. 2, p 234. (3) Meier, W. M.; Olson D. H. Atlas of Zeolite Structure Types; Butterworth: London, 1992. (4) (a) Flanigen, E. M.; Khatami, H.; Szymanski, H. AdV. Chem. Ser. 1971, 101, 201. (b) Flanigen, E. M. In Zeolite Chemistry and Catalysis;

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