J. Phys. Chem. 1993, 97, 9434-9440
9434
Molecular Dynamics Study of the Vibrational Spectra of Siliceous Zeolites Built from Sodalite Cages Konstantin S. Smirnovt and Daniel Bougeard' Laboratoire de Spectrochimie Infrarouge et Raman du CNRS, Bat. C5, Universite des Sciences et Technologies de Lille. 59655 Villeneuve d'Ascq cedex, France Received: March 2, 1993'
A molecular dynamics computer simulation of sodalite cage containing siliceous zeolites (sodalite, zeolite A, and faujasite) as well as silicalite was carried out. Two force fields based on a simplified version of the UreyBradley force field were examined in the calculations. It is shown that both of them lead to the same structural characteristics but to different vibrational spectra for the zeolite frameworks. The calculated infrared and Raman spectra are compared with available experimental and theoretical data. The influence of different terms in the potential function and of the lattice symmetry as well as common trends in the calculated spectra are discussed. 1. Introduction Zeolites are alumosilicates where Si04 and A104- tetrahedra are connected in a way creating cavities and channelsof molecular dimension. Due to this porous structure, zeolites have a number of industrial applicationsas molecular sieves and as heterogeneous catalysts the propertiesof which can be fitted for specialpurposes. These applications are an incentive to study physicochemical properties of zeolites, namely, the influence of the Si/Al ratio, the dynamics of the lattice, the characterizationof extraframework species, zeolite acidity, and the diffusional behavior of guest molecules in the zeolite framework. In recent years, a number of theoretical investigations of zeolites have been carried out to account for their properties. The methods used tostudy the zeolitecharacteristicsincludequantumchemical calculation (QCC), normal-mode analysis (NMA), energy minimization technique, and Monte Carlo (MC) and molecular dynamics (MD) simulations. In thestudies of thezeolitic systems QQC has limited possibilities due to the large number of atoms in a zeolite unit cell. The energy minimization technique and MC simulation provide information on statistical and thermodynamiccharacteristicsof a studied system. Morecomplete data includingtime-dependent properties can be derived with the help of MD calculation. As a consequence, MD simulations have been applied to investigate the diffusion of extraframeworkcations and adsorbed molecules in zeolites. The systems studied include Na ions in zeolite A,' xenon molecules in zeolite Y2.3 and ZSM5,4,5 water in ferrierite,6-7 and hydrocarbons in different zeolite~.~.*-16The results of these works have demonstrated a good agreement of the calculated diffusional behaviors with experimentaldata and detail information at the microscopic level derived from such computer experiments provides a better understanding of the diffusion processes. An assumption used in the works mentioned above is that the zeolite is considered as a rigid framework. It means that any coupling between host lattice and guest molecules is neglected and the influenceof the motion of the framework atoms on studied properties is not taken into consideration. Several attempts to take into account the flexibility of the framework in MD studies were made. Demontis et al. proposed a simple force field and investigated both structural and dynamical properties of zeolite AI7and silicalite**as well as the influenceof the lattice flexibility on the diffusion process of methane in ~ilicalite.1~ Schrimpf et t On leave from Institute of Physics, St. Petersburg State University, St. Petersburg 198904, Russia. .Abstract published in Advunce ACS Abstracts, August 15, 1993.
al. using a force field based on the Demontis one have studied the structure, dynamics, and thermalization process of sorbates for NaY zeolite.20 A more accurate force field was used by Nicholas and co-workers in their investigation of the structure and dynamics of the sodalite lattice2' However, the inclusion of long-range and nonbonded interactions limits the application of this force field in the very long simulations required for the study of diffusion processes. In all the cited works (excluding ref 21) the validity of the force field used was examined mostly by comparison of the calculated and experimental structural data. The calculations of the infrared spectra were only used as a qualitative supplementary check where overall agreement with observed data was considered as satisfactory. In the present work we report the results of an MD study of the vibrational spectra for sodalite cage containing zeolites (sodalite, zeolite A, faujasite). We began with pure silica compounds, and in order to establish the influence of structure the corresponding data for silicalite, a silica zeolite without sodalite cage was also computed. The outline of the paper is as follows: in section 2 we describe the computational procedure in detail. Oneoftheaimsofthis workis to treat simultaneously thestructure and the vibrational spectra. In section 3 we compare the results calculated with the help of two force fields: the first one was proposed by Demontis et al.I7and the second one is a force field used in our previous publication.22 Section 4 deals with the description of the calculated infrared and Raman spectra. A discussion of the data is presented in section 5 . Finally, we summarize our conclusions in section 6.
2. Computational Procedure 2.1. Structure. Thesodalitecage is a truncatedcuboctahedron (Figure la) with T atoms (Si or Al) located at the corners. In the sodalite structure the cages are sharing four-T member rings in a way creating a simple cubic lattice as shown in Figure 1b. The atomic coordinateswere taken from a combined single-crystal X-ray and powder neutron diffraction study of silica sodalite with encapsulated ethylene It was supposed that this encapsulated compound does not significantly affect the zeolite lattice and that these structural data can be directly used to set thesodalitestructure. The reported spacegroup of the framework is Im3m with lattice parameter a = 8.83 A. In zeolite A the sodalite cages are further apart and are linked by double 4-T member rings as shown in Figure IC. In addition to four- and six-T member rings there are eight-T member rings which are windows between large cavities. Because pure silica zeolite A does not exist (it is a hypothetic zeolite for our
0022-3654193f 2097-9434%04.00/0 0 1993 American Chemical Society
Siliceous Zeolites Built from Sodalite Cages
lb
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9435
1
C
I
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F w e 1. Structureof the frameworks of sodalitecagecontaining zeolites. Sodalite cage (a), sodalite (b), zeolite A (c), and faujasite (d). T atoms are localized at corners and connected by lines.
TABLE I: Structural Data for Zeolites and the Equilibrium Values of the Force-Field Parameters Used in Calculations sodalite zeolite A fauiasite silicalite space group Im3m Fm3c Fd3m Pnma 576 576 288 no. atoms per 36 unit cell 1 2 1 no. unit cells 8 used in calc Values of the Equilibrium Parameters ro = 1.587 A ro = 1.61 A ro = 1.61 A ro = 1.59 A SGVFF a = 109.5' j3 = 159.7'
DHFF
a = 109.5'
a
j3 = 150.6'
j3 = 142' 6 = 142' j3 = 142'
ro = 1.61 A 6 = 150.6' row = 2.618 A 6 = 150.6'
109.5'
a = 109.5 A
j3 = 149'
6 = 149' j3 = 149'
calculations), we have used the X-ray structural data for Na zeolite A24 with ratio Si/Al equal to one, replacing all A1 atoms by Si ones. The space group is Fm3c. The initial coordinates of the T atoms ((Oy,z), Wyckoff position is 96i) were taken as YT = '/&si ZA)and ZT = l/z(zsi + yd). The length of the unit cell was 24.555 A. The framework of zeolite Y is composed of sodalite cages connected together by hexagonal prisms (Figure Id). In this structure each sodalitecage has a tetrahedral environment leading to large cavities called supercages. These supercages are linked by windows consisting of 12-T member rings. The space group of the unit cell is Fd3m. In our calculations we have used a model of pure siliceous faujasite. The initial atomic coordinates were taken equal to those for the structure of Na zeolite YZs where the cell parameter u was reduced to 24.266 A in order to take into account the high silica content represented by the difference of the mean Si-0 distance in silicates and Na zeolite
+
Y. Unlike the cubic symmetry of the zeolite lattices described above, the framework of silicalite has orthorhombic symmetry Pnma and cell parameters u = 20.07, b = 19.92, and c = 13.42 A.26 Five- and six-T member rings which create two kinds of channels exist in the silicalite structure. These channels running along u (sinusoidal ones) and b (straight channels) axes are formed by 10-T member rings. The atomic positions for the structure were taken from ref 26. Two crystallographic cells arranged along the c axis were used in the simulation in order to work with an MD cell with a size comparable to the three cubic ones. The structural data and the number of atoms for each zeolite used in the simulation are listed in Table I. 2.1. Force Field. Two force fields were examinedin the present work. The first one is the harmonic force field proposed by Demontis et al.17 (DHFF). The other one is a simplified general
valence force field (SGVFF) used in our previous publication.22 Both force fields take into account only interactions between the nearest neighbors and supposethat forces are harmonicin variation of distance between atoms and bond angles. In this approximation the potential energy of the system can be written as
where V, is constant which does not influence the dynamics of the system. The second and third terms representthe participation of the bond and bond angles variation to the potential energy, respectively. The last term in eq 1 describes the shortest nonbonded interactions between the nearest atoms. r and B are the actual values of the distance and angle, respectively, and the zero index denotes their equilibrium values. Such a force field is the simplified version of the Urey-Bradley force field where all cross terms are neglected. The DHFF is represented by the second and fourth terms in eq 1:
with the following numerical parameters:17-19S i 4 bond term K, = 500 kcal mol-' A-2 (3.4737 mdyn A-') and 0-0nonbonded termKm= 103 kcalmol-l A-2(0.7156mdynA-l). Itisassumed that due to their large radii the oxygen atoms shield the silicon atoms and the interactions between the latter are neglected. The SGVFF uses the second and third terms in eq 1:
PGVFF = V, + ' / , x K r ( r - ro)2+ '/2CKe(B - 0,)'
(3)
and is represented with the help of an Si-0 bond term, K, = 4.1498 mdyn A-l-1,2l an 043-0 angle term, K, = 0.9596 mdyn rad-l,z1 and an S i - O s i angle term, KO = 0.126 mdyn rad-1-27 The values of equilibrium parameters for the zeolites frameworks for the DHFF were taken from ref 17 and those for the SGVFF were derived from the structural data of the zeolites. All the parameters used are listed in Table I. No long-range or cross terms are used in the potentials. It was shown2' that the electrostatic interactions included in potentials do not significantly influence the infrared spectrum of the framework because it mostly depends on the valence potentials. 2.3. Details of the Simulation. The equations of motion were integrated by using the velocity form of the Verlet algorithm28 with a time step of 2.0 fs with periodic boundary conditions in order to simulate the periodicity of the zeolite framework. At the beginning of the simulationthe initial velocities of the particles were taken from the Maxwell-Boltzmann distribution at 300 K. During the first 20 000 time steps the velocities of the atoms were rescaled to the reference temperature and then the simulation was performedin theNVEensemblefor50 960timesteps(lO1.92 ps). The data about the coordinates and velocities of the particles were stored every fifth step for the last 40 960 time steps. The total energy of the system during the MD simulations showed no drift and an average root-mean-square (RMS) fluctuation of the total energy was less than 0.3% of the RMS kinetic energy fluctuations over the NVE run. To put in evidence an eventual stress of the crystal, the internal pressure was calculated as "internal virial" according to ref 29. The infrared spectra were calculated by Fourier transformation of the autocorrelation function of the total dipole moment of the system.30 The charge values were set to 1.6 e- for Si and 0.8 efor 0 atoms.31 To compare experimental and theoretical spectra, the intensities in the latter were transformed into relative transmittance according to the Lambert-Beer law. The computational procedure for the Raman spectra was previously described indetail.22 It was shown that the calculation of the Raman intensities for powder spectra of zeolites with the help of the equation valid only for the liquid state leads to an
Smirnov and Bougeard 16 -
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Figure 6. Infrared spectrum of siliceous faujasite calculated with the SGVFF (a) and DHFF (b).
3. Force Fields: Structure and Vibrational Spectra Figure 2 shows the radial distribution function (RDF) for the S i S i interatomic distances in siliceous faujasite calculated by means of the DH and SGV force fields. In both cases sharp peaks appear at the interatomic distances predicted by the zeolite structure. The RDF for 0-0(Figure 3) displaysone sharp peak only for the first coordination sphere distance. Because of the large amplitude of the oxygen atoms motion, the peaks at larger distances are more diffuse. The S i 4 RDF (Figure 4) shows a narrow peak for S i 4 bond distance and a trend similar to the 0-0 RDF for the other peaks. The positions of the first peaks in RDFs are in good agreement with those expected from crystallographicdata. In the DHFF the absence of bending force constants and of any term for the S i s i interactions gives the more blurred picture for the second and next peaks in the RDFs. The mutual arrangement of TO4 tetrahedra is controlled by
sequences of nonbonded 0-0 interactions that leads to an as mmetrical shape of the first peak in the S i S i RDF. For the SG FF this arrangement is directly determined by an internal coordinate (angle Si-O-Si and its force constant Kp) so that a symmetrical peak is obtained. The M i 4 and Si-O-Si angle distribution functions (ADF) are presented in Figure 5 . The positions of maxima in the ADFs are in agreement with the mean values of the angles derived from structural data. The results calculated with the help of DHFF show a wider angle distribution than those obtained by SGVFF for the reasons mentioned above. These distribution functions were calculated for all the zeolites framework studied and led to similar results and conclusions. The infrared spectra of siliceous faujasite obtained with the DHFF and SGVFF are shown in Figure 6. A comparison of the theoretical spectra with the observed one for dealuminated faujasite shows that the experimentaldata33are better reproduced with the SGVFF. Although the overall spectrum computed with
5
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9431
Siliceous Zeolites Built from Sodalite Cages
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F i g w 7. Power spectrum for the siliceous faujasite calculated with the SGVFF (solid line) and DHFF (dashed line). 200
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Figure 9. Calculated infrared (a) and Raman (b) spectra of siliceous zeolite A.
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Figure 8. Calculated infrared (a) and Raman (b) spectra of siliceous
sodalite. DHFF is in satisfactory agreement with the observed spectrum there are some significant discrepancies. In particular the characteristic structure of the bands between 400 and 600 cm-l in the experimental spectrum is less distinct and shifted to lower wavenumberswith respect to the calculated one. The symmetric stretching vibration of the S i 4 bonds observed around 800 cm-l is also missing. The absence of this band in the spectrum could be caused by the selection rules. In this case the symmetric stretching band should exist in the power spectrum because there is no selection rule for this spectrum. The power spectra calculated with both force fields are presented in Figure 7. A comparison of the spectra shows that the density of vibrational states for siliceous faujasite in the region 700-800 cm-I can hardly be distinguished from the background. These bands are missing in all DHFF type model~,~~J*,~O while they are seen in SGVFF and in the experiment.21~33All the following results discussed in the present paper were obtainedby using the simplifiedgeneralvalence force field. 4. Vibrational Spectra
SiliceousSodalite. The calculated infrared and Raman spectra for siliceoussodalite are shown in Figure 8. The infrared spectrum shows four bands at 280, 476, 710, and 1121 cm-I. Both the position and the relative intensities of the bands are in agreement with the experimental data.33 The most significant difference (77 cm-1) between experimental and calculated frequencies is observed for the symmetric stretching S i 4 band. The position of the other bands differs from the experimental value by no more than 20 cm-1. The framework bending mode observed by Godber and Ozin34 for high-silica sodalite at 289 cm-l is
reproduced in our calculations at 280 cm-I. Similar spectra were obtained by de Man et al. for the silica-sodalite by a latticedynamical c a l c ~ l a t i o n .Some ~ ~ differencesbetween our data and the results of the MD study of the silica-sodalite infrared spectrum by Nicholas and co-workersZ1is explained by the fact that our potential does not take into account the nonbonded and torsional terms. The comparison of the calculated Raman spectrum with the experimental one is difficult because of the absence of highquality spectral data for pure siliceous sodalite. The Raman spectrum of the natural sodalite reported by AngelP reveals lines at 260,290,463,985, and 1060 cm-1. This compound has an Si/A1 ratio of about unity, and as a result, the mean value of the bond force constant is expected to be smaller than the one for the pure siliceous sodalite. This will at least lead to a shift of the whole spectrum to lower wavenumbers for the natural sodalite with respect to the pure siliceous compound. The calculated spectrum is in a satisfactory agreement with the one obtained from a lattice-dynamical c a l c ~ l a t i o nusing ~ ~ the shell model which reveals several Raman-active modes between 400 and 500 cm-1. A similar picture is obtained in the high-frequency region. In the low-frequency region these lattice-dynamical studies predict a Raman-active band at 125 cm-1, in agreement with our results. Some differencesbetween the calculated spectra can be caused by the use of different space groups for the sodalite unit cell: Im3m in our work, and P43n and I43m in latticedynamical calculations. Siliceous Zeolite A. It is a hypothetic zeolite used in our calculation because there are no experimental structural data and vibrational spectra. We compare our results with the experimental infrared spectrum of zeolite and with the data of Raman studies on the influence of the Si/A1 ratio on the spectrum of zeolite The presence of A1 atoms in the zeolite lattice will lead to a red shift and a blur of the bands in the experimental spectra. The calculated infrared and Raman spectra for siliceous zeolite A are shown in Figure 9. The IR spectrum has three strong bands between 1000 and 1200 cm-1 separated by approximately 45 cm-1. The experimental spectrum of zeolite A reveals a strong band at 995 cm-1 with two shoulders at 1050 and 1090 cm-l. Two week bands were calculated at 710 and 760 cm-1. The observed spectrum does not show any band between 700 and 800 cm-l, but a weak band was found at 750 cm-1 in the spectrum of zeolite loaded with tetramethylammonium ions. Lattice-vibrational calculations38 predict from one to three bands in the infrared spectrum of zeolite A for this spectral region. One strong band
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
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Smirnov and Bougeard 0
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Figure 10. Calculated infrared (a) and Raman (b) spectra of siliceous
Figure 11. Calculated infrared (a) and Raman (b) spectra of silicalite.
faujasite.
at 580 cm-I and two weak bands at 550 and 510 cm-I are present in the theoretical spectrum which can correspond to the experimental bands at 550 and 464 cm-I. The calculation by No et al.38 shows several bands between 400 and 600 cm-I. In the low-frequency region the calculated spectrum displays bands at 402, 330,285, and 180 cm-l. The first one can be related to the band observed at 378 cm-I. According to the lattice-vibrational calculations the weak band a t 260 cm-1 in the experimental spectrum is due to the double-four-ring pore opening vibration. The band a t 285 cm-1 can be assigned to this vibration. It should be noted that the agreement of the band positions calculated in the present work with the experimental data and with the results of No et al. is better for the region above 500 cm-1. The possible reasons for this fact will be discussed below. The calculated Raman spectrum shows three bands between 1000 and 1150 cm-I. The experimental spectrum obtained by Dutta and Del Barco for hydrated zeolite A3' with ratio Si/Al = 2.7revealsfourbandsat 1011,1046,1093,and 1139cm-'.The calculated bands a t 768 and 720 cm-1 correspond to a band observed a t 780 cm-I. The experimental data do not exhibit a second band between 700 and 800 cm-I, but two bands were observed a t 703 and 738 cm-1 for the sample with the ratio Si/Al = 1. The bands at 470, 330, 300, and 175 cm-1 are present in the theoretical spectrum below 500 cm-1. The experimental one reveals bands at 496, 412, and 335 cm-I. SiliceousFaujasite. The calculated infrared and Raman spectra of siliceous faujasite are shown in Figure 10. The infrared spectrum reveals three groups of bands in 1000-1200-, 750800-, and 400-600-cm-~regions, in accordance withthe observed spectrum of dealuminated f a ~ j a s i t e .In ~ ~particular, two bands observed between 750 and 850 cm-l are reproduced in the theoretical spectrum as well as five bands in the 400-700-cm-I region. The low-intensity triplet observed34 between 250 and 350 cm-1 is also present in the spectrum between 290 and 370 cm-I. One of the characteristic properties of the computed spectrum is the presence of a weak band at 127 cm-1 which could correspond to the peak observed a t 150 cm-1. It was pr0posed3~ that this peak originates from incompletely removed sodium ions. This assignment does not agree with our result, because extraframework cations were not included in the calculations. Experimental Raman spectra of hydrated pure siliceous faujasite recently reported by Dutta and TWU'~ reveal four characteristic regions, 200-400, 450-550, 750-900, and 9001250 cm-1, and we will follow this distinction. In the low-frequency region the normal-mcdea and lattice-dynamical calculation33 predict several Raman-active modes in good accordance with our
results. In particular, the Raman band at 100 cm-1 is present in all theoretical spectra. One strong peak is calculated at 530 cm-1 in opposition to the doublet observed between 450-550 cm-1. A normal-mode calculationa of the Raman spectrum for dealuminated faujasite also shows one single band in this region in contrast with the lattice-dynamical data33 of the same authors which predict several Raman bands a t 500 cm-I. A complicated structure from several bands occurs between 750 and 900 cm-1 in the calculated spectrum. In good agreement with our result four bands exist in the experimental spectra in this region. A lattice-dynamical calculation by de Man and cow o r k e r ~predicts ~~ the presence of four or five bands in the 800-900-cm-1 region for dealuminated faujasite. Between 900 and 1250 cm-1 our computed spectrum reveals only two bands corresponding to the experimental spectrum. Sicalite. The calculated infrared and Raman spectra of silicalite are shown in Figure 1 1 . The IR spectrum has bands at 1 1 13,1080,750,540,480, and 430 cm-1 in good agreement with e~perimental2~94~ and theoretical*I spectra. The Raman spectrum reveals bands at 1113, 1080, and 750 cm-1 for the high-frequency region and two broad bands with maxima a t 320 and 125 cm-1 in the low-frequency region of the spectrum. The experimental spectrum42of ZSM-5 with the ratio Si02/A1203 = 120 exhibits bands at 1090, 1030, 770, 350, and 330 cm-I. 5. Discussion
The described data show that the SGVFF yields a better agreement between calculated and experimental vibrational spectra than the DHFF. It is well-known that the chemical bond in S O 4tetrahedra has essentially a covalent character which is characterized by the fact that the chemical bonds have a fixed direction to each other (sp3hybridization of Si atomic orbitals). Therefore, it is necessary to use three-body terms in the potential function in order to describe the spatial distribution of bonds in a covalent compound. The DHFF uses effective pair potentials whereas the SGVFF takes into consideration the three-body interactions with the help of the angle bending terms between 04-0 and S i - O s i triads. Recently Catlow and co-workers43 have shown that including such a three-body term in the potential brings about a significant improvement to the agreement between the calculated data for the structure of vitreous silica. This is particularly significant for the Si-oSi angle distribution function. Thus the radial distribution functions are also improved. The same tendency was obtained in our calculations. Furthermore, our data show that the use of the angle bending terms results in a significantly better description of the vibrational spectra.
The Journal of Physical Chemistry, VO~. 97,NO. 37, 1993 9439
Siliceous Zeolites Built from Sodalite Cages
TABLE II: Calculated and Experimental Positions of the
Bands (cm-I) in the Infrared Spectra of the Zeolites sodalite zeolite A faujasite silicalite theor
exp
theor
280 476 710 1121
289 450 787 1107
180 285 330 402 510 550 580 710 760 1035 1085 1125
ex9 260 378 464 550 660 995 1050 1090
theor 127 300 340 370 405 480 530 575 640 750 800 1040 1080 1100
exp l5oC 26oC 29oC 32oC 4000J 4600J 525"J 6100.1 6800J 7900J 8300J
theor
expd
430 480 540 750 1085 1113
420 550
800 1100
1080 12000"J
a Reference 33. b Reference 36.c Reference 34.d Reference 21. e A wide band within indicated limits. f The value was derived from a figure in the cited work.
This fact can be explained by the following simple scheme. For an isolated tetrahedron the presence of the strong 0-0 nonbonded term necessary to compensate the nonexisting angle bending terms in the DHFF leads to the fact that some motions of the atoms are energetically unfavorable. In particular this takes place for the symmetric Si-0 stretch vibration where the 0-0distance undergoes large variations. In consequence, this causes a large deviationof the energy from the equilibrium Value. In contrary, the asymmetric stretch vibration does not cause such a deviation because the 0-0 "bond" only balances during the vibration. In the SGVFF both stretch vibrations occuring along the Si-0 axis are roughly independent on the bending motion and do not lead to such an effect. It is evident that a more flexible description of a system can be achieved by the use of both force fields (e& by using eq 1) which correspond tothe UreY-BradleY force field used for normal-mode analysis by spectroscopists. Both the infrared and Raman spectra calculated for all zeolites are in good agreementwith the experimentaldata. The calculated position of the bands in the infrared spectra of the Zeolite f ~ W " 0 r k sare listed in Table 11. We do not present such a table for the Raman spectra because Of the absence Of data for siliceous sodalite and zeolite A. For a more complicated structure of the zeolite framework containing the sodalite cage (sodalite-zeolite A-faujasite) the spectra become also more complicated: instead of 4 bands in the infrared spectrum for sodalite, more than 10 bands arise for faujasite. An interesting feature of the spectra is a blue shift of the bands in the 700-800and 100-1200-cm-1 regions for this series of zeolites. For example, intheRamanspectrathebandat750cm-' in thesodalitespectrum shifts to 768 cm-1 for zeolite A, and to 800 cm-1 for faujasite. A similar tendency is observed in the experimental spectra. The bands in this spectral region are observed at 787 cm-l for sodalite,33 at 780 cm-' for zeolite A36@/A1 = 2*7)3and 815-900 cm-' for siliceous f a ~ j a s i t e .A~ comparison ~ of the infrared and Raman spectra shows that they are complementary to each other. As mentioned above, the better agreement of the theoretical and experimental frequencies for Zeolite A iS observed in the spectral region above 500 cm-1. Several explanationsare possible to account for the discrepancy between calculated and experimental spectra in the low-frequency region. First, it can be caused by some inconsistency between the structural data and the equilibrium values of the force-field parameters. The high silica content of zeolite A was taken into account by calculating the initial coordinates of T atoms as a mean value of those for si and A1 atoms in Na zeolite A. This can lead to a strained structure mainly depending on nonvalence intertetrahedra interactions in the system. Incidently, the internal pressure for zeolite A was somewhat higher than for the other zeolite frameworks studied.
Second,the torsional terms which are neglected in the potential could be necessary for the simulation of the framework dynamics of zeolite A in contrast to faujasite. Let us consider the sodalite cage as an elementary structural unit. Then the structure of zeolite A is a simple cubic lattice. It is known that different deformations of this structure like shifting or twisting of layers are possible. In the zeolite framework torsional terms will play an important role for the description of such motions which are localized in the low-frequency region of the spectrum. On the other hand, in the faujasite framework these units (sodalite cages) form a diamond structure known as the most rigid lattice with respect to any deformation. In this case the absence of the torsional terms is less important for the reproductionof the low-frequencyregion of the frameworkspectra and can be partly compensated by the angular terms. Furthermore, we compare the calculated spectra of a pure siliceouscompound with the experimentalspectra of an Na zeolite A which has an Si/A1 ratio equal to 1. A coupling of Na ion vibrations with the framework was also, however, not taken into consideration in the present study. As already mentioned, a discrepancy appears between experiment and calculation for the Raman spectrum of faujasite where one band at 530cm-1 is calculated, whereas a doublet is observed. It was conjectured39 that this doublet might be due to average s i - o s i angles of 1410 and 1470 for pure siliceous faujasite. A calculation carried out with two different values of the S i - M i angle of 1420 and 1500 does not reveal any splitting of the band at 530 cm-1. This doublet could also originate from a coupling of Si-0 bonds which could be represented in the potential by a supplementary s i o / s i o Cross term. Unfortunately the intraduction of such force constants did not yield a noticeable improvement as it resulted only in Some fine structure, Another attempt was made using a simulation box doubled in one dimension. The results were absolutely identical, showing that the size of the MD cell is sufficient and does not create any artifact. In this situation the explanation of this doublet requires a more complete study probably including the use of long-rang interactions or/and Some superstructure in the crystal. A comparison of the spectra calculated for cubic zeolites with those for orthorhombic silicalite shows that the most significant difference is observed for the spectral region below 700 cm-1. In the silicalite spectra the bands in this region are less distinct and have a complicated structure. This structure looks like noise but cannot be explained as an artifact of the simulation because all the parameters of the MD were the Same for zeolite A, faujasite, and silicalite (the MD cell contained two times less of sodalite). It should be noted that the particles in the experimental of the silicalite infrared spectrum carried out at sample temperature from 293 to 4 K has showed such a fine structure of the bands. From our point of view it reflects the influence of the crystal symmetry on the vibrational spectra,It Seems reasonable that this influence manifests itself particularly in the spectral region of intertetrahedra vibrations that is characteristic of the difference in the zeolite substructures for the cage containing zeolites and silicalite (different T-member rings and their mutual arrangement). Thus there is more similarity between sodalite cage containing structures than between these and silicalite which contains 5-, 6-, and 10-T member rings. ~ i ~the~data l presented l ~ show a good transferability of the SGVFF. 6. Conclusions
Molecular dynamicscomputer simulationsof siliceous sodalite, zeolite A, faujasite, and silicalite were carried out. TWOforce fields were examined in the work. The first of them (DHFF) is based on the effective pair potential functions,whereas the second one (SGVFF) takes into account three-body interactions with help of the angle-bendingterms for O S i - 0 and Si-OSi triads.'
9440 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
The calculated properties of all zeolite frameworks studied show that the structural data are well reproduced by both force fields, while the dynamical properties (IR and Raman spectra) are significantly better obtained with the simplified general valence force field. The transferability of this force field is also demonstrated. The frequencies in infrared and Raman spectra are in good agreement with the experimental values and with the theoretical data obtained by other techniques like NMAor latticedynamicalcalculations. The comparison of the spectra for zeolite frameworks with cubic symmetry (sodalite, zeolite A, and faujasite) with those for silicalite with orthorhombic symmetry shows that the main differences occur in the spectral region below 700 cm-l where vibrations of zeolite substructures are localized. These results lead to more general remarks. The MD method yields complete vibrational spectra (frequency, intensity, shape of band) and can therefore be used as complementary to NMA for the problems where these data are important, in particular for the studies of disorder or of structural changes. Furthermore, thecomparisonof these four structures shows that spectral regions could be sensitiveto structural differenceand could help to identify spectral patterns characteristic of particular subunits. From the experimental point of view this could be important, because the observation of high-quality Raman spectra requires the use of dehydrated samples usually enclosed in glass capillaries which perturb the spectra because they contain silicates. The experimental and theoretical works concerning this problem have already been p u b l i ~ h e d . ~ ~ , ~ Finally, this study confirms that the choice of a force field can be critical and that a check of its applicability should include statical structural data as well as dynamical ones and that the application of two complementary methods, IR and Raman spectroscopy, provides a valuable information for comparison. The inclusion of angle bending terms seems to be necessary to reproduce the silicate spectra.
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