J. Phys. Chem. 1995,99, 12883-12891
12883
Structural and Electronic Properties of Sodalite: An ab Initio Molecular Dynamics Study Francesco FilipponeJ Francesco Buda: Simonetta Iarlori,*?#Giuliano MorettiJ and Piero Portat Department of Chemistry, University of Rome “La Sapienza”, P.le A. Mor0 5, I-00185 Rome, Italy, Istituto Nazionale per la Fisica della Materia, Laboratorio Forum, Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy, and IBM European Center for Scientijic and Engineering Computing, Viale Oceano Pacific0 171, I-00144 Rome, Italy Received: January 12, 1995; In Final Form: June 1, 1 9 9 P
Structural, vibrational, and electronic properties of crystalline sodalite are analyzed using ab initio molecular dynamics based on density functional theory (Car-Paninello method). This is the first theoretical study of sodalite based on first principles, in which the full periodicity of the lattice is explicitely taken into account. The computed structural and vibrational properties are in good agreement with available experimental data. The dependence of such properties upon different ions inside the sodalite framework show the correct trend. We have also analyzed the properties of the neutral sodalite framework with no interframework atoms: this ideal structure is found to be stable and metallic; its electronic structure elucidates the origin of the active sites of this material. Moreover we have synthesized and characterized two sodalites: hydroxysodalite and hydrosodalite. Photoelectron spectroscopy and fourier transform infrared spectroscopy data for these materials are shown.
1. Introduction The interest in the study of zeolites has rapidly increased in the past few years. The main reason is that these microporous materials, beyond being traditionally used for ion exchange, heterogeneous catalysis, gas separation, and purification, have recently been applied as host lattices for guest structures of nanometer size.’ The ability of these materials to incorporate small clusters inside the void spaces and channels present in the lattice should allow for engineering new materials with desired electronic and optical properties. On the other hand, recent developments in first principles electronic structure calculations make feasible an accurate theoretical study of these materials in spite of the large unit cell involved in such complex structures. Most of the previous ab initio calculations on zeolites were performed within a cluster model,2 therefore not including explicitly the full periodicity of the lattice. Only very recently a local density functional approach has been used for the study of a bulk zeolite, namely, ~ f f r e t i t ewhich ,~ takes into account possible long range effects. In this paper we use the local density functional based CarParrinello method to analyze the structural, vibrational, and electronic properties of sodalite. The sodalite framework is made of regularly alternating tetrahedrally coordinated A1 and Si atoms which are connected through oxygen atoms. The structural and physical properties of sodalite depend largely upon the nature of the ions inside the cage. This paper deals with different sodalite structures characterized by different interframework ions. Therefore, we think that this work represents a severe test on the reliability of the theoretical approach used, since subtle changes in the lattice constant and structural parameters as a function of the ions inside the cage can be monitored and compared with available experimental data. Furthermore, the Car-Parrinello approach, at variance from traditional quantum chemistry methods, allows also for ab initio +
* @
University of Rome “La Sapienza”. Scuola Normale Superiore. IBM European Center for Scientific and Engineering Computing. Abstract published in Advance ACS Abstracts, July 15, 1995.
0022-365419512099-12883$09.00/0
molecular dynamics (AIMD) simulations at finite temperature. We have performed finite temperature AIMD simulations and compared the computed vibrational spectra with infrared (IR) and Raman data. Finally, we show the electronic density of states for the different structures studied and the charge density associated with the relevant electronic states, which provides some insight into the nature of the active sites in the framework. The paper is organized as follows: in the second section we will briefly discuss the computational method and technical details of the calculation. In Section 3 we describe in some detail the sodalite structures. We present the experimental and theoretical results in sections 4 and 5, respectively, and we devote the final section to the conclusions.
2. Computational Method and Technical Details The Car-Parrinello (CP) meth0d~3~ combines the density functional (DF) approach for electronic structure calculations6 with molecular dynamics simulations, that is, the numerical solution of the classical equations of motion for the nuclei. The main idea of the CP method is the introduction of a Lagrangian for the extended system containing the nuclear degrees of freedom and the electronic single particle wave function, both treated as dynamical classical degrees of freedom. The Newtonian equations of motion generated by this Lagrangian are such that the nuclei move according to the forces derived from the instantaneous electronic ground state (assuming the validity of the Born-Oppenheimer approximation), and at the same time the electronic wave functions evolve staying always very close to the ground state defined by the minimum of the energy functional. The CP approach allows for a simultaneous optimization of the electronic wave functions, structural parameters, and other parameters like the volume of the unit cell of the crystal. Moreover, within the same theoretical framework, it is possible to study the dynamical behavior of a system at finite temperature. We would like to stress that the method is parameter free and no input is needed from experimental data. The only 0 1995 American Chemical Society
12884 J. Phys. Chem., Vol. 99, No. 34, 1995
Filippone et al.
approximation is contained in the exchange-correlation energy, which is an unknown functional of the electronic density. The most extensively used approximation is the local density approximation (LDA), where the exchange-correlation energy is written as
where e(r) is the electronic charge density and cxc is the exchange-correlation energy density for the homogeneous electron gas. In this work, we use for cxc(@(r)) the Perdew and Zunger7 parametrization of accurate quantum Monte Carlo simulations of the electron gas.* According to the experience accumulated in LDA based calculations, it is now quite generally accepted that LDA performs well in describing the geometry for covalently bonded materials and metals, even though it tends to slightly overestimate the binding energy. In the case of weakly bonded systems, like hydrogen or van der Waals, LDA gives large errors in binding energies and geometrical parameters. Recently, generalized gradient corrections to LDA have been used in a simulation of liquid water9 and have been shown to provide a remarkable improvement with respect to LDA. In this work, since we deal with strongly bonded materials, the use of LDA is fully justified. In the CP scheme periodic boundary conditions (PBC) are usually employed. This choice is natural for periodic systems, since the inclusion of the unit cell in the calculation is enough to reproduce the full crystal. All of the analyzed structures belong to the P43n space group, and therefore we use simple cubic PBC in order to simulate the full crystal. As mentioned in the Introduction, this makes possible full inclusion of long range effects of the electrostatic potential, which in cluster calculations have usually been neglected or approximated by point charges.I o The Kohn-Sham single particle wave functions are expanded on a plane wave basis set and are calculated only at the center of the Brillouin zone (I'point). Because of the large unit cell of the sodalite crystal, it seems reasonable to assume that the charge density is well described with only the I' point. Only the valence electrons are treated explicitely. The interaction between the valence electrons and the nuclei plus the core electrons is treated by means of pseudopotentials. In this work we use the ab initio norm-conserving pseudopotentials of Bachelet-Hamann-Schluter" for Si, Al, and Na atoms, while for 0 and C1 atoms we use the ultrasoft pseudopotentials developed by Vanderbilt. The use of ultrasoft pseudopotentials is very important in this work, since it reduces significantly the number of plane waves needed for describing the pseudo-wave functions and then the computational cost. In order to ensure a good convergence in the total energy, we use an energy cutoff of 25 Ry in the plane wave expansion. In the AIMD simulations, we use a time step of 4 au (%O.l fs), and a fictitious electronic mass p = 500 au, which ensures good adiabatic behavior of the electronic dynamic^.^ The structural relaxation was performed with a steepest descent algorithm4buntil the residual forces on the atoms were lower than -3 x au. We stress that in our calculations all atomic positions are allowed to fully relax. The molecular dynamics runs were performed for about 0.6 ps in order to obtain inforniation on the vibrational properties. The present simulations were performed on an IBM workstation RISC/6000, with 128 Mb of RAM memory. Each time step takes about 4 min of CPU time.
Figure 1. Sodalite unit. Small balls correspond to 0 atoms, medium balls to Si atoms, and large balls to A1 atoms.
3. Structures Description Several geometrical models have been proposed in the past 10 years in order to rationalize the sodalite-type structures. We give here a brief description of these models and refer to the papers in refs 13- 15 for more details. However, we emphasize that in our work no constraint is imposed on the geometry: we take the initial coordinates from crystallographic data, and then we optimize the geometry; we use the geometric model only as a tool to get a better insight into the structure and for comparison with our results. The aluminosilicate sodalite crystals are characterized by an ordered framework of TO4 tetrahedra (with T = Si or Al) linked together by a bridging oxygen (note that there exist also silica sodalite structures (see e.g. refs 4 and 5 in ref 16) and aluminate sodalites (see e.g. ref 17 and references cited therein)). The overall linkage of these tetrahedra results in a cubooctahedral cavity, which is named sodalite unit, or @-cage (Figure 1). The sodalite unit is made up of 24 TO4 tetrahedra and has six open windows composed of 4 T and 4 0 atoms, called 4-rings, and eight open windows of 6 T and 6 0 atoms, called 6-rings. The cubic structure of the sodalite mineral is obtained by linking the sodalite units through single 4-rings. Within the sodalite cage a variety of cations and anions can be substituted. The interframework ions can substantially modify the structural and physical properties of the material. One noticeable effect is a contraction or expansion of the cage that adapts itself to the size of the ions. Because of the presence of the interframework ions, the framework oxygen atoms tend to coordinate the interframework cations, so that the structure collapses to a smaller unit cell volume. In a completely expanded framework all tetrahedra are aligned with the cell edges, and the corresponding lattice parameter is about 9.4 A. The volume change (collapse) is obtained by a cooperative rotation of the tetrahedra around one of their axis parallel to one of the cell edges: this rotation is characterized by the so called collapsing angle.18 One of the geometrical models developed in the past has been discussed in ref 13 and later extended to zeolite structures containing a sodalite unit, as Faujasite or LTA.I5 This model is based on the following assumptions: the TO4 subunits are considered as regular tetrahedra; the AI-0 and Si-0 distances
4
Structural and Electronic Properties of Sodalite are constant irrespective of the interframework ions; and the 0-0 edges of the A104 and Si04 tetrahedra are also constant. Using the distances proposed by Hassan and GrundyI3 and having a measured lattice parameter, or an estimated interframework cation-interframework anion distance, or else the framework oxygen-interframework cation distance, it is possible to calculate the entire geometry of the particular aluminosilicate framework one is interested in. In particular it is possible to calculate the fractional coordinates of the oxygen in the general positions of the space group of the structure. An important feature of the geometric model is the capability of predicting the collapsing angle. As was noted by Depmeier,I4 the tetrahedra are not regular in the actual structures, but they are distorted so that there are two classes of 0-0 edges for each tetrahedron: one composed of two edges belonging to the 4-rings, and the other composed of four edges belonging to the 6-rings. Also, this distortion contributes to the reduction of the lattice parameter from the value of the fully expanded structure to the actual value, but its importance varies with the aluminum content of the structure. We have theoretically analyzed three different structures, all of them belonging to the P43n space group: (i) Si6A16024, i.e. the neutral sodalite framework with no atoms inside the cage (indicated in the following as SOD): the unit cell contains 6 Si, 6 Al, and 24 0 atoms. This structure is purely ideal, because of its electron deficiency: in the real chemical synthetization process at each A1 atom corresponds a A104- group whose charge is compensated by the interframework cations. We could formally speak of 6 of the 24 oxygen atoms in the unit cell being in an oxidation state -1 instead of -2, this meaning that SOD should be a very powerful oxidant. However, we decided to look also at this ideal structure since, as it will be clear in the following, its study can be useful in understanding some of the electronic properties of these materials. (ii) The chloro-sodalite or natural sodalite Si6A16024-Na~Clz (SOD-NaC1 in the following): besides the framework atoms, the unit cell contains 8 Na and 2 C1 atoms as interframework ions. This structure was first studied by Linus Pauling in 1930.18 (iii) The anhydrous sodalite Si6A16024.Na6 (SOD-Na in the following): the interframework ions in the unit cell are in this case 6 Na atoms. This metastable structure, studied by Felsche et al.,I9 can be obtained by dehydrating hydrosodalite. 3.1. Interframework Ions Coordination. The atoms in-the sodalite framework occupy positions according to the P43n space group; general positions 24(i) for 0 atoms; special positions 6(c) for A1 atoms; special positions 6 ( 4 for Si atoms. Interframework cations occupy the general positions 8(e): these sites lie just above the 6-rings, on the center of the hexagon. Because of collapsing of the structures, the atoms belonging to the 6-ring are not coplanar, but three of the six oxygens are upon the plane defined by the Si and A1 atoms, and three of them are underneath. Thus, the interframework cation is coordinated by three nearest neighbors (the first three oxygens) and by other three oxygens further away. Since the collapsing angle can be thought of as the measure of the angular distance of the 0 atom from the plane of the 4- or 6-ring (see Figure 2), we note that the more the structure is collapsed, the more differentiated the two types of oxygen are. Collapsing angles are rather small in anhydrous sodalite (the structure is nearly fully expanded), and thus, there is not a great difference between the nearest neighbors and the atoms further away. In natural sodalite the two interframework anions (Cl) occupy the special positions 2(a),that lie at the origin of the coordinates
J. Phys. Chem., Vol. 99, No. 34, 1995 12885
(b)
Figure 2. Collapsing angle as seen with the 4-ring. We do not distinguish here between Si or Al, both labeled as T. In a we show a schematic top view of the 4-ring; in b, a scheme of a side view which
shows clearly the collapsing angle 4.
and at the center of the ,4-cage. These anions tend to coordinate the interframework cations; thus, we have a “dragging” effect by which the cations are as near as possible to the anion, and the framework oxygens are as near as possible to the cation. In this way we can explain the partial collapse of the structure (much stronger than in anhydrous sodalite). We can then state, considering only the nearest neighbors, that the interframework cation in natural sodalite is coordinated by three oxygens and one chlorine, being at the center of a distorted tetrahedron. In anhydrous sodalite, instead, the cation is coordinated only by the three oxygens, and thus, it is a vertex of a triangular based pyramid (what is obtained by cutting off one of the vertices of a tetrahedron). It is important to note that in natural sodalite the occupation number of the 81e) sites is 1, while in anhydrous sodalite it is only 0.75: we shall see from theoretical results, how the presence of vacancies affects some of the anhydrous sodalite properties.
4. Experimental Section In this work we have also synthesized and characterized two sodalites: hydroxysodalite, NasAl6Si6024*(OH)24H20,and hydrosodalite, Na&16Si6024*8H20. Such a synthesis can be thought of as a route to eventually arrive at anhydrous sodalite, and moreover these structures can give us a qualitative comparison of their electronic band structures with the calculated one for SOD-Na. The synthesis has been obtained by modifing the one reported by Felsche et al.:I9 1 g of zeolite A and 50 mL of 16 M NaOH have been mixed in a steel autoclave with a 100 mL of internal Teflon container. The mixture was kept at 130 “C for 18 h and yielded a limpid solution, which, at room temperature and after adding 200 mL of water, gave precipitation of a white solid. The solid was filtrated, washed, and dried at 110 “C: by means of X-ray diffraction (XRD) and photoelectron spectroscopy ( X P S ) , it was identified as hydroxysodalite (note that in the original s y n t h e ~ i s the ’ ~ source of Si and A1 was kaolin). Moreover at room temperature and atmospheric pressure, zeolite A is soluble in 16 M NaOH, but the solution remains stable after adding H20. Hydrosodalite has been prepared by treating hydroxysodalite with water in an autoclave at 130 “C for 18 h. Identification of hydrosodalite is based on XPS quantitative analysis, since, as we can see from Figure 3, the XRD diffraction pattems for
12886 J. Phys. Chem., Vol. 99, No. 34, 1995 I
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Figure 5. FTIR spectra for (a) hydrosodalite and (b) hydroxysodalite. Figure 3. X-ray diffraction pattems for (a) hydrosodalite, (b) hydroxysodalite, and (c) natural sodalite from Bancroft, Ontario.
O(2s) and Na(2p). Our XPS results are substantially equal to the ones published in ref 16. Hydroxysodalite and hydrosodalite have been characterized also by Fourier transform infrared (FTIR) spectroscopy. In Figure 5 we show the spectrum region related to the structure vibrations, i.e. 450 t 1500 em-'. We note that the differences in some spectral regions allow a quick identification of the two different sodalites.
5. Theoretical Results
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Binding Energy (ev)
Figure 4. XPS spectra for (a) natural sodalite, (b) hydrosodalite, and (c) hydroxysodalite. hydrosodalite, hydroxysodalite, and natural sodalite (Bancroft, Ontario) are substantially identical to each other. By XPS we controlled the NdSi atomic ratios and we found 1.0 for hydrosodalite and 1.3 for hydroxysodalite. The XPS spectrum of Figure 4 shows that in the valence band the levels nearest to the Fermi level are essentially 0(2p), and the inner ones are
In this section we discuss the theoretical results obtained on the three different structures described in section 3. In is important to recognize, when we consider a structure containing vacant sites, like SOD-Na, that experimental values are averaged over the entire crystal, and then vacancies are distributed over all their possible positions: the information we can obtain is thus macroscopic, and it is not possible to discriminate contributions of vacant sites from the others. Instead, because of the nature of the simulation itself, theoretical data are obtained from a precise choice of the vacant sites, so it is possible to inspect the role played by the vacancy in modifing structural properties. 5.1. Lattice Parameter Trend and Geometry of the Optimized Structures. First we determine the equilibrium volume for each structure. We used the fractional coordinates found in crystallographic s t ~ d i e s ' ~ , 'to * *set ' ~up the initial atomic configuration. For SOD,obviously, there is no experimental data to start with; therefore we took the atomic positions and the space group pertaining to SOD-NaC1. We have determined the energy vs volume curve by minimizing the LDA energy functional for several values of the lattice parameter. During this process the atomic positions were taken fixed in the crystallographic configuration. In this way we can define the equilibrium lattice parameter as the one which minimize the E vs V curve, so that structural stresses due to an energy gradient with respect to cell volume ( P = -aE/aV) are absent. The results are shown in Table 1 together with the experimental values. We can see that the errors are rather small, being
Structural and Electronic F’roperties of Sodalite
J. Phys. Chem., Vol. 99, No. 34, 1995 12887
TABLE 1: Lattice Parameters for the Various Structures experimental data SOD-NaC1I3
SOD-NaI9
SOD-NaC1
SOD-Na
SOD
8.882
9.122
8.92
9.29
9.01
a, 8,
experimentalvalues 0 theoreticalvalues geometric modd
theoretical data
-0.5% for SOD-NaCl, and -1.8% for SOD-Na, which is a typical accuracy of LDA calculations. Since SOD is an ideal structure, there is no experimental value for the lattice parameter to compare with. However, it is remarkable that this (overall neutral) structure tums out to be stable, from a theoretical point of view, even without interframework atoms. Therefore one could infer that in the real material the presence of the interframework ions is crucial for balancing the negative charge of the f r a m e ~ o r k , but ’ ~ it is not necessary for preventing a collapse of the structure because of the absence of the steric support of the ions. The next step is the geometry optimization. We keep the computed equilibrium volume fixed and let the atomic positions to relax freely according to the Hellman-Feynman forces until these are lower than -3 x au in order to obtain the minimum energy atomic configuration. When we look at the optimized geometry for the structures with different interframework ions, the first observation is that the Al-0, Si-0, and 0-0 distances vary in going from one structure to the other, though the variation is small. This is also true in the experimental data, in which the variation is only of -3%, as we can see from Table 2. Therefore the assumption of the geometrical model of Hassan and GrundyI3 is satisfied only to some extent. In Figure 6 , we show the collapsing angles r#Jsiand C#JAI vs the lattice parameter as predicted from the geometrical model, together with the experimental data and with the present theoretical values. The theoretical values reproduce well the experimental trend of this subtle geometric property, and since we did not impose any geometric constraint to the structures, this result represents a clear demonstration of the reliability and accuracy of our calculations. One can also observe that the
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Figure 6. Trend of collapsing angles vs lattice parameter as predicted by the geometric model (full line), with experimental (square) and theoretical data (plus). Note that in Table 2 angles are reported in degrees.
geometric model is calibrated well for those structures whose lattice parameter is close to that of natural sodalite, but is less reliable in the region of bigger lattice parameters. Another relevant structural feature is the LSi-0-Al angle, which is connected to the collapsing angle, 4, since any rotation
TABLE 2: Bond Angles, Collapsing Angles, and Framework Bond Distances in the Sodalite Structure@ experimental values SOD-NaC1l3
theoretical values
SOD-Na19
SOD-NaCI
SOD-Na
SOD
Angles (deg) LSi-0- A1
138.2
156.30
134.56
ZSI
2 x 113.0 4 x 107.7
2 x 113.7 4 x 107.4
2 x 114.6 4 x 107.0
av
109.5 2 x 111.0 4 x 108.7
109.5 2 x 111.9 4 x 108.3
109.43 2 x 111.3 4 x 108.6
109.5 23.9 22.4
109.5 4.34 4.06
109.47 26.82 24.26
ZAl
av h
i
@AI
Si-0 A1-0 0-0 (Si)
1.62 1.74 4 x 2.62 2 x 2.70
Bond Distances (A) 1.58 1.61 1.71 1.80 4 x 2.55 4 x 2.59 2 x 2.65 2 x 2.71
av 0-0 (Al)
2.64 4 x 2.83 2 x 2.87
2.59 4 x 2.77 2 x 2.83
2.63 4 x 2.93 2 x 2.98
av
2.84
2.79
2.95
Experimental values are evaluated starting from data of referenced works.
154.19 12 x 150.6 6 x 156.6 6 x 159.1 2 x 116.1 3 x 104.8 110.4 109.37 2 x 113.3 3 x 105.8 1 x 112.6 109.37 5.03 4.59 1.59 1.78 3 x 2.53 2 x 2.71 1 x 2.60 2.60 3 x 2.84 2 x 2.97 1 x 2.93 2.90
140.33
2 x 111.0 4 x 108.7 109.47 2 x 108.2 4 x 110.1 109.47 23.86 21.50 1.59 1.79 4 x 2.59 2 x 2.63 2.61 4 x 2.94 2 x 2.90 2.93
Filippone et al.
12888 J. Phys. Chem., Vol. 99, No. 34, 1995
TABLE 3: Numerical Results for the Interframework Ions Coordinationa experimental values theoretical values SOD-NaC1I3 SOD-NaI9 SOD-NaCl SOD-Na Averaged Distances (A) Na-O(1) 2.35 2.56 2.28 2.56 Na-0(2) 3.09 2.69 3.14 2.69 Na-CI 2.74 2.80 Angles (deg) LO-Na-0 103.5 117.09 105.28 117.42 LC1-Na-0 114.9 113.39 LNa-C1-Na 109.47 109.47 0(1)indicates nearest neighbors framework oxygens, while O(2) stands for second neighbors. Experimental values are evaluated starting from atomic coordinates given in referenced works.
of a tetrahedron about one of his axis, which defines a collapsing angle, varies also LSi-0-AI. LSi-0-A1 ranges from -109.5' for closely packed structure to -160.5' for fully expanded structure. As shown in Table 2, the experimental values of the collapsing angles are smaller for the more expanded SOD-Na than for SOD-NaCl and consequently LSi-0-A1 is larger. This feature is well reproduced by the theoretically optimized structures, even though we overestimate the collapsing angle of about lo%, and therefore we slightly underestimate the LSi0-A1 angles. The vacancies in SOD-Na have an appreciable effect in LSi-0-AI: whereas both SOD-NaC1 and SOD have a unique value for this angle, at the contrary SOD-Na shows a splitting of this value in three classes. The computed values of these angles are 12x 150", 6 x 157" and 6 x 159' (this last value is very close to the one relative to the fully expanded structure). The class with the largest value includes the angles formed by the oxygens close to the vacant sites (the 0 atoms which are not first neighbors of Na atoms do not feel the "dragging" effect of the interframework ions). As we have already mentioned, tetrahedra in actual structures are not regular, but distorted. From the crystallographic data shown in Table 2, we see that this distortion, even though not very strong, induces a splitting of the six angles in two classes (4:2). Our results reproduce this feature accurately. Again we can observe a different behavior for the distortion of the tetrahedra related to vacancies. In fact, we find that tetrahedra in SOD-Na do not split their angles in two classes, but in three (3:2:1), one of the angles assuming an intermediate value. This angle has at one of its extremes an oxygen relative to a vacant site. The results for the interframework ions arrangement are collected in Table 3. Both in SOD-Na and SOD-NaCl we find a good agreement with the experimental values for the cation-oxygen distances in the first and second coordination shell. Moreover, we notice that in SOD-Na, as it was expected because of the small collapsing angles, the first neighbor distance Na-O( 1) is only slightly different from the second neighbor Na-O(2) distance. By looking at the Na-0 and Na-Cl distances, LO-Na-0 and LCl-Na-0 angles in SOD-NaCl, we see that the amount of the tetrahedron distortion around Na is reproduced well. The four Na atoms intemal to the cage coordinate the central chlorine atom in a perfectly regular tetrahedron, as observed experimentally. In SOD-Na the sodium coordination is very near to a trigonal planar one (see the LO-Na-0 angle). We can conclude that the structural properties are overall obtained with a high degree of accuracy (within typical errors of LDA-DF calculations).
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Figure 7. Computed vibrational spectrum for SOD-NaC1. The arrows indicate the peak positions of the IR spectrumZoand do not relate to experimental intensities. 5.2. Vibrational Spectra. In a MD simulation the vibrational properties can be obtained by the Fourier transform of the velocity-velocity autocomelation function. In order to uniformly excite all the vibrational modes, we start the dynamics from a randomly distorted initial configuration (with a random displacement of about 0.1 A), and we let the system evolve dynamically at finite temperature for about 0.6 ps. The average temperature in this run is about 200 K. We show the computed vibrational spectra for natural sodalite and for anhydrous sodalite and compare them with experimental data. We would like to mention that we performed a molecular dynamics simulation also for the ideal structure SOD, which once again tumed out to be stable even at finite temperature, since no collapse of the structure was observed during the simulation time. In Figure 7 we see that the computed vibrational spectrum for SOD-NaCl shows all of the bands observed experimentally, and the agreement is not only qualitative, but also quantitatively good. In Table 4, we compare the peak frequencies of the computed vibrational spectrum, with IRZ0(see also refs 21 and 22) and RamanZ2data. Because of the relatively short simulation time (about 0.6 ps), there is not enough resolution in the computed spectrum in order to resolve the d(0-T-0) double peak and the three vs(T-0) modes. We point out that the precise assignment of the individual vibrational modes that contribute to the observed infrared and Raman spectra is still a matter of current research (see the recent work by Creighton et aLZ2). We did not try to make a full assignment of the features present in the computed vibrational spectrum: this can be a subject of future investigation. Here we comment only on the splitting in the asymmetric stretching band, v,,(T-0), which in our calculation is about 80 cm-I. In the IR spectrum of ref 22, an intense double is observed near 1000 cm-' with a peak separation of 24 cm-I. The origin of this splitting has been assigned to the difference in force constants between A1-0 and Si-0 bonds. Moreover in the Raman spectrum22an LO-TO splitting (not apparent in the infrared spectrum) of about 70 cm-' is observed giving rise to a band above 1000 cm-I. In Table 5 we show the vibrational bands related to interframework ions vibrations. The far-IR data are from ref 20. In order to get a better signal for this region of the spectrum we have computed the Fourier transform of the velocity autocorrelation function obtained using only the trajectories relative to C1 and Na atoms. We observe two peaks which are in good agreement with the IR data. Statistical errors, induced by the quite short simulation time, are even more dramatic for low frequency modes. Therefore it is difficult to distinguish between the signal due to Na and that due to C1.
Structural and Electronic Properties of Sodalite
J. Phys. Chem., Vol. 99, No. 34, 1995 12889
TABLE 4: Frequency Values of Vibrational Bands (cm-9 framework vibrational bands spectrum
structure
SOD-NaCl IR20
284 262
SOD-NaC1 Raman22
SOD-NaCI (this work SOD-Na IR21 SOD-Na (this work)
6(0-T-0) 436
292
27 1 215
457 434
TABLE 5: Vibrational Bands Relative to Interf‘ramework Ions Vibration@ frequencies species SOD-NaCl IRZ0
Na
98 111
173 200
112
670 602
714
461
606 669
69 1 709 686
IE
16
192
Experimental data lie in far-IR spectral region. Frequency values are in cm-I.
~as(T-0) 734 730
994 986 1059 995 916 1058
964 1013 915
154 920
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10
-
\
I
I
SOD
E 6 -
0
”
”
l
a
a
I
m
Rqumcy en,-’
Figure 8. Computed vibrational spectrum for SOD-Na. The arrows indicate the peak positions of the IR spectrum21and do not relate to experimental intensities. In Figure 8 we show the computed vibrational spectrum for SOD-Na. Here we notice that the splitting of the v,,(T-O) band is much larger than in SOD-NaC1, and this suggests that its origin cannot be traced back to the difference in force constants between A1-0 and Si-0 bonds. The bending mode 6(0-T-0) is here visible as a shoulder around 450 cm-I. Moreover we can observe a peak at 330 cm-’ which can be interpreted as a framework breathing mode (it should be IR-inactive or too weak to be seen experimentally). The breathing mode experimentally found at about 275 cm-’ is probably hindered by the very strong Na+ band in the theoretical spectrum. In Table 4,we compare the computed peak frequencies with the IR data of ref 21. 5.3. Electronic Properties. Natural sodalite and anhydrous sodalite are insulators with a large energy gap between valence and conduction bands. An estimated energy gap value of 6.1 eV has been reported in ref 23 for natural sodalite. We have computed a number of empty Kohn-Sham eigenstates in the ground-state geometry, in order to get some information on the energy gap and on the nature of the conduction band. A brief comment is in order here: the DF theory is a ground-state theory, and in principle empty states do not have a physical meaning. However, it is customary in DF calculations to interpret them as conduction states. It tums out that the energy gap in LDA is strongly underestimated (e.g. in c-Si the energy gap is underestimated about 50%), but the nature of the conduction states is correctly described. The LDA error usually consists of an almost rigid downshift of the conduction band. In our calculations we have found an energy band gap of 4.39 and 3.78 eV for SOD-NaC1 and SOD-Na, respectively.
4 2 n-20
--
I
’
-
--
6 16
SOD-NaCl (This Work)
+ C1
470 46 1
shoulder
335
C1 Na
vs(T-0)
-
\, -15
A
-10
-5
0
5
10
Energy (eV)
Figure 9. Computed electronic density of states. The zero of energy is arbitrarily put on the highest occupied state (for SOD on the corresponding empty state: see text for explanation). As expected, these numbers are much smaller than the experimental estimate, nevertheless they confirm the insulator nature of these materials. For the structure with no interframework atoms (SOD) we find a different behavior: the Fermi energy, shown by the m o w in Figure 9, falls inside the valence band, conferring a metallic nature to this structure. In particular, as one could expect, we observe three empty almost degenerate electronic states on top of the valence band for SOD, then followed by an energy gap of more than 5 eV. In SOD-NaCl the top of the valence band is represented by an exactly threefold degenerate energy level which in this case is fully occupied. In SOD-Na, the degeneracy of the highest occupied states in the valence band is different because of the symmetry breaking due to the vacant sites: the triply degenerate level splits into one nondegenerate and a doubly degenerate level. In Figure 9, we can see that the electronic density of states for SOD and the one for SOD-Na are nearly identical, the only difference being that in SOD-Na the valence band is fully occupied. Even though this picture does not correspond to the real chemical synthetization process, one can think to the three empty states in SOD as the ones that “accommodate” the electrons provided by interframework atoms. Since each orbital can be doubly occupied, six electrons can be accepted, or in other words, the structure can accept only six monovalent atoms. This is what happens in anhydrous sodalite with the presence of six interframework Na atoms which fully compensate for the “missing” electrons in the neutral sodalite unit. However, we know that the sodalite framework has eight equivalent cationic sites; therefore the structure tends to occupy them all in order to maintain the full symmetry. The way this becomes possible, without putting electrons in conduction band orbitals, is to accept in the structure interframework anions which provide
12890 J. Phys. Chem., Vol. 99, No. 34, 1995
Filippone et al.
Figure 10. Electronic charge distribution associated with the three degenerate states at the top of the valence band for SOD-NaCl. The charge (light grey surface) is localized around each 0 site in the cage and has a p-like shape.
*
Figure 11. Electronic charge distribution associated with the nondegenerate state at the bottom of the conduction band for SOD-NaCl. charge (light grey surface) has a spherical shape centered around each 0 site in the cage.
the needed extra electronic states in the valence band. This is what happens in SOD-NaCl (see Figure 9), where the electronic density of states is somewhat different in the valence band because in addition to O(2p) states it becomes composed also
The
of Cl(3p) states. Furthermore we can see a new peak around - 13 eV which is related to the 3s states of C1. We can compare the theoretical electronic density of states with experimental data coming from XPS spectra (see Figure 4
Structural and Electronic Properties of Sodalite and, for natural sodalite, ref 16). We should consider this comparison as purely indicative since XPS measurements made on hydrosodalite and hydroxysodalite are relative to structures somewhat different from the simulated ones, which were waterless; besides the Na(2p) states, visible in XPS, are considered as core states in the calculations and then treated only implicitly through the pseudopotential. Nevertheless, the computed band wideness and the relative distance of the O(2s) and O(2p) bands are in reasonable agreement with the XPS data. Moreover we may note from experimental data that for natural sodalite there is not a drop of intensity between O(2s) and O(2p) bands as seen for the other two XPS spectra, thus revealing the presence of Cl(3s) states. The eigenvalues spectrum gives detailed information about the states and their degeneracy. In SOD-NaCl we find many triply degenerate states, while in SOD-Na the corresponding states are nearly completely split in nondegenerate and doubly degenerate levels. In SOD the corresponding states are all nondegenerate, although the splitting is very small. This shows the importance of the interframework ions in increasing local symmetry and then the degeneracy of electronic states. In order to characterize the nature of the electronic states close to the energy gap, we have computed the electronic charge density associated with the three uppermost states in the valence band and with the lowest conduction band state, which tums out to be nondegenerate. In Figure 10 we plot the charge density associated with the triply degenerate state on top of the valence band for SODNaC1. We can clearly see that these states are strongly localized around the 0 sites and have a p-like shape. The analysis of the corresponding states for SOD (which are empty in this case) and for SOD-Na shows that they are all O(2p) states and very similar to each other. Furthermore, we can observe in Figure 10 that the charge distribution is perfectly symmetric over all cationic sites. Finally, from Figure 11 we find that the nondegenerate state after the band gap, is essentially O(3s) in nature. It would be interesting to verify the nature of this state with inverse photoemission data or X-ray absorption spectroscopy at the Si or A1 2p edge. 6. Conclusions In this paper we have presented a theoretical first principles study of sodalite, which, at variance from the cluster method, takes explicitly into account the full periodicity of the crystal. The possibility of treating a quite large number of atoms in the unit cell stems mainly from the use of ultrasoft pseudopotentials which considerably reduce the computational effort. The capability of performing structure relaxation, electronic states analysis, and molecular dynamics, with no input from experiment, makes the Car-Parrinello method a powerful tool in quantum chemistry. We have shown how the structural, vibrational, and electronic properties are modified when varying the nature and number of the interframework ions contained in the sodalite cage. We find a very good agreement with experimental data on the lattice parameter and bond lengths and angles. The experimental trend of the lattice parameter, collapse angle, and other structural features for different interframework ions is reproduced very well by the calculation. We have underlined how the symmetry breaking induced by the vacant sites in the anhydrous-sodalite structure modifies bond lengths and angles and the degeneracy
J. Phys. Chem., Vol. 99, No. 34, 1995 12891 of the electronic states. These microscopic details are not easily detectable experimentally. The computed vibrational spectrum for natural sodalite shows a satisfactory agreement with infrared and Raman data, demonstrating that also dynamical properties can be successfully analyzed within this approach. We have demonstrated the stability of the ideal neutral sodalite structure without interframework atoms: this seems to indicate that the steric effect of the interframework atoms is not crucial in preventing a possible collapse of the structure. Moreover from the study of this structure we have enlightened the nature of the framework electronic states which are related to the active sites of this material, i.e. those sites which accept interframework ions. In fact, the three uppermost valence states in the O(2p) band are in this case empty and the electronic charge density associated with them is uniformly distributed on the eight equivalent cationic sites. In order to get the full symmetry with eight monovalent cations per unit cell, the cage must accept also interframework anions, which contribute to the valence band. We hope that this work will stimulate further investigations on these materials, and we think that the Car-Parrinello method appears to be a valuable theoretical tool which can help in the search for new materials based on zeolites with desired physical and chemical properties.
Acknowledgment. We wish to thank Prof. G. Graziani for donating the sample of natural sodalite and G. Minelli for technical support. Prof. A. Fasolino is acknowledged for useful discussions and critically reading the manuscript. References and Notes (1) Ozin, G. A.; Kuperman, A,; Stein, A. Angew. Chem., Int. Ed. Engl. 1989,28, 359. Stucky, G. D.; Mac Dougall, J. E. Science 1990, 247, 669. (2) See, e.g.: Sauer, J. Chem. Rev. 1989, 89, 199. (3) Campana, L.; Selloni, A,; Weber, J.; Pasquarello, A.; Papai, I.; Goursot, A. Chem. Phys. Lett. 1994, 226, 245. (4) (a) Car, R.; Paninello, M. Phys. Rev. Lett. 1985, 55, 2471. (b) Galli, G.; Pamnello, M. In Computer Simulations in Material Science; Meyer, M., Pontikis, V., Eds.; Kluwer: Dordrecht, The Netherlands, 1991; p 283. (5) Pastore, G.; Smargiassi, E.; Buda, F. Phys. Rev. A 1991,44, 6334. (6) See, e&: Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. Jones, R. 0.; Gunnarson, 0. Rev. Mod. Phys. 1989, 61, 689. (7) Perdew, J. P.; Zunger, A. Phys. Rev. E. 1981, 23, 5048. (8) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566. (9) Laasonen, K.; Sprik, M.; Paninello, M.; Car, R. J . Chem. Phys. 1993, 99, 9080. (10) Cook, S. J.; Chakraborty, A. K.; Bell, A. T.; Theodorou, D. N. J . Phys. Chem. 1993, 97, 6679. (11) Bachelet, G. B.; Hamann, D. R.; Schluter, M. Phys. Rev. B 1982, 26, 4199. (12) Vanderbilt, D. Phys. Rev. B 1990, 43, 7892. (13) Hassan, I.; Grundy, H. D. Acta Crystallogr. 1984, 840, 6. (14) Depmeier, W. Acta Crystallogr. 1984, B40, 185. (15) Beagley, B.; Titiloye, J. 0. Struct. Chem. 1992, 1, 429. (16) Herreros, B.; He, H.; Barr, T. L.; Klinowski, J. J . Phys. Chem. 1994, 98, 1302. (17) Depmeier, W. Z. Kristallogr. 1992, 199, 75. (18) Pauling, L. 2. Kristallogr. 1930, 74, 213. (19) Felsche, J.; Luger, S.; Baerlocher, C. Zeolites 1986, 6, 367. (20) Godber, J.; Ozin, G. A. J . Phys. Chem. 1988, 92, 2841. (21) Godber, J.; Ozin, G. A. J . Phys. Chem. 1988, 92, 4980. (22) Creighton, J. A.; Deckman, H. W.; Newsam, J. M. J . Phys. Chem. 1994. 98, 448. (23) Van Doom, C. 2.;Schipper, D. J.; Bolwijn, P. T. J . Electrochem. SOC.1972, 119, 85.
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