J. Phys. Chem. 1993,97, 13535-13538
13535
Structural Properties of CdO and CIS Clusters in Zeolite Y Andreas Jentys,’” Robin W. Grimes, Julian D. Gale, and C. Richard A. Catlow Davy-Faraday Laboratory, The Royal Institution of Great Britain, 21 Albemarle St., London, WIX 4BS Received: July 27, 1993’
A combination of lattice simulation and quantum cluster calculations has been used to predict the geometries and energies associated with CdO and CdS particle formation in zeolite Y. Excellent agreement between experimental and calculated geometries was found. Although the formation of (CdO), and (CdS)s clusters from diatomic species was found to be favorable, the clusters are constrained by the sodalite cages. This leads to a repulsive force between clusters in adjacent cages which will act against the formation of a completely dense packing of clusters throughout the zeolite lattice.
TABLE I: Potential Parameters
1. Introduction The pores and cages of zeolitic molecular sieves present a regular host system, able to accommodate a large range of guest molecules in uniform arrays by acting as solid solvents. In particular, taking advantage of the dimensional constraints of the zeolite channels, small uniform clusters of semiconductorscan be created, which as a consequence of their size exhibit remarkable quantum effects.’” In certain cases, due to the constraints offered by the zeolite host, the particles can be persuaded into a different coordinationcompared to that in their regular bulk structure. By supporting the clusters within the zeolite framework, the guest species are able to utilize the high chemical, mechanical, and thermal stability of the eol lite.^ These materials can be prepared by ion exchange3or metal organic chemical vapor deposition.5 The aim of both methods is to anchor precursor complexes within the lattice, which are subsequently transformed into semiconductor particles by treating the zeolite with gaseous reactants. It is interesting that CdS crystals with the rock salt structure have been biosynthesized6 and that under high pressure a phase transition from the wurzite to rock salt structures has been observed.’ In this study we describe the structure and the location of cubic (CdO), and (CdS)4 particles within zeolite Y. The results are compared to, and complement, the experimental studies of Herron et al.3 As this presents a new application for atomistic modeling techniques, considerableeffort was necessary in order to determine a reliable set of computational parameters that are able to describe the interactions between the atoms of the CdO and CdS particles themselves and those between the particles and the a t o m of the surrounding zeolite. To obtain these parameters, we first performed ab initio local density approximation (LDA) calculations on cubes consisting of four Cd and four 0 or S atoms and on clusters representing a portion of the zeolite lattice together with diatomic CdO or CdS molecules. Subsequently, the potential parameters were fitted to the resulting variations in binding energy as function of the geometry.
2. Metbnds 2.1. Lattice Simulation Technique. Two atomistic simulation techniqueswere used in these calculations. The first one assumes that guest particles occur periodically throughout the lattice and employ periodic boundary conditions.* The second method is based on Mott-Littleton methodology9and is used to describe a single particle embedded within an infinite lattice surround. Both Present addrau: lnstitut fiir Physikalihe Chemic und ChristianDoppler Laboratorium far Heterogene Katalyse, Technische Universitiit Wicn, Getreidemarkt 9/156, A-1060 Vienna, Austria. *Abstract published in Aduance ACS Absrracrs, November 15, 1993. t
specics Si4+ Oz,lcore O2-,ishell
charge 4.000 0.869 -2.869 0.736 1.664 -2.400 1.664 -2.400
Cd0.736+ S0.736-core
S0.736-shell 0°,736-,kcore @.736-,t,&ell
Buckingham Potentials (where E(r) = Ae+/P - C f i ) species
A (eV)
[email protected] Cd0.73642S0.736-42gO.736-42Si4+40.736Si4+40.736 Cd0.7364i4+ 00.736-40.736-
1283.90 22 164.47 35 178.11 32 401.73 18 672.26 62 564.81 58 762.92 6 821.54 9 721.45 1941 000.0 1283.90 50 800.0 40 618.0
D
(A-1)
Three-Body Terms (where E(0) = l/zK(Oo species
04-0 species
10.66 21.88 0.0 0.0 0.0
0.0 0.0 0.0 0.0 12.88 10.66 0.0 0.0
for both 0 species)
K (eV-rad-2)
eo
2.097 24
109.47
Shell Model Parameters shell charge
o*-e01
C( c V * A ~
0.3205 0.1490 0.1748 0.1927 0.2320 0.2955 0.1720 0.271 1 0.2576 0.1209 0.3205 0.1911 0.2638
k (eV.A-2)
-2.87 -2.40 -2.40
@‘736-mk s0.736-
74.9 75.0 35.0
methods utilize a description of the lattice in terms of effective potentials and are, in essense, a Born model of an ionic crystal. As such, long-range Columbic potentials are defined between ions and are summed to infinity using the Ewald technique.1° Short-range interactions, which are also defined between ions, are parametrized into a Buckingham potential form. Thus, the interaction between two ions separated by a distance rij can be written
4i41 + A exp(-r,j/p) - C/ril6 E(rij) = ‘ij
where qi is the charge on ion i. A, p, and Care the parameters mentioned in the Introduction. The values of A, p, and C (see Table I) associated with the clusters were chosen to reproduce the predicted variations in the quantum cluster energy as a function
0022-3654/93/2097-13535$04.00/00 1993 American Chemical Society
Jentys et al.
13536 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
the geometric distortion and will be described in greater detail below. The values of A, p, and C which describe the host lattice itself were taken from a previous study by Jackson et al.” and include a three-body bond bending term important for a correct description of the silica tetrahedra. Anions are treated as polarizable by virtue of the shell model of Dick and Overhauser.l* In this model, a massless shell of charge Y is allowed to move with respect to a massive core to charge X; the charge state of the ion is equal to (X+ r). The core and the shell are connected by an isotropic harmonic spring offorceconstant k (seeTable I). Displacementof the shell relative to the core gives a good description of electronic polarizability. Themodelsdescribed aboveareutilizedin the lattice simulation techniques. Using this ionic description,atom positionsand lattice vectors are minimized to zero force using Newton-Raphson procedures. Thus we are able to predict the energies and geometries of the guest clusters subject to the influence of the host lattice. The ability of this method to describe the relaxation response of the host lattice is an essential feature of the model and is the reason why it is not possible to use a small quantum cluster approach alone. Further details of these methods can be found in recent reviews.l3J4 2.2. Quantum Cluster Method. The quantum cluster calculation, from which the effective potential parameters arederived, is based on the local density functional (LDF) equations, which are solved variationally and self-consistently.lsJ6 In common with many other LDF methods, the kinetic energy is calculated directly from the wave function, while the Coulomb interactions are determined from the charge density. The many-electron exchange correlation term is calculated from the charge density as derived by Barth and Hedin.” A particularly attractive feature of this method is the use of a double numeric basis set,1*J6which includesan additionaldouble numeric core and also higher angular momentum number polarization functions. The richness of such a basis guarantees negligible basis set superpositions errors. In this study we have employed the DMol ~ 0 d e . I ~ 2.3. Determination of the Interatomic Potentials. The intraparticle potentials were derived from cubes consisting of four cadmium and four oxygen or sulfur atoms. In fact, the cubes were not perfectly cubic, since in their relaxed geometry the anions to cube center distance is slightly larger than the cation to cube center distance. The symmetry of thecube was Td. Thevariation of the binding energy of the cubes was calculated as a function of the distortion to the geometry of the cube. Three different “breathing” distortions were considered: (i) The distance of the Cd atoms from the center of the cube was varied while the 0 or s atoms were kept fixed; however, overall Td symmetry was maintained. (ii) The position of the Cd atoms remained fixed while the 0 or S atoms were distorted in the equivalent way as in (i). (iii) Finally, a distortion was considered in which the Cd and 0 or S atoms were “breathed” in the same direction starting again from the optimized geometry. To obtain a starting value for the fitting of the potentials, the variation of the binding energy of the diatomic CdO and CdS particles with interatomic distance was calculated and the corresponding Cd-O and C d S potentials were determined. The final interatomic potentials were then obtained by fitting the dependence of the binding energy to the geometry of the cube. Two models were derived, one in which the oxygen and sulfur atoms were assumed to be unpolarizable and a second where a shell model on these atoms was employed. The quantum mechanically optimized geometries of the (CdO)4 and (CdS)4 cubes and the geometries of the cubes calculated with both sets of potentials are given in Table 11. The value of the charge used to describethe Cd cluster ions was the averageMulliken population value for Cd obtained for the (Cd0)d and (CdS)4 clusters, those values being 0.877 and 0.638, respectively. To determine the potentials which describe the interface
TABLE II: Geometry (A)of the Cubes from LDA Cdculationa and Resulting from the Potential# (CdO)r Cube
LDA
without shell model
with shell model
Cd-Cd Cd-O 0-0
2.93 2.20 3.21
3.09 2.20 3.14
2.91 2.21 3.31
charge of Cd atoms from LDA calculation: 0.877 (CdS)d cube
LDA
without shell model
with shell model
Cd-Cd CdS
3.05 2.56 4.04
3.40 2.61 3.96
3.08 2.58 4.07
ss
charge of Cd atoms from LDA calculation: 0.638
n
Figure 1. Geometry of the lattice zeolite cluster together with a CIS molecule.
TABLE IIk Charges for the Geometry with the Lowest Binding Energy Cd 0,s 0 Si H CdO CdS O(SiHd6 CdS... O(SiH3)z S-Cd...O(SiH3)2 Cd-O... O(SiH& O-Cd...O(SiHs)z
0.792 0.557
-0.792 -0.557
0.489 0.599 0.738 0.811
-0.467 -0,613 -0.720 -0,787
-0.546 -0.603 -0.640 -1.044 -1.112
1.142 1.224 1.215 1.304 1.269
-0.290 -0.308 -0.298 -0.261 -0,237
Inductive Effect on Molecule Caused by Interaction between Cluster and Zeolite change in charge of Z i o n in diatomic C d S ...O(SiH& SCd...O(SiH3)z Cd-O. ..O(SiH3)2 04d...O(SiH3)z
-0.068 +0.042 -0.054 +0.019
between the semiconductor particles and the zeolite, a cluster representing the zeolite was selected and the energy and charges of the atoms within this cluster were calculated. A diatomic CdO (CdS) particle was placed in close proximity, and the variation of the binding energy as a function of the distance between the zeolite fragment and the diatomic molecule was determined. The geometry of the lattice zeolite cluster together with a CdS molecule is shown in Figure 1. Four sets of calculations were carried out: with the diatomic particle pointing either with the Cd or with the 0 (S) atom toward the 0 atom of the zeolite cluster. The charges of the host and the guest atoms for the geometry with the lowest binding energy are compiled in Table 111. To describe the interaction of the Si atoms of the zeolite framework with the semiconductor particle, diatomic Si-Cd and S i 4 species, with charges of +2 and + 1, respectively, were also studied. All potentials were derived from the quantum mechanical energy hypersurface by a least-squares fit to the binding energy for each of the conformations examined above. This procedure was carried out using a cluster version of the program GULP8
Structure of CdO, CdS Clusters in Zeolite
TABLE I V Energies in eV per Cd Atom for the CdO(S) Diatomic Particles rad Cubes Inside zeolite Y total coverage gas single species (lattice energy phase in zeolite of zeolite subtracted) -3.44 -3.66 -4.44 CdO-diatomic -2.06 -3.36 -2.83 CdS-diatomic -3.88 -4.80 -4.51 (Cd0)4 Cube -3.14 -4.18 -3.13 (CdS)4 cube -2.13 -3.17 (CdS)4 cube reversed -4.40 -3.86 CdrOOoS cube -3.19 -4.20 cdrooss cube -3.98 -3.51 cdrosss cube -3.41 C&OOOS cube reversed -3.88 Cd@OSS cube reversed -4.39 Cd4OSSS cube reversed Lattice Energies (eV) CdO -5.44 CdS -4.53 zeolite Y -6161-96 and follows the methodology used by Gale et to derive potentials for ar-alumina. Because the shell positions are indeterminate, unlike the core positions which are assumed to be coincident with the nuclear coordinates, their displacements are included as variable parameters in the least-squares procedure. For the energy surface of each molecule it is also necessary to include a fitted shift parameter which is added to the energy of each configuration. This term represents the sum of the ionization potentials of the ions at infinite separation; however, due to the use of the partial charge model this number cannot be calculated independently. All potentials are summarized in Table I.
3. Results Diatomic Cd-0 and C d S particles as well as (CdO)4 and (CdS)4 cubes were placed in the sodalite cage of zeolite Y. Calculationswere carried out on single (CdOk and (CdS)4 cubes inside the zeolite and for the case in which all sodalite cages contain one cube. It was reported by Herron et ~ lthat . for ~ (CdO(S))4 in zeolite Y the Cd atoms are located on the Si sites and the 0 or S atoms on the SI{sites. We used this proposed geometry and its reversed orientation as starting geometries for our calculations in order to check if our results depend on the starting geometry. The energiesfor the different geometriesare shown in Table IV and the optimized geometries in Table V. The volumes of the various cubes are compiled in Table VI. Only for the (Cd0)4 cubes was it found that the final geometry was not dependent on the starting geometry. In this case, identical geometries were obtained after minimizing the energy, starting from the experimental geometry or from the transposed configuration. For the (CdS)4 cubes and for the partially sulfur exchanged cubes (e.g., Cd4S202) a different behavior was observed. In thesecam, when starting with the reversed geometry the final structure was energetically less favored than that obtained from calculations initially starting with the experimentally geometry. In order to model the transformation of (CdO)4 into (CdS)4, which is achieved experimentally by sulfidization of the CdO clusters with HzS, a series of calculations were carried out in which the oxygen atoms were partially replaced by sulfur. The results were shown in Figure 2. 4. Discussion
For the CdO and CdS cubes, two different sets of potentials were derived. In one model the 0 and S species were treated as unpolarizable,while in the other model both types of atoms were assumed to be polarizable. In the latter case, this was accounted for by applying the shell model. Comparing the geometry of the
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13537
-4.5
E
9
5 L2
-4.3 -4.1
Y
a
El -3.9
B
W
-3.1
0
1 2 3 Number of S Atoms in Cube
4
Figure 2. Energim in eV per Cd atom for partially sulfur containing cubes.
cubes resulting from the two sets of potentials with the geometry obtained with the LDA calculations (see Table 11), to which the potentials were fitted, it is clear that the polarizability of the 0 and S atoms is an important factor which should not be neglected in our calculations. No charge transfer between the diatomic Cd-0 and Cd-S species and the cluster, used to simulate the zeolite, was observed in the LDA calculations. This is important, as it confirms that the interaction between the clusters and the zeolite was essentially nonbonding. As such, the effective pair potential approach is particularly appropriate to model the interaction between these two closed-shell species. While charge transfer between the host and guest did not occur, a significantchangein the overall electron densityofthediatomicparticlewas noticed. When thepolarizable atoms 0 and S were directed toward the zeolite cluster, a decrease in the total charge of the Cd atom, 0.068 for Cd-S and 0.054 for Cd-0, was observed. In the casewhen the Cd atomswere oriented toward the zeolite cluster, an increase of the total charge of 0.042 in the case of C d S and 0.019 for Cd-0 was observed. The strongest inductive effect was observed for the CdS particle with the S atom pointing toward the 0 atom of the cluster. This is due to the stronger polarizability of S atoms compared with 0 atoms. While optimizing the potential parameters it was essential to fit simultaneouslyto as many configuration as possible. The unconstrained shell position is a crucial factor during these calculations. Thisallowsus to simulatetheinductiveeffect across the interface as observed by the LDA calculations. When the Cd402S2 clusters were incorporated into the zeolite, a very good agreement with the experimentally determined distances from ref 3 was obtained. This is appropriate as the authors assume that the cubes they incorporated into the lattice were half-exchanged withS. Theresultsshow that theorientation with the Cd atoms located on the SI’sites and the 0 or S atoms on the SI{sites of zeolite Y is clearly preferred over the reverse geometry. For the (Cd0)4 cube, it was observed that there was no barrier for rotation between the two geometries during the energy minimization. For the larger (CdS)4 cubeand the partially exchanged cubes, a barrier was observed and a second less stable local minimum was found. When partially replacing the 0 atoms in the cubes with S,only a small deviation from a linear combination of the energies obtained for the (CdO)4 and (CdS)4 was noticed (see Figure 2). The biggest deviation of -0.04 eV per Cd atom was observed for the half-exchange cube. As such, we assume that a complete transformation of the CdO into CdS cubes will occur during the sulfidization process, but in the case of understoichiometric exchangeconditions species containing two oxygen and two sulfur atoms will be slightly preferred. The formation of ( C d o ) ~and (CdS)4 cubes, both as isolated
Jentys et al.
13538 The Journal of Physical Chemlrtry, Vol. 97, No. 51, 1993
TABLE V: Geometries of the Semiconductor Particles in Zeolite Y (Distances in A) Cd-O CdS Cd-Cd 0-0
CdO 2.1 1
CdS 2.35
3.13 3.16
ss
CdSi
(Cd0)4 2.23
3.23
3.22
3.58
(CdS)4
(CdS)4 rev
2.64 3.53
2.52 3.21
3.91 3.47
3.86 3.59
TABLE VI: Volume of the (CdO)4 and (CdS)4 Cubes volume of cube (A,) (CdO), cube isolated (CdS)4 cube. isolated (Cd0)4 cube in zeolite lattice (CdS)d cube in zeolite lattice (CdS)4 cube reversed in zeolite lattice
8.9 15.3 8.4 14.9 13.7
specieswithin the zeolite framework, is energetically favored with respect to the diatomic CdO and CdS species (seeTable IV). For CdO, the cube arrangement is energetically preferred over four separate diatomic CdO molecules by -0.13 eV per molecule. For CdS the gain in energy is -0.90 eV per molecule. This indicates that cubic particles will be formed immediately during the synthesis of the material and also that these particles have no tendency to dissociateinto smaller units. However, for geometric reasons it is clear that a cube is the largest fragment that can be accommodated in the sodalite cage. When the fragments were arranged periodically throughout the lattice (see Table IV) a significant interaction between the particles incorporatedinto the zeolite was observed. The repulsive interaction between diatomic CdO and CdS particles was found to be 1.0 and 0.79 eV, respectively. Between the cubic semiconductor particles interaction energies of 0.69 eV for (Cd0)4 and 0.59 eV for (CdS)4 were determined. This suggests that there is a long-range stress field between the particles which is slightly repulsive. This would act against the formation of a dense packing of the CdO and CdS particles within the zeolite framework. This repulsive interaction is a simple consequence of the constraint that each cluster experiences due to the sodalite surround. As shown in Table VI, isolated (CdO)4 and (CdS)4 clusters have a slightly larger volume compared to those species embedded within the zeolite framework.
5. Conclusions We have shown that interatomic potentials that describe the short-range interactions between a CdO (CdS) particle and a zeolite can be derived using LDA quantum cluster calculations of diatomic CdO (CdS) particles and a cluster representing the zeolite. In these calculations the larger polarizability of S compared to that of 0 is clearly shown. During the potential fitting process it was essential to model the polarizability of the anions using unconstrained shells. The important effect of longrange Coulombic interactions from the extended lattice was also included in this model.
CdrOOOS 2.24 2.55 3.20 3.15 3.55
Cd400SS 2.25 2.59 3.28 3.13 3.90 3.55
Cd4OSSS 2.26 2.60 3.40
C&OOSS from ref 3 2.23 2.52 3.29
3.91 3.55
3.42
Our calculations show that even at very low Cd concentrations the formation of (CdO)4 and (CdS)4 cubes in the sodalite cages is preferred over the formation of smaller CdO (CdS) units. Moreover, the experimentally recognized orientation with the Cd atoms located at the SI’sites and the 0 (S) atoms on the SI{ sites is favored for all possible (CdO(S))4 cubes in the zeolite lattice. Excellent agreement between experimental and calculated geometries for the clusters was noted. The modeling of the sulfidization process, achieved by partial replacement of the 0 atoms by S in the cubes, showed almost negligible preference for the intermediate-exchanged species.
Acknowledgment. Financial support from the EC under the science plan grant SCI-0199 and the Christian Doppler Laboratory for Heterogenous Catalysis is gratefully acknowledged. R.W.G. thanks the Gas Research Institute of Chicago USA for financial support. References and Notes ( I ) Ozin, G. A,; Ozkar, S.Adu. Mater. 1992, 4 ( I ) , 1 1 . (2) Gritzel, M. Nature 1989, 338, 540.
(3) Herron, N.; Wang, Y.; Eddy, M. M.; Stucky, G. D.; Cox, D. E.; Moller, K.; Bein. T. J . Am. Chem. SOC.1989, I l l , 530. (4) Schultz-Ekloff, G. Stud. Surf.Sci. Carol. 1991, 69, 65. (5) MacDougall, J. E.;Eckert,H.;Stucky,G.D.;Herron,N.;Wang,Y.; Moller, K.; Bein, T. J . Am. Chem. SOC.1989, 1 1 1 , 8006. (6) Dameron, C. T.; Reese, R. N.; Mehra, R. K.; Kortan, A. R.; Caroll, P. J.; Steigerwald, M. L.; Brus, L. E.; Winge, D. R. Nature 1989,338, 596. Phys. Chem. (7) Osugi,J.;Shimizu, K.;Nakamura,T.;Onodera,A.Reu. Jap. 1966,36, 59. (8) Gale, J. D. General Utility Lattice Program; Royal Institution of Great Britain: London 1993. (9) Mott, N . F.; Littleton, M. J. Trans. Faraday SOC.1938, 38, 485. (10) Tosi, M. P. Solid State Phys. 1964, 16, 517. (11) Jackson, R. A:, Catlow, C. R. A. Mol. Sim. 1988, I , 207. (12) Dick, B. G.; Overhauser, A. W. Phys. Reu. 1958, 112, 90. (13) Catlow, C. R. A.; Stoneham, A. M. (guest editors) J . Chem. SOC., Faraday Trans. 1989, 85 (S), special issue. (14) Harker, A. H.; Grimes, R. W. (guest editors) Mol. Sim. 1990 4 (5) and 5 (2), special issue. (15) Delley, B. J . J . Chem. Phys. 1990, 92, 508. (16) Sasa,C.;Andzelm,J.;Elkin,B.C.;Wimmer,E.;Dobbs,K.D.;Dixon, D. A. J . Chem. Phys. 1992, 96, 6630. (17) von Barth, U.; Hedin, L. J. Phys. C. 1972, 5, 1629. (18) Delley, B. J . Chem. Phys. 1990, 92, 508. (19) DMol version 2.1, BIOSYM Technologies, San Diego, CA, 1991. (20) Gale, J. D.; Catlow, C. R.A,; Mackrodt,W. C. Model. Simul. Mater. Sci. Eng. 1992, 1 , 73.
