J . Phys. Chem. 1987, 91, 891-899 photons prior to dissociation when radiation on the nanosecond time scale and in the 266-286-nm region is used. 4. When the parent ion dissociation dynamics are not well understood (e.g., cresols and benzyl alcohol derivatives), the wavelength dependence of REMPI fragmentation can potentially be used to develop a breakdown graph for ion dissociation provided that both the parent molecule and parent ion absorb over a suitable wavelength range.
Acknowledgment. This work was supported by the National Science Foundation under grant No. CHE8308049 and by the
891
National Institutes of Health under grant No. GM34457-03. T.-C. acknowledges support from a CIRES Visiting Fellowship. We thank Dr.Robert Barkley and J. Ronald Sadecky for obtaining CID spectra. Registry No. PhOMe, 100-66-3; PhOMe", 57378-73-1; oMeC6H40H, 95-48-7; o-MeC6H40H'*, 607 15-73-3; p-MeC,H,OH, 106-44-5; p-MeC6H40H'+, 51921-65-4; PhCH20H, 100-51-6; PhCHZOH", 105639-62-1; Ph(CHZ)zOH, 60- 12-8; Ph(CH2)20H'+, 105639-63-2; PhCH(CH3)OH, 98-85-1; PhCH(CH,)OH'+, 105760-405; o-MeC6H4CH20H,89-95-2; o-MeC6H4CH20H'+,105639-64-3; p MeC6H4CH20H,589-1 8-4; p-MeC6H4CH20H'+,105639-65-4.
Application of the Recursion Method to the Study of Heterogeneous Transition-Metal Catalysts Bernard
Yves Boudeville,la and Daniel Simonln,b
Institut de Recherches sur la Catalyse,Ic 69626 Villeurbanne Cedex, France, and Laboratoire de Chimie ThPorique,Ic Ecole Normale Supkrieure de Saint-Cloud, Grille d'Honneur- Le Parc, 9221 1 Saint- Cloud Cedex, France (Received: July 28, 1986)
The recursion method with an extended Hilckel Hamiltonian has been applied to the study of the local electronic properties of two small platinum clusters. The overlap between the various 5d, 6s, and 6p valence transition-metal orbitals is included in the computation. The feasibility and the influence of the various parameters of the procedure which involves a Schmidt orthogonalization have been considered. It has been checked that the results obtained with the recursion method and the classical LCAO-MO extended Hiickel method are identical. The analysis of the local density of states associated with the various atomic orbitals of the platinum atoms located on the surface clearly shows the differences in the adsorption properties of these atoms as a function of their local environment.
I. Introduction The understanding of the chemisorption properties of conducting or semiconducting surfaces is the first step toward a comprehensive molecular description of the catalytic heterogeneous processes.2 This type of description goes, in part, through the theoretical study of the various chemical elementary steps of their catalytic cycles. The detailed knowledge of these steps is a much desired goal if one wishes to compare, in heterogeneous catalysis, the mastery of the chemical reactivity presently acquired in classical organic, inorganic, or organometallic chemistry. A basic difficulty encountered in the theoretical study of catalytic heterogeneous systems is due to their large atomic size. Indeed, with the exception of the smallest metallic particles (2-50 atoms) which can be deposited on some specific supporting materials such as zeolite^,^ the size of the active heterogeneous catalysts corresponds to several hundred or thousand metal atoms! Various ways have been proposed for modeling these catalysts. Up to now, the most common models are either small aggregates5 with 2-10 metal atoms or infinite regular surfaces.6 In this case, (1) (a) Institut de Recherches sur la Catalyse. (b) Laboratoire de Chimie Thbrique. (c) These laboratories are part of CNRS (L.P. 5401). (2) Davis, S . M.; Somorjai, G.A. Bull. SOC.Chim. Fr. 1985, 271 and references therein. Boudart, M.; Djega-Mariadassou, G. CinPtique des RPactions en Catalyse HPttrog2ne; Masson: Paris, 1982. Gasser, H. An Introduction to Chemisorption and Catalysis by Metals; Clarendon: Oxford, 1985. Zarea, F.; Gellman, A. J.; Somorjai, G. A. Acc. Chem. Res. 1986, 19, 24. The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis; King, D. A., Woodruff, D. P., Eds.; Elsevier: Amsterdam, 1982; Vol. 4. (3) Gallezot, P. In Catalyse par les MPtaux; Imelik, B., Martin, G.A., Renouprez, A. J., Eds.; Editions of CNRS: Paris, 1984; pp 215-229. Fraissard, J. P.; Ito, T.; de Menorval, L. C.; Springuel-Huet M. A. In Metals Microstructures in Zeolites; Jacobs, P. A., Ed.; Elsevier: Amsterdam, 1982. Ito, T.;Fraissard, J. P. J. Chem. Phys. 1982, 76, 5225. (4) Renouprez, A. J. In Catalyse par les MPtaux; Imelik, B.,Martin, G. A., Renouprez, A. J., Eds.; Editions of CNRS: Paris, 1984; pp 163-179. (5) (a) Bigot, B.; Minot, C. J. Am. Chem. SOC.1984, 106, 6601 and references therein. (b) Siegbahn, P. E. M.; Blomberg. M. R. A.; Bauschlicher, C. W. J . Chem. Phys. 1984, 81, 2103. Flad, J.; Igel-Mann, G.; Dolg, M.; Preuss, H.; Stoll, H. Surf. Sci. 1985, 63, 285.
0022-3654/87/2091-089 1$01.50/0
the structures correspond to an extrapolation from the bulk arrangement. It is still an open question which minimal atomic size is needed for a theoretical model in order to take into account, in an appropriate manner, the essential electronic features involved in heterogeneous catalysis. Indeed, it is difficult with the small aggregate or regular surface models to treat, in a balanced way, at the same time the local character of molecular events which occur on the catalytic sites and the essentially global character of the electronic properties of conducting solids. The desired local molecular information can be obtained through two distinct approaches. One is to make, as a first step, a global description of the catalytic system and then to project parts of this information on the studied molecular system. A second approach is, as a first step, to isolate the molecular system under consideration (one or a few atoms of the solid and the molecular or atomic substrates) for studying its electronic properties and, then, to determine their modification under the influence of all the other parts of the catalytic system by some perturbational technique. The recursion method' is working within this scheme. This method has been used in solid-state physics for many years,' but it is still quite unfamiliar to chemists. It is the reason (6) Silvestre, J.; Hoffmann, R. Lungmuir 1985, 1, 621. Sung, S.; Hoffmann, R. J. Am. Chem. Soc. 1985,107,578. Froyen, S.; Cohen, M. L. Phys. Reu. B 1983, 29, 3258. Chelikowsky, R.; Louie, S. G.Phys. Reo. B 1984, 31, 3470. (7) (a) Haydock, R.; Heine, V.; Kelly, M. J. J . Phys. C 1972,5, 2845. (b) Haydock, R.; Kelly, M. J. J. Phys. C 1975, 8, L290. (c) Heine, V. Solid State Physics; Ehrenreich, E., Seitz, F., Turnbull, D., Eds.; Academic: New York, 1980; Vol. 35, pp 1-25. (d) Haydock, R. Ibid., pp 215-294. ( e ) Kelly, M. J. Ibid., pp 295-383. (fJPettifor, D. G.; Weaire, D. L. In The Recursion Method and its Application; Springer-Verlag: New York, 1985; Springer Ser. Solid-state Sci. Vol. 85. (8) See ref 7e, pp 320-353. Falicov, L. M.; F. Yndurain J. J . Phys. C 1975, 8, 147. Allan, G.; Dejonqueres, M. C.; Spanjaard, D. Solid State Commun. 1984, 50, 401. Choy, T. C. Phys. Reu. Lett. 1985, 55, 2915. Carette, T.; Lannw, M.; Friedel, P. Surf. Sci. 1985, 164, 260. Cuillot, C.; Chauveau, D.; Roubin, P.; Lecante, J.; DejonquEres, M. C.; Treglia, C.; Spanjaard, D. Surf. Sci 1985, 162, 46.
0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 4, 1987
why, at first in this paper, the principles and the computational details of this method are presented in chemical terms. Then, the capacities of the method are illustrated on the examples of two small platinum clusters.
11. The Recursion Method Theoretical chemists usually proceed in three steps to describe and analyze a molecular or crystalline material. First, the material is broken up into its atomic component parts; then, the properties of these parts and of their pair (or, if higher order systems are considered, their many-body) interactions are evaluated; finally, the collective properties of the system are computed by considering all interactions simultaneously. According to this scheme, in the recursion method, at first, one defines a basis set of atomic orbitals {d,] and a Hamiltonian operator H for the system S which is studied. H is defined by the values of its matrix elements H,, associated with the basis set. Then, a function luo) is selected. lao) could be any function belonging to the space generated by {d,).So, luo) is associated either with a single orbital dl or with any linear combination of them. From the consideration of the electronic spatial distribution associated with Iuo), a physical region, the part of S where the function luo) has its dominant contributions, is defined when luo) is considered. From the choice of luo),a new basis set of orthonormal functions (lu,))is generated step by step by taking into account the physical properties of S. Indeed, the new functions are obtained by using the operator H from the general three-term recurrence relation Hlu,) = 414)
+ bl+ll~I+l)+ ~ l l u l - l )
(1)
+
This relation is reduced to the expression Hluo) = aoluo) bllul),for l u l ) . Equation 1 determines the new orthonormal basis set {lu,))and fixes the values of the two sets of parameters {a,)and
PI1
where ai is the mean energy of the distribution lu,) and bi is the interaction energy or coupling between the functions lui) and lui+l). The recursion chain is equivalent to the progressive reorganization of the initial atomic basis set into new physically more adapted subsets. The subset associated with lui)is defined in such a way that it interacts directly only with the subsets associated with the functions and Due to the physical nature of H which involves pairwise interactions between overlapping atomic orbitals, the functions lui) generate a “concentric” de) .atomic orbital di overlaps composition of S around l ~ ~An significantly with another orbital d j only if the center of d j is located within a limited range around the center of di. So, lui) involves the orbitals which are more remote from luo) than the orbitals involved in the definition of and Iui-?). This fact allows us to take into account, in a continuous and progressive manner, the effects of atoms with decreasing influence on the energetic properties of the distribution associated with luo). The sequences { l u i ) ) ,{ai),and (6,)define a chain model which allows one, by starting from a particular point, to explore the entire system by a continuous step-by-step path as a wave progresses from its epicenter. At most, the length of this chain is equal to the dimension n of the basis set {di). This chain has interesting properties. Firstly, it does not depend upon periodicity and its generation does not require any particular symmetry properties for the atomic system. If local symmetry properties exist around luo), they will be taken into account and the new basis set { l u i ) )will span only the subspace of the atomic functions (di)which belongs to the same irreductible symmetry representation as luo). As a result, the length I of the chain is usually lower than the dimension n of the original atomic basis set. Secondly, since lui) represents a function interacting less and less with luo) as the index i grows, the truncation of the chain at an intermediate level t, t < 1, allows one to obtain an acceptable approximation of the complete system by considering a reduced part of it. An interesting feature of the chain model is that it
Bigot et al. selects this reduction for physical reasons. Naturally, the quality of the approximation increases with t , but the convergence is usually fast for a condensed atomic system, as encountered in solid-state chemistry. For example, for transition-metal solids, t = 15-30 gives already accurate results (see below). Thirdly, the chain model allows one to define the Hamiltonian H in a tridiagonal matrix form (Jacobi matrix) which is easily handled for diagonalization (Lanczos technique9): b1
UI
b2
0 0.
0 0
b2
(12
b3
0
b3
~
0
b
l
O
0
0 0 0 b4
0
0
0
. . . . . . . . . . . . . . . 0
-
0
b”-l
However, interest in the recursion method for studying the heterogeneous catalytic system goes beyond the elegant transformation of the physically unadapted original basis set {+,)into the basis set {lu,)),specifically adapted to the atomic system S . Indeed, it allows us to easily compute the local density of states n(t,uo) as a function of the energy. This function has decisive advantages over the classical oneelectron molecular orbitals when local information on a part of a large system is desired. Indeed, in the molecular orbital approach, \kk = Cckrdr,the local information associated with +, is spread all over the qk,i.e., a large number of functions. For large systems, such a dilution makes the extraction of easily handled results difficult. On the contrary, n(e,uo),which is defined as a functional of the \kk)s by the formula n(t,uo) = Ck{J”qk(r) uo(r) drI26(tk- e ) , gives local information relative to uo in a condensed way; 6 ( t k - t) is the Dirac function. If we express \kk as equal to CC‘~,~U,), the term { J q k ( r )uo(r)drl2 = c’ko2is the weight of the function luo) in the functions \ k k with energy t k . so, n(t,uo) is the energetical spectrum of the electronic distribution associated with luo) within the system S . The sum over i of the various n(t,u,) gives the usual electronic band structure of the solids. The density of states associated with the various atomic orbitals of a given atom can be summed up for defining an atomic local density of states. Another interesting feature of this function is that it can be computed directly by using Green’s operator G,the inverse of the operator (6 - H): n(t,uO)= (uol(t - H)-llu0). When the matrix [HI representative of H is tridiagonal as obtained by the Lanczos technique, this expression takes the form of a continuous fraction which can be rapidly evaluated:
n ( 4= l / ( t - a0
- bl2/(€ - a ] - b*2/(€ - a2 - b32/( .../...))))
(5)
To illustrate this procedure, let us consider the elementary example of the a electronic system of a conjugated unsaturated in the classical Hiickel formalism. Let hydrocarbon ring C98H98 us select any atom of the cycle. luo), the starting function of the recursion chain, is chosen as the 2p, orbital of this atom. The recursion method gives the following transformed Hamiltonian matrix on the basis of the new lu,) functions:
[w=r 2
.
.
.
.
.
p
0
q
0
P O C U P 0
.
.
.
.
P
.
.
I
O
0
0
0
1
P . .o . . . . . .
a
P
0
c
y
2 ‘ 4
2”2P
cy
(6)
The chain recursion vanishes after 50 steps for symmetry reasons: bSo= 0. The solutions t k of the tecular determinant gives the one-electron energy levels of the molecular orbitals of C9,H9,. ( 9 ) Cullum, J. K.; Willoughby, R. A. Lnnczos Algorithms for Large Symmetric Eigenualue Computations; Birkhaiiser Boston Inc.: Boston, MA, 1985; Vol. 1 and 2 and references therein.
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987 893
Heterogeneous Transition-Metal Catalysts
-*I-B
I
1
I
I
YI
I
Weight
-
I
Figure 1. Energy levels of the unsaturated conjugated ring Cg8Hg8obtained from a simple Hiickel calculation. The origin of the energies is the energy of a 2p, orbital. /3 represents the interaction of two adjacent carbon atoms. The weight reflects the participation of a given 2p, atomic
orbital. This allows us to compute the coefficients c / k j of the development of the molecular orbitals \kk on the recursion functions 1 ~ ~ ) : Iqk) = xc’k,lui)
0
c’k02 = lim n(crUO)/(ck - c )
(7)
e-ti
c’ko2gives the contribution of the selected 2p, orbital to the molecular orbitals with the energy ck. In other words, it is the number of states with energy t k weighted by the participation of the selected 2p, orbital to these states. The recursion method is, in principle, a good way of solving the one-electron approximation of the Schrodinger equation to extract local information from a many-electron system. Let us now look back to the truncation possibility in the recursion chain. As is mentioned above, the influence of the coupling of luo) with lu,) on the local density of states n(c,uo),, associated with luo) in the reduced system S, and generated by the basis U, = ( I u o ) , l u l ) , ..., I U , - ~ ) , \ u t ) ) ,decreases as the index i increases. Beyond a given value t , which depends on each studied system, this influence can be considered as a small perturbation which induces limited changes on the function n(c,uo),. Under these conditions, the properties of n(c,uo),, the local density of states, can be considered as a satisfactory approximation of the function n(c,uo), associated with luo) in the complete system S . The influence of the neglected part of the complete basis set when U, is used instead of U, can be viewed as a perturbative effect. This perturbation induces a broadening of the 6 Dirac function in n(c,uo),. This broadening can be simulated in various ways. One way is to transform each Dirac function in some Gaussian function. Another way is to add to the b, sequence a supplementary term b,+l. The value of this term is selected in order to simulate the effects of the neglected parts of S . b,+l represents the mean coupling of the system S, to these neglected parts. The value choosen for b,+l allows one to estimate the uncertainty on the position of the Dirac functions. As an illustration of the truncation procedure, the recursion method has been applied to the unsaturated hydrocarbon ring of 98 atoms. The recursion chain is stopped after t steps ( t d 50). The local energy density on a selected atom for several values o f t is depicted in Figure 2. The broadening is generated by the use of a Gaussian function instead of the Dirac function. We observe that the density of states of the selected 2p, orbital converges rapidly toward the exact spectrum as t increases. In the complete calculation, the continuous curve is obtained from a simple smoothing of the discrete histogram. Let us note that when we consider rings of increasing size C,H, (n > 2t), the local density of states obtained for a fixed recursion chain length t does not change. Thus, the recursion method is well adapted to the experimental observation that the local electronic properties of a large dense system are mainly determined by the nearby environment. Their description does not require the analysis of the whole system. The modifications of the spectrum of eigenvalues as the chain length increases from t to t + 1 are of two types: first, a new level
20 -~~~ I
DOSFigure 2. Densities of states (DOS) obtained in the recursion method for the C98H98 ring. Different levels of truncation have been used: r = 10 (A); t = 20 (B);t = 30 (C) and t = 40 (D). Curve E represents the actual density of states, obtained for t = 50. Continuous curves have been obtained by broadening the discrete spectrum (as in Figure 1) by a Gaussian function (with u = 0.1 6). Units are the same as in Figure 1.
of low density appears in the spectrum; second, some high-density levels already existing in the preceding spectrum are obtained with a better resolution, Le., with slight change in their position or splitting. The generation of the recursion chain from the Hij by the three-term relation is direct only if the atomic orbitals 4i are orthonormal. If they are not, two coupled left- and right-hand side recursion chains should be This requires the computation of S I , the inverse matrix of the overlap matrix S with elements S, = ( or the use of the chemical pseudopotential method.” To avoid the coupled recursion chains, the orthogonalization of the basis orbitals 4, and the computation of the associated Hamiltonian representation have to be peformed. Several orthogonalization techniques are available. The Schmidt technique has been selected. Choosing a given orbital as the start of the tridiagonalization procedure allows the recursion method to be applied to the initial functions and thus preserves the basis of the usual chemical analysis in terms of atomic orbitals.
+,
111. Computational Considerations In the present study, we decided to use the extended Hiickel formalism.I2 The different steps of a recursion calculation are the following: 1. To choose the function 4ofor which the local density of states is desired and to determine an orthonormal basis set {xi)by a Schmidt orthogonalization procedure. We use the overlap matrix on.the original basis set (q$) and start from xo = +o. The orthonormal basis defines a new Hamiltonian matrix H,. 2. To generate the sequence of the t coefficients ai and b, associated with xo where t defines the truncation level. The computation program for doing that step is based on eq 1. It needs a high numerical precision in order to limit cumulative errors. Presently, a FORTRAN 77 quadruple precision is used and gives satisfactory results. 3. To perform the computation of the poles of the Green functions and to calculate the density of states. This is done by a modified version of the standard programs of the Cambridge Recursion Library.’J3 The main subroutine is DENS. First, it calculates the poles and the associated weight on xo by using the continued fraction method. Then, for smoothing the corresponding histogram, it computes the integrated local density of states for various values of the energy by using the convergence properties of its indefinite integral.14 (10) Ballentine, L. E.; Kolar, M. J . Phys. C 1986,19, 991. (11) Anderson, P. W. Phys. Rev. 1969,181, 25-32. (12) Hoffmann, R. J . Chem. Phys. 1963,39, 1397. (13) We are indebted to C. M. M. Nex, Cambridge University , England, for providing us kindly with a listing of the original recursion program.
894
The Journal of Physical Chemistry, Vol. 91, No. 4 , 1987
Bigot et ai.
\
1.35
-14.0
IF l
DOS
-
e
i
'IDOS
(%I)"
Figure 3. Total densities of states (DOS) and integrated densities of states (IDOS) of atom 1 of the Pt,, cluster I (see Figure 8 below) for different values of the truncation parameters t .
Finally, it makes a derivation of this integrated density. For any value 6 of the energy which is not a pole of the Green function associated with the a, and b, sequence ( i = 1, f), the adopted procedure adds an extra couple (a,+,, where b,+, is selected by the user. Let us recall that this term represents the coupling of the reduced system S, with the neglected parts of S . a,+, is determined in such a way that e is a pole of the Green function associated with the a, and b, sequence ( i = 1, t + I ) . A simpler and faster way of smoothing is to use a convolution with Gaussian functions. A factor to be taken into account in this method is the dependence of the broadening on the compactness of the eigenvalues. Unfortunately, no explicit expression of this dependence could be found. However, if a constant broadening is assumed, one gets acceptable results which compare favorably with the more elaborated method. The convolution method has not been futher developed. The main computational parameters introduced in the full calculation, which gives the local density of states as a function of the energy c from the (a,,b,) coefficients, are the length of the recursion chain, t , the last coupling coefficient b,+l, and the resolution range of the energy A. The role of these parameters will now be illustrated. In Figure 3, different local densities of states are drawn for a model Pt13cluser (see below) with a chain length equal to 16, 25, 35, and 50. It is seen that, even with the shortest chain length, a satisfactory determination of the integrated density is obtained. The increase of t gives a more refined description of the local density of states but does not change its main features. In Figure 4, the corresponding curves are plotted for b,+, equal to 0, 1, and 3 eV. A comparison of the three curves of Figure 4 shows that the peaks in the local density function become wider and wider as b,+, increases while the integrated curve does not change much. In Figure 5, three densities of state are and presented with different values of A (respectively IO", eV) and the other parameters remained the same. The A parameter defines the minimal separation between two poles of the Green function so they are considered as distinct in the next smoothing calculations. Figure 5 shows that changing the A value mainly affects the dense part of the spectrum. We found that the optimum value is A = eV. It gives the best resolution. Finally, let us note that the three parameters discussed above are not independent in their action on the local density of states. For each calculation, an optimum set has to be found. In the computations that we have performed, typical selected values were t = 50, b,+, = 0.32 eV, and A = IO4 eV. The time of computation was about 10 min for one set of coefficients ( a z ,b,) on a 16-bit microcomputer.
IV. Comparison with LCAO-MO Extended Hiicke15s~12 Calculation
In an extended Hiickel calculation performed on a basis set (@,I (14) Nex, C. M. M. J . Phys A 1978, 11, 653. See also ref 3c, p 271
I
1
DOSIDOS ( W ) loo Figure 4. Total densities of states (DOS) and integrated densities of states (IDOS) of atom 1 of the Pt,, cluster I (see Figure 8 below) for different values of b,,,: (a) 0, (b) 1, and (c) 3 eV. The truncation has been made at t = 50. Comparisons can be made with Figure 3 where b,,, = 0.32 eV.
-3
-6.0
Y
-10.0
x
F m-,... 0
1000
DOS
and
IDOS
p4'
m
Figure 5. Densities of states (DOS) and integrated densities of states (IDOS) of atom 1 of the Pt,, cluster I (see Figure 8 below) for different eV. The values of the chain values of A: (a) lo", (b) lo-*, and (c) length and the last coupling coefficient are respectively t = 50 and b,,, = 0.32 eV.
(i = 1, n), the local density of states, projected on uo = the pole ck associated with the molecular orbital q k I(uoI*k)12
siois the
= (CcjPjo)2 =
c'kO2
is for
(8)
overlap integral (d0ldi);ckj and are defined as the coefficients of qkon d i and tui), respectively. It is thus easy to compare the results of a LCAO-MO extended Huckel calculation and those of a recursion calculationwhich use the same Hamiltonian. The extended Hiickel calculation requires a diagonalization of the complete Hamiltonian matrix H in order to get the n X n Cik coefficients, while the recursion method, which focuses on the local properties associated with a unique given orbital, requires at most the computation of n coefficients. This argument will naturally become more and more favorable to the recursion method as the size of the system increases. In Figure 6, a comparison between the local density of states of the 6s orbital of a platinum atom embedded in a PtI3cluster (see below) obtained by a recursion and an extended Hiickel calculation (1 17 orbitals) is presented. There is a full agreement between the two methods. The truncation only slightly modifies the broadening of the lines. The integrated densities are also identical in the two methods. In Figure 7, a comparison between the local densities of states cumulated for all the orbitals of an atom of the Pt13 cluster is depicted. The extended Hiickel spectrum has a higher resolution, but the recursion results are quite similar. They show a smoothing of the curves in the regions with several poles. As in the preceding case (Figure 6), the two integrated density functions are identical. The conclusion of these comparisons is that the recursion method, even on small systems, gives results analogous to a complete Hiickel calculation.
Heterogeneous Transition-Metal Catalysts
The Journal of Physical Chemistry, Vol. 91, No,. 4, 1987 895
TZ
EHT -6.0 '
t
Recursion
--8.0
-
n
%
Y-10.0
"
w Pt13 - I
-
x
F Q,
I
YC
C
u-11.0.
.
-14.0
! : : . : DOSIDOS '(W) la Figure 6. Comparison of the densities of states (DOS) and integrated densities of states (IDOS) of the 6s orbital of atom 1 of the Pt,, cluster I (see Figure 8 below) in a EHT and a recursion calculation. i
Pt,,-ll Figure 8. Structures of the Pt13 platinum clusters I and I1 with atom numbering.
-3
TABLE I: Parameters Used in the EHT Calculations
-0.0.
~
orbital Pt 5d Pt 6s Pt 6p
Y
x
F
Q,-lO.O
C
Hll,eV
exp,
exp2
CI
c2
-12.59 -10.00 -5.475
6.013 2.554 2.554
2.696
0.6334
0.5513
Lu
-11.0
i k
-Kp=--r -
DOS IDOS ( w ) loa Figure 7. Comparison of the cumulated densities of states (DOS)and integrated densities of states (IDOS) of the nine orbitals of atom 1 in Pt,, cluster I (see Figure 8 below) in a EHT calculation and in a recursion calculation.
Due to its local character, the recursion calculation naturally cannot determine the global properties of the cluster such as the Fermi level or the total energy. The local density of states is associated with an orbital which has a fixed extension in space defined by its spatial distribution. This extendon can be seen as a weighted volume. This fixed volume includes the whole overlapping region with the other orbitals. It constitutes the local point of view. The consequence is that we may not cumulate local results associated with different atomic orbitals for getting global properties. The overlap would be taken into account sevpral times. It is however possible to get global properties by cumulating local densities of states on a full set of orthonormalized nonlocalized functions xl. V. Results and Discussion
For illustrating the capacities of the recursion method, we have used two Pt13clusters with closqd packed geometries (Figure 8). The first one (I) is a stacking of two layers with 7 and 6 atoms, respectively. The second one (11) is the fcc cuboctahedron. The atoms of clusters I and I1 have the same mean coordination number. These clusters have been found to be among the most stable structures in a previous study.5a The 13-atom clusters have been selected for testing the recursion method because their size is large enough for performing elabo-
rated recursion calculations, without preventing the comparison with LCAO-MO extended Hiickel results. The extended Hiickel parameters are listed in Table I, and the HI]matrix elements are calculated from the by using the modified WolfsbergHelmholtz f0rmu1a.l~ The selected geometries offer a variety of environments for the atoms. If we use the coordination number of the atoms to differentiate them, we see that cluster I has coordination numbers of 9 (atom l), 5 (atoms 2, 3,4, 5 , 11, 12), 7 (atoms 6 , 7 , 9), and 4 (atoms 8, 10, 13). The center of the cuboctahedron (11) is 12-coordinated, and the other atoms are 5-coordinated (Figure 8). For each atom, the axis system has been oriented so that the z axis is normal to the mean local surface of the cluster. This direction is defined by the straight line which connects the considered atom and the barycenter of its nearest neighbors. It corresponds to the region of least steric hindrance for an incoming adsorbate. With this orientation of the axis, the atomic orbitals of the considered atom have specific symmetry behavior. They can be classified according to the irreducible representations of the C,, point group: (6s/z+,), (6p,/n,), (6py/ny), (6p,/z+,), (5d,2-y2/Ax2-y2)9 (5dZ2/Z+9),(5dxy/Axy),(5dxz/nXz),(5dyz/ny2). For each one of these symmetry orbitals and for each type of atom, we have determined the local density of states.I6 Comparisgns of these densities will now be made in order to illustrate the differences in the local electronic structures. Let us first consider some qualitative features. ( a ) Qualitatiue Features. First of all, the comparison of the different types of orbitals on the same atom is clearly illustrated Z+2z, and in Figure 9. The local density of states of the Z+s, A+2 are presented for atom 1 of cluster I. In the Z+, orbital spectrum, the different contributions are spread over a large range of energies. This behavior comes from (15) Hoffmann, R.; Hoffmann, P. J . Am. Chem. SOC.1976, 98, 598.
(16) We acknowledge the Computing Center of CNRS (CIRCE) at Orsay, France, on which the computations have been performed.
896
Bigot et al.
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987
r
I
I
I
-1
L0
I
I
lw%0 Dos ond
loo%
IDoS
Figure 9. Local densities of states (DOS) and integrated densities of states (IDOS) of some orbitals of atom 1 of cluster I. The dotted lines indicate the position of the Fermi level. An IDOS value of 100% corresponds to a two-electron occupancy.
the diffusiveness of this 6s orbital. The Z+zdensity of states shows that this atomic orbital has dominant contributions at high energy and is spread over a large range. On the contrary, the Z+,2 and AX2-9.curves, associated with more compact orbitals, are essentially restricted to an energy range from -14 to -1 1.5 eV. The local density functions show the mixing of the atomic orbitals in the molecular orbitals. For example, the Z + t and Z+satomic orbitals participate significantly in the lowest molecular orbital at -14.04 eV, while Pa, and Z+,2 have important contributions in the molecular orbital at -10.34 eV. The contribution of the atomic orbitals to the bonding can be illustrated qualitatively. The comparison between the energy position of an orbital in a free platinum atom (see Table I) and in the cluster makes it is possible to show how this orbital participates in bonding, nonbonding, or antibonding molecular orbitals. This behavior shows qualitatively what is the mean role of the atomic orbital under consideration in the cluster. For example, we can see in Figure 9 that the Z,' orbital contributes mainly to the bonding orbitals. (The value of the integrated density up to -10.5 eV is ca. 0.5.) The contribution to the nonbonding orbitals is small (ca. 0.1 from -10.5 to -9.5 eV), and that to antibonding orbitals is significant. The same analysis on the other atomic orbitals of atom 1 gives nonbonding and antibonding character for Z,' and bonding and antibonding behavior for Z+,z and Ax2-y~. Z+,2 and Ax2-y2 have only small nonbonding contributions (around -12.59 eV). Their spectrum presents no peak in the central region. It is interesting to compare these qualitative results to those obtained for another type of atom of the same cluster. The densities of states for the same orbitals as in Figure 9 are presented for atom 2 in Figure 10. W e see that for the PS orbital the bonding part is always large but less concentrated to the lowest energies than for atom 1, and the nonbonding part is a little more important. For Z+,2 the situation is inverted compared to that of atom 1, since the central nonbonding part has the largest contribution. Finally, this increase in the nonbonding character is also observed in the A,2,2 and Z,' curves. It must be noted that for atoms 6 and 13, for example, the behavior is analogous with atoms 1 and 2, respectively; so, the atomic orbitals have different electronic properties if they belong to a low coordination number atom (as atoms 2 or 13) or to higher coordinated atoms (as atoms 1 or 6). Nevertheless, no conclusion can be drawn
0
ao%o
DOS and
roo%
IDOS
Figure 10. Local densities of states (DOS)and integrated densities of states (IDOS) of some orbitals of atom 2 of cluster I. The dotted line indicates the position of the Fermi level. A IDOS value of 100% corresponds to a two-electron occupancy.
1
I
lo&
DOS and
W 6
IDOS
Figure 11. Cumulated local densities of states (DOS)of the nine atomic orbitals for each type of atom in cluster I. A value of 100% for the integrated densities of states (IDOS)corresponds to 18 electrons for the
whole atom. The dotted line indicates the Fermi level. without having analyzed more quantitatively the participation of the atomic orbitals at different energies by taking into account their actual population. Before doing that, let us give another illustration of the different behavior of different kinds of atoms by comparing the atomic local density of states (Figure 11). A qualitative analysis of the features of these curves shows that atom 1 of cluster I, with a high symmetry coordination, exhibits discrete peaks whereas the other atoms have a rather continuous density of states. Another point related to the symmetric situation of atom 1 is the fact that the contribution of this atom to the lower energy molecular orbital (at -14.04 eV) is large compared to the par-
Heterogeneous Transition-Metal Catalysts ticipation of other atoms at the same energy. If the atoms are classified according to their coordination number, some typical characteristics can be found. Atoms 1 and 6 of cluster I, with a larger coordination number (respectively 9 and 7), show a minimal region in their density between about -12.5 and -1 2 eV, whereas atoms 2 and 8 (coordination numbers 5 and 4) do not present this minimum. This hollow seems to be related to the nonbonding part of the d orbital densities. The observations above are also applicable to cluster I1 analysis. Let us now consider the quantitative analysis. ( b ) Quantitative Analysis. In this section, we study quantitatively the contributions, vs. energy, of the different atomic orbitals of each kind of atom. By doing that, we are going to establish, as a function of energy, the geometrical features of the filled or vacant molecular orbitals around a given atomic site. The aim of this study is to extract the characteristics of a given site for future interaction with an adsorbate: are the atomic orbitals full or empty, at what energies do they contribute, what are the energetic consequences in an interaction with an adsorbate having its own energy levels, and do the metallic atoms behave as donors or acceptors? The answers to these questions will finally allow us to get a molecular description of the mechanisms of the adsorption. In order to achieve that, the first step consists of fming the Fermi level, indicating to which energy the orbitals have to be filled. The determination of the Fermi level from the recursion method is not easy because this is a local method of calculation whereas the Fermi level position is a global property (it concerns the whole cluster). Nevertheless, an approximate technique may be used. The local density of states contains, at a given energy, the contribution of the initial recursion orbital plus the whole overlapping of this orbital with others, as was mentioned in section IV. The computation of the global density of states is possible by adding the local density of the initial atomic orbital and the local density associated with Schmidt orthogonalized orbitals: the Schmidt orthogonalized orbitals yield a local density having a contribution from one atomic orbital minus the overlapping with the others; the global density is therefore prevented from being overestimated. Moreover, by use of the geometry and symmetry properties of the cluster, this computation of the Fermi level energy cannot be too extensive. It may be supposed that, for different atoms equivalent in position, the corresponding Schmidt orthogonalized orbitals have equivalent density of states and that they have the same occupancy. This point has been verified on the example of the set of orthogonalized orbitals obtained by using the Schmidt procedure, with the 6s orbital of atom 1 in cluster I as the initial orbital. Let us compare, for example, the cumulated occupancy, up to the Fermi level at -1 1.6738 eV, of the nine Schmidt orthogonalized orbitals of atoms 3, 4, 6, and 8 (Figure 8): atoms 3 and 4 with equivalent geometrical position have an occupancy of 10.13 and 10.18 electrons, respectively, whereas atom 6 has 9.90 electrons and atom 8 has 9.56 electrons. Thus, the atoms with equivalent positions have their Schmidt orthogonalized orbitals which are associated with them filled equivalently. By considering the equivalent atoms 2, 3, 4, 5 , 11, and 12, the fluctuation in the total occupancy of these atoms has been computed to be 0.14 electrons. so, from a single Schmidt orthogonalization procedure, the global density may be reasonably approximated by n, 6n3 3n6 + 3n8where n, is the atomic density of states on atom i. By this method, the Fermi level is determined to be equal to -1 1.675 f 0.01 eV in cluster I as compared to the complete extended Huckel result of -1 1.6738 eV. In Figures 9-1 1, the Fermi level is indicated by a dotted line. Let us consider the total filling of each kind of atom when a new Schmidt orthogonalization procedure is performed for each atom (see Figure 11). Atoms 1 and 6 are the most populated (11.30 and 11.15 electrons, respectively), and atoms 2 and 8 are the least populated ones (10.96 and 10.88 electrons, respectively). The mean value of the atom occupancy in this cluster is 11.01 electrons per atom; this value is larger than 10 (the number of valence electrons of the platinum atom) because of the overlap between the orbitals from two distinct atoms. We see that the highest
+
+
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987 897 TABLE 11: Typical Values of the Occupancy N at the Fermi Level (in Electrons) and of the Mean Energy ( 6 ) for Some Orbitals of Cluster I atom 1 atom 13 orbitals N ( 6 ) . eV N ( e ) , eV 0.72 -13.20 1.06 -13.88 E+,
E+, z+,2
n,,
0.22 1.92 1.94
-13.23 -12.77 -12.69
0.18 1.98 1.86
-13.41 -12.62 -12.77
coordinated atoms are negatively charged whereas the lowest coordinated atoms are positively charged. Each atomic orbital has a characteristic occupancy N at the Fermi level (noted q):
N = x I n ( e ) de
(9)
and a mean energy ( e ) (E) =
I I n ( e ) c dc/S"n(e) -m de
(10)
n ( ~ is ) the local density of staes at energy e. N is related to the occupied or vacant character of the atomic orbital in the cluster, and ( E ) gives the stabilization relative to the free atom energy E@ To illustrate the differences between two types of atoms, we give in Table I1 the results for Z,' 2 + , 2 , and II,, orbitals of atoms 1 and 13. The 2 + , 2 and II,, orbitals are occupied in both atoms (Z+,2 is nearly full in atom 13), while the E+, is half-populated in atom 1. The other orbitals are unoccupied. The mean energy ( E ) shows that Z+, and Z+, are more stabilized that Z+,2 and ITxz, The most stabilized orbital is the half-unoccupied Z+, orbital of atom 1. To have a more precise idea of the quantitative features of each atomic orbital, we compute partial integrated density around the poles. In Table 111, we give the values of the contributions of each atomic orbital around the Fermi level. They are the most interesting since they are related to the H O M O or LUMO which determines the electron-donor or -acceptor character of the atoms. The results in Table I11 show typical characteristics for the different kinds of atoms. For instance, the 2+, orbital has a contribution only in the LUMO: the Z+, orbital of atom 1 contributes to the level at -10.34 eV and that of atom 6 to the level at -11.57 and -10.34 eV whereas that of atoms 2 and 13 contributes to the level at -1 1.57 eV. So, the 2+,orbital is a better electron acceptor on atoms 2 and 13 than on atoms 1 and 6. It has bad donor character in all cases. Another interesting example is found in the case. In the preceding discussion on the total population N a n d the mean energy ( e ) , the 2+,2orbitals of atoms 1 and 13 have a large electronic filling, 1.92 and 1.984 electrons, respectively, but their mean energy is hardly lower than in the free atom. Under these conditions, does the 2+22orbital constitute a good electron donor in both atoms? In Table I11 we see that this orbital participates mainly in the molecular orbitals at -1 1.67, -1 1.84, and -12.08 eV. Thus, 2'2 exhibits a better donor property in the case of atom 1 than in the case of atom 13 where the total contribution in the three orbitals is only 0.2 electron. From Table I11 we may sum up the donor or acceptor character of each type of atom: (1) atom 1: Z+,2 is a good electron donor, and E+, are light acceptors, and the Av, Ax.?, and nXz, II,, orbitals are good donors. (2) atom 2: P Z 2 has a mean donor character, whereas Z+, has a mean acceptor charcter; the A,, AX2-,2, and IIxz, II,, orbitals are good donors, and II, is a light acceptor. (3) atom 6: Z+,2 is a good electron donor, and E+, is a light acceptor; the Ax,, Ax2-,,2, and IIxr, II,, orbitals are good donors. (4) atom 13: Z+, is an acceptor, and A,, II,,, and II,, have acceptor character. We see in Table I11 that several atomic orbitals of the same type of symmetry contribute at the same energy. What are the relative phases of these atomic orbitals? The answer to this question will give information on the precise electronic distribution around a site. Two aspects will be illustrated here: first, if several
898 The Journal of Physical Chemistry, Vol. 91, No. 4, 1987
Bigot et al.
TABLE 111: Contributions (in Electrons) of Each Orbital of the Different Atoms of Cluster I to the Peaks around the Fermi Level
Atom 1 -10.34 -11.57 -11.67 -11.84 -12.08
0.16 0.00 0.00 0.00 0.02
0.00 0.12 0.00 0.00 0.00
0.14 0.12 0.00 0.00 0.00
0.00 0.00 0.00 0.04 0.02
0.06 0.00 0.52 0.00 0.20
0.00 0.00 0.00 0.54 0.32
0.00 0.52 0.18 0.00
0.00 0106 0.00 0.64 0.00
0.00 0.06 0.00 0.64 0.00
-10.34 -11.57 -11.67 -11.84 -1 2.08
0.08 0.22 0.00 0.00 0.02
0.02 0.02 0.00 0.02 0.00
0.12 0.06 0.00 0.06 0.00
Atom 2 0.04 0.02 0.00 0.02 0.00
0.02 0.00 0.06 0.40 0.10
0.00 0.00 0.08 0.20 0.00
0.00 0.14 0.00 0.28 0.22
0.02 0.06 0.00 0.18 0.16
0.02 0.06 0.00 0.32 0.12
-10.34 -11.57 -1 1.67 -1 1.84 -12.08
0.18 0.12 0.00 0.00 0.00
0.00 0.10 0.00 0.02 0.00
0.10 0.04 0.00 0.00 0.06
0.04 0.02 0.00 0.02 0.00
0.00 0.12 0.00 0.42 0.12
0.01 0.140 0.00 0.52 0.18
0.00 0.00 0.30 0.24 0.00
0.00 0.06 0.00 0.48 0.18
0.02 0.10 0.00 0.55 0.19
-10.34 -11.57 -11.67 -11.84 -12.08
0.06 0.24 0.00 0.00 0.04
0.00 0.00 0.02 0.02 0.00
0.04 0.00 0.02 0.04 0.00
0.00 0.02 0.00 0.00 0.02
0.00 0.00 0.00
0.00 0.02 0.00 0.00 0.10
0.00 0.04 0.00 0.25 0.23
0.00 0.00 0.10 0.28 0.24
0.02 0.00 0.10 0.28 0.00
0.00
Atom 6
Atom 13
(
n
I
0.02 0.08
1
b
-6.0
5
Y
-lo-Ol
1 0
DOS and
IDOS
1
x)(R.o
DOS and
lm%
Figure 12. Local density of states (DOS)and its integration (IDOS)for the hybridation 0.87 E+,-0.49 ,'E on atom 1 of cluster I.
atomic orbitals of the same atom participate at an energy level, we can find an hybridization which yields the largest contribution at this energy; second, if several atomic orbitals of adjacent atoms are present at the same energy, their linear combinations will define the topology of the adsorption site which gathers these adjacent atoms. As an illustration of the hybridization of atomic orbitals, Figure 12 presents the local density of states of the hybrid 0.87 Z+, -0.49 ;+,on atom 1. The coefficients of this hybrid have been chosen in ofder to get information on the behavior of atom 1 at -10.34 eV. '(They correspond to the largest contributions obtained at this energy.) The relative phases of the E+, and E+, orbitals yield a hybrid which protrudes out of the surface of the cluster. We see in Figure 12 that, at -10.34 eV, the contribution of this orbital is larger than the contributions of 2+, and Z+, (compare to the curves of Figure 9). So this shows that the electronic acceptor character of E+,and E+, in atom 1 is contained in an external orbital. Let us illustrate now the properties of a threefold site: in Figure 13, the local density orstates of the function 2+,(3) + 8+,(4) 2+,(10), built from the orbitals 2+,on atoms 3,4, and 10 of cluster 11, is depicted. It is compared with the curves of the 2+,orbitals of each atom. The spectra show some important differences; for example, the contribution around -13.5 eV in the atomic function is shifted to-13 eV in the sum function. In Figure 14, the local densities of states of the sum of E+,orbitals of atoms 6, 7, 9 (curve a) and 2, 3, 8 (curve b) of cluster I show important differences: (1) in curve a, the levels are concentrated at low energy (around
+
x)I
IDOS
Figure 13. Local densities of states (DOS)and their integration (IDOS) for the function: 2+,(atom 3) + Z+, (atom 4) + Z+, (atom IO) (curves b) compared with the curves of the Zts of each atom (a) of cluster 11.
tia) Y
-10.0
0
DOS
and
IDOS
Figure 14. Local densities of states (DOS) and their integration (IDOS) for the functions 2+, (atom 6) Z+, (atom 2) Z+, (atom 3)
+
+ E+,(atom 7) + 2+, (atom 9) (a) and + 2+, (atom 8) (b) on cluster I.
-14 eV) while in curve b they are spread' between -14 and -12.5 eV; (2) the first vacant level for curve a is at -1 1.57 eV while it is at -10.34 eV for curve b. So, the comparison of these local densities of states shows that the site 6-7-9 is less prepared for interaction with an adsorbate than the site 2-3-8.
VI. Conclusions In order to be able to get chemical information on the metallic sites involved in heterogeneous catalysis, the recursion method has been used in association with an extended Huckel Hamiltonian.
J. Phys. Chem. 1987, 91, 899-900 Because of the large overlap between the s and p valence orbitals of the transition-metal atoms and the valence orbitals of the adsorbed species, the application of the method requires the development of a performable Schmidt orthogonalization procedure involving sparse matrices. As a test, the method has been applied to the example of two small platinum clusters. It has been checked that the method gives identical results with the conventional
899
LCAO-MO method. The analysis of the local densities of states obtained for various atoms with different chemical environments clearly shows the capacity of the method to depict the main chemical features of the metallic surface sites. Applications to large systems involving up to 1000 metallic sites are under progress. Registry No. Pt, 1440-06-4.
EPR Evidence for New Rhodium Species In Na-Y Zeolitet A. Sayari,* J. R. Morton, and K. F. Preston Division of Chemistry, National Research Council of Canada, Ottawa, Canada Kl A OR9 (Received: August 21, 1986)
Several Rh(I1) species generated in Na-Y zeolite by heating in O2and subsequent evacuation at room temperature have been identified by EPR. Changes in the EPR spectra upon evacuation at high temperature (400-500 "C) are also discussed.
Zeolite-supported rhodium has been used extensively as a catalyst for a large number of chemical processes. The ability of rhodium to yield, upon suitable treatment, narrow distributions of small metallic particles throughout the zeolite as well as a variety of organometallic clusters inside the zeolite is a major reason for its widespread use in heterogeneous catalysis3 and also in the so-called heterogenized homogeneous ~ a t a l y s i s . ~ , ~ Several EPR investigations of rhodium species in Na-X and Na-Y zeolites have been published in recent year^.^-^ As for RhNa-Y, similar EPR spectra have been interpreted in different way^.^^^ Surprisingly enough, comparison of RhNa-X and RhNa-Y seems to indicate quite different behavior8 for the two types of zeolite. Because of the importance of catalyst characterization and also because of recent evidence that the oxidation state of Rh plays a major role in directing the hydrogenation of C O toward the production of either hydrocarbons or methanol or higher oxygenates,I0-l2we decided to undertake another EPR study of Rh-exchanged Na-X and Na-Y. Here we report only on RhNa-Y. The sample was prepared by ion exchange of zeolite Y (Linde LZY-52) with a 0.002 M aqueous solution of [Rh(NH3)5C1]Clz. The mixture was stirred continuously for 48 h at room temperature. The solid was then filtered, washed, and dried in air. The rhodium content was 2% w/w which corresponds to -3.5 Rh ions per unit cell. In most previous EPR studies, the Rh-loaded zeolites were heated under flowing oxygen typically at 200-500 OC, evacuated at the same temperature, and then cooled. Because some chemical processes may take place during the evacuation step at high temperature, we chose to evacuate the oxygen at room temperature usually for 18 h and then to heat the same sample under dynamic vacuum at various temperatures for different periods of time. Figure 1 shows the EPR spectra of two samples heated under flowing O2at 190 and 400 OC for 18 h, cooled to room temperature and then evacuated overnight. The sample treated at 190 OC (Figure la) exhibits an orthorhombic EPR spectrum with g values of g , = 1.968, g2 = 2.048, and g3 = 2.088 (species A). The narrow feature at g = 2.002, which may correspond to a carbonaceous impurity, is not present when the spectrum is observed at room temperature. The same spectrum was reported earlier by Naccache et aL7 for a RhNa-Y sample heated under oxygen at 210 "C and outgassed at the same temperature. This indicates that at such a relatively low temperature no further modification of the catalyst occurs after the O2 pretreatment, at least as far as 'NRCC No. 26414.
0022-3654/87/2091-0899$01.50/0
the paramagnetic species are concerned. Heating a RhNa-Y sample under oxygen at 400 OC generates several new paramagnetic species. At least three different species can be distinguished in Figure lb. Species B has an axially symmetric g matrix with g , = 2.550 and gll = 1.881. Only the high-field component exhibits a hyperfine splitting (All = 34 G) due to interaction with lo3Rh(I = natural abundance 100%). The central region of Figure 1b is very complicated. We tentatively assign g , = 2.266 and gll = 1.980 to a species C and g , = 2.186 and gll = 2.056 to a species D. Heating RhNa-Y under oxygen at temperatures above 500 O C eventually destroyed all paramagnetic species. As expected, under such conditions, all the Rh must have been oxidized to Rh(III).I3 The EPR spectra of a RhNa-Y sample heated under flowing O2at 400 OC and evacuated at room temperature (30 min), then at 400 OC (up to 72 h), and finally at 500 OC (2 h) are shown in Figure 2. The changes in the EPR spectra clearly demonstrate that during the evacuation of the sample at high temperature events other than the mere desorption of oxygen take place. Such events may involve the migration of paramagnetic species and/or further reduction of oxidized species. The resulting changes in the EPR spectra can be rationalized as follows. First, all signals in the central region of the spectrum disappear gradually. Second, the intensity of the EPR signal of species B decreases very slowly before it eventually vanishes at 500 OC. Third, a very strong signal (1) Shannon, R. D.; Vedrine, J. C.; Naccache, C.; Lefebvre, F. J . Catal. 1984, 88, 431 and references therein.
(2) Lefebvre, F.; Ben Taarit, Y. Nouu. J . Chim. 1984, 387. (3) Tebassi, L.; Sayari, A,; Ghorbel, A.; Dufaux, M.; Ben Taarit, Y.; Naccache, C. In Proceedings of the Sixth International Zeolite Conference; Olson, D., Bisio, A,, Eds.; Butterworths: London, 1984; p 368. (4) Gelin, P.; Lefebvre, F.; Elleuch, B.; Naccache, C.; Ben Taarit, Y. In Inrrazeolite Chemistry; Stucky, G. D.; Dwyer, F. G., Eds.; American Chemical Society: Washington, D. C., 1983; ACS Symp. Ser. No. 218, p 455. (5) Rode, E. J.; Davis, M . E.; Hanson, B. E. J . Catal. 1985, 96, 563. (6) Atanasova, V. D.; Shvets, V. A.; Kazanskii, V. B. Kinet. Catal. (Engl. Transl.) 1977, 18, 628. (7) Naccache, C.; Ben Taarit, Y.; Boudart, M. In Molecular Sieues II; Katzer, J. R., Ed.; American Chemical Society: Washington, D. C., 1977; ACS Symp. Ser. No. 40, p 156. (8) Goldfarb, D.; Kevan, L. J . Phys. Chem. 1986, 90,264. (9) Goldfarb, D.; Kevan, L. J . Phys. Chem. 1986, 90,2137. (10) Kawai, M.; Uda, M.; Ichikawa, M. J . Phys. Chem. 1985, 89, 1654. (1 1) van den Berg, F. G. A,; Glezer, J. H. E.; Sachtler, W. M. H. J . Coral. 1985, 93, 340. (12) van der Lee, G.; Schuller, B.; Post, H.; Favre, T. L. F.; Ponec, V. J . Catol. 1986, 98, 522. (13) van Brabant, H.; Schoonheydt, R. A,; Pelgrims, J. Stud. Surf. Sci. Catal. 1982, 12, 61.
Published 1987 by the American Chemical Society
