Molecular properties of the magnesia surface - The Journal of Physical

Ivano E. Castelli , Isabela-Costinela Man , Stefan-Gabriel Soriga , Vasile Parvulescu , Niels Bendtsen Halck , and Jan Rossmeisl. The Journal of Physi...
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10389

J. Phys. Chem. 1992,96, 10389-10397 that of the {lJI reflection. An estimation of the smallest detectable deviation (AyJmof yt from 90' can be made by simulating different possible patterns for the [1,11and the (1,T)reflections. If the two diffraction peaks associated with these reflections are very sharp; i.e. their full width at half-maximum fwhm(q,,) is close to the resolution limit A(qx ) = 0.007 A-' of the Soller collimator, then a split would have bem obcrvabie with (A?&, as low as 0.3'. For a wider fwhm(qv) of t h e peeks, (A& will be larger. If one demands that the two compming singlet peeks are sufficiently well resolved to be "&the minimum deviation (A& of the angle yrfrom 90' that would have been detected is 0.7' for a fwhm(q,,) of each singlet m0.03 A-'. Thus, there is little probability that in the crystallitesof CZ9H&O2H the unit cell is oblique. (62) We have strong evidence from the GID powder patterns of self-assembled crystallites of various amphiphiles with long hydrocarbon chains that the broadening of the observed reflections can be accounted for in terms of a smaller crystallite coherence length along the direction of the molecular tilt (as described in seaion 5.5). Indeed self--bled crystallites of triacontanoic acid CZ9Hs9CO2Hand hydroxyalkyl esters of eicosanoic acid*' C1J4J9C02C &OH (n = 9,lO) amphiphiles at low temperature over water yielded a {1,1$ (1,TJreflection less sharp than the {0,2)reflection, the moleculea being tilted along the short a axis of the unit cell. There are other examplea of diITraction t t m s from self-asw"led crystallites of amphiphilic molecules in which the El)+ (1,9 reflection is actually sharper than the (0,2l singlet. This occurs when the molecular tilt is along the long axis of the unit cell, as in uncompressed films of long chain alcohols (CfiMIOH, n = 23, 30, and 31) at low temperature over water.a For these systems, the {0,2) reflection is broad with a fwhm(q, ) = 0.03 A-I. Therefore it is highly improbable that the broadening of t i e (1,l)+ [1,11reflection for the self-assembled crystallites of triacontanoic acid arises from not perfectly coinciding {lJ) and [l,T)reflectim (and so, to a somewhat oblique character of the unit cell). In any event, the possibility of a packing in the plane group cl was considered in our analysis. (63) Internatfonal Tables for X-ray Crystallography; Kynoch Press: Birmingham, U.K., 1965; Vol. 1, p 57. (64)Becaw the rectangular unit cell contains two molecules, the plane groups pmm and cmm would require the molecules to stand upright with 2-fold crystallographic disorder, incompatible with the observed B r a g rod profiles. The plane group pm would require the two molecules in the unit cell to pack a m the mirror plane which imposes poor packing chara~teristics.5~ We a b generated all possible packing arrangements in the plane group p l Im with the triacontanoic acid molecules tilted by 26.5O along the short a axis and calculated, using 3 the ratio of the integrated intensities of the two reflections (0,2}{l,l)+Tl,f). The observed value of this ratio is 0.41. The calculated value was never less than a value of 8 which immediately rules out the possibility of plane grouppl lm. This result reflects the observation that the two molecules in the unit cell, related by mirror symmetry, are asentially separated by translation of b 2. Thus, [h,k)reflections with k = 2n + 1, such as the (1J) and the {l,T)re -ions, are very weak. (65) Any other tilt direction would impose poor intermolecular contacts. (66) The possible plane group for monolayer molecules packing in an oblique ceIP are p l and p2. Plane group p2 constrains the molecules to lie on a 2-fold axis or, if not, it yields a packing in which the molecules alternate their tilt direction, as for the pmg plane group. Plane group p l dcacribes simple translation packing with no symmetry constraint. (67) For such a packing there are two molecules per rectangular unit cell related only by pure translation of (I + b)/2 along the diagonal. The packing may be more conveniently dtacribed by plane group cl, as opposed to p l , particularly if a pseudosymmetry element is present. As an example, such a packing probably occurs in the 2-D crystal structure of arachida~nide"*~~ (C19H3,CONH2) as studied by GID. In the unit cell, the molecules are tilted

x

at an angle t = 18' from the vertical along the short a axis and oriented so that the angle 4 (see the inserts in Figure Sa) would be 0'. Thus the plane perpendicular to the hydrocarbon chain axis lies in the ac plane. Such a plane describes a "local" glide plane, relating neighboring CHI groups along the hydrocarbon chain, but it is not a true crystallographic symmetry plane. Although we may describe such a unit cell as p l , the information on the pseudosymmetry is better described in terms of the centered rectangular unit cell. (68) The conditions for possible are hO:h = 2n for plane group pllg. hkh + k = 2n for the plane groups cllm and cl, and Okk = 2n for plane group plgl and p2gm. (69) By comparison, the uncompressed monolayers of hydroxyalkyl esters of eicosanoic acid8' C19H39C02C,HhOH( n = 9, 10) at low temperature on water display GID patterns as well as packing arrangements very similar to thoat of CZ9H&O2H. The GID patterns did not yield any observable peek in qx regions in which the (1,Ol and {OJ) reflections should have appeared. ({Ob, Turner, J. D.; Lingafelter, E. C. Acta Crystallogr. 1955, 8, 549. (71) Turner, J. D.; Lingafelter, E. C. Acta Crystallogr. 1955, 8, 551. (72) The vector perpendicular to such a distorted glide plane lies parallel to the bc plane, which would be consistent with retention of a rectangular unit cell. Distortion from pure glide symmetry by rotation of all the molecules, and concomitantly the "glide* plane, about a vertical axis by an angle d would induce an angle 6 between the b axis and the vector perpendicular to the pseudoglide plane. Such a distortion would impose no intrinsic constraint on the unit cell angle y to retain a value of 90'. (73) In carboxylic acid crystal structures, where the C,CaC02 system is planar, the antiplanar C & , M conformation has not yet been nported; only the synplanar conformation has been observed. This preference has been interpreted in terms of intramolecular (74) Leiirowitz, L.; Schmidt, G. M. J. Acta Crystalfogr.1965,18, 1058. (75) Dunitz, J. D.; Strickler, P. In Structural Chemistry and Molecular Biology; Rich, A.. Davidson, N., Eds.;Freeman: San Francisco, 1968; p 443. (76) Leiserowitz, L. Acta Crystallogr. 1976, 832, 775. (77) An estimate of the libratory motion of long chain amphiphiles on water at a temperature of -5 'C can be gleaned from the GID data of the unwmpreased monolayers of C,,HMIOH (n 30,31). Analysis of the data78 yielded an average value for the three alcohol compounds of Uxr = 0.07 A2, namely, a root mean square amplitude of motion of 0.26 A. This value is in the same range as that obtained for the hydrocarbon chain of 3-D crystal structures of N - ( 2 - h y d r o ~ y e t h y l ) s d ~ ~ m (CH3(CH2) i d e ~ ~ &ONH(CH2)20H)and n-hexatriacontanesO (n-C,H,,) at room temperature. On the assumption that the in-plane motion of the molecules is taken up primarily by libration about the molecular axis, the root mean square amplitude of libration 530'. (78) Wang, J.-L.; Leveiller, F.; Jacquemain, D.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. Manuscript in preparation. (79) Dahl€n, B.;Pascher, I.; Sundell, S.Acta Chem. Scand. 1977, A31, 313. (80) Boistelle, R.; Simon, B.; P€pe, G. Acta Crystallogr. 1976, 832, 1240. (81) The symbols used for the dfffmnt phases are in accordance with those of Stiillberg-Stenhagen and Stenhagen.82 (82) Stilllberg-Stenhagen, S.;Stenhagen, E. Nature 1945, 156, 239. (83) Bibo, A. M.; Peterson, I. R. Adv. Mater. 1990, 2, 309. (84) Wang, J.-L. Work in progress. (85) Majewski, J. Work in progress. (86) Weinbach, S.P.; Jacquemain, D.; Leveiller, F.; Lahav, M.;Leiserowitz, L.; Kjaer, K.; Als-Nielsen, J. Manuscript in preparation. (87) Hartman, P.; Bennema, P. J. Cryst. Growth 1980,19, 145. (88) Hartman, P. J. Cryst. Growth 1980, 49, 157. (89) Eisenstein, M.; Hirshfeld, F. L. Acta Crystallogr. 1983, 839, 61.

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Molecular Propertles of the MgO Surface Alexander L. Shluger,*Tt Julian D. Gale, and C. Richard A. Catlow The Royal Institution of Great Britain, 21 Albemarle St., London WIX 4BS,U.K., and University of Latvia, 19 Rainis bulv., Riga, Latvia (Received: June 4, 1992; In Final Form: September 1, 1992)

Properties of the MgO surface and of its interaction with H2are explored using both semiempirical and ab initio Hartree-Fock techniques. Special attention is paid to the properties of the MgO molecule and to its W i o n a i " the surface and interaction with step and kink sites. Hartrce-Fock calculations indicate that such molecules provide effective sites for low-energy H2 dissociation with two possible channels corresponding to the formation of H M g - O H or H 2 0 Mg. However, the stability of the latter channel is not supported by multideterminantal calculations in which correlation effects are included.

+

IatdUCtiOll

It is well-lolown that the chemical activity of atoms on a surface is s w y dependent on their coordination numbs, yet knowledge 'University of Latvia.

of these effects is often imprecise. This paper reports a detailed investigation of this problem for a topical yet relatively simple system, namely magnesium o x i d t a highly ionic material with effective ion charges close to f2,1*2 with t h e second electron on the oxygen ion being localized by the crystalline potentiaL1v3 The

0022-3654/92/209610389$03.00/0 0 1992 American Chemical Society

10390 The Journal of Physical Chemistry, Vol. 96,No. 25, I992 change of coordination number of the oxygen ion from six in the bulk to five on the (100) surface and four at the edge of the infinite step on the (100) surface results in its polarization but does not lead to a tigniilcant electron density redistribution.w In contrast, the chemical bond in the MgO molecule is much more covalent than in the bulk of the crystal and the effective charges on the ions comprising the molecule are close to f1 Therefore it seems likely that two- or three-coordinated oxygen ions on the surface of M may have chemical properties intermediate to that shown by 0 - and 0-ions. From a structural point of view, the two-coordinated oxygen on the (100) surface of MgO may be represented by the MgO molecule adsorbed on the plain surface. Consequently, the molecule attached to a ledge or kink on the (100) surface corresponds to the three- or four-coordinated case. Although the concentration of individual molecules on the plain terraces of the real surface at equilibrium conditions is most probably small, the concentration of ledges, kinks, comers, and molecular clusters very much depends on the method of surface preparation and may be quite high! These surface imperfections should exhibit some molecular properties which we aim to demonstrate in this paper using quantumchdcal techniques. Our strategy is to probe the chemical properties of different sites of the surface of MgO by studying their interaction with the H2 molecule. The related and important question of the mechanisms of MgO molecular diffusion across the surface of the oxide is also considered in detail. The intcracticm of the hydrogen molecule with the (100) surface of MgO has received considerable recent attention for several reasons. Magncaium oxide is one of the simplest ccramic materials which nevertheless has important potential applications. As a catalyst it is responsible for the oxidative coupling of methane to produce C2 hydrocarbon^.^.^ It has potential applications as a singlecrystal insulator and tunnel barrier in device structures.l0 MgO is also usually considered as a prototype model oxide often serving as an initial subject for applications of new experimental and theoretical techniques. Hydrogen, in turn, is the simplest molecule which is widely used to probe perfect crystal surfaces as well as the chemical activity of various surface defects. In particular,diffractive and inelastic Scatteringof H2have been used to study the perfect MgO surface structure."J2 These studies as well as recent theoretical calculation^^^ have shown that the H2 molecule has a small adsorption energy and does not dissociate on the perfect (100) surface. Experimental studies performed using a temperature-programmed desorption method', have shown that highly dispersed polycrystalline surfaces of MgO have a series of active sites for hydrogen adsorption. As suggested in ref 14 all of these sites have a common structure of an O-Mg pair with low coordination numbers on which H2 is heterolytically dissociated. According to Ito et ala1,a pair of three-coordinated surface atoms are the most probable active sites for the H2 heterolytic dissociation. Four-coordinated surface atoms may also participate in this adsorption, but with a lower interaction energy. The interaction and dissociation of hydrogen with MgO in low coordination numbers has recently been investigated theoretically by employing a (MgO), cube as a model for the surface, leading to results in accord with the above experimental ~bservations.~~ Reactions of Hz with point defects on the (100) surface of MgO have also been considered in a series of theoretical studies.1620 It was concluded that the interaction of H2 with the anion vacancy, the self-trapped hole (0ion on the surface), the V- center (hole trapped near a cation vacancy), and the V center (two holes trapped near a cation vacancy) is accompanied by exothermic dissociative chemisorption of Hp19.z0 High chemical activity of 0- toward the H2 molecule has been shown by experimental studies of gas-phase kinetia of the reaction of the 0-ion and NaO molecule with H2,21 Recent quantumchemical calculations of the interaction of gas-phase MgO, AlO, and LiO molecules with methane have demonstrated their ability to abstract a hydrogen atom to form methyl However, the experimentsmade for the gas-phase reactions between the AI0 and the H2 and CH4Ubmolecules have shown that the hydrogen

.'

P

Shluger et al. abstraction reaction has a very low reaction rate. There are several additional reasons prompting an interest in the behavior of MgO molecules on the surface of MgO. First, since the chemical bond in the MgO molecule is much more covalent than in the bulk it may be considered as a close analog of the LP-0- center on the surface, which is widely believed to be one of the active sites of the Li/MgO catalyst.23 Secondly, although water is experimentally proven to be an important intermediate product generated during the process of catalytic synthesis of the mechanisms of its production are not completely clear. Gas-phase experimentsz1have shown that water is one of the products of the chemical reaction between the NaO molecule and Hp It therefore seems plausible that the same reaction could also take place between H2 and MgO molecules both in the gas phase and when MgO is initially adsorbed on the surface. Hydrogendeuterium exchange, as studied in detail by Boudart et al.,z5 is also promoted by the surface of MgO. Gu and have proposed a mechanistic scheme based on their experimental results which requires the dissociativec h e " p t i o n of H2/D2 on a magnesium and oxygen adjacent to a surface hydroxyl group. Such a reaction is likely to be more favorable if the MgO entity comprises a surface molecule. Furthermore, it is of interest to study how such reactions are affected by the particular position of the MgO molecule on the surface, i s . the coordination of the oxygen ion. A further incentive for the study concerns the need for information on the mechanisms of diffusion and reaction of MgO and other ionic molecules on ionic surfaces in order to improve understanding of low-temperature growth of ionic crystals by molecular-beam The present paper therefore presents a comparative study using theoretical methods of the electronic structures and properties of the MgO molecule in different environments on the (100) surface of MgO. In particular, we consider the mechanisms for its diffusion and interaction with the hydrogen molecule. In addition we compare the properties of the M g 0 molecule with those for the LiCl molecule adsorbed on the (100) surface of MgO. Our calculations considerably extend the theoretical investigation of these systems both by the use of embedding techniques with large clusters and by employing multideterminantal quantum mechanical techniques. Our general approach is fmt to undertake a qualitative analysis of the subject using both a semiempirical quantum-chemical method (employing the CLUSTER code) and an embedded molecular cluster model (employing the EMC technique). In order to achieve more quantitative results we have performed an ab initio study of the electronic structure of the MgO molecule and its interaction with H2. In particular, the role of electron correlation has been examined in the latter study by extending the techniques beyond the Hartree-Fock level. The plan of the paper is as follows. First we will discuss the methods of calculation. This is followed by the results of semiempirical calculations of the adsorption of MgO and LiCl molecules on the (100) surface of MgO, and of the mechanisms and barriers for their diffusion; we also give preliminary results on their interaction with the HZmolecule. Then we discuss the results of ab initio calculations on the interaction of the H2 molecule with the MgO molecule, which we follow with a general discussion and conclusions. Both the adsorption and chemical reactions of molecules on surfaces are complex processes, which include different kinetic For example, stages, requiring individual thsomical the Monk-Carlo simulation technique may be successfully applied to molecular aggregation in order to study the problem of comm e n s u r a t t e covhBgc.30 Energy dissipation during the adsorption of molecules and their subsequent chemical reactions is another Micult problem, which is especially important where the reaction rate is c o n ~ m e d .In ~ ~this paper we focus mainly on the calculation of adiabatic barriers for diffusion of the individual MgO and LiCl molecules on the surface and their reaction with the H2 molecule. These values may be used in

Molecular Properties of the MgO Surface

The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10391

Embedded cluster

Periodic slab of frozen ions

Figure 1. Illustration of the embedding of the molecular cluster in the five-layer slab of frozen ions.

further simulations and in analysis of the kinetics of real processes happening on surface. For these purposes two quantum-chemical methods and com-, puter codes were employed. The study of the MgO and LiCl molecules on the surface of MgO as well as preliminary calculations of their interaction with the H2 molecule were performed using the CLUSTER method and code.32 The ab initio calculations of the electronic structure of the MgO molecule in the singlet and triplet states were performed with GAUSSIAN90,33 while the study of the adiabatic potential energy surface for the interaction of MgO with the H2 molecule were made using GAMESS.34 The CLUSTER code has been described in several recent publications. Therefore we will focus our discussion only on the details which are essential for the present study. The program employs both the embedded molecular cluster (EMC) model35 and the periodical large unit cell (LUC) method36and is based on the intermediate neglect of differential overlap (INDO) approximation of the unrestricted HartreeFock-Roothaan meth0d.3~ It allows us to determine the electronic structure of a quantum mechanically described cluster or unit cell containing several tens of ions. The latter is essential for studies of the atomic and electronic structure of complicated defects and mechanisms of ion diffusion. Recent calculation^^^^-^^ have shown that it gives reliable results for point defects in ionic crystals, where the correct representation of the crystalline potential produced by the environment of the defect under study is most important. However, it employs a minimal valence Slater basis set and uses a singledeterminantal approximation for the wave function and therefore is able to give only preliminary results for adiabatic paths and for the barriers of dissociative processes. The calculation scheme of the CLUSTER code and the parameterization of the INDO method are described in ref 32. The procedure for a defect study on a crystal surface using the CLUSTER code includes the following steps: (i) Calculations of the electronic structure, relaxation and rumpling of the perfect surface are made using periodic boundary conditions where the crystal with the surface is treated as a slab comprising several atomic planes. For this purpose the LUC method is used, as both sides of the two-dimensional infinite slab are equivalent. It is therefore necessary for the slab to be thick enough to reproduce both the bulk and surface properties of the crystal. As has been shown both in our previous semiempirical calculation^^^ and in recent ab initio studies,40a slab comprising 5-7 atomic planes of the rock-salt ionic crystal lattice satisfies these requirements. (ii) A study of defects or adsorbed molecules on the surface may be performed either in the periodic or EMC model. In the first case the defect is periodically translated along the surface$l while in the second calculations are made for a cluster embedded in the slab (seeFigure 1 ) . The atomic structure of the slab outside the cluster is treated as in the first step of the study. The lattice outside the cluster is constructed from the ions carrying the same

TABLE I: Relative Energies and Geometries of Singlet and Triplet MgO singlet-triplet energy bond lengths, A method difference, eV singlet triplet HF/INDO 1.32 1.78 1.93 HF/tzvp 1.85 1.739 1.872 MP2/tzvp -1.28 1.747 1.898 experiment 1.749

basis of atomic orbitals (AOs) as inside the cluster, but with the Lowdin pop~lations~~ of these AOs frozen to those A 0 populations in the slab simulating the perfect surface. The Coulomb interaction with these ions is calculated exactly up to a distance, R, where the Coulomb integral between two interacting ions becomes practically equal to 1/R. The potential of the crystalline field produced by the rest of the slab is then calculated using the Ewald met hod.32 The electronic structure and rumpling of the MgO (100)surface were calculated using the CLUSTER code, the slab model, and the LUC method in ref 32c. They are in good agreement with the results of periodic ab initio Hartree-Fock calculations, using the CRYSTAL code? Both calculations suggest that the surface rumpling is very small, i.e. the cations and anions displace very little from their sites perpendicularly to the ideal surface plane. The same result was obtained in Mott-Littleton calculation^,^^^^^ which also revealed that there is a very small surface dilatation of -0.02a0, (where a. is an interionic distance in the bulk of the crystal which in our CLUSTER calculationsis 2.03 A). However, different experimental techniques yield a much greater variety in their results, although the results of ref 43 yielded a surface rumpling of about 0 . 0 2 in ~ ~agreement with theory. In contrast, experiments on hydrogen diffraction have shown a much larger surface corrugation,exceeding 0.10%. The discrepancies between such results may be explained by the fact that molecular scattering processes are controlled by interactions with the valence electrons, whereas other experimental techniques are more sensitive to nuclear positions. In all the present semiempirical calculations we employed the EMC model. The crystal surface was simulated by a Mg25Ozs molecular cluster comprising two planes of 25 ions and embedded in the slab of five lattice planes (see Figure 1). Steps and kinks on the surface were simulated by molecular islands which were “adsorbed” on the basic Mg25025 cluster and included several (usually -8-10) MgO molecules. We consider that such an approach gives an adequate representation of local interactions between the attaching molecule and steps or kinks on the surface. Although static by nature, it provides additional information useful for the understanding the dynamics of the growth of molecular islands on the perfect surface as a result of the assembling of individual adsorbed molecules.

Results of Semiempirical Calculations In this section we will first discuss the interaction of individual MgO and LiCl molecules with the relaxed (100) surface of MgO and the mechanisms for their diffusion along the surface and attachment to a step or kink. Next we will consider the interaction of the H2 molecule with the individual MgO and LiCl molecules adsorbed on the surface and how this is modified when the molecule binds to a step or kink and ultimately becomes incorporated into one of these surface features. 1. MgO and LiCl Adsorption and Diffusion on tbe Surface of MgO. Although the ground electronic state of the MgO molecule is known experimentally to be a ‘C,singlet in the Hartree-Fock approximation it has a higher total energy than the lowest lying triplet 3Cgstate (Table I). This result was obtained both at the INDO and ab initio levels of calculation employing a triple-{ basis set including polarization functions (tzvp) .45 Inclusion of electron correlation using Maller-Plesset t h e o e to second order results in a greater stabilization of the singlet configuration, making it the ground state by 1.28 eV. The correlation correction also leads to close agreement between the

10392 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992

Shluger et al.

TABLE II: Comparison of the Details of the Adsorption and Diffusion Processes for MgO and LiCl on the Surface of M p barriers for diffusion, eV characteristics of adsorption Figure 2a Figure 2c Re, around Figure around around (X,Y,4, Eads, around eV cation anion 2b a0 cation anion molecule gas surface MgO 1.78 1.91 0: (0.0;0.03;1.09) 0.90 0.22 0.32 0.70 0.32 0.39 Mg: (0.0;0.97;1.06) LiCl 1.98 2.01 C1: (0.0;0.03;1.15) 1.3 0.02 0.33 0.73 0.13 1.07 Li: (0.0;0.97;0.84)

"Fractional Cartesian coordinates refer to the system of axes as shown in Figure 1. TABLE 111: Transition-State Geometries [(x,y,z],so]for MgO and LiCl Diffusing on the Surface of MgO" Figure 2a Figure 2c around cation around anion Figure 2b around cation around anion Mg: (-0.03,1.03,1.06) Mg: (0.53,0.53,1.06) Mg: (0.50,1.43,1.20] Mg: (0.00,1.00,1.06] Mg: (0.00,0.00,1.95] 0: (0.58,0.42,1.09) 0: (-0.08,-0.08,1.10) 0: (0.50,0.57,1.20) 0: (0.00,1.00,1.92] 0: (0.00,0.00,1.09) Li: (0.50,1.47,0.87) Li: (-0.02,1.02,0.84) Li: (0.495,0.495,0.91) Li: {0.00,1.00,0.87) Li: (0.00,0.00,2.24) C1: (0.645,0.355,1.15) C1: (-0.17,-0.17,1.15) C1: (0.50,0.53,1.17) C1: (0.00,1.00,1.81) C1: (0.00,0.00,1.30)

" Fractional Cartesian coordinates refer to the system of axes as shown in Figure 1. calculated and experimental bond lengths for gaseous MgO. Because of the nature of perturbation theory, it is important to check the convergence of the series. Performing single-point calculations at the MP2/tzvp optimized geometries we have examined both the third- and fourth-order corrections. At the MP3 level the triplet state again becomes the ground state by 0.02 eV, though this is much smaller than at the Hartree-Fock level (1.85 eV). Further inclusion of fourth-order terms (MP4(SDTQ)) preferentially stabilizes the singlet state by 1.77 eV. Although the series is far from converged, the trend is toward the increasing stability of a singlet ground state. In the subsequent semiempirical calculations the MgO molecule will be considered in this electronic configuration. The bond lengths of both MgO and LiCl molecules in the gas phase are less than the interatomic distance in bulk MgO (see Table 11). Therefore when the molecules are adsorbed on the surface they do not reside directly above the lattice sites of the layer below, but adopt a distorted atomic configuration as shown in Figure 1. The coordinates of the molecules are given in Table I1 relative to the magnesium ion of the surface plane nearest the oxygen or chlorine, in the two respective cases, as well as the adsorption energies. The displacementsof the surface ions caused by the adsorption of the molecules are negligibly small. We now consider the diffusion of the MgO and LiCl molecules on the (100) surface of MgO, for which three mechanisms were considered in this study, as depicted in Figure 2. The calculated adiabatic barriers for the elementary steps of diffusivejumps are presented in Table 11, while the transition-state geometries are given in Table 111. The most effective mechanism for both molecules involves two successive 90' rotations parallel to the surface plane as shown in Figure 2a. In each stage of the migration by this mechanism one end of the molecule remains close to a lattice site while the other end traverses the square of surface ions of the layer below. The second pathway investigated (Figure 2b) involves the simultaneous translation of the molecules diagonally across the surface, while the third mechanism (Figure 2c) requires one atom to rotate 180' about the other out of the surface plane in a manner resembling a cartwheel. Although the qualitative features of all three mechanisms are clear, there are several particular points which deserve attention. As can be seen from a comparison of the values of the barriers for diffusion of both molecules, Mg+ and Li+ ions interact more strongly than 0-and C1- ions with the surface of MgO as they form the pivotal ions. It should also be noted that there is a close agreement between the 0--(Mg2+),,,fa, equilibrium distances obtained in the present work and those in a periodic ab initio study of the adsorption of S i 0 on the (100) surface of Mg0.41 In both these calculationsthis distance is -2.2 A. Secondly, we note that in the transition state for the 90' reorientation mechanism shown in Figure 2a the migrating ion is close to the point located above

Transition state

a

b

n

-0 I

I

1 C

Figure 2. The three mechanisms of diffusion of molecules on the surface of MgO: (a) successive 90° reorientationsin the surface plane with the relaxation of the ions below indicated at the transition state, (b) translation across the surface, (c) 180' out-of-plane rotation. Open circles indicate the final positions of ions subsequent to the diffusive step shown.

the center of the square comprising the four nearest ions on the surface, where the crystallinepotential is equal to zro. To achieve this saddle point configuration there must be a strong displacement of the molecule along the (110) axis parallel to the surface. Furthermore, there is significant lattice relaxation at the barrier points for molecular diffusion by the "90'" reorientation mechanism (see Figure 2a). The magnitudes of the displacements of the two cations and anions, nearest to the moving ion, are -0.033ao, where a, is the equilibrium nearest neighbor distance for the crystalline material. Our calculations show that diffusion above a rigid, nonrelaxing lattice would require the molecules to overcome barriers of approximately 1.5 times the height of those shown in Table 11. Finally we note that the calculated adiabatic barriers for the mechanisms shown in parts a and c of Figure 2 are quite close, while that for the mechanism in Figure 2b involves a significantly higher barrier. This indicatesthat the actual process

Molecular Properties of the MgO Surface

The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10393

TABLE I V Oxygen Charge as a Function of the Surface Environment Calculated at the INDO Level" step plain position surface I I1 I11 IV V I coordination 2 2 2 3 3 4 2 oxygen -1.05 -1.05 -1.20 -1.30 -1.35 -1.73 -1.05 charge

kink

I1

I11

IV

3 -1.25

3 -1.50

4 -1.57

Reference numbers correspond to the geometries indicated in Figure 4. Cluster boundarv

a

a

b Figure 3. Embedded surface clusters used to model (a) a step and (b) a kink on the 001 surface of MgO. Shaded blocks indicate the elevated ions representing the appropriate surface feature.

of molecular diffusion on the surface is likely to be complex as there are two energetically feasible mechanisms, and at high temperatures even the third type of diffusive jump may be possible. The calculated barriers for diffusion of both MgO and LiCl molecules are low, and therefore one can suppose that once they have been adsorbed onto the surface they will be mobile even at relatively low temperatures. In a manner which depends on their concentration, they will cluster and diffuse to the steps and kinks, which will consequently grow. In fact, very good growth of MgO by molecular-beam epitaxy has been observed even at 140 K.l0 As has already been mentioned, we considered clusters, adsorbed on the (1 00) surface and containing several MgO molecules, as an example of the surface inhomogenities. Indeed, the structure of these clusters reflects both the crystal properties of the adsorbent and the molecular properties of the component molecules (see for example the discussion in ref 28). The important feature of the singlelayered clusters of molecules adsorbed onto the surface is that their structure and electron density distributionschange gradually from the edge to the center, reflecting changes in the coordination of the ions. In this paper we report the results of calculations performed for the clusters schematicallydepicted in Figure 3. The first of these (see Figure 3a) was used in order to simulate a step on the surface, whereas that shown in Figure 3b simulated a kink. The optimum structures of both surface defects were calculated by energy minimization. As one would expect, their geometries are somewhat distorted with respect to those found for the bulk material. In fact, the cluster

b Figure 4. Geometries of the MgO molecule at which the charge distribution has been calculated in the proximity of (a) a step and (b) a kink.

shown in Figure 3b more resembles a collection of molecules, although their z-coordinates are much closer to the equilibrium lattice separation than those for the individual molecule. We make the assumption that the central, most highly coordinated part of the clusters correctly reproduces the local interaction of the approaching molecule with a more extended step or kink. We should note that the effective charges of these ions (marked 1 and 2 in the figures) are much closer to those on the perfect surface than on the boundary of the cluster. A Lowdin population analysis showed that the charges of the edge, three-coordinated oxygens are -1.5 e, while those for the four-coordinated ions are -1.75 e. The strong dependence of the effective charge of the oxygen ion on its coordination number is one of the most important characteristics of small molecular clusters adsorbed on the surface, which has to be taken into account in Monte-Carlo and molecular dynamics simulations of these systems. This may be illustrated by the example of the individual molecule, approaching the cluster. The effective charges of the oxygen ion in the molecule at different points of its path from the position far from the cluster to that corresponding to incorporation into the step (see Figure 4) are collected in Table IV. Although these values may be overestimated since we use a localized valence basis set, the qualitative trend is expected to be reliable. We will return to this point when discussing the interaction of H2 with the MgO molecule. From an energeticpoint of view, the two situations, i.e. approach .of the molecule to either the step or the kink, are different. We have calculated the barriers for the final jump of the molecule before it becomes part of the kink or attached to the step (see Figure 3). The trend in both cases is the same, namely the barriers

10394 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992

8

Shluger et al.

O H

0 0-

I I I I

0

Mg2+

@!J 0-

e

I

I

I

I

- 0 - L L e -

-0-LL.b

f

I I

I

b C

I

I I

0 I I

b d Figure 5. Dissociative pathways for hydrogen on a surface adsorbed molecule of MgO yielding (a-d) MgH-OH, (e-g) H 2 0 + Mg.

are much lower than those for the diffusion of the molecule on the nondefective surface; however, for the kink it is almost vanishingly small. The final energy gain accompanying the attachment of the molecule to the step is 1.2 eV and for the kink rises to 2.5 eV. These results indicate that on associating with the kink the molecule is trapped and becomes immobilized. In contrast, the molecule can still diffuse along the step, but with a much higher activation energy than for migration across the plain surface. The lowest barriers are for diffusion of the molecule by the in plane reorientation mechanism shown in Figure 3. The rotation from the surface around the Mg ion of the molecule requires it to overcome the barrier of 1.0 eV; the analogous rotation around the oxygen ion requires 1.3 eV. Therefore the diffusion of MgO along the steps may take place only at relatively high temperatures. This is not surprising since the melting temperature for MgO is known to be very high (about 3000 "C). However, a "gas" of the molecules adsorbed on the surface in thermodynamic equilibrium with surface inhomogeneities may exist at much lower temperatures, since the adsorption energy of the individual molecule on the surface is -0.9 eV. Monte-Carlo simulations are needed in order to study this point in great detail. 2. Hydrogen Interaction with MgO Molecules Adsorbed onto the Surface of MgO. As discussed earlier, the hydrogen molecule has only a small adsorption energy on the plain (100) surface of MgO. Therefore in studying its interaction with the MgO molecule adsorbed onto the surface we considered only the case when H2 attacks the MgO molecule from the gas phase perpendicularly to the surface. In order to simplify the search for a transition state we followed the same procedure in all our cal-

--

culations of the adiabatic energy surface for H2 interaction with the MgO molecule in different positions. First we minimized the total energy of the system for the configuration corresponding to the H2molecule approaching the oxygen ion of the MgO molecule in the plane, containing both molecules and perpendicular to the surface (see Figure 5a). Next we kept the hydrogen closest to the oxygen fmed and simultaneously allowed the bond length and orientation of the H2 molecule to vary as shown in Figure 5a. If the barrier occurred on the corresponding adiabatic curve we performed a more detailed study of the barrier region scanning the energy surface at different distances from the MgO molecule parallel to its axis. Subsequently the geometry of the product was optimized. These calculationswere performed for the H2 molecule interacting with the MgO molecule in a variety of locations, as illustrated in Figure 4a, adsorbed on the plane surface, attached to the step in position IV, and to the kink in the positions I11 and IV, as well as with the MgO molecular unit incorporated into the step (position V in Figure 4a) and the nondefective surface. The results of these calculations may be summarized as follows: (i) In every case we observed a very strong polarization of the hydrogen molecule as it approaches the MgO molecule on the surface. The 0-H distance corresponding to the total energy minimum when H2 is above the oxygen ion and oriented perpendicularly to the surface (see Figure 5a) is in all cases -0.93 A, i.e. close to the equilibrium distance in the free OH- ion. (ii) Further stretching of the H-H bond occurs, except when above the edge of the step and above the nondefective surface, leading to the formation of the OH-MgH configuration, as shown in Figure 5a, without any energy barrier. According to our results,

Molecular Properties of the MgO Surface dissociation of the H2 molecule interacting with the edge of the step or the plain surface, despite the strong polarization, has an energy barrier that is close to the molecular dissociation energy of -4.0 eV. (iii) In the HC&MgH configurationthe Mg-O bond remains intact, although the interaction with the H2 molecule lengthens the bond by -0.14 A. The effective charges of the hydrogen atoms, bonded to the oxygen and magnesium ions of the molecule, are approximately equal (with a value of 0.35 e). There is therefore a considerable Coulombic interaction between these ions and the nearest surface ions, which stabilizes this configuration on the surface. The Mg-H equilibrium distance is close to 1.3 which is smaller than the equilibriumdistance in the free MgH' molecular ion of 1.65 A 4 2 (1.53 A in our calculations). (iv) In order to study the possibility of the formation of water in the same series of reactions, we calculated the section of the adiabatic potential energy surface corresponding to the classical trajectory of the hydrogen atom schematically shown in Figure 5e. It represents the rotation of the Mg-H bond around the Mg ion, which was held fmed. This path brings the second hydrogen atom toward the oxygen ion and generates a configuration which resembles the water molecule. Geometry optimization was performed when this configuration was roughly achieved. To follow this path the system has to overcome an energy barrier of about 1 eV, which is located at the intermediate point of the M e H bond rotation trajectory, shown in Figure 5e. After this, the system approaches the much deeper energy minimum, corresponding to the formation of the water molecule and the Mg atom. The energy of the configuration corresponding to the optimized geometry of the water molecule with the oxygen ion kept fixed in the same position, as in the HO-MgH configuration, is calculated as -4.2 eV lower than the energy of the latter configuration when the present semiempirical techniques are employed. Rather different results are obtained when ab initio methods including electron correlation are employed (discussed later). The final question, which we can address employing our semiempirical technique concerns the difference between the interaction of the hydrogen molecule with the MgO and the LiCl molecules on the surface. The study of the interaction of the hydrogen molecule with the individual LiCl molecule adsorbed on the plain (100) surface of MgO was performed in an analogousmanner to the previous study with Mg0. In addition to the adiabatic path shown in Figure 5a, we also considd the situation when the H2 molecule approaches the LiCl molecule while oriented parallel to the LiCl molecular axis. In both c a w the LiCl molecule attracts and polarizes the H2 molecule, but neither H2 dissociation nor chemical bond formation with LiCl have been o k e d . This is hardly surprising since both Li+ and C1- ions have completely occupied electronic shells. This result reveals that the polarization of the H2 molecule is not the main reason for its dissociation. It also agrees with the previous finding which indicated that the H2 molecule does not d w i a t e , interacting with the edge of the step or with the plain (100) surface, where the oxygen ion has the effective charge close to -1.8 e. In the M g 0 molecule both Mg+ and 0-ions have open electronic shells. One of the particular manifestations of this peculiarity of its electronic structure is the proximity of the singlet and triplet states. As a result, one of the channels of the reaction between the H2 and MgO molecules corresponds to the situation when both 0-and Mg+ each form chemical bonds each with a hydrogen atom. On the other hand, as is proved by experimenf2' the 0- ion and the NaO molecule have very similar chemical properties with respect to the H2 molecule. In both caw the two reaction channels, hydrogen atom abstraction and water molecule formation, were obacrved. These reactions were attributed solely to the chemical activity of the 0-ion.*' It seems plausible to suppose that the same reactions could be characteristic also for the [Li]O center on the surface of MgO which is essentially Li+-O- incorporated in the surface. Although not considered in this paper, hydrogen abstraction by the similar V- and V centers on the surface of MgO has been predicted in

The Journal of Physical Chemistry, Vol. 96, NO. 25, 1992 10395 previous ab initio c a l c u l a t i ~ n s .The ~ ~ ~second ~ ~ channel, corresponding to the formation of the water molecule, is much more difficult to consider because polarization of the surface by the defect and the diffusion of the water molecule will play an cwntial role in the calculation of the reaction energy. The results therefore suggest that there may be two different reaction pathways for the H2 molecule with the MgO molecule on the surface of MgO, whose chemical activity depends on the particular location of this species. It is, however, desirable to perform more detailed studies with the aid of ab initio quantum-chemical methods with particular emphasis on the effects of electron correlation. The latter are most important in the reactive region of conformation space where the separation of the two channels of the chemical reaction MgO H2apparently takes place. Some of the results of these calculations are presented in the next section.

+

Results of ab Initio Calculations While it is possible to consider the MgO molecule on the surface of magnesium oxide at the INDO level of approximation, incorporating an accurate description of the interaction with a periodic surface, this is not currently feasible at the ab initio level. However, the results of the semiempirical calculations indicate that the surface only constitutes a weak perturbation to the electronic structure of the adsorbed molecule as the electric field decays exponentially as a function of the distance above the surface. The influence of the surface is strongest in the final geometry of HMgOH after hydrogen dissociation as the hydrogens incline toward the nearest surface ions, while the transition state will be less affected. Hence in this ab initio study we have initially considered the isolated MgO molecule in the gas phase to complement the information available from the semiempirical calculations. All of the calculations have been performed using a triple{ basis set with polarization functions (tzvp)? In addition, selected calculations were run utilizing the 3-21G basis setiCf,4'*@as chosen in a previous theoretical inve~tigation,'~ to allow an assessment to be made of the effects of basis set quality. All results have been corrected for basis set superposition error (BSSE)using a full counterpoise c o r r e c t i ~ n . ~ ~ In accord with the INDO results there are found to be two reaction pathways for hydrogen with singlet magnesium oxide at the HartreeFock level, the course of the reactionbeing determined by the direction of approach of the hydrogen molecule. If the approach is at 90° to the Mg-O bond above the oxygen then the product is HMgOH, while hydrogen interaction along the direction of the Mg-O bond yields magnesium and water. In both cases there is no barrier to hydrogen dissociation. Formation of HMgOH is predicted to have the largest heat of reaction which is 498.3 kJ mol-' as compared to 428.9 kJ mol-' for the alternative process. The earlier discussion of the relative stabilities of the singlet and triplet states of MgO highlights the importance of electron correlation in this system. Consequently it is necessary to investigate its effect on the interaction with hydrogen. Given the uncertain convergence of the Maller-Plesset expansion, we have chosen to use CASSCFSofor this purpose. While CASSCF only yields a small percentage of the full correlation energy, due to the restricted number of determinants that may be included for computational reasons, it produces a reliable description of the changes in electronic structure along a reaction pathway providing the active space encompasses all important Slater determinants. An active space spanning the four highest occupied orbitals and the four lowest unoccupied orbitals was found to be adequate, resulting in 1107 symmetry-allowed determinants. The reaction pathway for hydrogen and magnesium oxide including CASSCF is illustrated in Figure 6, for both tzvp and 3-21G basis sets. The most signifcant difference between the two basis sets is the existence of a physisorbed complex in the 3-21G calculation when the hydrogen molecule is 2.4 A from the oxygen. The subsequent transition state for hydrogen d i d a t i o n is only 3.4 kJ mol-' higher in energy than the reactants leading to a small

10396 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992

Shluger et al.

4

3-21G

,\

0.929A

155.0" Q

I 1.253A I

H, .?..MgO H,

?:A

37 1.03 KJMol-1

MgO

CASSCF 1 3 - 21 G H - Mg - 0 - H

b

'

TS 1.439A

\ \

70.2"

CASSCF 1 tzvp

L

H - Mg - 0 - H Figure 6. Ab initio energy profiles for the interaction of hydrogen and MgO in the gas phase: (a) CASSCF/3-21G, (b) CASSCF/tzvp.

overall barrier, assuming the energy of the physisorbed state is not dissipated by an alternative process. The higher quality tzvp basis set gives a barrier of 72.6 kJ mol-' and a significantly different transition-state geometry (Figure 7) in which the hydrogen molecule is further from MgO, though it is closer to a parallel arrangement of bonds. With the inclusion of correlation, the second reaction pathway to yield magnesium and water is no longer observed regardless of the orientation of the hydrogen during the saddle point, indicating it to be much higher in energy. Both the differences in the energetics and geometries obtained from the 3-21G basis set demonstrate its inadequacies for calculations involving electron correlation due to the poor description of the virtual orbitals. This may explain the low barrier calculated for hydrogen dissociation on an MgO cube obtained in an earlier study.I5 Analysis of the CASSCF wave function at the transition state reveals that there are two dominant Slater determinants. The Hartree-Fock solution (occupation pattern in active space 2 2 2 2 0 0 0 0) contributes 79% of the total wave function, while a second determinant (2 1 1 0 2 2 0 0) represents 16%. The second wave function represents a state in which the hydrogen molecule antibonding orbital occupancy increases and the magnesiumhydrogen bond begins to form. To improve the quantitative accuracy of the evaluation of the activation energy and the heat of reaction we have performed CASSCF with second-order CI for the CASSCF/tzvp optimized geometries in order to obtain a greater degree of the true correlation energy. The CI expansion, involving single and double excitations (CI active space included orbitals 8-36), employed all of the determinants of the CASSCF wavefunction as reference states. Inclusion of CASSCF second-order CI leads to a lowering of the activation energy to 62.1 kJ mol-', which is very low relative to the experimental binding energy of hydrogen which is 435.8 kJ mol-', while the heat of reaction becomes -295.2 kJ mol-' as compared to -380.0 kJ mol-' with just CASSCF. The overall effect of electron correlation is to lower the energy associated with the formation of HMgOH by stabilizing the singlet state of MgO.

+

Figure 7. Transition-state geometries for the dissociation of hydrogen on molecular MgO: (a) CASSCF/3-21G, (b) CASSCF/tzvp.

The results confirm that magnesium oxide molecules should readily promote the dissociation of hydrogen. The above ab initio calculations confirm the validity of the parameterization of the INDO scheme and its ability to mimic correctly more accurate Hartree-Fock results. However they also emphasize the limitations of single-determinant methods when concerned with reactive processes. In particular, the second channel involving water formation appears to be unimportant when correlation is included in the calculations.

Discussion and Conclusions The basic qualitative conclusions of this study may be formulated as follows: (i) The reaction of H2 with the MgO molecule in the gas phase and with the molecule adsorbed on the (100) surface of MgO has two possible product channels: (1) heterolytic dissociation of the hydrogen molecule and (2) water molecule formation. If the reaction proceeds by the first channel the Mg+-O- chemical bond remains intact and the products of the dissociation HMg+-OHare stabilized by the surface. Although Hartree-Fock calculations indicate that the latter channel is exothermic, this reaction becomes kinetically disfavored when electron correlation is included in the calculations. (ii) The chemical activity of the MgO molecule on the surface depends on its environment. In particular, the MgO molecule retains its chemical activity with respect to the hydrogen molecule until it incorporates in the edge of the step on the surface. Thus the MgO molecules attached to the ledges or to the kinks may serve as the active sites for the heterolytical dissociation of hydrogen molecules on the surface. Several questions remain unsolved, however. In particular, as has been shown in our ab initio calculations of the interaction between the H2and MgO molecules, there is a considerable barrier for the hydrogen heterolytic dissociation. It is not clear to what extent the magnitude of this barrier could be affected if the M g 0 molecule is attached to the ledge or to the kink. The same question arises in the case of the water molecule formation. Much more extensive ab initio calculations beyond the Hartree-Fock level are needed to address these questions. The properties of the defective MgO crystal surface discussed in this paper demonstrate characteristics more closely related to those of molecular magnesium oxide rather than those of the bulk material. The same properties may be attributed to other binary oxides with the fcc structure, such as CaO, BaO, or NiO.

Molecular Properties of the MgO Surface However, the role played by the cation is still not absolutely clear. In particular, according to the experimental dataZZb for NaO and AlO, and the results of our calculations for MgO, the bamer for the hydrogen abstraction reaction between the Me0 (Me = Na, Mg, Al) and H2 increases along the row Na-Mg-Al. This question clearly needs a more detailed study. Finally we should note that if the reaction of MgO + H2were to proceed by the second channel leading to the water molecule formation, the Mg atoms, which remain on the surface, could react with the O2molecules present in the surrounding gas phase or adsorbed on the surface. This is one of the possible mechanisms whereby MgO molecules may be renewed on the surface during catalytic reactions. Acknowledgment. A.L.S.is grateful to the Royal Society, the Royal Institution of Great Britain, and to the Canon Foundation in Europe for financial support. J.D.G. would like to acknowledge I.C.I. Chemicals and Polymers Ltd. and SERC for financial support. The authors would like to thank Drs. R. W. Grimes and G. J. Hutchings for valuable discussions. Registry No. H1,1333-74-0; MgO, 1309-48-4; LiCl, 7447-41-8.

References and Notes (1) (a) Caus6, M.; Dovesi, R.; Pisani, C.; Roetti, C. Acta Crystallogr. 1986, 842,247. (b) C a d , M.; Dovesi, R.; Pisani, C.; Roetti, C. Phys. Reo. 1986,833, 1308. (c) Pandey, R.; Jaffe, J. E.; Kunz, A. B. Phys. Reu. 1991, 843,9228. (2) Abarenkov, I. V.; Antonova, 1. M. Phys. Status Solidi B 1979,93,315. (3) Abarenkov, I. V.; Antonova, I. M. Phys. Statu Solidi 8 1979,92,389. (4) CausB, M.; Dovesi, R.; Pisani, C.; Roetti, C. Surf. Sci. 1986, 175, 551. (5) C a d , M.; Dovesi, R.; Kotomin, E.; Pisani, C. J . Phys. C SolidState Phys. 1987, 20,4983. (6) (a) Abarenkov, I. V.; Antonova, I. M. Sw. Phys. Solid Stare 1986, 28,2020. (b) Abarenkov, I. V.; Antonova, I. M.; Frenkel, T. Yu. Phys. Chem., Mech. Surf. 1990, 6, 66. (c) Abarenkov, I. V.; Frenkel, T. Yu. J . Phys.: Condens. Matter 1991. 3. 3471. (7) Baukhlicher, C.'W., Jr.; Lengsfield, B. H., III; Liu, B. J. Chem. Phys. 1982,77,40a4. (8) Hargreaves, J. S.J.; Hutchings, G. J.; Joyner, R. W.; Kiely, C. J. Catal. Today 1991, 10, 259. (9) Hargrcaves, J. S.J.; Hutchings, G. J.; Joyner, R. W. Nature 1990,348, 428. (10) Yadavalli, S.;Yang. M. H.; Flynn, C. P. Phys. Rev. 1990, B41.7961. (1 1) Kolodney, E.; Amirav, A. Surf. Sci. 1985, 155, 7 15. (12) Rowe, R. G.; Ehrlich, G.J. Chem. Phys. 1975,63,4648. (13) Karimi, M.; Vidali, G.Phys. Rev. 1989,839, 3854. (14) (a) Ito, T.; Kuramoto, M.; Yoshioka, M.; Tokuda, T. J. Phys. Chem. 1983,87,4411. (b) Ito, T.; Murakami, T.; Tokuda, T. J. Cktn. Soc., Faraday Trans. I 1983, 79,913. (15) Kobayashi, H.; Yamaguchi, M.; Ito, T. J . Phys. Chem. 1990, 94, 7206. (16) Kunz, A. B.; Guse, M.P. Chem. Phys. Lett. 1977,45, 18. (17) Derouane, E. G.;Fripiat, J. G.; Andre, J. M. Chem. Phys. Lett. 1974, 28, 445. (18) Colbourn, E. A.; Mackrodt, W. C. Surf. Sci. 1982,117, 571. (19) Pope, S.A.; Guest, M. F.; Hillier, I. H.; Colbourn, E. A.; Mackrodt, W. C.; Kendrick, J. Phys. Rev. 1983, 828, 2191. (20) Colbourn, E. A.; Mackrodt, W. C. Ado. Ceramics 1985, 10, 190. (21) Ager, J. W., 111; Howard, C. J. J. Chem. Phys. 1987,87, 921.

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