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Embedded cluster study of water adsorption at Cr2O3(0001)
Surface Science 401 (1998) 82–95
Embedded cluster study of water adsorption at Cr O (0001) 2 3 Thomas Bredow Theoretische Chemie, Universita¨t Hannover, Am Kleinen Felde 30, D-30167 Hannover, Germany Received 6 September 1997; accepted for publication 19 November 1997
Abstract Quantum chemical calculations on the molecular and dissociative adsorption of water at the Cr O (0001) surface are performed. 2 3 A specially parametrized version of the semi-empirical SCF MO method SINDO1 is used for the calculations. The surfaces are simulated with model clusters embedded in finite arrays of pseudo-atoms. Different possible surface terminations are taken into account and their adsorption behaviour is compared. Single-molecule adsorption is studied as well as monolayer adsorption. A comparison of the calculated results for the relative stabilities of molecular and dissociative adsorption, dissociation barriers, electronic structures and adsorption geometries of water with experimental data leads to conclusions for the most probable surface termination of Cr O (0001). © 1998 Elsevier Science B.V. All rights reserved. 2 3 Keywords: Chemisorption; Chromium oxide; Low index single crystal surfaces; Models of surface chemical reactions; Semi-empirical models and model calculations; Single crystal surfaces; Solid–gas interfaces; Surface defects; Surface relaxation and reconstruction; Water
1. Introduction The surface chemistry of transition-metal oxides is of fundamental importance for many technical processes. Chromium oxide is used as a catalyst for hydrogenation reactions, water–gas shift reactions, or C–C bond formation [1–3]. In most cases, the mechanisms of the catalytic surface reactions are not clear. The first step in this research field is the identification of the surface structure. In the last few years, there has been significant progress in experimental structure determination using surface science techniques for ideal surfaces prepared either by epitaxial layer growth on metal supports [4] or by cleaving single crystals in ultrahigh vacuum [5]. Theoretical quantum chemical calculations have been used successfully as a complementary tool in connection with experimental investigations to 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0 0 3 9- 6 0 28 ( 97 ) 0 09 1 3 -8
clarify surface and bulk properties [6 ]. Recent developments in theoretical methods and computational efficiency have led to a large number of theoretical investigations on the bulk and surface properties of transition-metal oxides [7–16 ]. Ab-initio Hartree–Fock and density functional methods as well as semi-empirical methods have been used for the calculations. The models used for the simulations can be classified into three categories: isolated clusters [17], embedded clusters [18–23], and periodic arrangements of two- or three-dimensional unit cells [7,8,14,24,25]. The next step in the understanding of catalytic processes at surfaces is the controlled adsorption of small molecules [26 ]. Since adsorbed water molecules or hydroxyl groups play an important role for many catalytical reactions as byproducts, intermediates or reaction inhibitors, this study will
T. Bredow / Surface Science 401 (1998) 82–95
concentrate on the adsorption of water on Cr O 2 3 surfaces. From spectroscopic measurements on well-ordered epitaxially grown Cr O (0001) sur2 3 faces [27], it is known that water adsorbs almost entirely molecularly at low temperatures. Dissociation of adsorbed water only takes place near oxygen defect positions. In this study, results of semi-empirical quantum chemical calculations will be presented on the geometries, stabilities and electronic structures of adsorbed water species on different modifications of the Cr O (0001) surface. It will be shown that 2 3 only one surface modification gives the adsorption characteristics found in the experiments. From this combination of theoretical and experimental data, the most probable surface structure will be deduced. Section 2 gives a brief description of the semiempirical method SINDO1 used in this study and details of the models which have been selected to describe the surface structures. In Section 3, results of the quantum chemical calculations will be given for bulk properties of Cr O , single-molecule 2 3 adsorption at clean and defective surfaces, and monolayer adsorption. Section 4 summarizes the results and outlines the main conclusions from the calculations in connection with experimental facts from the literature.
2. Computational details
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study. In contrast to previous investigations, all simulations are performed with embedded cluster models. The clusters are embedded in finite arrays of pseudo-atoms which are described with the same atomic parameters as the real atoms. All interaction integrals between real and pseudoatoms are calculated on the same level of approximation as between real cluster atoms. Details of the embedding scheme were described in Ref. [38]. In this context, it is important to note that geometry optimization of the cluster is possible with the embedding procedure used here. As shown earlier [38], embedded cluster geometries are much closer to the corresponding bulk values as compared to free clusters. This allows for the relaxation of the internal cluster coordinates before the adsorption of molecules. The optimized cluster geometry is then used as the starting point for local and global relaxations due to adsorption effects. For the adsorption of water at oxide surfaces, hydrogen bonds between adsorbed water molecules or between water and surface oxygen have to be taken into account. In SINDO1, the hydrogen basis set can be augmented with specially parametrized 2p functions [39] in order to describe hydrogen bonds. Geometries and stabilization energies for the dimers of small molecules like H O, NH and formic acid were reported in 2 3 Ref. [39], and agree well with the experimental data. The influence of hydrogen bonds on adsorbed water on the (110) surface of rutile has also been described [34].
2.1. Method 2.2. Models The quantum chemical calculations have been performed with the semiempirical SCF MO method SINDO1 [28–31]. This method has been successfully applied to adsorption studies on magnesium oxide, anatase, rutile and vanadium pentoxide [32–35]. A scheme for the optimization of the empirical parameters in SINDO1 was presented previously [36,37]. A series of calculations for clusters with increasing size was performed, and the cluster properties were extrapolated to the bulk. The empirical parameters were varied so that the extrapolated values showed the best agreement with experimental data from the literature. A similar procedure has been utilized in this
Chromium oxide (Cr O ) has the corundum 2 3 structure. The oxygen atoms form a hexagonal close-packed array with the metal atoms occupying two thirds of the octahedral interstices between two layers. The metal atoms (M ) form buckled graphite-like layers parallel to the oxygen layers. It is possible to build up the corundum structure with M O units which are regular trigonal bipyra2 3 mids, the three O atoms forming the basis and the M atoms the top. This building unit has been used in this study to construct model clusters for simulating the Cr O bulk and surface. The internal 2 3 coordinates which globally define the cluster struc-
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Fig. 1. Internal coordinates for the definition of the Cr O 2 3 structure.
ture are the distance R of the oxygen atoms to XO the bipyramids center X, the Cr–X distance R , XCr the horizontal distance R between two centers X h in the same oxygen plane, and the vertical distance R between two oxygen layers (Fig. 1). v All clusters discussed in this study are based on the Cr O unit. In some cases it was necessary to 2 3 take out atoms from some bipyramids near the cluster boundaries in order to achieve higher symmetry for the system. The non-defective Cr O 2 3 bulk and surface structures were simulated with stoichiometric (Cr O ) clusters, with n ranging 2 3n from 24 to 87. The clusters were constructed with symmetry constraints, so that the three-fold symmetry axis of the corundum (0001) plane is retained and no total dipole moments occur, which prevents artificial charge redistribution in the clusters. For bulk simulations with embedded cluster models, it is necessary to embed the central cluster of real atoms in three dimensions. Since the oxygen atoms form two different layers, A and B, and the metal atoms three different layers, a, b and c, the corundum structure is repeated only after 12 layers (AaBbAcBaAbBcA). For a complete description of the corundum structure in the direction perpendicular to the parallel layers, it is necessary to use clusters with at least thirteen atomic layers. We chose the 15-layer clusters Cr O , Cr O and 48 72 90 135 Cr O with increasing layer size for bulk simu174 261
lations. The clusters were embedded in threedimensional arrangements of 4370, 4450 and 5410 pseudo-atoms, respectively. This is equivalent to two shells of pseudo-atoms around the real cluster atoms. It has been shown [38] that the changes in the cluster electronic energy are small when the pseudo-atom array is extended to more than two shells. The orbital charges q of the pseudo-atoms were n fixed to the average values of the corresponding real O and Cr cluster atoms. The charges q were n readjusted after embedding so that the resultant orbital charges are consistent. Since the differences for these averaged charges between the different cluster models are relatively small (about 0.01 atomic units), the same values were taken for all clusters. From experiments [40] it is known that the epitaxially grown (0001) surface of Cr O is termi2 3 nated by chromium atoms which form a highly symmetric layer. It is assumed that the Cr atoms in the first layer occupy equivalent positions on the second layer, which consists of oxygen atoms. The number of Cr atoms in the top layer is only half of a corresponding Cr layer in the bulk, which is essential for the electrostatic stability of the surface. Three different sites for the top Cr atoms were discussed [40]. The numbering in this study (see Fig. 2) follows the previous usage [40]. Position 1 is equivalent to the top position of a Cr O unit. The three base oxygen atoms are part 2 3 of the uppermost oxygen layer. Position 2 is the lower part of a Cr O unit where the oxygens and 2 3 the second Cr atom belong to layers above the surface and are therefore missing. Position 3 is equivalent to a tetragonal interstitial in the bulk structure. The top Cr atom is not part of a Cr O unit, but is close to three oxygen atoms of 2 3 the second layer which belong to different Cr O 2 3 bipyramids. In the bulk, both positions 1 and 2 are occupied by Cr atoms. Position 3 is not occupied in the bulk, but may be populated on the surface after reconstruction. The inclusion of local relaxation is necessary for the proper description of surface properties. There is agreement between theoretical and experimental investigations [40] that top-layer Cr atoms move towards the uppermost oxygen layer. This is in
T. Bredow / Surface Science 401 (1998) 82–95
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Fig. 2. Schematic representation of the first three atomic layers of the Cr O (0001) surface indicating the three possible Cr posi2 3 tions in the top layer. Large circles denote oxygen atoms, and small circles are chromium atoms. Cr atoms of the third layer are shaded. The surface is slightly rotated so that all third-layer atoms can be seen.
line with earlier theoretical investigations on adsorption processes on perfect and defective rutile surfaces [34], where it has been found that relaxation of surface titanium atoms is essential for the dissociation of molecularly adsorbed water. As a consequence of the vertical movement of surface Cr atoms, changes for other internal surface coordinates like R and R can be expected. For all XO v surface simulations, changes in the global coordinates and local relaxations of surface atoms have been taken into account in this study. The model clusters used for the simulation of the three surface types are Cr O for surface 100 150 type 1, Cr O for surface type 2 and Cr O 92 138 88 132 for surface type 3. They consist of seven, five and seven atomic layers, respectively. The embedding in pseudo-atoms is two-dimensional in the sense that only atomic layers already present in the real cluster are extended. This approach is similar to the slab models in infinite periodic calculations, with the difference that only a finite number of atoms and pseudo-atoms is included. The total
Fig. 3. Embedded cluster models for the Cr O (0001) surface. 2 3 (a) Cr O +1560 pseudo-atoms for surface type 1, (b) 100 150 Cr O +1600 pseudo-atoms for surface type 2, (c) 92 138 Cr O +2000 pseudo-atoms for surface type 3. Small circles 88 132 are chromium atoms and pseudo-atoms, while large circles are oxygen atoms and pseudo-atoms. The lighter atoms of each size are pseudo-atoms.
numbers of pseudo-atoms for the three models are 1560, 1600 and 2000, respectively. The structures of atoms and pseudo-atoms are shown in Fig. 3. Chromium oxide (Cr O ) is antiferromagnetic 2 3 at low temperatures. Formally, it consists of
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Cr3+ and O2− ions. Each Cr3+ ion has three unpaired electrons of parallel spin. The atomic spins are coupled so that the two Cr atoms in a Cr O bipyramid have opposite z components. 2 3 Experimentally, the energetic effect of the antiferromagnetic coupling has been determined to 1.2 kJ mol−1 [41]. Periodic ab-initio studies [7] show that geometrical changes due to the coupling are small. Therefore, in this study the high-spin state has been taken for all models, which leads to a multiplicity of 3n+1 for a Cr O cluster. The n 3/2n systematic error due to this simplification is smaller that the expected uncertainty of a semi-empirical method. For open-shell calculations, the restricted open-shell Hartree–Fock (ROHF ) formalism of Roothaan [42] has been used. The ROHF orbital energies have been corrected so that they can be interpreted as ionization energies or electron affinities [43].
3. Results 3.1. Bulk properties Experimental data for bulk Cr O are used to 2 3 adjust empirical parameters of SINDO1 such as orbital exponents and bonding parameters. These parameters have been optimized previously [28– 31] with respect to a set of small molecules in the gas phase. Previous investigations on bulk and surface properties with SINDO1 clearly showed that a readjustment of parameters is necessary to describe the bonding situation in condensed matter, which is apparently different from small molecules. This procedure is in line with many ab-initio studies on bulk materials and surfaces, where a special optimization of the orbital exponents is performed [44]. The optimization will concentrate on the binding energies and geometries of Cr O . The available experimental data include 2 3 heats of atomization D H298 [45] of a-Cr O at a 0 2 3 298 K and crystal structure data from neutron powder diffraction at 2 K [46 ]. There are also two periodic ab-initio calculations with [7,8], which present data for the lattice constants a and c. The optimization of parameters was restricted to the Cr atoms in order to retain the oxygen basis
Table 1 Comparison of calculated and experimental geometry parameters of bulk Cr O 2 3
a=E3R h c=6R v R XO R XCr
Experimenta
This study
b
c
4.952 13.599 1.519 1.357
5.01 13.65 1.45 1.36
5.04 13.72
5.05 13.74
Note; a and c are lattice parameters of the hexagonal unit cell. R , R , R and R are internal coordinates described in the h v XO XCr ˚. text. Distances are given in A aRef. [46 ]. bRef. [7]. cRef. [8].
set, which was adjusted for small molecules like water. The best agreement with experimental data was achieved with orbital exponents of f =1.326, f =1.308 and f =2.555 for s, p and d s p d orbitals, respectively. The bonding parameters a and a were set to 0.20 and 0.18, respectively. CrO OCr The atomization energy per Cr O unit was cal2 3 culated for the embedded clusters Cr O , 48 72 Cr O and Cr O . The previously described 90 135 174 261 extrapolation scheme [36,37] was applied to calculate the atomization energy for the bulk. The averaged relative coordination numbers k were estimated for the non-embedded clusters. In order to account for zero point and temperature corrections, which are included in the experimental value of D H298 , a full force-constant analysis f 0 was performed for the smallest bulk model (Cr O +4370 pseudo-atoms). The zero-point 48 72 correction per Cr O unit and the temperature 2 3 correction were assumed to be independent of the cluster size. The sum of corrections was estimated to be 54 kJ mol−1 per Cr O unit. With this correc2 3 tion, the calculated value for D H298 became f 0 2699 kJ mol−1, which is within the error limits of the experimental value (2681 kJ mol−1 [45]). The extrapolated calculated values for the lattice constants a and c and the internal coordinates R and R are presented in Table 1 together XO XCr with experimental data [46 ] and results from the calculations [7,8]. 3.2. Surface properties With the models Cr O +1560 pseudo100 150 atoms, Cr O +1600 pseudo-atoms and 92 138
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Cr O +2000 pseudo-atoms, the effect of local 88 132 relaxation for the three types of the Cr-terminated Cr O (0001) surface was investigated. The posi2 3 tions of first-layer chromium and second-layer oxygen atoms were optimized independently. The vertical height z with respect to the atomic layers and the coordinate R parallel to the atomic XO layers have been varied. In Table 2 the distances between the Cr and O atoms of the first and second layers and the optimized value for R of XO O atoms in the second layer are given and compared with the calculated values for the bulk given in Section 3.1. In accordance with the results of experimental and ab-initio results [40], the lowcoordinated top-layer Cr atoms tend to reduce their distance to the uppermost oxygen layer, which is indicated by the smaller values of h as compared to the bulk. The interlayer distances h, ˚ for position 1 and 0.910 A ˚ for which are 1.357 A position 2, respectively, are reduced by 22% and 49%. For position 3, no comparison to the bulk is possible since the position is not occupied. The contraction of h is much more pronounced for surface type 2 than for type 1 because there is no Cr atom in the third layer below position 2, in contrast to position 1. There is excellent agreement between the calculated reduction of h in this study (49%) and in the periodic ab-initio Hartree–Fock study [7] (49.8%). In contrast to surface type 1, a pronounced reconstruction of the uppermost Table 2 Surface relaxation for the three types of Cr-terminated Cr O (0001) surface 2 3 Surface type
ha Contractionb DRc XO Rs d CrO
1
2
3
1.06 22 +0.01 1.80
0.47 49 +0.20 1.78
1.22 – +0.07 1.97
aThe vertical distance between the first and the second layer ˚ ). (in A bGiven relative to the calculated bulk distance (%). cThe change in this coordinate with respect to the calculated ˚ ). bulk value (in A dThe Cr–O bond distance between atoms of the first two ˚) layers (in A
87
oxygen layer occurs in surface type 2. In the Cr O bipyramids at the surface of type 2, the top 2 3 Cr atoms are missing and the surface Cr atoms bridge three different CrO units. The oxygen 3 atoms in the remaining CrO units increase their 3 distance to the center X (R ) in order to decrease XO the Cr–O distance to the Cr atoms in the top layer. This results in a surface Cr–O bond distance ˚ , which is the same value as obtained in of 1.78 A the ab-initio study [7]. In surface type 1, the Cr O bipyramids are still present and there are 2 3 only small changes for the oxygen positions. For surface type 3, the distance h of the top Cr atoms to the oxygen layer is much larger than for the other surface types due to the repulsion from subsurface Cr atoms in the third layer which are placed perpendicularly below position 3. The Cr–O ˚ is almost unchanged surface bond length of 1.97 A ˚. compared to the calculated bulk distance of 1.99 A 3.3. Adsorption of isolated water molecules 3.3.1. Non-defective surfaces Molecular adsorption of an isolated water molecule was simulated with the embedded clusters Cr O (surface type 1), Cr O (surface type 100 150 92 138 2) and Cr O (surface type 3). The oxygen atom 88 132 of a single H O molecule was placed towards the 2 central surface Cr atom of the clusters. The internal coordinates of water, the orientation relative to the surface and the coordinates of the nearest surface atoms were then optimized. The derivatives of the energy with respect to internal coordinates including pseudo-atoms were calculated analytically. Details of the analytical derivative procedure will be given elsewhere [47]. Dissociative adsorption was simulated by removing one hydrogen atom from H O and placing it near a surface 2 oxygen atom O . The most stable arrangement is s obtained when O is part of the CrO unit of the s 3 central Cr atom. In Table 3 the results for the most important coordinates and the energetics for molecular and dissociative adsorption at the three surface types are given. Adsorption energies E ads are calculated as the energy difference between the isolated systems and the adsorbate–substrate system. They are positive when adsorption leads to a stabilization. In Figs. 4 and 5 the optimized
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Table 3 Optimized geometry parameters and adsorption energies for the adsorption of a single water molecule at Cr O (0001) surface types 2 3 1, 2 and 3 Surface type 1 Adsorption ˚) R a (A Cr O ˚ R s w (A ) O Hb ˚ R w (A ) OsHb ac (°) b (°) O Hd b w (°) O Hd c s d (°) Cr O ˚ Dz s we (A ) Cr ˚ Dz se (A ) O ˚) DRfs (A XOs E (kJ mol−1) ads
2
Molecular 2.29 1.01
Dissociative 1.80 0.96 1.00
102
3
Molecular 2.28 0.99
1.90 0.95 0.97
103 28
101 71 +0.05 +0.03 +0.01 234
Dissociative
9 +0.12 +0.12 +0.25 575
Molecular 2.29 0.98
1.81 0.95 0.97
106 69
23 52 +0.06 +0.03 +0.21 195
Dissociative
29 +0.18 +0.24 +0.04 172
26 112 24 -0.02 +0.00 +0.09 177
9 +0.08 +0.33 +0.24 500
aThe water oxygen–surface distance. bThe O–H distances to the water and surface oxygen. cThe water HOH angle. dThe angles between the O –H, the O –H and the Cr –O bond and the surface normal. w s s w eChanges in vertical positions of surface Cr and O. with respect to the calculated bulk value. fThe change for R XOs
water geometries and the nearest surface atoms are shown. The geometries and energetics of molecular adsorption are similar for the three surface types. The water oxygen is tilted towards the surface, as can be seen from the angle with the surface normal c . Its position is close to that CrsOw of an oxygen in the next oxygen layer above the surface in the ideal bulk structure. The hydrogen atoms are bound to surface oxygens by hydrogen bonds. The adsorption energies are comparable for the three surfaces. They range from 177 kJ mol−1 for surface type 3 to 234 kJ mol−1 for surface type 1. For dissociative adsorption, however, there is a remarkable difference between type 2 and the other structures. In surface types 1 and 3 the dissociated hydrogen moves into the surface oxygen layer, while it stays above the oxygens in surface type 2 (Fig. 5). This can be seen by the angle b of the O –H bond with the OsH s surface normal, which is larger than 100° for structures 1 and 3 and only 23° for structure 2. This difference can be explained by the structure of the third layer, which consists of Cr atoms. For
surface type, 2 Cr atoms of the third layer are located below the centers of gaps in the surface oxygen layer. Thus, the hydrogen Hd+ cannot move into the oxygen layer due to the electrostatic repulsion with the Cre+. This is not the case for the other surface types. There is a strong stabilization of the Hd+ from the negatively charged oxygens in the surface. This leads to strong stabilization of the dissociated form for the two surface types, while for surface type 2 the dissociative form is less stable than the molecular form. Another explanation for the differences in stabilization of the dissociated form between the surface types can be given in terms of surface oxygen coordination. Since the surface oxygen O and the s water hydrogen H form a covalent bond, the coordination of O to surface Cr atoms plays an s important role for the stability of the O –H bond s in addition to long-range contributions. On surfaces 1 and 3, O is only two-fold coordinated, s while the coordination is three on surface type 2. This can explain the weaker O –H bond in the s latter case. The hybridization of O after water s
T. Bredow / Surface Science 401 (1998) 82–95
Fig. 4. Molecular water adsorption at Cr O (0001). (a) Surface 2 3 type 1, (b) surface type 2, (c) surface type 3. Small dark spheres are Cr, large grey spheres are O, and small white spheres are H. Only the surface atoms closest to the adsorption site are shown.
dissociation is close to sp2 in cases 1 and 3, and sp3 in case 2. In order to investigate the reaction barrier for water dissociation, the transition-state geometries have been determined for all surface types. Fig. 6 shows the optimized geometry for surface type 2. The water oxygen O is tilted down to the surface w oxygen O and the dissociating hydrogen is located s between O and O . The transition structure is w s 171 kJ mol−1 higher in energy than the molecular
89
Fig. 5. Dissociative water adsorption at Cr O (0001). (a) 2 3 Surface type 1, (b) surface type 2, (c) surface type 3. Small dark spheres are Cr, large grey spheres are O, and small white spheres are H. Only the surface atoms closest to the adsorption site are shown.
form. This is again different from the other surface types, where the barrier heights are only 59 and 40 kJ mol−1 for surface types 1 and 3, respectively. Since our calculated barriers can only be taken as upper limits for the real activation enthalpies because electron correlation is included through parametrization only for minimum structures, it can be expected that water would dissociate on
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Fig. 6. Transition-state geometry for water dissociation at the perfect surface type 2.
surfaces 1 and 3 even at low temperatures, while dissociation is kinetically hindered on surface 2. The experimental fact [27] that water dissociation plays only a minor role on defect-free epitaxially grown Cr O leads us to the conclusion that 2 3 the Cr-terminated (0001) surface is identical to surface type 2. Periodic ab-initio calculations [7] also favor surface type 2 compared to other possible structures. Therefore, further investigations presented here will mainly concentrate on this surface type. Another experimental fact which has to be considered is that the UP spectra [27] show only one signal for OH groups after water dissociation. The structures shown in Fig. 5 for the defect-free (0001) surfaces all have in common that the two OH groups O –H and O –H are not equivalent due to w s their differences in coordination. The O –H group w has only one bond to a surface Cr atom, while O is bound to two or three Cr atoms. This s inequivalence can be seen from the calculated orbital energies of the highest OH s orbital in the valence-band region. The s orbital of the O –H s group is 4.3 eV lower in energy than the s orbital of the O –H group. Angle-resolved UPS experiw ments also suggest that the OH groups are perpendicular on the surface. The calculated angles with the surface normal b and b show large OwH OH deviations from the expected values of zero. This leads us to the conclusion that surface defects, especially oxygen defects, play a role for water dissociation. This has been suggested by experimentalists [27].
3.3.2. Surfaces with oxygen defects From experiments, it is known [27] that the Cr O (0001) surface contains a small amount of 2 3 oxygen defects. For rutile [34], it has been shown that oxygen defects enhance the dissociation of water molecules. For this reason, the effect of a single oxygen vacancy on water adsorption was studied for surface type 2. A surface oxygen atom was removed from the cluster Cr O embedded 92 138 in the same array of 1600 pseudo-atoms as for the stoichiometric cluster. Water adsorption was assumed to take place at the defect position, the water oxygen atom occupying the vacant surface oxygen site. Local relaxation of the nearest surface atoms was taken into account for the free cluster reference and the cluster–water system. The optimized structures of the molecular and dissociative form of water (Fig. 7) are summarized in Table 4. In the molecular adsorption, the water oxygen ˚ above the O takes a position approximately 1 A w position of the missing surface oxygen. The hydrogen atoms of water are not equivalent: one forms a hydrogen bond to a surface oxygen while the other is points away from the surface. In the dissociative form, the two OH groups have the same coordination and their angles with the surface
Fig. 7. Water adsorption at surface type 2 with an oxygen defect. (a) Molecular and (b) dissociative adsorption.
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Table 4 Optimized geometry parameters and adsorption energies for the adsorption of a single water molecule at Cr O (0001) surface 2 3 type 2 with an oxygen vacancy; see Table 3 for details Adsorption
˚) R (A Cr O ˚ R s w(A ) O H ˚ R w (A ) OH b s (°) OwH b (°) OH ˚ Dzs (A ) Crs ˚ Dz (A) O ˚) DR w (A XOw E (kJ mol-1) ads
Molecular
Dissociative
2.14 0.98/1.03 – – – +0.03 +1.06 +0.19 251
1.82 0.95 0.96 36 44 +0.06 +0.15 +0.06 556
normal b and b are similar. The chemical O H OH equivalencew can be sseen from the calculated s orbital energies of the two OH groups. The energy difference is now only 0.5 eV, which can explain the single broad signal in the UP spectra. The values of b and b , 36° and 44°, respectively, O H OsH deviate fromw the experimentally suggested value of 0°. This is larger than the error limits of angleresolved UPS, and could be due to inaccuracies in the theoretical approach. It is also possible that the measurements include averaging on different positions, partly near surface defects such as steps and kinks. It seems reasonable that the OH bonds are not perpendicular on the surface, since the repulsion from the surface Cr atom is reduced after tilting. For the defect site, the relative stabilities of the molecular and dissociative forms of water are reversed compared to the non-defective surface. The dissociation is now exothermic by 305 kJ mol−1. The calculated transition barrier for dissociation is only 40 kJ mol−1, which is close to the values for the non-defective surfaces 1 and 3. The geometry of the transition structure is given in Fig. 8. The dissociation involves movements of the surface oxygen O and the water oxygen O s w and the formation of a hydrogen bond to O . s 3.4. Monolayer adsorption of water The monolayer adsorption on the defect-free Cr O (0001) surface type 2 has been simulated 2 3
Fig. 8. Transition-state geometry for water dissociation at surface type 2 with an oxygen defect.
with the cluster model Cr O embedded in 1600 92 138 pseudo-atoms used previously for single-molecule adsorption studies. The model contains 19 adsorption positions, the central position and two symmetric shells with six and 12 sites, respectively. Two islands of seven and 19 H O molecules were 2 used for monolayer representation ( Figs. 9 and 10). The coordinates of the water molecules and the surface atoms near the different sites were optimized equivalently. In order to avoid artificial effects from the boundaries of the water islands, the adsorption energy in Table 5 is calculated for the removal of the central H O only. The coordina2 tion of the central water is close to that of a molecule in a real monolayer. Another reason for this procedure is that the experimentally available isosteric heat of formation is defined for an infinitesimal change of the coverage. In Table 5 it can be seen that the geometrical changes between the seven-molecule and the 19-molecule islands are small. The water orientation of both the molecular and dissociative form does not show significant differences compared to single-molecule adsorp˚, tion. The Cr –O distance is reduced by 0.05 A s w while the angles deviate by less than 5°. Also, the local surface relaxations differ only by less than ˚. 0.05 A The calculated adsorption energies of the central H O for monolayer simulation are much lower 2 than for single-molecule adsorption. For the molecular form, the two islands give more or less the same result, 188 and 180 kJ mol−1, respectively, indicating that the long-range effects are
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Fig. 9. Simulation of monolayer adsorption at surface type 2: cluster Cr O with seven H O. (a) Molecular and (b) dissoci92 138 2 ative adsorption. Only real atoms are shown.
Fig. 10. Simulation of monolayer adsorption at surface type 2: cluster Cr O with 19 H O. (a) Molecular and (b) dissociative 92 138 2 adsorption. Only real atoms are shown.
already accounted for by the island model. The largest island shows a reduction of E by ads 15 kJ mol−1 with respect to single-molecule adsorption. The situation is completely different for a monolayer of dissociated water. Desorption of OH and H as H O from the center of the 2 19-molecule island costs only 80 kJ mol−1, compared to 130 kJ mol−1 for the seven-molecule island and 170 kJ mol−1 for a single H O unit. 2 Two effects are responsible for these differences. Lateral long-range Coulombic repulsions between the protruding O Hd− groups (d is approximately w 0.5 a.u.) reduce the adsorption energy. As a second
effect, there is a strong electron transfer from the surface to water of about 0.3 a.u. per H O unit, 2 which destabilizes the Cr O surface when a mono2 3 layer of dissociated water is adsorbed. The trend of decreasing adsorption energies with increasing coverage is in qualitative agreement with calorimetric measurements on Cr O samples 2 3 [48–50]. The absolute values of E calculated in ads this study cannot be compared directly with the experimental values DH from Refs. [48–50], ads since the surface structure of the samples may be different from the models used in this study due to their preparation. However, the order of magni-
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Table 5 Optimized geometry parameters and adsorption energies for monolayer adsorption of water at Cr O (0001) surface type 2; see Table 3 2 3 for details 7HO 2
19 H O 2
Adsorption
Molecular
Dissociative
Molecular
Dissociative
˚) R (A Cr O ˚ R s w(A ) O H ˚ R w (A ) OsH a (°) b (°) O H b w (°) OH c s w (°) CrsO ˚ Dz (A) Cr ˚ Dz s (A ) O ˚) DR s (A XOs E (kJ mol-1) ads
2.25 0.99 – 104 – – 53 +0.06 +0.03 +0.19 188
1.88 0.95 0.98 – 68 28 33 +0.20 +0.16 +0.09 134
2.23 1.00 – 103 – – 53 +0.03 +0.03 +0.18 180
1.86 0.95 0.98 – 67 26 33 +0.13 +0.19 +0.06 77
tude of the calculated E , i.e. 180–195 kJ mol−1 ads for molecular adsorption and 80–170 kJ mol−1 for dissociative adsorption, agrees very well with the differential heats of adsorption [48–50], i.e. 80–160 kJ mol−1 for the first layer of water on Cr O . The upper limit of the experimental investi2 3 gation is for the limit of zero coverage.
4. Summary and conclusions The molecular and dissociative adsorption of water on different kinds of Cr-terminated Cr O 2 3 surfaces was studied theoretically with embedded cluster models. A semi-empirical SCF MO method has been used for the calculations with empirical parameters specially adjusted for the description of Cr O bulk properties. The clusters were chosen 2 3 to be large enough to describe the electron redestribution in the surface area due to charge transfer from the adsorbate molecules. Long-range electrostatic effects have been introduced into the models by an embedding procedure. Three different geometrical arrangements of the surface Cr atoms have been taken into account, referring to previous suggestions from experimentalists. On two surface structures, types 1 and 3, water dissociation is highly exothermic and the activation barrier is relatively small. On surface type 2, the molecular form of water is slightly more stable than the
dissociative form, and a high activation barrier of 171 kJ mol−1 exists. The low adsorption energies and the conversion of relative stabilities of the molecular and dissociative forms on surface type 2 compared to the other structures can be explained by the strong stabilization due to relaxation of surface Cr atoms and the geometrical structure of the oxygen and the third Cr layer. Only the data for surface type 2 can explain the experimental finding that water does not dissociate considerably on non-defective Cr O (0001). 2 3 Therefore, it is concluded that the structure of Cr-terminated epitaxially grown Cr O (0001) is 2 3 that of type 2. This conclusion agrees with other theoretical calculations for this system. On all defect-free surfaces, the two OH groups formed after water dissociation are different in orientation and coordination, and would give different signals in UPS spectra. Agreement with the experimental spectra, which show only one OH signal, is achieved when water dissociates at oxygen vacancies. Water dissociation on surface structure 2 is energetically favored at oxygen defect sites, and the OH groups formed after dissociation are similar in their coordination and orientation. The calculated orbital energies are so close that the experimental spectra can be explained. Lateral interaction between adsorbed water molecules in a monolayer and charge transfer to the surface leads to a reduction of the adsorption
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T. Bredow / Surface Science 401 (1998) 82–95
energy compared to the single molecule adsorption. E decreases from 195 to 180 kJ mol−1 for ads the molecular form. The dissociated form is more destabilized when larger islands are formed. E ads decreases from 170 kJ mol−1 for a single molecule to 130 kJ mol−1 for a seven-molecule island and to 80 kJ mol−1 for a 19-molecule island. It can be expected that a full monolayer of dissociatively adsorbed water will not be formed. In general, the decrease of E with increasing coverage is in ads agreement with experimental measurements on Cr O crystals. 2 3
Acknowledgements The author would like to thank H.-J. Freund, Berlin, and H. Kuhlenbeck, Bochum, for many helpful and stimulating discussions. This work was partially supported by the Commission of the European Communities and the Deutsche Forschungsgemeinschaft. The calculations were performed on a Siemens VPP300 and a Cray T3E at the Universita¨t Hannover. Part of the structure drawings was done using 92.
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Embedded cluster study of water adsorption at Cr O (0001) 2 3 Thomas Bredow Theoretische Chemie, Universita¨t Hannover, Am Kleinen Felde 30, D-30167 Hannover, Germany Received 6 September 1997; accepted for publication 19 November 1997
Abstract Quantum chemical calculations on the molecular and dissociative adsorption of water at the Cr O (0001) surface are performed. 2 3 A specially parametrized version of the semi-empirical SCF MO method SINDO1 is used for the calculations. The surfaces are simulated with model clusters embedded in finite arrays of pseudo-atoms. Different possible surface terminations are taken into account and their adsorption behaviour is compared. Single-molecule adsorption is studied as well as monolayer adsorption. A comparison of the calculated results for the relative stabilities of molecular and dissociative adsorption, dissociation barriers, electronic structures and adsorption geometries of water with experimental data leads to conclusions for the most probable surface termination of Cr O (0001). © 1998 Elsevier Science B.V. All rights reserved. 2 3 Keywords: Chemisorption; Chromium oxide; Low index single crystal surfaces; Models of surface chemical reactions; Semi-empirical models and model calculations; Single crystal surfaces; Solid–gas interfaces; Surface defects; Surface relaxation and reconstruction; Water
1. Introduction The surface chemistry of transition-metal oxides is of fundamental importance for many technical processes. Chromium oxide is used as a catalyst for hydrogenation reactions, water–gas shift reactions, or C–C bond formation [1–3]. In most cases, the mechanisms of the catalytic surface reactions are not clear. The first step in this research field is the identification of the surface structure. In the last few years, there has been significant progress in experimental structure determination using surface science techniques for ideal surfaces prepared either by epitaxial layer growth on metal supports [4] or by cleaving single crystals in ultrahigh vacuum [5]. Theoretical quantum chemical calculations have been used successfully as a complementary tool in connection with experimental investigations to 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0 0 3 9- 6 0 28 ( 97 ) 0 09 1 3 -8
clarify surface and bulk properties [6 ]. Recent developments in theoretical methods and computational efficiency have led to a large number of theoretical investigations on the bulk and surface properties of transition-metal oxides [7–16 ]. Ab-initio Hartree–Fock and density functional methods as well as semi-empirical methods have been used for the calculations. The models used for the simulations can be classified into three categories: isolated clusters [17], embedded clusters [18–23], and periodic arrangements of two- or three-dimensional unit cells [7,8,14,24,25]. The next step in the understanding of catalytic processes at surfaces is the controlled adsorption of small molecules [26 ]. Since adsorbed water molecules or hydroxyl groups play an important role for many catalytical reactions as byproducts, intermediates or reaction inhibitors, this study will
T. Bredow / Surface Science 401 (1998) 82–95
concentrate on the adsorption of water on Cr O 2 3 surfaces. From spectroscopic measurements on well-ordered epitaxially grown Cr O (0001) sur2 3 faces [27], it is known that water adsorbs almost entirely molecularly at low temperatures. Dissociation of adsorbed water only takes place near oxygen defect positions. In this study, results of semi-empirical quantum chemical calculations will be presented on the geometries, stabilities and electronic structures of adsorbed water species on different modifications of the Cr O (0001) surface. It will be shown that 2 3 only one surface modification gives the adsorption characteristics found in the experiments. From this combination of theoretical and experimental data, the most probable surface structure will be deduced. Section 2 gives a brief description of the semiempirical method SINDO1 used in this study and details of the models which have been selected to describe the surface structures. In Section 3, results of the quantum chemical calculations will be given for bulk properties of Cr O , single-molecule 2 3 adsorption at clean and defective surfaces, and monolayer adsorption. Section 4 summarizes the results and outlines the main conclusions from the calculations in connection with experimental facts from the literature.
2. Computational details
83
study. In contrast to previous investigations, all simulations are performed with embedded cluster models. The clusters are embedded in finite arrays of pseudo-atoms which are described with the same atomic parameters as the real atoms. All interaction integrals between real and pseudoatoms are calculated on the same level of approximation as between real cluster atoms. Details of the embedding scheme were described in Ref. [38]. In this context, it is important to note that geometry optimization of the cluster is possible with the embedding procedure used here. As shown earlier [38], embedded cluster geometries are much closer to the corresponding bulk values as compared to free clusters. This allows for the relaxation of the internal cluster coordinates before the adsorption of molecules. The optimized cluster geometry is then used as the starting point for local and global relaxations due to adsorption effects. For the adsorption of water at oxide surfaces, hydrogen bonds between adsorbed water molecules or between water and surface oxygen have to be taken into account. In SINDO1, the hydrogen basis set can be augmented with specially parametrized 2p functions [39] in order to describe hydrogen bonds. Geometries and stabilization energies for the dimers of small molecules like H O, NH and formic acid were reported in 2 3 Ref. [39], and agree well with the experimental data. The influence of hydrogen bonds on adsorbed water on the (110) surface of rutile has also been described [34].
2.1. Method 2.2. Models The quantum chemical calculations have been performed with the semiempirical SCF MO method SINDO1 [28–31]. This method has been successfully applied to adsorption studies on magnesium oxide, anatase, rutile and vanadium pentoxide [32–35]. A scheme for the optimization of the empirical parameters in SINDO1 was presented previously [36,37]. A series of calculations for clusters with increasing size was performed, and the cluster properties were extrapolated to the bulk. The empirical parameters were varied so that the extrapolated values showed the best agreement with experimental data from the literature. A similar procedure has been utilized in this
Chromium oxide (Cr O ) has the corundum 2 3 structure. The oxygen atoms form a hexagonal close-packed array with the metal atoms occupying two thirds of the octahedral interstices between two layers. The metal atoms (M ) form buckled graphite-like layers parallel to the oxygen layers. It is possible to build up the corundum structure with M O units which are regular trigonal bipyra2 3 mids, the three O atoms forming the basis and the M atoms the top. This building unit has been used in this study to construct model clusters for simulating the Cr O bulk and surface. The internal 2 3 coordinates which globally define the cluster struc-
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Fig. 1. Internal coordinates for the definition of the Cr O 2 3 structure.
ture are the distance R of the oxygen atoms to XO the bipyramids center X, the Cr–X distance R , XCr the horizontal distance R between two centers X h in the same oxygen plane, and the vertical distance R between two oxygen layers (Fig. 1). v All clusters discussed in this study are based on the Cr O unit. In some cases it was necessary to 2 3 take out atoms from some bipyramids near the cluster boundaries in order to achieve higher symmetry for the system. The non-defective Cr O 2 3 bulk and surface structures were simulated with stoichiometric (Cr O ) clusters, with n ranging 2 3n from 24 to 87. The clusters were constructed with symmetry constraints, so that the three-fold symmetry axis of the corundum (0001) plane is retained and no total dipole moments occur, which prevents artificial charge redistribution in the clusters. For bulk simulations with embedded cluster models, it is necessary to embed the central cluster of real atoms in three dimensions. Since the oxygen atoms form two different layers, A and B, and the metal atoms three different layers, a, b and c, the corundum structure is repeated only after 12 layers (AaBbAcBaAbBcA). For a complete description of the corundum structure in the direction perpendicular to the parallel layers, it is necessary to use clusters with at least thirteen atomic layers. We chose the 15-layer clusters Cr O , Cr O and 48 72 90 135 Cr O with increasing layer size for bulk simu174 261
lations. The clusters were embedded in threedimensional arrangements of 4370, 4450 and 5410 pseudo-atoms, respectively. This is equivalent to two shells of pseudo-atoms around the real cluster atoms. It has been shown [38] that the changes in the cluster electronic energy are small when the pseudo-atom array is extended to more than two shells. The orbital charges q of the pseudo-atoms were n fixed to the average values of the corresponding real O and Cr cluster atoms. The charges q were n readjusted after embedding so that the resultant orbital charges are consistent. Since the differences for these averaged charges between the different cluster models are relatively small (about 0.01 atomic units), the same values were taken for all clusters. From experiments [40] it is known that the epitaxially grown (0001) surface of Cr O is termi2 3 nated by chromium atoms which form a highly symmetric layer. It is assumed that the Cr atoms in the first layer occupy equivalent positions on the second layer, which consists of oxygen atoms. The number of Cr atoms in the top layer is only half of a corresponding Cr layer in the bulk, which is essential for the electrostatic stability of the surface. Three different sites for the top Cr atoms were discussed [40]. The numbering in this study (see Fig. 2) follows the previous usage [40]. Position 1 is equivalent to the top position of a Cr O unit. The three base oxygen atoms are part 2 3 of the uppermost oxygen layer. Position 2 is the lower part of a Cr O unit where the oxygens and 2 3 the second Cr atom belong to layers above the surface and are therefore missing. Position 3 is equivalent to a tetragonal interstitial in the bulk structure. The top Cr atom is not part of a Cr O unit, but is close to three oxygen atoms of 2 3 the second layer which belong to different Cr O 2 3 bipyramids. In the bulk, both positions 1 and 2 are occupied by Cr atoms. Position 3 is not occupied in the bulk, but may be populated on the surface after reconstruction. The inclusion of local relaxation is necessary for the proper description of surface properties. There is agreement between theoretical and experimental investigations [40] that top-layer Cr atoms move towards the uppermost oxygen layer. This is in
T. Bredow / Surface Science 401 (1998) 82–95
85
Fig. 2. Schematic representation of the first three atomic layers of the Cr O (0001) surface indicating the three possible Cr posi2 3 tions in the top layer. Large circles denote oxygen atoms, and small circles are chromium atoms. Cr atoms of the third layer are shaded. The surface is slightly rotated so that all third-layer atoms can be seen.
line with earlier theoretical investigations on adsorption processes on perfect and defective rutile surfaces [34], where it has been found that relaxation of surface titanium atoms is essential for the dissociation of molecularly adsorbed water. As a consequence of the vertical movement of surface Cr atoms, changes for other internal surface coordinates like R and R can be expected. For all XO v surface simulations, changes in the global coordinates and local relaxations of surface atoms have been taken into account in this study. The model clusters used for the simulation of the three surface types are Cr O for surface 100 150 type 1, Cr O for surface type 2 and Cr O 92 138 88 132 for surface type 3. They consist of seven, five and seven atomic layers, respectively. The embedding in pseudo-atoms is two-dimensional in the sense that only atomic layers already present in the real cluster are extended. This approach is similar to the slab models in infinite periodic calculations, with the difference that only a finite number of atoms and pseudo-atoms is included. The total
Fig. 3. Embedded cluster models for the Cr O (0001) surface. 2 3 (a) Cr O +1560 pseudo-atoms for surface type 1, (b) 100 150 Cr O +1600 pseudo-atoms for surface type 2, (c) 92 138 Cr O +2000 pseudo-atoms for surface type 3. Small circles 88 132 are chromium atoms and pseudo-atoms, while large circles are oxygen atoms and pseudo-atoms. The lighter atoms of each size are pseudo-atoms.
numbers of pseudo-atoms for the three models are 1560, 1600 and 2000, respectively. The structures of atoms and pseudo-atoms are shown in Fig. 3. Chromium oxide (Cr O ) is antiferromagnetic 2 3 at low temperatures. Formally, it consists of
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Cr3+ and O2− ions. Each Cr3+ ion has three unpaired electrons of parallel spin. The atomic spins are coupled so that the two Cr atoms in a Cr O bipyramid have opposite z components. 2 3 Experimentally, the energetic effect of the antiferromagnetic coupling has been determined to 1.2 kJ mol−1 [41]. Periodic ab-initio studies [7] show that geometrical changes due to the coupling are small. Therefore, in this study the high-spin state has been taken for all models, which leads to a multiplicity of 3n+1 for a Cr O cluster. The n 3/2n systematic error due to this simplification is smaller that the expected uncertainty of a semi-empirical method. For open-shell calculations, the restricted open-shell Hartree–Fock (ROHF ) formalism of Roothaan [42] has been used. The ROHF orbital energies have been corrected so that they can be interpreted as ionization energies or electron affinities [43].
3. Results 3.1. Bulk properties Experimental data for bulk Cr O are used to 2 3 adjust empirical parameters of SINDO1 such as orbital exponents and bonding parameters. These parameters have been optimized previously [28– 31] with respect to a set of small molecules in the gas phase. Previous investigations on bulk and surface properties with SINDO1 clearly showed that a readjustment of parameters is necessary to describe the bonding situation in condensed matter, which is apparently different from small molecules. This procedure is in line with many ab-initio studies on bulk materials and surfaces, where a special optimization of the orbital exponents is performed [44]. The optimization will concentrate on the binding energies and geometries of Cr O . The available experimental data include 2 3 heats of atomization D H298 [45] of a-Cr O at a 0 2 3 298 K and crystal structure data from neutron powder diffraction at 2 K [46 ]. There are also two periodic ab-initio calculations with [7,8], which present data for the lattice constants a and c. The optimization of parameters was restricted to the Cr atoms in order to retain the oxygen basis
Table 1 Comparison of calculated and experimental geometry parameters of bulk Cr O 2 3
a=E3R h c=6R v R XO R XCr
Experimenta
This study
b
c
4.952 13.599 1.519 1.357
5.01 13.65 1.45 1.36
5.04 13.72
5.05 13.74
Note; a and c are lattice parameters of the hexagonal unit cell. R , R , R and R are internal coordinates described in the h v XO XCr ˚. text. Distances are given in A aRef. [46 ]. bRef. [7]. cRef. [8].
set, which was adjusted for small molecules like water. The best agreement with experimental data was achieved with orbital exponents of f =1.326, f =1.308 and f =2.555 for s, p and d s p d orbitals, respectively. The bonding parameters a and a were set to 0.20 and 0.18, respectively. CrO OCr The atomization energy per Cr O unit was cal2 3 culated for the embedded clusters Cr O , 48 72 Cr O and Cr O . The previously described 90 135 174 261 extrapolation scheme [36,37] was applied to calculate the atomization energy for the bulk. The averaged relative coordination numbers k were estimated for the non-embedded clusters. In order to account for zero point and temperature corrections, which are included in the experimental value of D H298 , a full force-constant analysis f 0 was performed for the smallest bulk model (Cr O +4370 pseudo-atoms). The zero-point 48 72 correction per Cr O unit and the temperature 2 3 correction were assumed to be independent of the cluster size. The sum of corrections was estimated to be 54 kJ mol−1 per Cr O unit. With this correc2 3 tion, the calculated value for D H298 became f 0 2699 kJ mol−1, which is within the error limits of the experimental value (2681 kJ mol−1 [45]). The extrapolated calculated values for the lattice constants a and c and the internal coordinates R and R are presented in Table 1 together XO XCr with experimental data [46 ] and results from the calculations [7,8]. 3.2. Surface properties With the models Cr O +1560 pseudo100 150 atoms, Cr O +1600 pseudo-atoms and 92 138
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Cr O +2000 pseudo-atoms, the effect of local 88 132 relaxation for the three types of the Cr-terminated Cr O (0001) surface was investigated. The posi2 3 tions of first-layer chromium and second-layer oxygen atoms were optimized independently. The vertical height z with respect to the atomic layers and the coordinate R parallel to the atomic XO layers have been varied. In Table 2 the distances between the Cr and O atoms of the first and second layers and the optimized value for R of XO O atoms in the second layer are given and compared with the calculated values for the bulk given in Section 3.1. In accordance with the results of experimental and ab-initio results [40], the lowcoordinated top-layer Cr atoms tend to reduce their distance to the uppermost oxygen layer, which is indicated by the smaller values of h as compared to the bulk. The interlayer distances h, ˚ for position 1 and 0.910 A ˚ for which are 1.357 A position 2, respectively, are reduced by 22% and 49%. For position 3, no comparison to the bulk is possible since the position is not occupied. The contraction of h is much more pronounced for surface type 2 than for type 1 because there is no Cr atom in the third layer below position 2, in contrast to position 1. There is excellent agreement between the calculated reduction of h in this study (49%) and in the periodic ab-initio Hartree–Fock study [7] (49.8%). In contrast to surface type 1, a pronounced reconstruction of the uppermost Table 2 Surface relaxation for the three types of Cr-terminated Cr O (0001) surface 2 3 Surface type
ha Contractionb DRc XO Rs d CrO
1
2
3
1.06 22 +0.01 1.80
0.47 49 +0.20 1.78
1.22 – +0.07 1.97
aThe vertical distance between the first and the second layer ˚ ). (in A bGiven relative to the calculated bulk distance (%). cThe change in this coordinate with respect to the calculated ˚ ). bulk value (in A dThe Cr–O bond distance between atoms of the first two ˚) layers (in A
87
oxygen layer occurs in surface type 2. In the Cr O bipyramids at the surface of type 2, the top 2 3 Cr atoms are missing and the surface Cr atoms bridge three different CrO units. The oxygen 3 atoms in the remaining CrO units increase their 3 distance to the center X (R ) in order to decrease XO the Cr–O distance to the Cr atoms in the top layer. This results in a surface Cr–O bond distance ˚ , which is the same value as obtained in of 1.78 A the ab-initio study [7]. In surface type 1, the Cr O bipyramids are still present and there are 2 3 only small changes for the oxygen positions. For surface type 3, the distance h of the top Cr atoms to the oxygen layer is much larger than for the other surface types due to the repulsion from subsurface Cr atoms in the third layer which are placed perpendicularly below position 3. The Cr–O ˚ is almost unchanged surface bond length of 1.97 A ˚. compared to the calculated bulk distance of 1.99 A 3.3. Adsorption of isolated water molecules 3.3.1. Non-defective surfaces Molecular adsorption of an isolated water molecule was simulated with the embedded clusters Cr O (surface type 1), Cr O (surface type 100 150 92 138 2) and Cr O (surface type 3). The oxygen atom 88 132 of a single H O molecule was placed towards the 2 central surface Cr atom of the clusters. The internal coordinates of water, the orientation relative to the surface and the coordinates of the nearest surface atoms were then optimized. The derivatives of the energy with respect to internal coordinates including pseudo-atoms were calculated analytically. Details of the analytical derivative procedure will be given elsewhere [47]. Dissociative adsorption was simulated by removing one hydrogen atom from H O and placing it near a surface 2 oxygen atom O . The most stable arrangement is s obtained when O is part of the CrO unit of the s 3 central Cr atom. In Table 3 the results for the most important coordinates and the energetics for molecular and dissociative adsorption at the three surface types are given. Adsorption energies E ads are calculated as the energy difference between the isolated systems and the adsorbate–substrate system. They are positive when adsorption leads to a stabilization. In Figs. 4 and 5 the optimized
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Table 3 Optimized geometry parameters and adsorption energies for the adsorption of a single water molecule at Cr O (0001) surface types 2 3 1, 2 and 3 Surface type 1 Adsorption ˚) R a (A Cr O ˚ R s w (A ) O Hb ˚ R w (A ) OsHb ac (°) b (°) O Hd b w (°) O Hd c s d (°) Cr O ˚ Dz s we (A ) Cr ˚ Dz se (A ) O ˚) DRfs (A XOs E (kJ mol−1) ads
2
Molecular 2.29 1.01
Dissociative 1.80 0.96 1.00
102
3
Molecular 2.28 0.99
1.90 0.95 0.97
103 28
101 71 +0.05 +0.03 +0.01 234
Dissociative
9 +0.12 +0.12 +0.25 575
Molecular 2.29 0.98
1.81 0.95 0.97
106 69
23 52 +0.06 +0.03 +0.21 195
Dissociative
29 +0.18 +0.24 +0.04 172
26 112 24 -0.02 +0.00 +0.09 177
9 +0.08 +0.33 +0.24 500
aThe water oxygen–surface distance. bThe O–H distances to the water and surface oxygen. cThe water HOH angle. dThe angles between the O –H, the O –H and the Cr –O bond and the surface normal. w s s w eChanges in vertical positions of surface Cr and O. with respect to the calculated bulk value. fThe change for R XOs
water geometries and the nearest surface atoms are shown. The geometries and energetics of molecular adsorption are similar for the three surface types. The water oxygen is tilted towards the surface, as can be seen from the angle with the surface normal c . Its position is close to that CrsOw of an oxygen in the next oxygen layer above the surface in the ideal bulk structure. The hydrogen atoms are bound to surface oxygens by hydrogen bonds. The adsorption energies are comparable for the three surfaces. They range from 177 kJ mol−1 for surface type 3 to 234 kJ mol−1 for surface type 1. For dissociative adsorption, however, there is a remarkable difference between type 2 and the other structures. In surface types 1 and 3 the dissociated hydrogen moves into the surface oxygen layer, while it stays above the oxygens in surface type 2 (Fig. 5). This can be seen by the angle b of the O –H bond with the OsH s surface normal, which is larger than 100° for structures 1 and 3 and only 23° for structure 2. This difference can be explained by the structure of the third layer, which consists of Cr atoms. For
surface type, 2 Cr atoms of the third layer are located below the centers of gaps in the surface oxygen layer. Thus, the hydrogen Hd+ cannot move into the oxygen layer due to the electrostatic repulsion with the Cre+. This is not the case for the other surface types. There is a strong stabilization of the Hd+ from the negatively charged oxygens in the surface. This leads to strong stabilization of the dissociated form for the two surface types, while for surface type 2 the dissociative form is less stable than the molecular form. Another explanation for the differences in stabilization of the dissociated form between the surface types can be given in terms of surface oxygen coordination. Since the surface oxygen O and the s water hydrogen H form a covalent bond, the coordination of O to surface Cr atoms plays an s important role for the stability of the O –H bond s in addition to long-range contributions. On surfaces 1 and 3, O is only two-fold coordinated, s while the coordination is three on surface type 2. This can explain the weaker O –H bond in the s latter case. The hybridization of O after water s
T. Bredow / Surface Science 401 (1998) 82–95
Fig. 4. Molecular water adsorption at Cr O (0001). (a) Surface 2 3 type 1, (b) surface type 2, (c) surface type 3. Small dark spheres are Cr, large grey spheres are O, and small white spheres are H. Only the surface atoms closest to the adsorption site are shown.
dissociation is close to sp2 in cases 1 and 3, and sp3 in case 2. In order to investigate the reaction barrier for water dissociation, the transition-state geometries have been determined for all surface types. Fig. 6 shows the optimized geometry for surface type 2. The water oxygen O is tilted down to the surface w oxygen O and the dissociating hydrogen is located s between O and O . The transition structure is w s 171 kJ mol−1 higher in energy than the molecular
89
Fig. 5. Dissociative water adsorption at Cr O (0001). (a) 2 3 Surface type 1, (b) surface type 2, (c) surface type 3. Small dark spheres are Cr, large grey spheres are O, and small white spheres are H. Only the surface atoms closest to the adsorption site are shown.
form. This is again different from the other surface types, where the barrier heights are only 59 and 40 kJ mol−1 for surface types 1 and 3, respectively. Since our calculated barriers can only be taken as upper limits for the real activation enthalpies because electron correlation is included through parametrization only for minimum structures, it can be expected that water would dissociate on
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Fig. 6. Transition-state geometry for water dissociation at the perfect surface type 2.
surfaces 1 and 3 even at low temperatures, while dissociation is kinetically hindered on surface 2. The experimental fact [27] that water dissociation plays only a minor role on defect-free epitaxially grown Cr O leads us to the conclusion that 2 3 the Cr-terminated (0001) surface is identical to surface type 2. Periodic ab-initio calculations [7] also favor surface type 2 compared to other possible structures. Therefore, further investigations presented here will mainly concentrate on this surface type. Another experimental fact which has to be considered is that the UP spectra [27] show only one signal for OH groups after water dissociation. The structures shown in Fig. 5 for the defect-free (0001) surfaces all have in common that the two OH groups O –H and O –H are not equivalent due to w s their differences in coordination. The O –H group w has only one bond to a surface Cr atom, while O is bound to two or three Cr atoms. This s inequivalence can be seen from the calculated orbital energies of the highest OH s orbital in the valence-band region. The s orbital of the O –H s group is 4.3 eV lower in energy than the s orbital of the O –H group. Angle-resolved UPS experiw ments also suggest that the OH groups are perpendicular on the surface. The calculated angles with the surface normal b and b show large OwH OH deviations from the expected values of zero. This leads us to the conclusion that surface defects, especially oxygen defects, play a role for water dissociation. This has been suggested by experimentalists [27].
3.3.2. Surfaces with oxygen defects From experiments, it is known [27] that the Cr O (0001) surface contains a small amount of 2 3 oxygen defects. For rutile [34], it has been shown that oxygen defects enhance the dissociation of water molecules. For this reason, the effect of a single oxygen vacancy on water adsorption was studied for surface type 2. A surface oxygen atom was removed from the cluster Cr O embedded 92 138 in the same array of 1600 pseudo-atoms as for the stoichiometric cluster. Water adsorption was assumed to take place at the defect position, the water oxygen atom occupying the vacant surface oxygen site. Local relaxation of the nearest surface atoms was taken into account for the free cluster reference and the cluster–water system. The optimized structures of the molecular and dissociative form of water (Fig. 7) are summarized in Table 4. In the molecular adsorption, the water oxygen ˚ above the O takes a position approximately 1 A w position of the missing surface oxygen. The hydrogen atoms of water are not equivalent: one forms a hydrogen bond to a surface oxygen while the other is points away from the surface. In the dissociative form, the two OH groups have the same coordination and their angles with the surface
Fig. 7. Water adsorption at surface type 2 with an oxygen defect. (a) Molecular and (b) dissociative adsorption.
T. Bredow / Surface Science 401 (1998) 82–95
91
Table 4 Optimized geometry parameters and adsorption energies for the adsorption of a single water molecule at Cr O (0001) surface 2 3 type 2 with an oxygen vacancy; see Table 3 for details Adsorption
˚) R (A Cr O ˚ R s w(A ) O H ˚ R w (A ) OH b s (°) OwH b (°) OH ˚ Dzs (A ) Crs ˚ Dz (A) O ˚) DR w (A XOw E (kJ mol-1) ads
Molecular
Dissociative
2.14 0.98/1.03 – – – +0.03 +1.06 +0.19 251
1.82 0.95 0.96 36 44 +0.06 +0.15 +0.06 556
normal b and b are similar. The chemical O H OH equivalencew can be sseen from the calculated s orbital energies of the two OH groups. The energy difference is now only 0.5 eV, which can explain the single broad signal in the UP spectra. The values of b and b , 36° and 44°, respectively, O H OsH deviate fromw the experimentally suggested value of 0°. This is larger than the error limits of angleresolved UPS, and could be due to inaccuracies in the theoretical approach. It is also possible that the measurements include averaging on different positions, partly near surface defects such as steps and kinks. It seems reasonable that the OH bonds are not perpendicular on the surface, since the repulsion from the surface Cr atom is reduced after tilting. For the defect site, the relative stabilities of the molecular and dissociative forms of water are reversed compared to the non-defective surface. The dissociation is now exothermic by 305 kJ mol−1. The calculated transition barrier for dissociation is only 40 kJ mol−1, which is close to the values for the non-defective surfaces 1 and 3. The geometry of the transition structure is given in Fig. 8. The dissociation involves movements of the surface oxygen O and the water oxygen O s w and the formation of a hydrogen bond to O . s 3.4. Monolayer adsorption of water The monolayer adsorption on the defect-free Cr O (0001) surface type 2 has been simulated 2 3
Fig. 8. Transition-state geometry for water dissociation at surface type 2 with an oxygen defect.
with the cluster model Cr O embedded in 1600 92 138 pseudo-atoms used previously for single-molecule adsorption studies. The model contains 19 adsorption positions, the central position and two symmetric shells with six and 12 sites, respectively. Two islands of seven and 19 H O molecules were 2 used for monolayer representation ( Figs. 9 and 10). The coordinates of the water molecules and the surface atoms near the different sites were optimized equivalently. In order to avoid artificial effects from the boundaries of the water islands, the adsorption energy in Table 5 is calculated for the removal of the central H O only. The coordina2 tion of the central water is close to that of a molecule in a real monolayer. Another reason for this procedure is that the experimentally available isosteric heat of formation is defined for an infinitesimal change of the coverage. In Table 5 it can be seen that the geometrical changes between the seven-molecule and the 19-molecule islands are small. The water orientation of both the molecular and dissociative form does not show significant differences compared to single-molecule adsorp˚, tion. The Cr –O distance is reduced by 0.05 A s w while the angles deviate by less than 5°. Also, the local surface relaxations differ only by less than ˚. 0.05 A The calculated adsorption energies of the central H O for monolayer simulation are much lower 2 than for single-molecule adsorption. For the molecular form, the two islands give more or less the same result, 188 and 180 kJ mol−1, respectively, indicating that the long-range effects are
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Fig. 9. Simulation of monolayer adsorption at surface type 2: cluster Cr O with seven H O. (a) Molecular and (b) dissoci92 138 2 ative adsorption. Only real atoms are shown.
Fig. 10. Simulation of monolayer adsorption at surface type 2: cluster Cr O with 19 H O. (a) Molecular and (b) dissociative 92 138 2 adsorption. Only real atoms are shown.
already accounted for by the island model. The largest island shows a reduction of E by ads 15 kJ mol−1 with respect to single-molecule adsorption. The situation is completely different for a monolayer of dissociated water. Desorption of OH and H as H O from the center of the 2 19-molecule island costs only 80 kJ mol−1, compared to 130 kJ mol−1 for the seven-molecule island and 170 kJ mol−1 for a single H O unit. 2 Two effects are responsible for these differences. Lateral long-range Coulombic repulsions between the protruding O Hd− groups (d is approximately w 0.5 a.u.) reduce the adsorption energy. As a second
effect, there is a strong electron transfer from the surface to water of about 0.3 a.u. per H O unit, 2 which destabilizes the Cr O surface when a mono2 3 layer of dissociated water is adsorbed. The trend of decreasing adsorption energies with increasing coverage is in qualitative agreement with calorimetric measurements on Cr O samples 2 3 [48–50]. The absolute values of E calculated in ads this study cannot be compared directly with the experimental values DH from Refs. [48–50], ads since the surface structure of the samples may be different from the models used in this study due to their preparation. However, the order of magni-
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Table 5 Optimized geometry parameters and adsorption energies for monolayer adsorption of water at Cr O (0001) surface type 2; see Table 3 2 3 for details 7HO 2
19 H O 2
Adsorption
Molecular
Dissociative
Molecular
Dissociative
˚) R (A Cr O ˚ R s w(A ) O H ˚ R w (A ) OsH a (°) b (°) O H b w (°) OH c s w (°) CrsO ˚ Dz (A) Cr ˚ Dz s (A ) O ˚) DR s (A XOs E (kJ mol-1) ads
2.25 0.99 – 104 – – 53 +0.06 +0.03 +0.19 188
1.88 0.95 0.98 – 68 28 33 +0.20 +0.16 +0.09 134
2.23 1.00 – 103 – – 53 +0.03 +0.03 +0.18 180
1.86 0.95 0.98 – 67 26 33 +0.13 +0.19 +0.06 77
tude of the calculated E , i.e. 180–195 kJ mol−1 ads for molecular adsorption and 80–170 kJ mol−1 for dissociative adsorption, agrees very well with the differential heats of adsorption [48–50], i.e. 80–160 kJ mol−1 for the first layer of water on Cr O . The upper limit of the experimental investi2 3 gation is for the limit of zero coverage.
4. Summary and conclusions The molecular and dissociative adsorption of water on different kinds of Cr-terminated Cr O 2 3 surfaces was studied theoretically with embedded cluster models. A semi-empirical SCF MO method has been used for the calculations with empirical parameters specially adjusted for the description of Cr O bulk properties. The clusters were chosen 2 3 to be large enough to describe the electron redestribution in the surface area due to charge transfer from the adsorbate molecules. Long-range electrostatic effects have been introduced into the models by an embedding procedure. Three different geometrical arrangements of the surface Cr atoms have been taken into account, referring to previous suggestions from experimentalists. On two surface structures, types 1 and 3, water dissociation is highly exothermic and the activation barrier is relatively small. On surface type 2, the molecular form of water is slightly more stable than the
dissociative form, and a high activation barrier of 171 kJ mol−1 exists. The low adsorption energies and the conversion of relative stabilities of the molecular and dissociative forms on surface type 2 compared to the other structures can be explained by the strong stabilization due to relaxation of surface Cr atoms and the geometrical structure of the oxygen and the third Cr layer. Only the data for surface type 2 can explain the experimental finding that water does not dissociate considerably on non-defective Cr O (0001). 2 3 Therefore, it is concluded that the structure of Cr-terminated epitaxially grown Cr O (0001) is 2 3 that of type 2. This conclusion agrees with other theoretical calculations for this system. On all defect-free surfaces, the two OH groups formed after water dissociation are different in orientation and coordination, and would give different signals in UPS spectra. Agreement with the experimental spectra, which show only one OH signal, is achieved when water dissociates at oxygen vacancies. Water dissociation on surface structure 2 is energetically favored at oxygen defect sites, and the OH groups formed after dissociation are similar in their coordination and orientation. The calculated orbital energies are so close that the experimental spectra can be explained. Lateral interaction between adsorbed water molecules in a monolayer and charge transfer to the surface leads to a reduction of the adsorption
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energy compared to the single molecule adsorption. E decreases from 195 to 180 kJ mol−1 for ads the molecular form. The dissociated form is more destabilized when larger islands are formed. E ads decreases from 170 kJ mol−1 for a single molecule to 130 kJ mol−1 for a seven-molecule island and to 80 kJ mol−1 for a 19-molecule island. It can be expected that a full monolayer of dissociatively adsorbed water will not be formed. In general, the decrease of E with increasing coverage is in ads agreement with experimental measurements on Cr O crystals. 2 3
Acknowledgements The author would like to thank H.-J. Freund, Berlin, and H. Kuhlenbeck, Bochum, for many helpful and stimulating discussions. This work was partially supported by the Commission of the European Communities and the Deutsche Forschungsgemeinschaft. The calculations were performed on a Siemens VPP300 and a Cray T3E at the Universita¨t Hannover. Part of the structure drawings was done using 92.
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