Theoretical Models of the Polar Cu2O(100) Cu+-Terminated Surface

In both cases a practical starting point for a quantum chemical calculation is a ..... to converge the integrals over the crystal potential to four de...
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J. Phys. Chem. 1996, 100, 294-298

Theoretical Models of the Polar Cu2O(100) Cu+-Terminated Surface Martin A. Nygren*,† and Lars G. M. Pettersson Department of Physics, UniVersity of Stockholm, Box 6730, S-133 85 Stockholm, Sweden

Alexander Freitag and Volker Staemmler Lehrstuhl fu¨ r Theoretische Chemie, Ruhr-UniVersita¨ t Bochum, D-44780 Bochum, Germany

David H. Gay and Andrew L. Rohl The Royal Institution, 21 Albemarle Street, London, W1X 4BS, U.K. ReceiVed: June 19, 1995; In Final Form: September 19, 1995X

Different reconstructions of the polar, cation-terminated (100) surface of Cu2O have been investigated. All surfaces have been fully relaxed employing a pair-potential and shell-model description of the interactions within the crystal. A (1 × 1) missing-row reconstruction gave the lowest surface energy, while the experimentally reported (3x2 × x2)R45° surface structure could not be made stable. Quantum chemical models of the (1 × 1)-reconstructed surface were studied and the Cu+ (d10 f d9 s1) excitation energy computed; relaxation of the surface leads to an increased excitation energy (1.89 eV) and a more ionic description compared with the reconstructed but unrelaxed surface (1.38 eV). The hydrogen atomic chemisorption energy was also computed; for the relaxed surface the computed binding energy of 2.06 eV is sufficiently below half the binding energy of H2 that hydrogen dissociation can be excluded. This is in agreement with experiment. For the unrelaxed surface the binding energy is higher, 2.26 eV, which would allow energetically for H2 to dissociate. The convergence of the Madelung potential for these nontrivial surfaces is investigated with the conclusion that it is favorable to perform the full Ewald summation. A program to compute the Gaussian integrals over the Madelung potential is reported.

I. Introduction In this work we address the problem of describing the polar, Cu+-terminated (100) surface of Cu2O and its reactivity toward atomic hydrogen. In particular, we address the question of reconstructions and the importance not only of performing a structural or topological reconstruction keeping the ions in the bulk positions but also for relaxing the ions completely within the given topology. The calculations have been made in several steps, by first exploring the relative stabilities of several different possible structural reconstructions using pair potentials to describe the interaction. The best surfaces were then further relaxed using shell-model pair potentials and a static energy minimization of the surface structure. Finally, quantum chemical calculations of surface excitation energies and the hydrogen chemisorption energy were performed on embedded cluster models of the relaxed surface structure. Theoretical modeling of metal oxide surfaces is in many respects more complicated than the modeling of the pure metal surfaces. In both cases a practical starting point for a quantum chemical calculation is a cluster model of the site of interest where of the order of 5-50 atoms are taken to represent the surface. In the case of a metal, questions such as convergence of the properties of interest with respect to cluster size have to be addressed, but normally no further consideration of the embedding of the cluster needs to be made.1,2 For a metal oxide, at least the electrostatic potential generated by the remainder of the crystal must be considered. This entails expanding the potential approximately by using a finite number of suitable point charges representing the remaining ions, or † Current address: The Royal Institution, 21 Albemarle Street, London W1X 4BS, U.K. X Abstract published in AdVance ACS Abstracts, December 1, 1995.

0022-3654/96/20100-0294$12.00/0

by performing the Ewald summation3 over the semiinfinite crystal. In either case some assumption of the degree of ionicity of the crystal must be made. Since the anions in the crystal in general will have cations as nearest neighbors, some further consideration has to be made as to the termination or embedding of the cluster in order to avoid spurious effects of polarization of the negative ions toward unscreened positive point charges.4 In the case of ionic crystals, the particular facet that is exposed becomes particularly critical due to the long-range Coulomb interaction; only nonpolar surfaces, i.e, surfaces without a dipole moment perpendicular to the surface, may be stable with only minor rearrangements of the ions. All surfaces, or bulk terminations, which are built from alternating layers of positive and negative charges must reconstruct or be otherwise stabilized in order to exist.5 Most previous theoretical work on metal oxide surfaces has in fact been devoted to the study of nonpolar terminations, such as the MgO(100),4,6 NiO(100),7 and ZnO(101h0)8 surfaces. Several different mechanisms can be imagined to obtain a finite electrostatic contribution to the surface energy for a polar cut of a metal oxide crystal; it has been demonstrated5 that a stable surface results from reducing the charge at the surface according to Qs ) σQ with σ taken as σ ) a/(a + b), where a and b are the (constant) interlayer distances. This would, e.g., in the case of cleavage of MgO to expose the (111) surface, correspond to cleave the crystal not between two ion layers but in an ion layer in such a way that half the ions of this layer goes with either side of the crystal at the cut. Instead of a anionterminated and a cation-terminated surface one thus obtains either two anion-terminated or two cation-terminated surfaces (corresponding to the two different possible cuts), but each with a reduced charge. Alternative mechanisms to generate the © 1996 American Chemical Society

Polar Cu2O(100) Cu+-Terminated Surface

J. Phys. Chem., Vol. 100, No. 1, 1996 295

TABLE 1: Potential Parameters Charges qi

Cu

Ocore

Oshell

1.00

0.04

-2.04

integrals over the Ewald sums using a newly written extension of the ECPAIMP program.20 The AIMP formalism includes long- and short-range Coulomb, exchange, and projector components19 for each type of ion (I ) Cu+, O2-):

Buckingham Potentials, V(r) ) A exp[-r/F] - C/r6 A (eV) Oshell-Oshell Cucore-Oshell

9547.96 610.47

I,MP I,MP Vˆ lr-Coul (i) + Vˆ sr-Coul (i) + Vˆ I,MP ˆ I(i) exch (i) + P

C (eV Å6)

F (Å) 0.21916 0.30450

32.0 0.0

Core-Shell Harmonic Spring for Oxygen, V(r) ) 1/2kx2

is simply the point-charge potential from the ionic charge, while the short-range term describes the deviation from complete screening through

k (eV/Å2) Ocore-Oshell

6.30

necessary charge reduction are a change in oxidation state, reconstruction to locally expose more stable facets, or stabilization by, e.g., decomposition of water which converts the O2anions at the surface to OH-, leading to the required stabilization. The latter process is active in the stabilisation of NiO(111).8 For the polar, Cu+-terminated (100) surface of Cu2O, Cox and Schulz have performed a number of experimental studies of the surface structure,9 interaction with atomic hydrogen,10 water,11 propene,12 C3 acids,13 allyl alcohol and 1-propanol.14 The clean surface was found to reconstruct and give rise to a (3x2 × x2)R45° LEED pattern with many missing spots.9 No reactivity toward H2 was observed, but by predissociating H2 the surface could react with atomic hydrogen to form a Cu+-H surface species;10 adsorption of hydrogen also induced a reconstruction of the surface back to (1 × 1) periodicity. II. Computational Details The study of the surface reconstructions was performed using the MARVIN15 program which calculates surface structure relaxations. The interatomic interactions are described through two- or three-body potentials. For ionic systems, such as the present, the electrostatic interaction is obtained through the proper Ewald summation. In the present application the potentials used for Cu+-O2- and O2--O2- are of Buckingham type with a shell-model description of the anion polarizability. The parameters were taken from ref 16 and are displayed in Table 1. The polar Cu+-terminated (100) surface of Cu2O is Madelung unstable and the net dipole over the crystal must be eliminated to generate a stable surface. We have in the present work chosen to reduce the surface charge by moving half the top-layer Cu+ cations down to the opposite face of the slab. MARVIN’s program divides the slab into two regions, and the topmost region (region 1) is allowed to relax and placed upon a second region (region 2) kept fixed to reproduce the potential of the bulk structure on region 1. It is necessary that the second region is deep enough so that there is no interaction between ions in the upper region and the bottom of the fixed region. The bulk structure was achieved by a three-dimensional energy minimization using the program GULP.17 The lattice parameter computed was 4.270 Å compared to the 4.267 Å18 found experimentally. In the surface calculations region 1 consisted of four to eight unit cells and region 2 was 10 unit cells deep. The surface energy computed is defined as the difference between the energy per surface unit minus the bulk energy for a corresponding number of bulk unit cells. The quantum chemical models of the surface consisted of a CuO, Cu2O, or Cu3O unit embedded in a surrounding of total ion ab initio model potentials (AIMP);19 the crystal potential was included either through explicit point charges to represent the remaining crystal or by directly evaluating the one-electron

(1)

I,MP (i) Vˆ lr-Coul

2

I,MP Vsr-Coul (i)

)

∑j

AIj

exp[-RIj rIi ] rIi

(2)

where the set of parameters {AIj ,RIj } are obtained by fitting to the local short-range Coulomb potential, -(NI/rIi ) + Jˆ I, where the Coulomb operators Jˆ I are built from the orbitals of ion I in the appropriate environment. The nonlocal exchange operator Vˆ Iexch is spectrally represented:19 I

ˆ IVˆ exchPˆ I Vˆ I,MP exch (i) ) P

(3)

where Pˆ I is the projection operator on the primitive basis set {|χI〉} used for ion I, with

Pˆ I ) χI(SI)-1(χI)†

(4)

SI is the corresponding overlap matrix. The projection operator, finally, is defined as

Pˆ I ) R

(-2∈Ik)|φIk,occ〉〈φIk,occ| ∑ k∈I

(5)

where ∈Ik is the orbital energy of the occupied atomic (ion) orbital φIk,occ. R is a scaling parameter, which is set to 0.65 in the present case following.21 The calculations to obtain the Cu(d10fd9 s1) excitation energy and the hydrogen binding were performed at the SCF and MCPF22 levels. Relativistic effects were obtained through a first-order perturbation theory treatment of the mass-velocity and Darwin terms and have been added to all results. For a gas phase copper ion, the d10 f d9 s1 (1S f 3D) excitation energy decreased from 2.36 to 1.71 eV when the relativistic effects were included. The basis set used were (5s 1p)/[3s 1p]23 for hydrogen, (15s 12p 6d 3f)/[6s 5p 3d 1f] for copper,24 and (10s 6p 1d)/[5s 4p 1d] for oxygen.4 The small cluster was embedded in a surrounding of total ion AIMP’s out to a distance of 10 a0. This embedding was automatically generated by the ECPAIMP program. The ion positions in the optimized surface large unit cell (i.e., all unit cells from the surface toward the bulk that were modified by the presence of the surface cut) from the MARVIN calculation were read in and the nuclear attraction integrals over the Madelung potential were computed through the proper Ewald summation at the integral level using the approach of ref 25; again this was achieved through a recent extension of the ECPAIMP program.20 In order to find the optimal position for the hydrogen atom a numerical minimizer has been implemented. The method used is Powell’s method as described in ref 26. Parabolic interpolation has been used for the line minimizations. III. Results and Discussion Structure of the Polar Cu2O(100) Surface. Cu2O crystallizes in the cuprite structure with a lattice parameter of 4.267

296 J. Phys. Chem., Vol. 100, No. 1, 1996

Nygren et al.

TABLE 2: Surface Energies (J/m2) for Differently Reconstructed Surfaces reconstruction

unrelaxed

relaxed

(1 × 1) missing row (1 × 1) on-top (x2 × x2)R45° missing row (x2 × 2 x2)R45° missing row (2 × 1) missing row (3x2 × x2)R45°

1.65 2.84 2.15 2.75 2.50 1.65b

1.09 2.24 N.C.a N.C.a 1.30 N.C.a

No converged surface structure was obtained. b Started from (1 × 1) missing row unrelaxed topology. a

Å.18 The cubic unit cell has oxygen ions at the center and corners and four of the eight interstitial positions are occupied by the Cu+ cations. For the (111) surface there is a nonpolar cut, but the (100) surface, in a simple bulk termination, would lead to alternating cation and anion layers with a resulting dipole across the crystal and would thus be Madelung unstable. In order to have a finite surface energy the perpendicular dipole across the crystal must be eliminated. For Cu2O(100) the interlayer distances a and b are equal so Qs ) aQ/(a + b) ) 1/25 and the charge of the topmost layer must be halved to produce a stable cut. In the present work we have chosen to reconstruct the Cu+-terminated surface by removing half the Cu+ cations from the top layer and placing them at the bottom of the slab model that was used to investigate the surface structure and relaxations. Several different reconstructions were investigated using the pair potentials in Table 1 and the MARVIN program. For each of these, the surface energy (see preceding section) was first computed without relaxing the ions from their bulk positions. As a second step, the ions were allowed to move and the final, relaxed surface energy was also obtained (Table 2). Several of the proposed reconstructions were ruled out due to significant reconstruction taking place all through the surface region to a depth greater than eight unit cells. When the entire surface region was affected, even though the depth was extended in several successive steps, this was taken as an indication of a

reconstruction to expose a more stable facet than the desired (100). This was the case for, e.g., the (x2 × x2)R45°, the (x2 × 2x2)R45°, and the (3x2 × x2)R45° reconstructions; the latter is the one reported in the LEED experiment of ref 9. The surface unit cell of the most stable (1 × 1) reconstruction is depicted in Figure 1 before and after relaxation. The initial structure was taken as a simple cation bulk termination with half the top layer Cu+ ions moved to the bottom of the slab. Quite large motions of the ions in the first three unit cells may be discerned. The general trend is for the top layer Cu+ to move downwards (by 1.36 Å), the second layer copper ions by 0.28 Å, while in the third layer one copper moves down by 0.32 Å and the other up by 0.44 Å. Similarly, the topmost oxygen moves downwards by 0.90 Å, while the second-layer oxygen moves upwards by 0.24 Å. These motions are combined with quite large lateral motions in the lattice; this can be seen in the top view of the surface unit cell before and after relaxation. The main result of the relaxation of the reconstructed surface is a more compact surface where the cation sinks in and the oxygen anion becomes somewhat more exposed. This has effects also on the electronic structure at the surface as measured by the Cu+(d10 f d9 s1) excitation energy: for the unrelaxed surface the MCPF-level excitation energy was computed to be 1.38 eV, while after relaxation this had increased to 1.89 eV. This is mainly due to the more compact environment surrounding the cations in the relaxed surface. Since the formation of a covalent bond to the Cu+ cation is dependent on this type of excitation the change in the excitation energy can be expected to affect the binding energy to, e.g., atomic hydrogen, as studied in the present work. Before discussing this we will, however, turn to a discussion of the convergence of the Madelung potential using point-charge expansions for the present type of polar surface. For nonpolar cuts of rock-salt structured crystals, such as, e.g., MgO(100), the convergence of the Madelung potential with the number of point charges used in an approximate expansion

Figure 1. Side view of the (1 × 1) missing row reconstruction, the darker atoms being oxygens: (A, left) unrelaxed structure; (B, right) relaxed structure.

Polar Cu2O(100) Cu+-Terminated Surface

J. Phys. Chem., Vol. 100, No. 1, 1996 297

TABLE 3: Convergence of Madelung Potential for Differently Reconstructed, but Unrelaxed Cu2O(100) Surfaces, Total SCF Energy (EH) Relative to Gas Phase Cu+, and Effect on Singlet-Triplet Separation (eV) reconstruction (1 × 1) (1 × 1) (1 × 1) (x2 × 2x2)R45° (x2 × 2x2)R45° (x2 × 2x2)R45°

radiusa layersb charges 50 100 100 50 100 100

8 8 16 8 8 16

2770 10962 22902 2072 7176 15004

∆E

∆(S-T)

-0.354 01 -0.336 60 -0.354 62 -0.194 00 -0.184 88 -0.196 76

-0.77 -0.79 -0.81 -1.12 -1.13 -1.14

a Radius in a0 of point-charge embedding cylinder. b Number of layers on ions.

is quite rapid; around 5000 point charges within a square with side 60 a0 around the central site is sufficient to converge the integrals over the crystal potential to four decimal places. A few hundred point charges are actually sufficient to ensure that computed properties, such as shifts in vibrational frequencies, binding energies, etc., for adsorbates are converged.27,28 In the present case, with a less compact and cation-terminated surface, a substantially larger number of point charges are required to generate a converged potential in the cluster region. In Table 3 we give the energy differences (at the SCF level) obtained from different sizes of the point-charge expansion. Here we compare the total energy of a Cu+ cation at the surface with that of the free ion. The Evjen technique28,29 of fractional charges is always used to speed up the convergence, but no embedding apart from the usual point charges (taken as the full ionic charge) is performed. As is seen from Table 3, the convergence with respect to the radius of the embedding cylinder is quite slow, while the sensitivity of the results with respect to the number of layers is less pronounced. This is also what is found for, e.g., MgO(100) where convergence is reached already after a few (4-5) layers.30 In the present case, however, we cannot claim that the results have converged even with a radius of 100 a0 and taking 16 layers into account. Even though the total energy still varies substantially, the differential effect on the singlettriplet separation is much smaller, as expected. However, of the order of 10 000 point charges seem to be required for a reasonably accurate representation of the crystal potential. A more reliable and also faster approach thus seems to be to evaluate the required nuclear attraction integrals directly through an Ewald summation over the crystal potential. This has been included in the ECPAIMP program following the approach given in ref 25. In the following, all results will refer to calculations where this complete summation has been performed. Hydrogen Adsorption. The Cu2O copper-terminated (100) surface does not dissociate hydrogen, but by passing the H2 through a platinum mesh placed just above the surface,10 it has been possible to study the interaction of hydrogen with the surface. The hydrogen was found to react with the Cu+ cations to form CuH+ species; this reaction also removes the (3x2 × x2)R45° symmetry seen in LEED to give a (1 × 1) pattern. The binding of atomic hydrogen to a Cu+ cation at the (1 × 1)-reconstructed and relaxed (100)-surface has been studied in the present work using four different models: a Cu3O cluster where the three top layers are included, a Cu2O cluster with one third-layer Cu, a CuO cluster, and finally just a single Cu+ cation. The clusters were embedded in a surrounding of total ion model potentials and the contribution from the crystal potential was evaluated using the full Ewald summation in the integral evaluation. The cation at the (relaxed) (1 × 1)-reconstructed surface has a 3d10 closed-shell configuration with some (0.5 electrons)

TABLE 4: Cu+(d10fd9s1) Excitation Energy (eV) for Different Cluster Models of the (1 × 1)-Reconstructed (Missing Row) and Relaxed (100) Surface, and MCPF Results Including Relativistic Correction cluster

∆E

De (eV)

Cu+ CuO Cu3O

2.07 1.89 1.76

1.61 2.06 1.92

TABLE 5: Chemisorption of Hydrogen on Cu2O(100) (1 × 1) Missing Row Reconstruction, and MCPF Results Including Relativistic Correction with and without Relaxation of the Surface re (Å)

φa

ωe (cm-1)

De (eV)

1.48 1.50

20 32

2132 1994

2.27 2.06

unrelaxed relaxed a

Cu-H angle against surface normal (degrees).

population in the 4sp orbitals. The charge is thus close to +0.5. The bond to hydrogen is formed through the excited d9 s1 (3D) state of the ion which may form a strong σ-bond to the hydrogen atom. The gain in energy from the formation of the bond is thus balanced by the cost to excite the Cu+ ion to the bonding atomic state; this leads to a rather low total binding energy for the hydrogen interaction with the surface and will explain why the surface does not dissociate H2. In Table 4 we have collected the results for this excitation energy for the four different models. It is seen that, apart from the single Cu+ ion the results are very similar, which then gives as a smallest model the (embedded) single CuO unit. A complete optimization of the hydrogen geometry relative to the fixed (after relaxation) surface model leads to a Cu-H bond distance of 1.50 Å and an angle of 32° against the surface normal (Table 5). The computed MCPF-level binding energy is 2.06 eV, which should be compared to the H2 D00 of 4.478 eV;31 thus, it is clear that this surface cannot be expected to dissociate H2. This is in accordance with the need to predissociate the hydrogen in order to obtain a reaction with the surface. For the unrelaxed surface a similar bond-distance is found while the angle against the surface normal is smaller, 20°. The binding energy is 0.20 eV higher, which partly reflects the rather large difference in d f s excitation energy, 1.38 eV compared with 1.89 eV for the fully relaxed surface. The computed binding energy is now also somewhat larger than half the H2 D00 so that without including relaxation of the surface, incorrect conclusions about the surface reactivity might be drawn. Normally one expects a higher vibrational frequency to correlate with a stronger bond. This picture is consistent with the higher, 2132 cm-1, vibrational frequency for the unrelaxed surface compared to 1994 cm-1 for the relaxed. Comparing the charge distributions in the two cases (relaxed and unrelaxed), we find the relaxed structure having a higher ionicity, with a positive charge of 0.48 on Cu+ compared with 0.17 for the unrelaxed structure. The 3d populations are very similar with 9.75 and 9.77 d-electrons (MCPF), so that the difference is exclusively in the 4s and 4p populations. In the interaction with hydrogen the relaxed surface is still the more ionic and more of the d f s excitation has to come in order to form the bond to hydrogen; the 3d population has decreased to 9.29 compared with 9.39 for the unrelaxed surface. IV. Conclusions In the present work we have performed a study of the Cu2O cation-terminated (100) surface. Since a simple bulk termination would generate a polar, Madelung-unstable surface, the surface

298 J. Phys. Chem., Vol. 100, No. 1, 1996 must reconstruct in order to remove the perpendicular dipole across the crystal. Several topologically different reconstructions have been studied, using pair potentials within the shell model for polarizable ions to generate the relaxed ion positions for each reconstruction. The lowest surface energy was found for a missing-row (1 × 1) reconstruction, where half the toplayer cations have been transferred to the opposite face of the slab model of the crystal. It proved not to be possible to obtain the experimentally reported (3x2 × x2)R45° structure; this was due to reconstruction taking place all through the rather large surface layer used in the modeling. This reconstruction could be due to the potentials not adequately representing the interaction of the surface ions. However, this would only have affected the topmost layer not the whole simulation unit. More likely, the (3x2 × x2)R45° reconstruction is stabilized with thermal effects. Further research is needed to answer these questions. Since this reconstruction is observed experimentally10 to be lifted by chemisorption of atomic hydrogen, to generate a (1 × 1) LEED structure, it was deemed sufficient to model the latter surface. The relaxation of the surface generates a more compact structure with quite substantial downwards displacements of the order of 1 Å of the top-layer ions. This has several effects: the d f s Cu+ excitation energy is increased from 1.38 to 1.89 eV and the surface ions become substantially more ionic. Since the bonding to hydrogen requires a d f s excitation to take place, the computed hydrogen chemisorption energy is affected by whether or not this relaxation has been allowed to occur before making a quantum chemical model of the surface. The computed hydrogen chemisorption energy for the model of the reconstructed but unrelaxed surface was 2.27 eV, which would lead to the conclusion that dissociation of H2 over Cu2O(100) would be energetically possible; this is contrary to what is observed experimentally. The relaxed surface, on the other hand, gives a binding energy of 2.06 eV, which is sufficiently below half the binding energy of H2 to allow the conclusion to be drawn that Cu2O(100) should not dissociate H2. A common method to generate the Madelung potential felt by the quantum chemical cluster model is to include a number of ions from the immediate surroundings as point charges. For nonpolar cuts of, e.g., rock-salt structured crystals this converges quite rapidly and rather few (of the order of a thousand) point charges need to be included. For the present type of reconstructed surfaces we find, not surprisingly, that substantially larger numbers of charges must be used in such an expansion. At this point it becomes advantageous to perform the full Ewald summation at the integral level; this has been implemented in the ECPAIMP program and applied in the present work. Acknowledgment. This work was partly supported by funds from the Swedish Consortium on Oxidic Overlayers. D.H.G. thanks BIOSYM Technologies, San Diego, for their financial support. References and Notes (1) Siegbahn, P. E. M.; Nygren, M. A.; Wahlgren, U. In Cluster Models for Surface and Bulk Phenomena; NATO ASI Series 283; Pacchioni, G., Bagus, P. S., Eds.; Plenum: New York, 1992; p 267.

Nygren et al. (2) Whitten, J. L. Chem. Phys. 1993, 177, 387. (3) Ewald, P. P. Ann. Phys. 1921, 64, 253. Parry, D. E. Surf. Sci. 1975, 49, 433. Parry, D. E. Surf. Sci. 1976, 54, 195. (4) Nygren, M. A.; Pettersson, L. G. M.; Barandiara´n, Z.; Seijo, L. J. Chem. Phys. 1994, 100, 2010. (5) Fripiat, J. G.; Lucas, A. A.; Andre´, J. M.; Derouane, E. G. Chem. Phys. 1977, 21, 101. Tasker, P. W. J. Phys. C 1979, 12, 4977. (6) See for example: Dovesi, R.; Orlando, R.; Ricca, F.; Roetti, C. Surf. Sci. 1987, 186, 267. Pisani, C.; Dovesi, R.; Nada, R.; Tamiro, S. Surf. Sci. 1989, 216, 489. Lakhlifi, A.; Girardet, C. Surf. Sci. 1991, 241, 400. Pacchioni, G.; Cogliandro, G.; Bagus, P. S. Int. J. Quantum Chem. 1992, 42, 1115. Stro¨mberg, D. Surf. Sci. 1992, 275, 473. Neyman, K. M.; Ro¨sch, N. Chem. Phys. 1992, 168, 267. Neyman, K. M.; Ro¨sch, N. Surf. Sci. 1993, 297, 223. Pacchioni, G. Surf. Sci. 1993, 281, 207. (7) See for example: Pacchioni, G.; Cogliandro, G.; Bagus, P. S. Surf. Sci. 1991, 255, 344. Po¨hlchen, M.; Staemmler, V. J. Chem. Phys. 1993, 97, 2583. Pettersson, L. G. M. Theor. Chim. Acta 1994, 87, 293. Nygren, M. A.; Pettersson, L. G. M. J. Electron. Spectrosc. 1994, 69, 43. Po¨hlchen, M.; Staemmler, V.; Wasilewski, J. to be published. (8) See for example: Jen, S. F.; Anderson, A. B. Surf. Sci. 1989, 223, 119. Nakatsuji, H.; Fukunishi, Y. Int. J. Quantum Chem. 1992, 42, 1101. Nyberg, M.; Nygren, M. A.; Pettersson, L. G. M.; Gay, D. H.; Rohl, A. L. to be published. Cappus, D.; Xu, C.; Ehrlich, D.; Dillman, B.; Ventice, C. A., Jr.; Al-Shappery, K.; Kuhlenbeck, H.; Freund, H.-J. Chem. Phys. 1993, 177, 533. Rohr, F.; Wirth, K.; Libuda, J.; Cappus, D.; Ba¨umer, M.; Freund, H.-J. Surf. Sci. 1994, 315, 977. (9) Schulz, K. H.; Cox, D. F. Phys. ReV. 1991, B43, 1610. (10) Schulz, K. H.; Cox, D. F. Surf. Sci. 1992, 278, 9. (11) Schulz, K. H.; Cox, D. F. Surf. Sci. 1991, 256, 67. (12) Schulz, K. H.; Cox, D. F. Surf. Sci. 1992, 262, 318. (13) Schulz, K. H.; Cox, D. F. J. Phys. Chem. 1992, 96, 7394. (14) Schulz, K. H.; Cox, D. F. J. Phys. Chem. 1993, 97, 647. (15) Gay, D. H.; Rohl, A. L. J. Chem. Soc., Faraday Trans. 1995, 91, 925. (16) Binks, J. Cu2O potential parameters, private communication. (17) General Utility Lattice Program (GULP), developed by J.D. Gale, Royal Institution of Great Britain/Imperial College, 1992-5. (18) Restori, R.; Schwarzenbach, D. Acta Crystallogr. B 1986, 42, 201. (19) Barandiara´n, Z.; Seijo, L. J. Chem. Phys. 1988, 89, 5739. Barandiara´n, Z.; Seijo, L. In Computational Chemistry: Structure, Interactions and ReactiVity; Fraga, S., Ed.; Studies in Physical and Theoretical Chemistry, Vol. 77(B); Elsevier: Amsterdam, 1992; pp 435-461. (20) ECPAIMP is an integral program for ECP and AIMP calculations written by L. G. M. Pettersson and L. Seijo. Integrals over the Ewald sum have been written by M. A. Nygren. (21) Pascual, J. L.; Seijo, L.; Barandiara`n, Z. private communication. (22) Chong, D. P.; Langhoff, S. R. J. Chem. Phys. 1986, 84, 5606. (23) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. (24) Wachters, A. J. H. J. Chem. Phys. 1970, 52, 1033. (25) Saunders, V. R.; Freyria-Fava, C.; Dovesi, R.; Salasco, L.; Roetti, C. Mol. Phys. 1992, 77, 629. (26) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical recipes in FORTRAN: the art of scientific computing, 2nd ed.; Cambridge University Press: London, 1992; p 410. (27) Pacchioni, G.; Cogliandro, G.; Bagus, P. S. Int. J. Quantum Chem. 1992, 42, 1115. (28) Fink, R. to be published. (29) Evjen, H. M. Phys. ReV. 1932, 39, 675. (30) Causa`, M.; Dovesi, R.; Pisani, C.; Roetti, C. Surf. Sci. 1986, 175, 551. (31) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; Van Nostrand Reinhold Co.: New York, 1979.

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