An ab Initio Periodic Study of NiO Supported at the Pd(100) Surface

Dipartimento di Chimica IFM and Centre of Excellence NIS (Nanostructured Interfaces and Surfaces), Università di Torino, via Giuria 5, 10125 Torino, ...
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J. Phys. Chem. B 2006, 110, 7918-7927

An ab Initio Periodic Study of NiO Supported at the Pd(100) Surface. Part 2: The Nonstoichiometric Ni3O4 Phase Anna Maria Ferrari,*,† Mauro Ferrero,† and Cesare Pisani†,‡ Dipartimento di Chimica IFM and Centre of Excellence NIS (Nanostructured Interfaces and Surfaces), UniVersita` di Torino, Via Giuria 5, 10125 Torino, Italy ReceiVed: December 20, 2005; In Final Form: February 20, 2006

The present computational study describes the structure and properties of a substoichiometric 2D monatomic in the height phase of nickel oxide, c(4 × 2)-Ni3O4, which has been newly found to epitaxially grow under special deposition conditions on the (100) face of palladium. A slab model is adopted where palladium is simulated by a thin film covered on both sides by epilayers, in combination with a DFT hybrid-exchange Hamiltonian; to make convergence of the SCF procedure easier, a thermal smearing technique is used, whose consequences on the results are critically analyzed. Three adsorbed systems are considered and characterized: (i) RH, that is, the c(4 × 2)-Ni3O4 phase with a rhombic distribution of Ni vacancies, as is experimentally observed; SQ, or p(2 × 2)-Ni3O4, which differs from the previous one for a square, instead of a rhombic distribution of vacancies; (iii) OX, or p(2 × 2)-O, that is, a surface oxidized phase of Pd(100) which is believed to be the precursor for the formation of RH. For a better understanding of the interaction of the metal with the adlayers, the isolated substoichiometric oxides, i-RH and i-SQ, have also been studied. It is shown that RH is more stable than SQ by a few tenths of electronvolts per Ni3O4 unit, which justifies its preferential formation and that the surface reaction, OX + 3NiO(ads) f RH, is thermodynamically possible. Special attention has been devoted to characterize RH from an energetic, geometric, electronic, and magnetic viewpoint. The strong bond which is formed between surface Pd and O ions in the adlayer is responsible for some peculiar aspects of the electronic and magnetic structures of that phase.

1. Introduction It has recently been shown that vapor deposition of nickel on Pd(001) in oxidizing atmosphere results, under special conditions, in a peculiar two-dimensional epitaxial c(4 × 2) structure of monoatomic height. Through a combination of different experimental techniques (LEED, XPS, XPD, and STM), the novel phase has been found to differ from the perfect epitaxial (1 × 1) NiO monolayer (NiOML) for a rhombic c(4 × 2) distribution of nickel vacancies; its formula unit is therefore Ni3O4.1-4 On the contrary, the stoichiometric NiO phase is not observed at the early stages of deposition but only appears for a nominal coverage that widely exceeds the monolayer. A recent combined theoretical and experimental work5 has provided justifications for the formation of c(4 × 2)-Ni3O4. It has been argued that small NiO clusters, which are forming during the deposition in contact with the surface covered by atomic oxygen in a regular p(2 × 2) arrangement, reorganize themselves into the novel Ni3O4 phase according to the reaction

3NiO[cluster] + O[p(2×2)] f Ni3O4[c(4×2)]

(1)

The present computational study is mainly concerned with the ab initio simulation of the energetic, electronic, magnetic, and structural properties of c(4 × 2)-Ni3O4. Attention is also devoted to a hypothetical adsorbed phase, p(2 × 2)-Ni3O4, which * To whom correspondence should be addressed. Tel: +39-011-6707563. Fax: +39-011-6707855. E-mail: [email protected]. † Dipartimento di Chimica IFM. ‡ Centre of Excellence NIS.

differs from the other one only for a square (SQ), instead of rhombic (RH) arrangement of Ni vacancies: for the sake of brevity, the two phases are indicated in the following as RH and SQ. Since SQ is also compatible with reaction 1, the problem dealt with becomes, why it is not observed at all. A brief analysis is also included of the other regular epitaxial phase involved in reaction 1, namely, p(2 × 2)-O. The structures investigated are schematically depicted in Figure 1. In a previous paper (to be referred to in the following as 1), we studied the properties of the bare Pd(100) surface in relation with those of bulk Pd and characterized the epitaxial NiO monolayer.6 Paper 1 is an important reference for the present study in two respects: first of all, it serves as a validation of the computational techniques here adopted (see next section); second, it permits us to relate the characteristics of the nonstoichiometric phase to those of the “perfect” (1 × 1)-NiO-ML. The organization of this paper is as follows. In section 2, the computational models and techniques adopted are presented and discussed: all phases considered are described with a periodic twodimensional (2D) slab model, a hybrid DFT Hamiltonian is adopted, and a basis set of localized functions is used. Section 3 presents and discusses the results obtained for the different phases. 2. Computational Models and Techniques The calibration of the computational model for such complicated systems as those considered here is far from trivial and is a compromise between conflicting requirements of accuracy and feasibility. We report here the choices adopted with a brief justification for each of them. Reference is made to paper 1 for

10.1021/jp0573994 CCC: $30.25 © 2006 American Chemical Society Published on Web 03/25/2006

NiO Supported at the Pd(100) Surface Part 2

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Figure 1. Geometric and magnetic structure of the different phases considered: top left, the epitaxial stoichiometric NiO monolayer (NiO-ML); top center, p(2 × 2)-O; top right, p(2 × 2)-Ni3O4 in its ferromagnetic configuration (SQ-FM). Below, from left to right: c(4 × 2)-Ni3O4 in the three magnetic configurations here considered, RH-FM, RH-A1, and RH-A2. Pd atoms in the surface and subsurface layers are drawn as large white circles with black and gray contours, respectively. Ni and O atoms are drawn as small black and gray circles, respectively. In the Ni3O4 phases, 1 and 2 indicate Ni atoms with 1 or 2 multiplicity, a prime distinguishing those of opposite spin. In the magnetic phases, the up or down triangles indicate the direction of the magnetic moment on nickel atoms; the large, thick circumferences around the Ni vacancies indicate the magnetic moment associated with the two-electron hole at the oxygens, directed in two opposite directions, if they are either continuous or dotted. The 2D unit cell is identified in all cases by the continuous gray lines. See text for details.

a more detailed discussion. As in that paper, all the present calculations have been performed by means of the CRYSTAL03 periodic code,7 by adopting a periodic slab model, a hybridexchange DFT Hamiltonian, and using a localized basis set of Gaussian type functions (GTFs). A three-layer Pd slab was used to model the metal substrate; despite its thinness, this film has been shown to provide a satisfactory description of the main features of the metal surface (results from test calculations comparing performances of a three-layer Pd slab and a five-layer Pd slab are reported in Table 1 of the Supporting Information). The geometry of the slab dictates the 2D unit cell of the epitaxial phases considered. In all cases, the same epilayer was made to interact with both faces of the slab; this means that the central Pd layer is always a symmetry plane. Geometry optimizations have been carried out using the procedure recently implemented in CRYSTAL: at the present, it requires the numerical calculation of gradients for conductors, since analytical gradients are only available for insulating systems. All O and Ni ions in the adlayers have been allowed to relax whereas the Pd atoms have been kept fixed at their bulk values (3.93 Å). The systems under study comprise a magnetic insulator (NiO oxide) interacting with a nonmagnetic conductor (Pd substrate), resulting in a magnetic conductor. In a DFT approach, the use of hybrid functionals is required to account for the localized nature of the unpaired electrons in magnetic systems.6,8,9 The Becke hybrid-exchange functional10 with a percentage R ) 35 of exact Hartree-Fock exchange, together with a Perdew-

Wang correlation functional11 (altogether referred to below as F35PW), has been found to adequately describe both the magnetic oxide and the metal substrate and to provide a balanced picture of the compound system. The magnetic and conducting nature of the systems under study determines additional difficulties from a computational viewpoint. The presence of 4d bands close to the Fermi level (F) creates instabilities in the wave function and makes convergence of the self-consistentfield (SCF) procedure difficult. Furthermore, the magnetic character of the compound requires the use of spin-unrestricted (SU) calculations: due to the fact that Pd is easily magnetizable, and that the high fraction of exact exchange in the hybrid Hamiltonian tends to stabilize spin-polarized structures, the SCF process may result in an unphysical solution, corresponding to strong spin polarization of the metal substrate. Both problems are alleviated by adopting a smearing procedure12-16 that consists of assigning a fractional occupancy to one-electron states in a proximity of F, owing to a Fermi-Dirac finitetemperature distribution, with T ) {β}/{kB} (kB is the Boltzmann constant, and β is the smearing parameter, usually measured in hartrees). While β ) 0.01 Ha is usually sufficient to overcome convergence difficulties, higher values of β are required to prevent the Pd spin polarization in spin-unrestricted calculations. For the systems under study, test calculations have indicated that β ) 0.035 Ha is necessary for this purpose. However, while values of β of the order of 0.02-0.04 Ha have scarce effects on the electron properties of the interface, they produce a dramatic underestimation of the binding energy BE.6 Extrapola-

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tion to zero smearing temperature is required to provide meaningful results, which is often quite difficult, as discussed below. The basis set here adopted for the Ni and O atoms in RH and SQ is the same as that used for studying the NiO-ML supported on Pd and calibrated in our previous study of ultrathin films of NiO at the Ag(001) surface:9,17 it consists of all-electron 8-411G functions for the O2- ion and in the Hay-Wadt small core pseudopotential18 together with 3sp/2d contracted GTFs for Ni2+. The O atom of the p(2 × 2)-O phase has been described by the standard 6-311G* basis set.19 The effect of basis set on the palladium electron structure has been analyzed in paper 1, and the final choice (a good compromise between size and accuracy) consists of a Hay-Wadt small core pseudopotential18 together with 4sp/2d to describe the outer electrons. Further details are found in the CRYSTAL database.20 However, results from test calculations comparing performances of the adopted Pd basis set and the larger one described in ref 6 are reported in Table 1 of the Supporting Information. The number of electrons explicitly considered is 18 for Pd and 18 for Ni (corresponding to the electron configuration 5s24p64d10 and 3s24s23p63d,8 respectively). To compare among themselves energy data referring to quite different systems, the “formation energies” starting from the bare slab and the separated atoms are provided for the various phases, obtained according to the formula

∆E′(π) )

[E(π|Pd|π) - mE(Pd)] 2

∑Eat

TABLE 1: Geometric, Energetic and Electronic Properties of the p(2 × 2)-O Phase for Three Configurations of the Square Array of Oxygens with Respect to the Metal Substrate: at the Hollow Sites (H), on Top of Surface Atoms (T), and at Bridge Positions (B)a z (Å)b d(Pdsurf-O) (Å) q(O)c q(Pdsurf)c ∆E′c (eV)d F (eV)e

H

T

B

0.70 2.09 -0.64 0.18 -2.81 -4.90

1.77 1.77 -0.52 -0.10 -0.93 -6.89

1.27 1.89 -0.56 0.07 -2.65 -5.75

a The smearing parameter β was set at 0.01 Ha. b z is the equilibrium distance between the surface plane of the substrate and the overlayer. c Mulliken net charges q are in atomic units. d ∆E′c is the BSSE corrected “formation energy” per unit cell, with reference to the bare Pd slab and the isolated O atom (see eq 1). e The Fermi level of the isolated three-layer Pd slab is -3.85 eV.

(2)

Here, E(π|Pd|π) is the total energy per unit 2D cell of the phase considered (the Pd slab sandwiched between the two adsorbed structures), m is the number of unit 2D cells of the bare Pd slab comprised in the repeat unit of the compound system, and E(Pd) is the total energy of each of them; Eat values are the energies of the isolated atoms of the adsorbed π phase. All energy data reported in this work have been corrected for the basis set superposition error (BSSE) by applying the standard counterpoise method.21 For describing electronic and magnetic structures, total and difference charge and spin density maps, band structures, and densities of states (DOSs) are reported. A Mulliken analysis has also been used to provide a rough indication of the distribution of charge and spin populations on the various atoms and to partition the total DOS into projected DOSs (PDOS). All Mulliken populations are reported in atomic units (au). 3. Results and Discussion 3.1. p(2 × 2)-O Phase. Table 1 reports the main results of the present simulations of the p(2 × 2)-O phase. Three configurations (H, T, and B) have been tried, only the first two are compatible with the LEED evidence. As expected, the H configuration (O at a hollow site) is by far preferred over the T one (O on top of surface Pd). Let us briefly discuss the H-configuration data. The BSSE corrected binding energy per O atom (the opposite of the ∆E′ value reported in the Table 1) is larger than the atomization energy of the gas-phase O2 molecule: its experimental value is 5.21 eV (2.60 eV/atom), and the calculated one with the present setup is 4.8 eV (2.4 eV/atom). This justifies the spontaneous formation of this phase in an O2 atmosphere. The equilibrium distance of O from the surface plane is in good agreement with the experimental LEED result (0.83 ( 0.02 Å).22 The analysis of the electronic structure indicates that O mainly interacts with d orbitals of the four

Figure 2. Charge difference density map for the O/Pd system in the most stable H configuration. The plot shows the difference between the electron density for the compound system and the superposition of the electron densities of the two subunits with the same internal geometry. The sections are in a vertical plane through the 4-fold hollow site and the nearest neighbor Pd atoms (see Figure 1). The continuous and dashed lines refer to the positive and negative density differences, respectively. The contour lines are drawn at intervals of 0.002 |e|/bohr3.

surface Pd atoms nearby and to a lesser extent with an spd hybrid orbital of the metal atom beneath. A considerable polarization of these bonds makes the O atom negatively charged (q(O) ) -0.64 au), which causes a decrease in the Fermi energy by more than 1 eV with respect to the bare surface; see Table 1. It is worth noticing that the usage of a five-layer Pd slab and the L-basis does not provide any significant variations in the computed adsorption properties (see Table 1 of the Supporting Information). Further insight into the oxidized Pd surface is provided by the difference electron density map of Figure 2. The charge transfer from the metal surface to the oxygens is clear, and the directionality of the Pd-O bond is made evident by the depletion of a d-Pd orbital along the bond direction. It can be finally observed that the B configuration (O at a bridge position) is less stable than the H one by only 0.16 eV, which suggests the possibility of surface migration of adsorbed O atoms, so facilitating the formation of very regular patterns. 3.2. Unsupported Ni3O4 Monolayer. Although the isolated RH (i-RH) and SQ (i-SQ) phases are totally artificial, they have nonetheless been studied to obtain information about their magnetic structure and relative stability and to derive by difference the importance of their interaction with Pd. In both cases, charge neutrality has been enforced and the internal coordinates have been allowed to relax with respect to their ideal epitaxial configuration shown in Figure 1, while maintain-

NiO Supported at the Pd(100) Surface Part 2 ing coplanarity and unit cell parameters. Before discussing the results, it is expedient to introduce a few preliminary considerations. Both i-RH and i-SQ are formally derived by removing one out of four Ni atoms from the perfect stoichiometric NiO monolayer (i-NiO-ML), which is well described owing to a pure ionic picture (Ni2+O2-). Consequently, each Ni3O4 unit is characterized by a two-electron hole; for symmetry reasons, the hole is uniformly distributed over the four O ions adjacent to the Ni vacancy. This corresponds to a partial depletion of the valence 2p-O bands of the stoichiometric oxide; in a simplified scheme, two of them (to be indicated as the O-hole) would be singly occupied, resulting in a net magnetic moment on oxygens. These facts will have important consequences on the electronic structure of the nonstoichiometric phases and on the relative stability of their different magnetic arrangements. In particular, the monolayer may become a semimetal (conduction occurs in only one of the two spin subsystems). The deep influence that a distribution of cation vacancies may have on the electronic and magnetic properties of oxides has been recently discussed by different authors.23,24 We shall come back to these aspects in the following. Consider first the results for the two ferromagnetic phases, i-SQ-FM and i-RH-FM. They are reported in the top panels of Figures 3 and 4 and in the two first columns of Table 2. The spin density maps of Figure 3 indicate clearly that the prevailing direction of spin at oxygens is opposite with respect to that on Ni ions, which has to be expected because of Pauli repulsion between nearby localized orbitals of like spin. The most interesting feature in the band structures of Figure 4 is the semimetallic character of i-SQ-FM, strictly related to the symmetry properties of that phase. The majority spin band, characterized by (Γ) ) -0.096 Ha, corresponds to one of the two O-holes, essentially localized on oxygens with a small participation of Ni(2) ions (the other O-hole orbital is directed toward Ni(1) ions). At Γ, its point symmetry is of type B2, as shown in the inset. At the other extreme of the band, at M ) (1/2, 1/2), it becomes of symmetry E, hence degenerate with a corresponding occupied crystalline orbital. Such degeneracy cannot take place at the Fermi level because of the Jahn-Teller effect, and the electronic system responds by making the film a conductor (no smearing technique was used here, however). This feature is not present in i-RH-FM, which remains a widegap semiconductor. Table 2 provides quantitative information about the two structures. It can be noted first of all that i-RH is more stable than i-SQ by 0.80 eV/cell, which can be attributed mainly to electrostatics, due to the larger average distance between Ni vacancies in the former structure; the quasi-JahnTeller instability of i-SQ-FM previously commented on may also play a role. Ion relaxation contributes to the stability of i-RH and i-SQ by 2.00 and 1.45 eV, respectively. As expected from electrostatics, the four O ions move away from the vacancy in both structures and the two Ni(2) ions move toward it in i-RH (the positions of Ni(1) in i-RH and of both Ni ions in i-SQ are constrained by symmetry to coincide with their ideal values). The electronic structure is very similar in the two phases. With respect to i-NiO-ML, where the Mulliken charges on the two ions are (1.75 au, the Ni ions are only slightly more positive, while O is less negative by 0.4 au, which shows that the twoelectron hole is practically localized on the four oxygen ions. As concerns the magnetic structure, if a magnetic moment µ ) +2 au is formally attributed to each Ni, then the hole can be assigned the value µ ) -2 au, -0.5 au/O ion, corresponding to an excess of four majority spin bands per unit cell. The

J. Phys. Chem. B, Vol. 110, No. 15, 2006 7921

Figure 3. Spin density of the isolated Ni3O4 monolayers in the plane through the nuclei. From left to right and from top to bottom: i-SQFM, i-RH-FM, i-RH-A1, and i-RH-A2. The continuous and dashed lines refer to the positive and negative spin densities, respectively. The contour lines are drawn at intervals of 0.002 au. The gray lines identify the unit cell.

TABLE 2: Results for the Fully Relaxed Unsupported Phases of Ni3O4 (i-RH and i-SQ) in Different Magnetic Arrangements ∆d(O) (Å)a ∆d(Ni(2)) (Å)a q(O)b q(Ni(1))b q(Ni(2))b µ(O)b µ(Ni(1))b µ(Ni(2))b Eg(eV)c ∆E′(eV)d

i-SQ-FM

i-RH-FM

i-RH-A1

i-RH-A2

+0.19

+0.24 -0.14 -1.35 1.81 1.79 -0.096 1.84 1.27 2.8 -41.66

+0.24 -0.14 -1.35 1.81 1.79 (0.08 (1.86 (1.19 3.7 -41.49

+0.24 -0.14 -1.35 1.81 1.79 (0.09 (1.85 (1.21 3.3 -41.54

-1.34 1.82 1.72 -0.13 1.10 1.72 -40.86

a

∆d(O) and ∆d(Ni(2)) are the change in the distance of the ions from the nearest cation vacancy with respect to their ideal epitaxial positions. b Mulliken net charges q and spin population µ are in atomic units. c E is the main gap (it is 3.7 eV in i-NiO-ML). d ∆E′ is the formation g energy per Ni3O4 unit from the free atoms.

calculated Mulliken magnetic moments on ions are obviously much less than the formal values, due to spin delocalization. Using a higher percentage R of HF exchange in the hybrid Hamiltonian would increase localization; for instance, if R ) 80 is used instead of 35, the magnetic moments in i-RH-FM

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Figure 4. Band structure and projected densities of states (PDOS, arbitrary units) of the isolated Ni3O4 monolayers. From left to right and from top to bottom: i-SQ-FM, i-RH-FM, i-RH-A1, and i-RH-A2. The thick gray horizontal line marks the Fermi level or the top of the occupied bands. The majority and minority spin bands and majority and minority spin PDOSs are drawn as continuous and dashed lines, respectively; they obviously are equal in the AFM structures. The two insets in the i-SQ-FM band structure indicate schematically the electronic structure of the majority spin crystalline orbitals at the Γ and M special points, which are commented on in the text.

TABLE 3: Geometric and Energy Data for the RH-FM and SQ-FM Phases of Ni3O4 Interacting with the Pd Surface, for Two Different Values of the Smearing Parameter βa RH-FM Ni(1) Ni(2)

O

Pd (surface) Pd (central) BEc (eV)b ∆E′c (eV)b F (eV)c

SQ-FM

β (Ha)

0.01

0.035

0.01

0.035

z q µ z ∆d q µ z ∆d q µ q µ q µ

2.22 1.75 1.80 2.19 -0.17 1.71 1.76 2.09 0.14 -1.38 0.28 0.11 0.59 -0.07 0.29 3.34 (a) 2.63 (b) -45.00 (a) -44.29 (b) -3.97

2.20 1.75 1.76 2.16 -0.18 1.71 1.71 2.08 0.14 -1.37 0.14 0.09 0.11 -0.08 0.03 2.39 -43.5 -3.19

2.13 1.66 0.82 2.26 0.00 1.75 1.82 2.16 0.12 -1.35 0.16 0.10 0.61 -0.09 0.23 3.78 (a) 3.10 (b) -44.64 (a) -43.96 (b) -3.43

[2.13] 1.49 0.00 [2.26] 0.00 1.75 1.78 [2.16] [0.12] -1.32 0.10 0.07 0.09 -0.02 0.02 2.37 -43.2 -3.92

a Only the coordinates of Ni and O ions have been optimized: z is the distance from the substrate; ∆d is the change in the distance of the ion from the nearest cation vacancy with respect to its ideal epitaxial positions; coordinates are in angstroms. The corresponding experimental data from ref 3 and referring to the RH structure are as follows: z(Ni(1)) ) 2.099 ( 0.05 Å; z(Ni(2)) ) 2.14 ( 0.03 Å; ∆d(Ni(2)) ) -0.1 ( 0.1 Å; z(O)) 2.102 ( 0.06 Å; ∆d(O) ) 0.20 ( 0.1 Å; ∆y(O) ) 0.12 ( 0.1 Å. For SQ-FM (β ) 0.035 Ha), the equilibrium geometry for the case (β ) 0.01 Ha) has been taken. b BEC are the binding energies per Ni3O4 unit after the BSSE correction and are calculated with reference to the noninteracting subsystems, the bare Pd slab and the i-RH-FM or i-SQ-FM. ∆E′c are the BSSE corrected “formation energies” per Ni3O4 unit, with reference to the isolated Ni and O atoms and to the bare Pd slab (see eq 1). In both cases, for the bare Pd slab, either the unpolarized (data marked “a”) or the polarized (data marked “b”) solution for the corresponding β value has been considered. c F is the Fermi level; for the isolated unpolarized Pd slab, F ) -3.85 eV (β ) 0.01 Ha) and F ) -3.51 eV (β ) 0.035 Ha).

NiO Supported at the Pd(100) Surface Part 2

Figure 5. Difference charge density (top panel) and net spin density maps (bottom panel) for the Ni3O4-RH/Pd system in the FM configuration. The smearing parameter β is set at 0.01 Ha. The top plot shows the difference between the electron density for the compound system and the superposition of the electron densities of the two subunits with the same internal geometry. The continuous and dashed lines refer to the positive and negative density differences, respectively. The sections are in a vertical plane through nearest neighbor Ni and O atoms and crossing the Ni vacancy site (see Figure 1). The contour lines are drawn at intervals of 0.002 |e|/bohr3 in both plots.

become: µ(O) ) -0.32 au, µ(Ni(1)) ) 1.92 au, and µ(Ni(2)) ) 1.68 au, that is, much closer to the formal values. The artificial

J. Phys. Chem. B, Vol. 110, No. 15, 2006 7923 partition of electron charges among atoms according to the Mulliken analysis is probably also the main explanation for the magnetic nonequivalence of the two Ni ions. As a matter of fact, the most stable configuration of the Ni ions in all Ni3O4 phases considered in this work is essentially describable as [(z2)1(zx)2(zy)2(xy)2(x2 - y2)1] (by taking as x and y as the directions of the Ni-O bonds), the same as in NiO bulk and in NiO-ML, both isolated and supported on Pd(100). Two possible AFM structures of the RH phase are shown in Figure 1. They are called A1 and A2 because they can be obtained from the corresponding ones of NiO-ML (see Figure 1 of paper 1) by removing one out of four Ni ions, with the removed ions forming an RH lattice. Since the removed ions have opposite spins, an RH-AFM structure is obtained in both cases, with a 2D cell twice the size of the FM one. The same is not possible for the other case, since a p(2 × 2) sublattice of any AFM structure of NiO-ML comprises only Ni ions with the same spin. Artificial SQ-AFM structures can be devised, but they would imply the presence of zero-spin Ni ions, with very high energetic cost. The analysis has therefore been restricted to i-RH-A1 and i-RH-A2. The results are provided in the bottom panels of Figures 3 and 4 and in the last two columns of Table 2. The most notable result is that both AFM configurations are less stable than the FM one by more than 0.1 eV/Ni3O4 unit, while the opposite was true for i-NiO-ML8 and NiO bulk.25 The reason is that the superexchange effect which favored spin alternation on second-neighbor Ni2+ ions via the intermediate O2- ions in the stoichiometric structures can no longer be effective in the present case. On the other hand, with respect to the FM case, the lonely occupied orbitals on oxygens are interfering to some extent with lonely occupied orbitals of the same spin on nearby Ni ions, as is evident in Figure 3. For the rest, charge and spin populations and geometries are practically unchanged with respect to the FM case. The width Eg of the band gap is appreciably different in the three i-RH structures, mainly depending on the energy of the highest occupied crystalline orbital, which depends in turn on symmetry (Eg ) 3.7 eV in the perfect monolayer). 3.3. Supported Ni3O4 Phase. The formation of the Ni3O4 phase according to reaction 1 and to the proposed mechanism is compatible with both a rhombic and a square arrangement of Ni vacancies. The energy difference between the relaxed

Figure 6. Band structure of i-RH-FM (left), of Ni3O4-RH/Pd(100) in the FM configuration (center), and of the spin-paired Pd three-layer slab (right). The 2 × 1 2D cell, pertinent to the former two systems, has been adopted for consistency for the Pd slab as well. The dashed line gives the position of the Fermi level. In the central panel, majority and minority spin bands are drawn as continuous and dashed curves, respectively. The smearing parameter β for the two conducting systems is set at 0.01 Ha.

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Figure 7. Projected densities of states of RH-FM/Pd (solid black line) and of the two noninteracing subunits (dashed gray line). The smearing parameter β is set at 0.01 Ha. The position of the Fermi level is indicated by the vertical lines: solid black for the compound system and dashed gray for the subunits. The insert shows the spin-resolved PDOSs for O and the system of d electrons of surface Pd. The projections are affected according to a Mulliken population analysis.

isolated structures (0.80 eV) might be significantly altered by the stabilizing effect of the metal support, since it is well-known that electrostatic interactions are partially screened at metal surfaces (see, for instance, ref 26): in fact, as is shown below, the two isomeric arrangements at the Pd surface are almost isoenergetic, even if RH remains the more stable one. Determining the correct energetics in the present case is difficult for three fundamental reasons. First, the interaction of the nonstoichiometric epilayer with the substrate is very strong; second, there are a number of quasi-degenerate solutions for both geometries which differ widely in their magnetic and electronic properties; third, convergence of the SCF procedure is not easily achieved, and the use of the thermal smearing technique is mandatory. The three orders of problems are strictly interweaved. For instance, due to the strong interaction, the electronic structures of both the metal and the adsorbate are deeply affected, and to evaluate the effect of the smearing technique and of the Pd spin polarization from the properties of the bare slab, as was done in paper 1, is therefore less justified in the present case. Particularly, the situations are delicate where magnetically different structures have to be compared. When commenting on the results, reported in Tables 3 and 4 and in Figures 5-10, we shall take these critical aspects into account. Table 3 reports results obtained for the two ferromagnetic structures, RH-FM and SQ-FM, with values β ) 0.01 and 0.035 Ha of the smearing parameter. As is seen in the line BEc, which reports the binding energy between the isolated moieties, corrected for the BSSE, the interaction with the surface is quite strong, several electronvolts as compared to a value of 0.20 eV/ NiO unit for the stoichiometric monolayer (see paper 1). Incidentally, the BSSE correction is in all cases about 1.21 eV/ Ni3O4 unit: this value is in agreement with that found for NiOML/Pd (0.32 eV/NiO unit) by considering that BSSE affects, in particular, neighboring Pd and O atoms. Before analyzing the energy data more carefully, it is expedient to look at the other features of the equilibrium structures. As concerns geometry, O ions move away from the vacancy and Ni ions

toward it (when this is allowed by symmetry); these displacements are qualitatively similar to those observed in the isolated structures (see Table 2), but much less important when it concerns oxygens, probably due to their strong interaction with the underlying metal atoms, which cannot move far from their ideal positions. The direct O-Pd interaction may also explain why the nonstoichiometric adlayer is closer to the surface (z ) 2.1/2.2 Å) than NiO-ML (z ) 2.3/2.4 Å, see paper 1). The calculated equilibrium geometry for the RH-FM structure is in good agreement with the experimental LEED data,3 as already discussed in our previous work.5 The mutual influence between metal and adlayer is more evident when considering Mulliken charges and magnetic moments of the different species. The presence of the metal reduces the ionicity of the oxide, compensated for by the formation of a partially ionic bond between O and the underlying surface Pd. This “donation” of electrons from metal atoms to oxygens is evident in the charge difference maps of Figure 5, and is absent in NiO-ML, where the effect of the overlayer was rather that of displacing part of the electron charge at the metal surface from the core to the interstitial regions (see Figure 5 of paper 1). In the present case, the charge redistribution corresponds to the partial filling of the hole distributed over the oxygens and to the depletion of the minority spin d(z2) orbital of surface Pd, as seen in Figure 5, bottom panel. As a result, a strong magnetic moment appears on Pdsurf, while that of oxygen decreases in absolute value and even changes its sign with respect to the i-RH and i-SQ situations. The effect of the smearing procedure is that of the partial quenching of these effects. It is much more marked in the SQ-FM case, probably due to the fact that in a vicinity of F there is in this case an important participation of bands from Ni3O4 (see Figure 3): it can be noted that µ(Ni(1)) becomes almost zero with β ) 0.035 Ha. All data discussed below are referred to β ) 0.01 Ha, unless otherwise stated. The importance of the substrate-adsorbate interaction is evident from the band structures and DOSs reported in Figures 6 and 7, respectively. The results for the compound cannot be regarded any longer as

NiO Supported at the Pd(100) Surface Part 2

J. Phys. Chem. B, Vol. 110, No. 15, 2006 7925

Figure 9. Influence of the smearing parameter β on the energetic properties of the bare Pd three-layer slab and of RH-FM/Pd. Top panel: dependence on β of the total energy of RH-FM/Pd (circles) and of the bare Pd three-layer slab, resulting from a spin-restricted (triangles) or spin-unrestricted (diamonds) calculation. For the first two curves, the respective zero is set at β0 ) 0.01 Ha, while for the third curve, the same reference value is taken as for the second one. Bottom panel: dependence on β of the binding energy (BE) of RH-FM/Pd per Ni3O4 unit, calculated either with reference to the spin-restricted (superscript a) or spin-unrestricted (superscript b) solution for the bare Pd slab. The binding energies are still not corrected for BSSE.

Figure 8. Electrostatic potential at Ni3O4-RH-FM/Pd. The three vertical sections are along the long (top left), the short (top right) diagonal of the rhombus, and in a vertical plane through nearest neighbor Ni and O atoms and crossing the Ni vacancy site (center); the horizontal section is at 2 Å above the oxygens of the epilayer (see Figure 1). Isopotential curves are separated by 0.01 au (0.27 V). The positive and negative potentials are drawn with continuous and dashed curves, respectively. The zero of the potential is set at an infinite distance above the surface. The smearing parameter β is set at 0.01 Ha.

the superposition of those of the interacting subunits, as was essentially the case for NiO-ML/Pd. The strong participation of majority spin oxygen states immediately below F (as is seen in the right panel of Figure 7) shows that electrons associated with the “hole” play an important role in determining the value of the Fermi energy. This characteristic feature may also explain why the STM images performed with direct or inverse bias look so differently; simulations to clarify this question are under way. Figure 8 provides information on the electrostatic potential at the surface. At a distance of 2 Å or more above the epilayer, the electrostatic potential looks rather like a rhombic distribution of negative centers (in correspondence of the Ni vacancies) in a relatively uniform positive background. From this point of view, the surface can be seen as an ordered array of strong Lewis bases, with possible catalytic applications. Even more important in this respect is the fact that those centers may act as electron acceptors or donors. In analogy with the surface V center (magnesium vacancy) in MgO, the Ni vacancy could exhibit an interesting reactivity toward metal atoms: depending on the electron affinity of the vacancy and on the ionization potential of the metal atom, the interaction may result in the formation of mono- or dications that should be strongly stabilized by the electrostatic interaction with the surface.27 This could be true

in particular if the metal cations can replace the missing Ni atoms and become part of the surface as a lattice impurity. Let us now come back to the energy data. We have shown in paper 1 that it is possible to obtain accurate estimates of the interaction energy between NiO-ML and Pd, by extrapolating to β ) 0 results obtained with different values of the smearing parameter. In that case, however, it was possible to separate the effects on energy of the smearing technique from those of the artificial spin polarization of the Pd support, because the interaction between the two subsystems did not change appreciably their essential electronic and magnetic features. As we have just discussed, the situation is different here. This is clearly shown in Figure 9. The effect of β on the energy of the compound system and of the bare slab is very different, which is clearly due the fact that the states in a vicinity of the Fermi level of RH-FM/Pd is not a superposition of those of the separate subsystems. Extrapolation to β ) 0 of the calculated binding energy is delicate, because it is difficult to establish to what amount the spin polarization observed in the metal interacting with the oxide is that induced by the hole on oxygens (which appears to be physically justified) or corresponds to the artificial one which sets in even in the bare slab for β < 0.025 Ha (see paper 1). For this reason, two energy data are provided in Table 3 for the β ) 0.01 Ha case: one taking as a reference the metastable paired-spin solution for the Pd slab (marked with (a)), the other referred to the spin-polarized solution (b). From the trend shown in Figure 9, the extrapolated value of the binding energy should be intermediate between the two but probably closer to the former one. Let us then discuss for definiteness the data reported as BEca in Table 3 and corresponding to β ) 0.01 Ha, 3.34 eV for RH-FM, and 3.78 Ha for SQ-FM. We consider these two values comparable to each other, because the electronic structure of the two solutions is very similar (the

7926 J. Phys. Chem. B, Vol. 110, No. 15, 2006

Ferrari et al.

TABLE 4: Calculated Properties of Supported Ni3O4-RH, with Different Magnetic Arrangements and with the Smearing Parameter β Set at 0.01 or 0.035 Haa RH-A1 q(O)b q(Ni(1))b q(Ni(2))b q(Pdsurf); q(Pdinner)b µ(O)b µ(Ni(1))b µ(Ni(2))b µ(Pdsurf); µ(Pdinner)b EFM - EAFMx (eV)c

RH-A2

β ) 0.01 Ha

β ) 0.035 Ha

β ) 0.01 Ha

β ) 0.035 Ha

-1.37 1.74 1.70 0.12; -0.007 (0.18 (1.79 (1.76 (0.56; (0.10 -0.04

-1.36 1.74 1.70 0.09; -0.02 (0.04 (1.76 (1.71 (0.05; (0.01 -0.05

-1.37 1.75 1.71 0.12; -0.07 (0.17 (1.80 (1.76 (0.57; (0.10 -0.12

-1.36 1.75 1.71 0.09; -0.02 (0.05 (1.76 (1.71 (0.05; (0.01 -0.09

a The geometry is the one optimized for the FM arrangement and reported in the RH-FM 0.01 column of Table 3. b Mulliken net charges q and spin population µ are in atomic units. c In the last row, the difference in stability per Ni3O4 unit with respect to the FM structure for the same β value is reported.

Figure 10. Spin density of the supported Ni3O4 monolayers in the plane of the oxygens. From left to right: RH-FM, RH-A1, and RH-A2. The continuous and dashed lines refer to the positive and negative spin densities, respectively. The contour lines are drawn at intervals of 0.002 au. The smearing parameter β is set at 0.01 Ha.

same is not true with β ) 0.035 Ha, where it was seen that the smearing correction heavily affects the SQ-FM solution). As expected, the stabilizing effect of the interaction with the metal is higher for SQ-FM but not to such an extent as to make it preferred over RH-FM which has a more favorable distribution of vacancies from an electrostatic viewpoint. On the whole, RHFM is more stable than SQ-FM by a few tenths of electronvolts per Ni3O4 unit. Note that the present value, resulting from new calculations and a more accurate analysis of the results, is smaller than that quoted in our previous joint experimentaltheoretical work on Ni3O4/Pd5 (≈1 eV). On the other hand, it had been argued there that the two structures should be close in energy, since some STM images reveal the local presence of the SQ phase as a line defect. The formation of Ni3O4-RH according to reaction 1 can be now more accurately estimated. To guess the energetics of reaction 1, it has been assumed that the formation energy per NiO unit of NiO[cluster] is the same as that of the isolated NiO monolayer in its most stable (AFM) configuration (-13.83 eV). This is probably an overestimation, because of the high defectivity of small NiO clusters and of their weak interaction with the oxidized surface. As concerns RH-FM, two reference formation energy values are considered, ∆E′c(a) and ∆E′c(b), as reported in Table 3. The corresponding reaction energies are

∆E(a) reaction

) -0.71 eV,

∆E(b) reaction

) 0.01 eV

The former estimate is probably more realistic, as discussed above, and is close to that previously reported on the basis of less accurate calculations (-0.95 eV).5 In any event, while the

difference between the two estimates provides a measure of the uncertainties of the present data, they support the hypothesis that the formation of RH according to reaction 1 is thermodynamically faVored. Let us finally consider briefly the question of the different possible magnetic configurations of the compound system. The discussion is restricted to RH/Pd, because no sensible AFM configurations can be devised for SQ/Pd, as in the case of the isolated monolayer (see section 3.2). Table 4 reports the electronic structure and stability data of the two RH-AFM phases. Comparison with the data of RH-FM from Table 3 shows that charge and spin populations are very similar in the three cases. FM is still the most stable solution among the three, with regards to the isolated monolayer; however, at variance with that case, RH-A1 is more stable than RH-A2. This is another evidence of the important influence of the substrate on the magnetic properties of the adsorbed phase. Figure 10 shows the spin density in the plane of the oxygens for the three magnetic configurations. Comparison with the corresponding maps of Figure 3 reveals how deeply the magnetic structure has changed owing to interaction with the metal, especially as concerns oxygens. 4. Conclusions The role of the Pd substrate is crucial for the formation of c(4 × 2)-Ni3O4. Not only does it provide a proper support to an oxidized Pd phase with a precise oxygen structure which is able to incorporate the impinging NiO units and reorganize them in a rhombic tissue but also it stabilizes the nonstoichiometric

NiO Supported at the Pd(100) Surface Part 2 phase through a donation to the oxygens of electrons taken from the d(z2) bands close to the Fermi level. Ni3O4/Pd is therefore really a noVel phase with no bulk counterpart since it exists only as an epilayer of monatomic height. Its exceptional features in terms of magnetic structure, charge distribution, and composition of states at the Fermi level make it an interesting example of a new class of 2D nanostructures which can be realized following well-assessed procedures. Among the envisaged developments of the present study, the following ones can be cited: (i) study of the reactivity with respect to metal atoms and small molecules, (ii) simulation of XPS energies and comparison with experimental data, and (iii) simulation of STM images both of the perfect Ni3O4/Pd phase and of the different point and line defects that are experimentally observed. Acknowledgment. The authors are grateful to Gaetano Granozzi and to Silvia Casassa for useful discussions and comments. Financial support from Italian MURST (PRIN-2003, Prot. No. 031153, coordinated by G. Pacchioni) is acknowledged. We also acknowledge CINECA for a high-performance computing grant. Supporting Information Available: Table giving the geometric, energetic, and electronic properties of the p(2 × 2)-O phase at the hollow sites using three- and five-layer Pd slabs and two different basis sets. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Sambi, M.; Sensolo, R.; Rizzi, G. A.; Petukhov, M.; Granozzi, G. Surf. Sci. 2003, 537, 36. (2) Orzali, T.; Agnoli, S.; Sambi, M.; Granozzi, G. Surf. Sci. 2004, 569, 105.

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