Bulk-surface relationship of an electronic structure for high-throughput screening of metal oxide catalysts

Accepted Manuscript Title: Bulk-Surface relationship of an electronic structure for high-throughput screening of metal oxide catalysts Author: Joshua Minwoo Kweun Chenzhe Li Yongping Zheng Maenghyo Cho Yoon Young Kim Kyeongjae Cho PII: DOI: Reference:

S0169-4332(16)30262-8 http://dx.doi.org/doi:10.1016/j.apsusc.2016.02.093 APSUSC 32611

To appear in:

APSUSC

Received date: Revised date: Accepted date:

24-7-2015 30-1-2016 6-2-2016

Please cite this article as: J.M. Kweun, C. Li, Y. Zheng, M. Cho, Y.Y. Kim, K. Cho, Bulk-Surface relationship of an electronic structure for highthroughput screening of metal oxide catalysts, Applied Surface Science (2016), http://dx.doi.org/10.1016/j.apsusc.2016.02.093 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Bulk-Surface relationship of an electronic structure for high-throughput screening of metal oxide catalysts Joshua Minwoo Kweuna, Chenzhe Lia, Yongping Zhenga,b, Maenghyo Choa, Yoon Young Kima, Kyeongjae Choa,b a

Department of Mechanical and Aerospace Engineering, Seoul National University, Gwanak-gu, Seoul 08826, South Korea b Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas 75080, United States *

[email protected], Tel.: +1 972 883 2845 [email protected], Tel.: +82 2 880 7154

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Highlights Bulk surface relationship was predicted by the ligand field nature of metal oxides. Antibonding and bonding d-bands occupancy clarified the bulk surface relationship. Different surface relaxations were explained by the bulk electronic structures. Transition from the bulk to the surface state was simulated by oxygen adsorption.

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Abstract Designing metal-oxides consisting of earth-abundant elements has been a crucial issue to replace precious metal catalysts. To achieve efficient screening of metal-oxide catalysts via bulk descriptors rather than surface descriptors, we investigated the relationship between the electronic structure of bulk and that of the surface for lanthanum-based perovskite oxides, LaMO3 (M = Ti, V, Cr, Mn, Fe, Co, Ni, Cu). Through density functional theory calculations, we examined the d-band occupancy of the bulk and surface transition-metal atoms (nBulk and nSurf) and the adsorption energy of an oxygen atom (Eads) on (001), (110), and (111) surfaces. For the (001) surface, we observed strong correlation between the nBulk and nSurf with an R-squared value over 94%, and the result was interpreted in terms of ligand field splitting and antibonding/bonding level splitting. Moreover, the Eads on the surfaces was highly correlated with the nBulk with an R-squared value of more than 94%, and different surface relaxations could be explained by the bulk electronic structure (e.g., LaMnO3 vs. LaTiO3). These results suggest that a bulk-derived descriptor such as nBulk can be used to screen metal-oxide catalysts. Keywords Bulk surface relationship (BSR), Density functional theory (DFT), Metal oxide catalyst, High-throughput screening (HTS), Ligand field, Correlation study. 1. Introduction Much research in recent decades has focused on metal oxide due to its relative abundance, which can offer the opportunity to replace catalysts composed of precious platinum group metals (PGMs). Metal oxide is crystalline or amorphous materials and consists of metals and oxygen ligands. The materials provide a wide range of tunable compositions, mechanical strength, thermal stability [1], and selective oxidation property [2]. Metal oxide has many possible uses for catalytic applications such as the solid oxide fuel cell (SOFC) [3,4], environmental catalysts [2,5], water splitting [6,7], and thin film photovoltaic cell [8,9]. In most of the research fields, however, an inefficient trial-and-error approach has been faced with the difficulty to develop new metal oxide catalysts. One way to accelerate the material design process is to conduct a study on density functional theory (DFT) for a better understanding of the atomic scale nature [5,7,10–21]. For example, high-throughput screening (HTS) was carried out for various applications such as intermetallic compounds, photovoltaic cells, thermoelectric materials, and heterogeneous catalysts and with different descriptors such as formation energy, band gap, and adsorption energy [10–13]. Especially, electronic structure based descriptors were developed for optimizing catalysts. For example, Vojvodic et al. demonstrated that metal oxides had the Brønsted-Evans-Polanyi (BEP) relationship, which is a linear relationship between molecule dissociation energy and its relative energy of transition states [14]. Similarly, Vojvodic et al. showed that metal carbides Page 1 of 32

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had a linear correlation in both the center of electronic surface states (SS) and surface resonances (SR) with respect to an adsorption energy of atoms or molecules, which could be further applied for a BEP relationship to optimize the catalysts [15]. In addition, Man et al. found that there is a constant adsorption energy difference between two intermediate states of oxygen evolution reaction (OER), which is a descriptor to construct a clear theoretical overpotential volcano curve [16]. However, although a catalytic reaction occurs on the surface of catalysts, current surface-derived descriptors [7,12,14–16] could be considered as a relatively time-consuming job for the HTS of metal oxides since these approaches need to construct slab models of different surface orientations, which consist of a super-cell of bulk unit cells and a vacuum with a proper size on the slab. Unfortunately, little attention has been paid to develop an efficient bulk-derived descriptor for HTS [17,25]. This study presents an electronic structural bulk surface relationship (BSR) of lanthanum perovskite oxides based on the DFT calculation and ligand field theory (LFT), which is an intuitive molecular orbital theory that could be applied to interpret a DFT result [19–21]. Figure 1 illustrates a general scheme of the BSR of this study in detail [47]. The different metal d-orbitals splitting in various ligand fields (MLX: X=3, 4, 5, 6) is calculated by the angular overlap (AO) model in order to simply estimate the energy level of d-orbitals in coordination complexes in line with LFT [18]. However, some of the ligand complexes have the ideal configuration in terms of the high reactivity of the center metal. Metal with a different coordination in the oxides should play a key role in catalysis, which interacts with the intermediates in the middle of the catalytic reactions. The peak magnitude of the density of states (DOS) of the d-orbitals (black curves) increases, and the coordination numbers of the ligands decrease. These changes could give a basic understanding of the existence of electronic SS and SR for under-coordinated surfaces and sites such as steps, kinks, edges and corners of nanoparticles for different metal carbides, nitrides [15] and oxides. Based on the general concept given in Fig. 1, the aim of this study is to develop an efficient bulk-derived descriptor for the HTS of new metal oxide catalysts [1,5]. From the perspective of LFT, we quantitatively examine the BSR of the perovskite by calculating different d-bands electrons occupancy of the bulk and (001) surface via DFT (Section 3.2). Moreover we investigate the relationship between the bulk d-electrons occupation and adsorption energy on various perovskite surfaces (Sec. 3.4) of an oxygen atom, which is an important intermediate species of OER, oxygen reduction reaction (ORR), and environmental clean-up catalysis [2,3,22–24]. Consequently, BSR and the correlation between the occupancy of bulk d-electrons and the oxygen adsorption energy were obviously revealed. 2. Computational modeling and methods The current investigation involved calculating and analyzing electronic structures of eight different perovskite oxides in order to figure out a BSR of the electronic structures of the oxide materials. The perovskite oxides are extensively investigated for versatile catalysts such as SOFC electrodes [3,4,6,7,14,16,22,25]. In this study, lanthanum perovskite oxides (LaMO3: M = Ti, V, Cr, Mn, Fe, Co, Ni, Cu) in the Pm 3 m space group were studied. This provides clearer electronic structure information than other space groups such as Pbnm and R 3 ch due to the relatively simple Jahn-Teller (JT) distortion, which is the elongation and compression of the structures along the bonding directions. The bulk structures of the perovskites were collected from experimental data via the Inorganic Crystal Structure Database (ICSD) [28]. The surface structures of the perovskites were constructed using the bulk information. Three different surface orientations, (001), (110), and (111), which properly represent different oxygen ligands fields, were selected in this study. Transition-metal terminated surfaces were chosen, which have been extensively studied and are generally the stable surfaces in the range of typical operating temperatures of various catalysts [3,6,7,14,16,25,29,30]. In addition, transition-metal terminated surfaces enabled an appropriate application of LFT, owing to the similar bonding nature between transition-metals and their ligands [18]. The detailed BSR study was carried out only for the (001) surface model due to the difficulties of coordinate mismatches between the global coordinates of atomic positions and the local coordinates of ligand fields. Nevertheless, assuming there was the BSR of the three entire surfaces under the detailed BSR study of the (001) surface, correlations between the oxygen adsorption energy on the three surfaces and the bulk-derived descriptor mentioned earlier were investigated. An oxygen atom has close associations with essential intermediate species of various catalytic reactions. Thus, an adsorption study has given the crucial information related to the activation barriers of catalyses according to the BEP relationship described above [2,3,5–7,12,14–16,23–25,29,30]. Page 11 of 32

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The Angular Overlap (AO) model is a calculation method of metal d-orbitals splitting in the coordination complexes [18]. This calculation is based on the amounts of orbital overlaps which depend strongly on the angular distributions of metal d-orbitals and the orientations of different ligand fields. A general scheme of the BSR calculated and predicted by the AO model is described in Fig. 1. Based on the conceptual prediction, accurate and detailed calculations of the BSR and correlations with the adsorption energies were investigated by the DFT using the Vienna ab-initio simulation package (VASP 5.3.3) [31]. The atomic wave-function was described by the projector augmented-wave (PAW) method [32,33], and the PerdewBurke-Ernzerhof (PBE) potential, which is the generalized gradient approximation (GGA) for improving the local spin density (LSD) description of the exchange-correlation energy of atoms, molecules, and solids, was applied [34]. The cut-off energy of the plane-wave basis set was 500 eV, and the k-points meshes with the Γ-point in the reciprocal space were selected due to the skewed unit cells. The k-point meshes with grid spacing less than 0.4 Å-1 were selected for the ionic relaxations in which the force convergences of the DFT calculations were smaller than 0.08 eV/Å for the proper self-consistency of the structural optimizations via the conjugate-gradient algorithm [31].

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In typical operating temperatures of the heterogeneous catalyses [2,22-24], magnetic phase transition of the perovskites generally occurs from ordered magnetic structures to the disordered structures over the Néel temperatures [35–40]. For the random distribution of magnetic moments of transition-metals, various magnetic orderings such as ferromagnetic (FM), anti-ferromagnetic (AF), and non-magnetic (NM) structures were adapted. Primitive unit cells of the bulk perovskites were applied for the FM and NM model, and a 1x1x2 supercell was constructed to calculate AF electronic structures. The effects of different magnetic orderings were negligible to the perovskites, which have small magnetic moments of their B-site transitionmetals. For surface electronic structures and the adsorption of oxygen atoms, stoichiometric slab models, which have four to six transition-metal layers with respect to the three different surface orientations, were applied [41]. The lower half of the layers of each slab were fixed at the bulk structure during the ionic relaxation, which clearly described electronic transition between the bulk and surface states (Fig. 4) from even a thinner slab than the Debye length (>10nm) of the surface dipole layer for semiconductors [23,24]. The effect of the unrelaxed part could be diminished for a relative correlation and adsorption study. A 15 Å vacuum region in the unit cell of each model was constructed to reduce vertical interactions between the slab and its periodic images. For good convergence to specific magnetic structures such as FM and AF, the lattice parameters of the bulk primitive unit cell were adapted to the lattice vectors of the slab parallel to the surface plane. The monopole (or dipole) correction was applied due to the periodic interactions of oxygen adsorbates (or asymmetric slabs), which constructed the (1x1) substrate structure on the slabs [31,42]. The coverage effects of adsorbates were not considered in this study. Projection to the proper atomic orbitals of the periodic wave-function should be required to deeply analyze the electronic structures calculated by DFT [21,27]. For this purpose, angular (l) and magnetic (m) quantum number level-decomposed calculations were carried out even though the projection coordinates were restricted to the Cartesian coordinates of the unit cell in the simulation package, which were accurate enough for analyses of the bulk and (001) slab of the Pm 3 m perovskites. According to the calculations, the local density of states (LDOS) of metal d-orbitals was integrated to calculate the d-band electrons occupation, which was an indicator to investigate the BSR and the descriptor of the adsorption study. The band decomposed charge density was calculated to extract the partial electrons distribution in the real space even though the charge density cannot be fully decomposed with respect to the degenerated states or the different bonding symmetries such as σ- and π-bonding [31]. The weights of the sampling points in the reciprocal space and those of the bands were chosen carefully to reduce the ambiguities. Band splitting of the bonding and antibonding was necessary to interpret the DFT results using the AO model in an accurate way. Traditionally, the crystal orbital overlap population (COOP) method has been conducted to produce the splitting in the tight-binding or linear combination of atomic orbitals (LCAO) regime [27]. However, currently this approach might have a somewhat complicated post-processing in the DFT regime [31,43]. Hence, we determined the splitting as simple and intuitive standards based on the fundamentals of molecular orbital (MO) theory [18]: Existence of a notable valley in the DOS due to the obvious splitting (Fig. 2), degree of the orbital hybridization between a metal d-band and an oxygen p-band, Page 12 of 32

and a DOS comparison with that of the oxides with adjacent transition-metals. The first criterion can be easily applied to the materials with large bonding and antibonding splitting, which means there was basically a strong binding nature of the oxides, especially, strong bonds between metals and their oxygen ligands in this study. The second standard was established based on a different hybridizing ratio between a center metal and its ligands. For example, oxygen p-band’s contribution in the bonding state was relatively larger than that of the metal d-bands and vice versa for the contribution to the antibonding. The last condition could give a better electronic structural correlation of the perovskites with a series of the metals inside even if there might exist ambiguity to determine the transition between the bonding and antibonding bands.

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3. Results and discussion The center transition-metal and its oxygen surroundings are intrinsic natures of metal oxides, which can be an important factor in the electronic structure analyses of their different surfaces. The coordination number of oxygen ligands provided the basic relationship between the bulk and surface of the perovskite oxides in this study and is related to the coordination dependency of heterogeneous metal catalysts [24,45]. It seems that the polyhedrons were composed of metal and oxygen ligands even under surface reconstruction [23,46]. Assuming that the metal oxides have a stable transition-metal terminated surface under operating condition and the active site is the metal, it seems likely that the angular overlap (AO) method suggested different electronic structures of the various surface with different coordination of the ligands (Fig. 1). Additionally, there is a clear possibility that the antibonding state of the metal and its ligands became an important descriptor for analyzing the change of the electronic structures in this study and is supported by the basic assumption of the crystal field theory (CFT) [18,48], which describes the d-orbital splitting in terms of electrostatic repulsion interaction of point-charge ions. 3.1. Analysis of the bulk and surface electronic structures of lanthanum perovskite oxides According to the three standards mentioned in the previous section, we present the bonding and antibonding splitting of the bulk perovskites (Fig. 2). LDOS of d-orbitals for 3d-transition-metals is displayed, and the bonding (antibonding) d-bands of the metals are illustrated by green (red) colors. The inset shows the front view of the DOS, and the LDOS of p-orbitals of one oxygen ligand is displayed by blue lines for each of the DOS of the perovskites. The ferromagnetic (FM) ordering was adapted for the electronic structure. Using the first criterion that led us to find the clear cleavage between the states, we differentiated between the bonding and antibonding sides in most cases. However, LaCuO3 (denoted by Cu on its DOS in Fig. 2b) shows slight ambiguous transition between the bonding and the antibonding due to the strong interaction between the copper (Cu) core and its valence electrons. The second guideline related to the oxygen hybridization had a higher priority than the first guideline, which suggested that the transition level was slightly lower than that of the valley. Moreover, the DOS’s of the perovskites with cubic symmetry (Pm 3 m) in the bulk unit cells indicate their metallic behavior with no band gaps. It seems that the high symmetry of the materials without severe JT distortion [18,49] and Peierls distortion [27,50] caused the metallic property rather than the semiconductor property of the orthorhombic structure (Pbnm). Additionally, the cubic perovskite was in the high temperature phase, which was apparently a time-averaged orthorhombic structure with reduced distortion [51]. It appears that our electronic structures in Fig. 2b were consistent with other experimental results and simulations [52]. In a similar manner, the bonding and antibonding splitting of the surfaces were obtained [53]. Figure 3 shows the bulk and (001) surface electronic structures of lanthanum manganite (LaMnO3). The FM structure was chosen for the DOS’s, and the decomposed charge density was collected from spin-up electrons. The anti-bonding and bonding 3d-bands are indicated in red and green colors, respectively. The blue curves in the DOS’s illustrate the metal d-orbitals participating in the σ-bonding (dx2-y2, dz2). A bunch of insets minutely shows the decomposed charge distribution of different d-bands of the bulk and surface. The labels (Mn, O) denote the position of the Mn-metal and oxygen ligand atoms. In the bulk case, the four top insets illustrate cross-sectional areas of bonding and antibonding (*) of eg and t2g orbitals distribution at the {001} cube faces. For the surface, various bonding and antibonding configurations at the top surface are described by the isosurface plots. The σ-bonding character of the cylindrical symmetry around the internuclear axis and the π-bonding feature with the nodal plane containing the axis are revealed considerably. Page 13 of 32

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As described in the AO model of square-pyramidal ligands field (ML5) (Fig. 1), the bands broadening of the (001) surface DOS (Fig. 3) indicates the degeneracy breaking of the highest symmetric octahedral ligands field (ML6) in the bulk. The triply degenerated bands (t2g) of the bulk were separated into a doubly degenerated band (dyz + dzx) and dxy band, and the doubly degenerated bands (eg) in the bulk were split into dx2-y2 and dz2, respectively. Consequently, the surface Mn-metal has more different electronic states than the metal in the bulk as shown in the insets (Fig. 3), which described the presence of surface states and resonances [15,23]. A considerable decrease of the dz2* level of the surface Mn-metal from the eg* level of the bulk could significantly contribute to the formation of surface states or resonances in accordance with the results of the AO model. According to the results of the AO model in Fig. 1, sharper antibonding dbands of the surface could be expected. However, it is apparent that the peak height of the d-bands was reduced due to the periodic interaction in the crystalline solid (Fig. 3). Additionally, the band width of the dxy* band of the surface was larger than that of the dyz* and dzx*, which should be the result of the stronger metal-ligands hybridization without absence of four bulk-ligands in the xy-plane.

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Furthermore, electronic structures of the surface slab model could be seen as an analogy to electronic transition between the bulk and surface states (Fig. 4). The reduction of electronic energy of the dz2* band as approaching the first metal layer is revealed by the LDOS of the metal layers, which is in good agreement with the results from Fig. 1, qualitatively. An asymmetric and stoichiometric slab model was adapted for this study, and the third and fourth metal bilayers were fixed in the ionic relaxation of the slab to describe a quasi-bulk condition with the relaxed bulk structure. An AF structure was chosen for the clear observation of the DOS changes due to the presence of the pseudo gaps and confined DOS, which also can be observed in another simulation study [55]. The d-bands of the fourth layer metal give a sharp antibonding peak, which could indicate quite degenerated t2g* bands in line with the previous result in Fig. 3. Moreover, the strong SS of the dz2* band of the first layer metal without one apical ligand suggests that the local ligands configuration is a dominant factor in the electronic nature of metal oxides. This result should support the BSR of metal oxides based on the AO model in this study.

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3.2. Bulk and surface relationship based on the descriptor of the d-electron occupation of the La-perovskite oxides A descriptor is like a language that properly represents a target functionality to be easily understandable in huge database achieved by HTS [10]. For example, band center and electron occupancy, which are the electronic structural descriptors, have been successfully introduced into heterogeneous catalysis by metals, metal carbides and metal oxides [3,6,7,12,15,25,57,58]. Thus, we investigated the number of occupied delectrons up to the Fermi level as the appropriate descriptor for this basic BSR study rather than the d-band center, which could be quite dependent on the electronic spin configurations and the U-value correction of the highly correlated electrons in the systems. Figure 5 shows correlation diagrams for the number of occupied d-electrons in the bulk metal (nBulk) versus that of the (001) surface metal (nSurf). The red (or blue) lobes (Figs. 5a-f) represent the angular shapes of the atomic orbital projections for the t2g (or eg) band. The error bars in the nSurf vs. nBulk plots indicate the 95% confidence intervals of the spin-polarized calculations with different magnetic moments, and the plots describe the number of occupied d-electrons in the antibonding (triangles), bonding (inverted triangles), and the overall (diamonds) bands, separately. The linear regression data are given by dash-dot, solid, and dashed lines for the antibonding, bonding, and overall bands, respectively. The dashed boxes (Fig. 5e) represent the maximal possible number of electrons occupied in the different symmetry-resolved d-orbitals. Figure 5 clearly reveals the correlation of the electronic structure between the bulk and surface of the perovskite oxides. The electrons in the whole d-bands (dx2-y2, dz2, dxy, dyz, dzx) of the bulk and the surface metal have quite equal occupancy. It seems that relatively weak ligand-field perturbation from the 6coordinated octahedral ligands around the bulk metal to the 5-coordinated square-pyramidal ligands of the surface metal caused a slight deviation of the trend lines from the diagonal line (Fig. 5a). The line shifts from the identity line (nSurf = nBulk) in the plot of t2g-bands (Fig. 5b) are smaller than those of the eg-bands (Fig. 5c). This implies that the eg-bands should be influenced more by the elimination of an apical ligand of the bulk metal than the t2g-bands due to the different bonding strength between σ- and π-bonding. Similarly, the lines of the eg-bands are more deviated from the diagonal than those of the dz2-band (Fig. 5d), suggesting that the σ-bonding of the dz2 would be influenced more by the elimination than the δ-bonding of the dx2-y2 in Page 14 of 32

the surface normal direction. Additionally, antibonding and bonding lines moved in the opposite direction with respect to the identity line, and the large error bars represented the data of highly magnetic oxides with mid-3d transition-metals (e.g., Fe).

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Electronic band analyses of the manganese perovskite are visible in Fig. 6. The bluish (or reddish) circles or ellipses represent the electron distribution with small (or large) overlap between interacting orbitals of the neighboring atoms. The antibonding-bonding energy separation (Fig. 6a) is dependent on the different orbital overlap, which is caused by the different interatomic distance (Case 1, Fig. 6a) or orbital shape (Case 2, Fig. 6a). Figure 6b displays band formation in crystal with different bandwidths due to the different lattice constant (Case 1, Fig. 6b) or orbital symmetry of the atoms (Case 2, Fig. 6b). Each case shows the crystal wave-function (χ) of the highest band (fingers) at Γ-point or the first Brillouin zone boundary in the reciprocal space, which has the strongest antibonding character. The bottom graphs illustrate the atomic wave-functions (dashed curves) and the 1D crystal wave-function (solid curves, partially displayed) [61]. The lattice constant (or the orbital symmetry) could determine the nodes density (or the slope at the nodes) of the wave-function, which is a factor of the formation of dispersive bands in the crystal. The transition region (Figs. 6c-d) was defined between the antibonding (or nonbonding) band and the bonding band. The number of occupied electrons could be influenced by dangling bond formation (yellow dashed lines in Fig. 6c) and charge transfer from the eliminated ligands (O2−) (arrows in Fig. 6d). The reduction of the dz2*-band level from the bulk to the surface DOS is around 1.5 eV in this study and about 1.0 eV from the AO parameters. The reduction of dxz- and dyz-band is approximately 0.4 eV in this study and 0.25 eV from the parameters [18], assuming that the main cause of the t2g-band broadening should be the degeneracy breaking and not from the periodic interaction. Note that the band diagrams were constructed using the spin-polarized calculation even though the diagrams mainly show the up-spin state of electronic bands in order to illustrate clearly. Figures 6a-b show that the different overlaps between interacting orbitals of neighboring atoms in molecules and crystals [18,27] caused the different antibonding-bonding energy separation and electronic band dispersion. The orbitals could be calculated by the projection of the DFT results with a plane-wave basis on the atomic orbitals. Hence, we focused on the differences between the bulk and surface electronic structure by investigating their band locations, bandwidths, and electron occupation numbers for a better understanding of the BSR (Fig. 5). The band broadening is caused by strong hybridization of bonding orbitals and by the degeneracy breaking of a group orbital (e.g., eg, t2g-bands in the octahedral (Oh) ligands field). Even though, a group orbital only can be defined by a symmetric ligand-field, we used the same symmetric representation for the bulk (octahedral field) and the surface (square pyramidal field) group orbitals that contain the same set of orbitals (e.g., eg for dx2-y2 and dz2). Figure 6c provides the differences in the dz2-band of the bulk and (001) surface. First, the dz2*-bands of both the bulk and surface show considerably larger bandwidths than those of the bonding dz2-bands. It seems that there should be significant repulsive interactions [27,55] with antibonding, ferromagnetic, and complete cubic symmetric nature in the simulation. Second, the bandwidths of the surface are reduced with respect to those of the bulk due to the weakened hybridization of the metal and ligands with the elimination of an axial ligand normal to the surface. This decreased coordination caused the formation of a dangling bond on the surface (see yellow lines in Fig. 6c). Furthermore, the bonding strength of the surface is apparently reduced in terms of the energy separation between the antibonding and bonding state when compared to the splitting of the bulk. Therefore, according to the differences in the dz2-band diagram, the trend lines of the antibonding and bonding dz2 could be easily explained (Fig. 5d). The reduced bandwidth and antibondingbonding energy splitting of the surface could increase the electron occupation of the antibonding band, and the dangling bond could decrease the bonding occupation, which the trend lines of the antibonding and bonding band were located in the upper and lower part of the diagonal, respectively. The substantial deviation from the identity line could imply that there was considerable influence of the ligand elimination to the dz2-band on the surface as mentioned earlier. Hence, the enhanced antibonding nature should affect the bonding distances (or bond orders) of the metal (Mn) and the square pyramidal ligands on the surface. As a result, the apical and equatorial bonding distance increased 8 percent and 0.5 percent with respect to the distances of the bulk (about 1.95 angstrom), respectively. When we considered the eg- and t2g-band diagrams in the same manner, a somewhat different behavior of the bands could be observed due to the nature of group orbitals. The t2g*-band seems to be broadened at the surface on account of the degeneracy breaking even if the hybridization strength of each band in the group Page 15 of 32

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should be reduced on the surface of the lower coordination (Fig. 6d). Moreover, the electrons of the bulk t2g*-bands might transfer to the eg*-bands of the surface (Fig. 6d). It seems that the transfer results from the occupation of the nonbonding dz2-band of the eg-states (Fig. 6c). This interpretation was consistent with the BSR of the antibonding bands as illustrated by Figs. 5b-c. The trend lines of the t2g*- and eg*-bands locate in opposite direction with respect to the diagonal. Furthermore, Figs. 3-4 strongly confirmed that the downspin electrons of the t2g*-band were almost not occupied at the top surface layer, which is the energy level raised above the Fermi level. In addition, the quantitative shifts of the dz2*-band and the dyz*- (or dzx*-) band was about 1.5 eV and 0.4 eV, respectively, which is in good agreement with the AO parameters [18]: 1.0 eV for eσ and 0.25 eV for eπ in the cases of water and fluoride-ion ligands (see the numbers in Figs. 6c-d and refer to the “ML5” case in Fig. 1). It seems that more electronic interaction in the crystal caused larger shifts in comparison with the AO parameters of complex molecules. On the other hand, the trends of bonding t2g- and eg-bands were contrary to the shifts of antibonding bands (Figs. 5b-c). The losing bonding eg-electrons at the surface could be due to the formation of dangling bonds mainly through the bonding dz2-band. The other eg-band (dx2-y2) should not significantly affect the bond formation due to the symmetry mismatch on the (001) surface (refer the inset in Fig. 3). However, the bonding t2g-electrons were increased at the surface even though the t2g-bands should also contribute to the dangling bond formation for the π-interaction. Therefore, we should consider the effect of the surrounding ligands, given the fact that the bonding t2g-bands were strongly hybridized with the p-bands of the ligands. Consequently, we could conclude that there was a charge transfer from the lost ligand on the surface. According to the Bader charge analysis [62], the Mn-metal on the top surface had about 0.14 electrons more than the quasi-bulk metal (fourth layer in Fig. 4b), which implies that the increased bonding t2g-electrons should be responsible for the Bader charge difference [63]. Similarly, the dz2- or eg-bands of the surface metal could occupy more electrons from the lost ligand. However, the net number of electrons in the bands was reduced at the surface due to the large contribution for the dangling bond formation as discussed earlier. In summary, the BSR of the metal oxides was carried out in detail by means of a correlation diagram and electronic band analysis based on the orbital overlap. In particular, the symmetry-resolved (t2g- and egbands) study clearly described the relationships. The band positon and the electron occupation numbers were closely related to one another, thus inferring that there was a possibility to develop a new descriptor based on the band location and width for metal oxide such as the d-band center theory for metal [23,24,57,58]. 3.3. Bulk-surface relationship of the electronic structure and connection with surface relaxation Atomic structure analysis based on electronic structure has been a crucial approach to better understand atomic nature and vice versa. For example, the structure of staked platinum square-planar complex studied as a conducting polymer was closely related to the metal-metal antibonding state and oxidation state [27]. Also, the temperature-dependent electronic conductivity of titanium oxide (Ti2O3) was studied in terms of nonbonding state formation as an increasing temperature [64]. In this study, according to the DOS of the surface and even the bulk, it could be explained that the opposite behaviors of the slab relaxation between LaMnO3 and LaTiO3 resulted from the different occupations of the antibonding dz2*-states and antibondingbonding energy separation. After relaxation of the Ti-perovskite slab, the apical bonding distance (perpendicular to the (001) surface) decreased 2.8 percent with respect to the distance of the bulk (about 1.98 angstrom), whereas the relative distance of the Mn-perovskite increased 8 percent as mentioned previously. These findings were consistent with other simulation results obtained in [65,66]. Based on the bulk DOS in Fig. 2b, the different surface relaxation of Ti-perovskite could be speculated with no dz2*-band occupation and that the large energy separation resulted in the contraction of the surface layers. 3.4. Bulk-surface relationship in an adsorption study and its potential application for efficient catalyst screening Atomic and molecular adsorption is a fundamental step in a heterogeneous catalysis [2,23,24], and adsorption energy in a rate-determining step has been an important factor in overall catalytic reaction based on the BEP relationship [7,12,14–16]. In particular, an oxygen adsorption state has been a crucial intermediate step for various heterogeneous catalyses [2,3,22–24]. Furthermore, oxygen adsorption on the surface of metal oxide could be regarded as a ligand field modification of the surface metal. The continuous transition between the square-pyramidal field on the (001) surface and the octahedral field of the adsorption state, which might pretend the field in the bulk, will be carried out for a better understanding of the BSR. Finally, with proper assumptions including elementary reaction [67], correlation between the adsorption energy and the electron occupation number of the bulk perovskites was investigated to briefly show the possibility of efficient screening based on the BSR study. Page 16 of 32

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Figure 7 shows the DOS changes from the adsorption state to the clean surface of LaMnO3 during atomic oxygen adsorption. In Fig. 7a, the greenish curves represent DOS’s of the dz2-band, and each circled number indicates: ① dxy*-band of the Mn-metal that was a nonbonding state of the adsorption due to the orbitalsymmetry mismatch, ① adsorption-induced antibonding state including the d*-bands hybridized with the oxygen p-bands, ① bonding band formed by the adsorption, ① eg*-like bands that can present a quasioctahedral ligand field in the bulk, ① energetic reduction of the dz2*-band, which similarly shows the dangling bond state of the clean surface, ① bonding dz2-bands that result from the remaining apical ligand of the surface metal (Fig. 7c), ① low-spin configuration of the octahedral ligands field under the strong ligands field, ① rapid reduction of the peak height of the bonding state by decreasing the bonding length of the metal and adsorbate, ① beginning of the hybridization of the nonbonding dxy*-band with the adsorbate p-bands, and ① the antibonding-bonding separation increased by the approaching atom toward the surface. The inset (Fig. 7a) shows that the bonding and antibonding dz2-band are merging into the dangling bond state as the adsorbate gradually desorbs from the metal site on the surface. Figure 7 reveals the continuous evolution in the DOS, which illustrates the transition from the octahedral ligands field (① in Fig. 7a) to the square-pyramidal ligands field (①), which strongly confirms the BSR of metal oxides. It seems that the bonding dz2-band of the adsorbate state (–2 ~ –3 eV) could not be stabilized to the level of the remaining apical ligand (–5 ~ –6 eV) due to neglecting other interactions with ligands and cations below the top surface. Moreover, the nonbonding and adsorption state (①-①) was hybridized with larger bandwidths by decreasing the bonding distance of the adsorbate (①-①). This implies that the reduced distance caused the strong ligands field with large orbital overlap. Also, a low-spin configuration was observed due to the large octahedral field splitting (∆o) (①). Additionally, the binding energy curve suggests that the discontinuity (arrow in Fig. 7b) represents the beginning of the hybridization between the metal and adsorption states, in which the DOS’s are very similar to that of the clean surface in Fig. 3.

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Figure 8 contains a numerical relationship between the bulk d-electron occupation number and the adsorption energy of the adsorbate for La-perovskite oxides. The adsorption energy (Eads) of the oxygen was 1 o2 adsorbed clean adsorbed clean O2 defined as Eads = Etot − Etot − Etot , where Etot , Etot , and Etot denote the total energy of the 2 surface with the adsorbed oxygen, the clean surface, and an oxygen molecule, respectively. The calculated adsorption energy was parallel to other simulation results [7,14,30,56] and experimental data [60,70] (i.e., heat of adsorption): Approximatly, -2 eV (or ~ 45 kcal/mol, exothermic) for Cr-pervoskite and -1 eV (or ~ 24 kcal/mol, exothermic) for Mn-perovskite. The error bars describe the 95% confidence intervals from the (non- or) magnetic calculations. The larger error bars indicate more magnetic properties as mentioned earlier (Fig. 5). The optimal window is constructed based on the experimental overpotential data for ORR (or OER) [3,6]. In Fig. 8c, the purple, red, and green spheres represent Mn-, O-, and La-atoms, respectively. The bulk descriptor was well correlated to the adsorption energy (Fig. 8). This repeatedly confirmed that the bulk electronic nature could be related to the surface phenomena such as adsorption according to the BSR proposed in this study. In Fig. 8a, the R-squared value of the t2g-bands was larger than that of the eg-bands. It seems that more electrons participated in the π-bonding rather than the σ-bonding, which caused a better correlation of the t2g-bands. Hence, both σ- and π-bonding nature should be theoretically considered for an accurate description. Moreover, we have confidence that the bulk DOS could explain surface relaxation (Sec. 3.3) and surface adsorption. The perovskites with early 3d transition-metals (Ti, V) had large adsorption energy (more negative value). It could be speculated that the strong binding nature (i.e., large antibonding-bonding level splitting) caused the favorable adsorption. Fig. 8b demonstrates the correlation of the bulk d-bands occupation and the adsorption energy on the (001), (110), and (111) surfaces. A good correlation of the bulk occupation and the adsorption energy on the (110) and (111) surfaces indicates that the BSR came into existence for different surfaces under different ligand fields. Additionally, the right sides of the trend lines for the (110) and (111) facet are closer to each other than the left sides. It seems that the deviation was attributed to the strong binding nature of the early 3d-metal perovskites and saturation of the charge transfer from the metal-sites to the adsorbate (O2−). Linear relations in the electronic structure of catalysts have dominated the elementary catalyses. For example, the d-band center model and BEP relationships have been investigated [12,14–16,21,23–25,57– 59]. According to the d-center model and the BSR, we could infer that the adsorption energy (Eads) was Page 17 of 32

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linearly related to the d-electron occupancy of the bulk (nBulk). In the adsorption, the metal s-, p-, and dbands interacted with the adsorbate states, and the contribution of the coupling between the metal d-bands d and adsorbate states ( Eads ) was proportional to the filling of the d-bands (f), which should correspond to the d-electron occupation number (nBulk). However, deviation from the linearity could be responsible for the sp ) and the energy cost of the orthogonalization (V2) with a different metal s- and p-band contribution ( Eads effective nuclear charge of the transition-metals in the period. The eg-bands occupation of the bulk metal has been experimentally investigated to optimize electrochemical catalysts [3,6]. Hard X-ray spectroscopy like X-ray absorption near edge structure (XANES) and Mössbauer spectroscopy with a large penetration depth in the conventional mode [68] was employed to study the electronic structure of perovskite oxides. However, little work has been conducted to clarify the connection between the bulk descriptor and the overpotential. LaCoO3 and LaNiO3 turned out as the best OER or ORR catalyst of the ternary La-perovskites (LaMO3). An optimal window in Fig. 8b was introduced based on experimental data [3,6] with additional assumptions mentioned earlier [67]. Consequently, the adsorption energy (Eads) range in the window is near 0 eV (Fig. 8b). It could be inferred that the binding nature preferred in the catalysis was governed by the Sabatier principle [12,69] and thus not too weak and not too strong.

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4. Conclusions We have demonstrated that the electronic structure of the oxides surface can be closely related to that of the bulk in the ligand field nature of metal oxides (Fig. 1). First, we thoroughly analyzed the bulk and surface density of states (DOS) of the perovskite oxides as discussed in Sec. 3.1. To distinguish the splitting of bonding and antibonding states (Fig. 2), different decomposed charge distribution of the bulk and (001) surface was analyzed in line with the angular overlap (AO) model (Fig. 3). In addition, we studied electronic transition between the bulk and the (001) surface using the slab model with four metal-layers (Fig. 4). In Sec. 3.2 (key results for this study), the bulk surface relationship (BSR) of the metal oxides was clearly revealed. We obtained the correlations of the bulk and surface in terms of the d-electron occupancy of the metals in the perovskites (Fig. 5), and the electronic band analyses were conducted to understand the correlations in detail (Fig. 6). In Sec. 3.3, we found that the different surface relaxation behaviors could be explained by the ligand field theory (LFT) and the BSR. Finally, an oxygen adsorption study was adopted for a better understanding of the BSR in terms of the DOS change between the clean surface and the adsorption state (Fig. 7). The correlation of the bulk d-bands occupation and the adsorption energy on the different surfaces were also investigated (Sec. 3.4) for the potential application of efficient catalyst screening based on the BSR (Fig. 8). Surprisingly, we have confidence that the bulk electronic nature could even predict or explain the surface atomic nature (e.g., surface relaxation) as well as the surface electronic structure based on the BSR. The surface properties are different from the bulk properties (surface░≠░bulk). However, the surface properties can be correlated to the bulk properties (surface~a bulk+β). This study broadens and confirms the scope of current catalyst screening based on surface descriptors [7,10,12,14–16,29,58,59] to the efficient screening of metal oxides with bulk descriptors [3,10,17,21,25], which provide an excellent correlation of the (001) surface and bulk electronic structures. Moreover, our study reveals the novel findings of the BSR for the perovskite oxides and the important fundamental approaches [20,27,57] to analyze electronic structures. However, the BSR of the (110) and (111) surfaces remains to be determined even though the correlation with the adsorption energy of the surfaces strongly implied the existence of the BSR. To investigate the BSR of different surfaces in detail, the mismatch of local (ligands) and global (lattice) coordinates should be carried out. In addition, our results should be validated in an A-site (cation) effect of the perovskites (ABO3), which could contribute to the activity and stability of the catalysts [3,6,25] and perturb the d-band structures. Moreover, further investigations should be conducted to understand the different corner, edge, and face sharing nature of oxides [1,5,16,20,49] that affect the electronic structure or active-site geometry of the catalysts. This study can be applied to a wide range of metal-oxide catalyst applications, suggesting an electronic structure relationship between metal-oxide surfaces and ligand fields of the complex molecules. Although density functional theory (DFT) could describe the electronic structures more generally than LFT based on the group theory, the ligand-field nature could provide a certain framework to analyze complicated DOS’s calculated by DFT, as shown in this study. We further recommend that sensitive DFT calculation of d-band Page 18 of 32

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occupancy should be investigated to provide accurate BSR data in terms of different magnetic structures, energy criteria for the DOS calculation, and U-values for the oxides that generally have highly correlated electrons. This could eventually lead to the fast screening of metal-oxide catalysts based on bulk descriptors and to a better understanding of both bulk and surface properties. For future research, new candidates of metal-oxide catalyst, such as the Mullite family [1,5], should be investigated to find the BSR for efficient high-throughput screening (HTS). Acknowledgements J.M.K. gratefully acknowledges Prof. Jihyun An for her valuable “Inorganic Chemistry” lecture in the Dept. of Chemistry Education, and Prof. Do Heui Kim for his instructive “Introduction to Catalysis” lecture in School of Chemical and Biological Eng. at Seoul National University (SNU). The authors thank Dr. Young Jun Oh, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, for his helpful comments. K.C. thanks the New Generation Scholar Funding funded by the College of Engineering in SNU. This work was supported by the Global Frontier R&D Program on Center for Multiscale Energy System funded by the National Research Foundation under the Ministry of Science, ICT & Future Planning, Korea (2012M3A6A7054855). This research was supported by the National Research Foundation of Korea (NRF) Grant No. 2015-021967 funded by the Korean Ministry of Science, ICT and Future Planning (MSIP), contracted through Institute of Advanced Machines and Design at SNU in Korea. Reference [1] H. Schneider and S. Komarneni (Eds.), Mullite, Wiley-VCH, Weinheim, 2005. [2] C.H. Bartholomew, R.J. Farrauto, Fundamentals of Industrial Catalytic Processes, second ed., John Wiley & Sons, New Jersey, 2005. [3] J. Suntivich, H.A. Gasteiger, N. Yabuuchi, H. Nakanishi, J.B. Goodenough, Y. S.-Horn, Design principles for oxygen-reduction activity on perovskite oxide catalysts for fuel cells and metal–air batteries, Nat. Chem. 3 (2011) 546–550. [4] S.C. Singhal, K. Kendall (Eds.), High-temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications, first ed., Elsevier, Oxford, 2003. [5] W. Wang, G. McCool, N. Kapur, G. Yuan, B. Shan, M. Nguyen, U.M. Graham, B.H. Davis, G. Jacobs, K. Cho, X. Hao, Mixed-Phase Oxide Catalyst Based on Mn-Mullite (Sm, Gd)Mn2O5 for NO Oxidation in Diesel Exhaust, Science 337 (2012) 832–835. [6] J. Suntivich, K.J. May, H.A. Gasteiger, J.B. Goodenough, Y. S.-Horn, A Perovskite Oxide Optimized for Oxygen Evolution Catalysis from Molecular Orbital Principles, Science 334 (2011) 1383–1385. [7] A. Vojvodic, J.K. Nørskov, Optimizing Perovskites for the Water-Splitting Reaction, Science 334 (2011) 1355–1356. [8] N.-G. Park, Organometal Perovskite Light Absorbers Toward a 20% Efficiency Low-Cost Solid-State Mesoscopic Solar Cell, J. Phys. Chem. Lett. 4 (2013) 2423–2429. [9] H.J. Snaith, Perovskites: The Emergence of a New Era for Low-Cost, High-Efficiency Solar Cells, J. Phys. Chem. Lett. 4 (2013) 3623–3630. [10] S. Curtarolo, G.L.W. Hart, M.B. Nardelli, N. Mingo, S. Sanvito, O. Levy, The high-throughput highway to computational materials design, Nat. Mater. 12 (2013) 191–201. [11] S. Curtarolo, W. Setyawan, S. Wanga, J. Xue, K. Yang, R.H. Taylor, L.J. Nelson, G.L.W. Hart, S. Sanvito, M.B.-Nardelli, N. Mingo, O. Levy, AFLOWLIB.ORG: A distributed materials properties repository from high-throughput ab initio calculations, Comp. Mater. Sci. 58 (2012) 227–235. [12] J.K. Nørskov, T. Bligaard, J. Rossmeisl, C.H. Christensen, Towards the computational design of solid catalysts, Nat. Chem. 1 (2009) 37–46. [13] J.W. Bennett, K.M. Rabe, Integration of first-principles methods and crystallographic database searches for new ferroelectrics: Strategies and explorations, J. Solid. State. Chem. 195 (2012) 21–31. [14] A. Vojvodic, F. C.-Vallejo, W. Guo, S. Wang, A. Toftelund, F. Studt, J.I. Martínez, J. Shen, I.C. Man, J. Rossmeisl, T. Bligaard, J.K. Nørskov, and F. A.-Pedersen, On the behavior of Brønsted-Evans-Polanyi relations for transition metal oxides, J. Chem. Phys. 134 (2011) 244509 (8pp). [15] A. Vojvodic, A. Hellman, C. Ruberto, and B.I. Lundqvist, From Electronic Structure to Catalytic Activity: A Single Descriptor for Adsorption and Reactivity on Transition-Metal Carbides, Phys. Rev. Lett. 103 (2009) 146103 (4pp). [16] I.C. Man, H.-Y. Su, F. C.-Vallejo, H.A. Hansen, J.I. Martinez, N.G. Inoglu, J. Kitchin, T.F. Jaramillo, J.K. Nørskov, J. Rossmeisl, Universality in Oxygen Evolution Electrocatalysis on Oxide Surfaces, ChemCatChem 3 (2011) 1159–1165. Page 19 of 32

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Fig. 1 An illustration of the bulk surface relationship (BSR) of electronic structures. The center model represents the (001) surface and bulk of ABO3 perovskite oxides (Pm m space group) as a heterogeneous solid catalyst. The large spheres denote transition-metals (M) as the B-site of perovskite, and oxygen ligands (L) are denoted by the small spheres. The transition-metals terminated surface model shows the different surface sites with respect to the various coordination of ligands (L) such as terrace-sites (ML5), step-sites (ML4), and kink-sites (ML3). The bulk-site (ML6) represents the octahedral ligands field. The A-site cations of the perovskites are omitted in the model for easy viewing. Fig. 2 Splitting of electronic states in metal oxides: (a) Scheme of bonding and antibonding states formation in bulk oxides and (b) DOS of the bulk lanthanum perovskite oxides (LaMO3: M =Ti, V, Cr, Mn, Fe, Co, Ni, Cu) in the Pm m space group. In Fig. 2b, arrows represent valleys between the bonding and antibonding states. The abscissa is the relative energy level with respect to the Fermi energy (E - EFermi), and vertical level denote the Fermi level. The DOS of the perovskites are aligned with dashed lines at the zero regards to the Fermi level of one another. Fig. 3 An anatomical diagram of LDOS of the bulk and (001) surface lanthanum manganite perovskite (LaMnO3) for manganese (Mn) 3d-bands. The abscissa and ordinate represent the relative energy at the Fermi level (E-EFermi) and the DOS of spin-up and -down electrons, respectively. The vertical dashed lines at level denote the Fermi level [54]. the 0 Fig. 4 Electronic structures of (001) surface atomic layers for lanthanum manganite perovskite (LaMnO3): (a) LDOS of Mn-metal d-bands on each layer of the slab and (b) geometry and isosurface of the charge density of the slab model. The inset (Fig. 4a) displays the DOS of antibonding dz2-bands of Mn-metals on the different layers. As the distance of the metal from the top surface increases, the energy level of the dz2*band of the metal rises and locates near the Fermi level (EFermi) [54]. Fig. 5 Correlation diagrams of La-perovskite oxides (LaMO3: M = Ti, V, Cr, Mn, Fe, Co, Ni, Cu) for the number of occupied d-electrons in the bulk metal (nBulk) versus the number of the electrons on the (001) surface metal (nSurf): (a) A nSurf vs. nBulk plot for the whole d-bands (dx2-y2, dz2, dxy, dyz, dzx), (b) plot for the t2g-bands (dxy, dyz, dzx), (c) plot for the eg-bands (dx2-y2, dz2), (d) plot for the dz2-band, (e) collection of the plots for different symmetry-resolved d-bands (d, t2g, eg, dz2), and (f) illustration of the BSR of the metal oxides. Fig. 6 Electronic band analyses of the La-perovskite based on the data from the manganese perovskite (LaMnO3): (a) Diagram of molecular orbital theory for a diatomic molecule, (b) scheme of electronic band formation in crystalline solid, (c) dz2-band diagrams of the bulk and surface of the perovskite, and (d) eg- and t2g- band diagrams of the bulk and surface of the perovskite. Fig. 7 Simulated transition between the bulk and surface states during atomic oxygen adsorption (or desorption): (a) Plot of local density of states (LDOS) of the Mn-metal d-bands at the top surface of LaMnO3, (b) binding energy curve of the perovskite in the adsorption process, and (c) scheme of the oxygen adsorption on the (001) surface of the lanthanum manganite. Page 22 of 32

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Fig. 8 Numerical relationship between the d-electron occupation number of the bulk ( ) and the ) for La-perovskite oxides (LaMO3: M = Ti, V, Cr, Mn, Fe, adsorption energy of the oxygen adsorbate ( Co, Ni, Cu): (a) Correlation diagram for the bulk electron occupancy of the different symmetry-resolved dstates (eg, t2g, and overall d-bands) versus the adsorption energy on the (001) surface, (b) correlation plot of the bulk d-electron occupation number and the adsorption energy on the (001), (110), and (111) surfaces, and (c) illustrations of the surfaces [54].

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