Electronic Structure and Bonding in Co-Based Single and Mixed

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Electronic Structure and Bonding in Co-Based Single and Mixed Valence Oxides: A Quantum Chemical Perspective Vijay Singh and Dan Thomas Major* Department of Chemistry, Lise Meitner-Minerva Center of Computational Quantum Chemistry, and Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel S Supporting Information *

ABSTRACT: The mixed valence cobalt oxide, Co3O4, is a potential candidate as a photovoltaic (PV) material, which also exhibits intriguing chemical and catalytic properties. Here, we present a comparative study of the electronic, magnetic, and chemical bonding properties of mixed valence Co3O4 (i.e., Co2+/3+) with the related single valence CoO (i.e., Co2+) and Co2O3 (i.e., Co3+) oxides using density functional theory (DFT). We have employed a range of theoretical methods, including pure DFT, DFT+U, and a rangeseparated exchange-correlation functional (HSE06). We compare the electronic structure and band gap of the oxide materials, with available photoemission spectroscopy and optical band gaps. Our calculations suggest that the bonding between Co3+ and O2− ions in Co2O3 and Co3O4 and Co2+ and O2− ions in CoO and Co3O4 are rather different. We find that Co2O3 and Co3O4 are weakly correlated materials, whereas CoO is a strongly correlated material. Furthermore, our computed one-electron energy level diagrams reveal that strong Co−O antibonding states are present at the top of the valence band for all the cobalt oxides, hinting at a defect tolerant capacity in these materials. These results, which give a detailed picture of the chemical bonding in related single and mixed valence cobalt oxides, may serve as a guide to enhance the PV or photoelectrochemical activity of Co3O4, by reducing its internal defect states or changing its electronic structure by doping or alloying with suitable elements. Co3O4 has two valence Co ions in its unit cell, namely, Co2+ and Co3+, where Co2+ is magnetic and sits in a tetrahedral environment while Co3+ is a diamagnetic center in an octahedral crystal field of oxygens.11−13 In a recent paper, we employed a range of theoretical methods, including pure density functional theory (DFT), DFT+U, and a rangeseparated exchange-correlation functional (HSE06), as well as many-body Green’s function theory (i.e., the GW method), to study the electronic structure of Co3O4.14 We have shown that the fundamental band gap in Co3O4 is direct with a value of ∼0.8 eV, which resolved the long-standing problem of the correct band gap for this material.10,15−19 However, Co3O4 is seemingly not an ideal PV material. According to the Shockley−Queisser limit, semiconductors with band gaps in the near-infrared to visible region (i.e., between 1.5 and 2.0 eV) exhibit maximal efficiency. These materials also possess the greatest potential to form efficient single-junction cells.20 Nevertheless, despite the range of photon absorption mentioned above, Co3O4 absorbs lowenergy (305 Å3), the nature of the equation of state is complex, with significant variation in the line curvature, and we have not explored this behavior further in this study. As mentioned previously, the magnetic structures of CoO and Co3O4 are well-established. The only magnetic ions, Co2+, lie ferromagnetically in the [111] plane and interact via AFM with its nearest neighboring layer of Co2+ ions. In the following, we shall analyze all the results based on the ground state

III. RESULTS AND DISCUSSION A. Magnetic Structure of Co2O3. A high-pressure phase of Co2O3 contains Co3+ ions in their low-spin state. It has been suggested that upon heating to 400 °C, its volume increases and a transformation from a low-spin Co3+ ion into a high-spin state occurs.47 It is important to note that the conclusion mentioned above was drawn from indirect evidence by comparing the cell volume and d spacing of Co2O3 with that of α-Fe2O3. We have attempted to confirm this hypothesis by plotting the equation of states for Co2O3. Here, we have employed all possible magnetic structures for Co2O3, such as an 3309

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Figure 3. Change in (a) the magnetic moment per Co site and (b) the band gap as a function of U for different oxides. For Co3O4, we consider different sets of Ueff values for Co2+ and Co3+ ions: 0.0 and 0.0 (i.e., PBE), 1.0 and 1.0 eV, 2.0 and 1.0 eV, 3.0 and 3.0 eV, 4.4 and 6.7 eV, and 6.0 and 6.0 eV, respectively.

Figure 4. Schematic depiction of the partial densities of states for (a) Co3O4, (b) Co2O3, and (c) CoO using the PBE, PBE+U, and HSE06 functionals.

of Ueff on Co3+ (i.e., Ueff > 3.0 eV), the band gap increases rapidly and overshoots the experimental value. We also find that with an increase in the value of Ueff on the Co2+ and Co3+ ions, both metal centers remain in their respective HS and LS state. A slight increase in the magnetic moment of the Co2+ ion was observed (Figure S6a). In contrast, in Co2O3 we observe a transformation from a low-spin state of the Co3+ ions to a high-spin state above Ueff = 3.0 eV (Figure 3a). In CoO, the Co2+ ions remain in a high-spin state with increasing Ueff and, as a result, a finite magnetic moment is observed. We also observed that the computed band gap (∼1.72 eV) for Co2O3 is in good agreement with the experimental band gap (∼1.82 eV) for Ueff (Co3+) = 3.0 eV (Figure 3b). Additionally, we find that Co2O3 remains an insulator throughout the phase diagram, similar to Co3O4. For CoO, a transformation from metal to insulator is clearly seen from our calculations (Figure

magnetic structure of Co3O4, CoO, and Co2O3, as shown in Figure S5 of the Supporting Information. We note that we do not show the magnetic structure of Co2O3, because Co is diamagnetic in the ground state. B. Phase Diagrams for Co3O4, Co2O3, and CoO. Using the GGA+U method, a band gap of ∼0.75 eV is obtained for Co3O4, which is in agreement with the experimental band gap of 0.74 eV. However, the electronic structure obtained with GGA+U does not provide reasonable agreement with experimental XPS results.10 A change in the magnetic moment of the Co ions and in the band gap in the antiferromagnetic phase of Co3O4 as a function of U (i.e., a so-called phase diagram)10 is shown in Figure S6a. It is clearly seen that the band gap of Co3O4 is increasing as a function of Ueff. For a constant and small value of Ueff on Co3+, an optimized value of the energy band gap can be obtained by increasing the value of Ueff on the Co2+ ions (Figure S6a). However, for larger values 3310

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the Co d and O 2p states do not mix strongly with each other (Figure 4b). In contrast, employing HSE06 with a greater amount of exchange (α = 25%) yields a band gap of 3.6 eV, which is clearly an overestimation. The PBE functional gives a metallic solution for CoO, which is at odds with experimental observations (Figure 4c).42 This erroneous result is consistent with earlier theoretical predictions.45 Inclusion of a Hubbard U parameter (above Ueff = 2.0 eV) opens the energy gap, and the electronic structure changes, yielding a Mott insulating state. For larger values of U, the computed energy band gap is 2.57 eV, in agreement with the experimental fundamental band gap values ranging from 2.50 to 2.70 eV.42,45 However, we obtained an anomalous electronic structure, in which the O 2p states are located above the Co 3d states (Figure 4c, center panel), which is at odds with the experimental observation, where the Co 3d states are above the O 2p states.42 The XPS results42 suggest that the Co 3d states are close to the Fermi level and the O 2p states are spread throughout the valence region with a peak at approximately −4.0 eV. Therefore, our calculations suggest that inclusion of larger values of Hubbard U parameters is not suitable for CoO. Next, we performed hybrid DFT calculations using the HSE06 functional with two sets of short-range (SR) exact exchange (α = 5 and 25%); 5% exact exchange gives a metallic solution, similar to the PBE functional. When we increase the amount of exact exchange to 25%, the electronic structure is altered and the energy band gap opens to 2.94 eV, which is in agreement with the experimental band gap values ranging from 2.5 to 2.7 eV.42 Seemingly, HSE06 with a greater amount of exact exchange yields a more reasonable electronic structure for CoO, where the major peak of the Co d states remains at −3.6 eV for the spin up channel and approximately −2.0 eV for the spin down channel, while the O 2p states are dispersed over large regions of the valence band (VB). This is in agreement with earlier XPS42 and XES-XAS64 studies of CoO. It is useful to note that in Co3O4, an optimal bandgap and electronic structure was obtained with 5% of exact exchange using HSE06. On the other hand, in CoO, a larger value of exact exchange (i.e., 25%) is required to obtain a correct band gap and electronic structure. We find that the associated crystal field of the Co2+ ions in Co3O4 and CoO is weaker than the Hund exchange, and hence, a HS state is observed. Moreover, in all Co-based oxide systems, a large Hubbard U value changes the electronic structure substantially, and the Co d and O 2p states hybridize strongly. In summary, Co2O3 has characteristics similar to those of Co3O4, and this is reflected both in the similar electronic structures of these materials (Figure 4a,b) and in the ability of different computational approaches to reproducing these similar features. For example, for both systems, the PBE and HSE06 (α = 5%) functionals give a reasonable electronic structure, where the Co 3d and O 2p states are well-separated. However, using PBE+U, the electronic structure of both systems is perturbed significantly for larger values of the Hubbard U. On the other hand, we find that for CoO, the PBE and HSE06 (α = 5%) functionals predict a metallic solution. For this material, introduction of larger amounts of exact exchange in HSE06 (or greater U values in PBE+U) improves our theoretical description. Importantly, these findings point to intrinsic differences in these materials: Co2O3 and Co3O4 are weakly correlated materials, whereas CoO is a strongly correlated material. Finally, we find that the associated crystal

3b). A correct experimentally observed insulating ground state for CoO was obtained by the inclusion of Hubbard U (above Ueff = 2.0 eV). For Ueff = 8.0 eV, our computed energy band gap, 2.57 eV, is in the range of the experimental values obtained by PES+BIS, XAS+XES and optical absorption, which are 2.50, 2.60, and 2.70 eV, respectively.44 In the next section, we present a careful analysis of the electronic structure, which is necessary to further validate the computational methods. To conclude, it seems that the phase diagrams of the single valence Co-based compounds, Co2O3 and CoO, are more complex than that of the mixed valence compound Co3O4, and great care must be taken in choosing an electronic structure method and U parameters. C. Electronic Structure for Co3O4, Co2O3, and CoO. To compare the electronic structures of the single and mixed valence compounds, we present a schematic illustration of the partial densities of states (Figure 4). The computed partial and total densities of state for each material using different methods are shown in Figures S7−S10 of the Supporting Information. In an earlier study, we pointed out that for Co3O4 the HSE06 functional with 5% exact exchange provides an energy band gap and electronic structure in good agreement with the experimental observation (Figure S7d). We also noted that the PBE+U method is not suitable for Co3O4, because it perturbs the electronic structure significantly.14 For instance, we found that all oxygen states are pushed up in energy and strongly hybridize with Co d states near the Fermi level (Figure 4a, center panel). In contrast, pure PBE gave a very reasonable electronic structure, albeit a too low band gap. In this work, a similar analysis of the single valence compounds was performed. For Co2O3, the PBE functional gives an electronic structure in which we can clearly distinguish between Co d and O 2p states, with a band gap ∼0.2 eV. We note that PBE in general underestimates the band gap (Figure 4b).63 A significant energy separation between the Co 3d and O 2p states was expected because octahedrally surrounded Co 3d-(t2g)6 states of LS Co3+ ions should be completely occupied in both spin channels and 3d-eg states should be above the Fermi level and remain unoccupied. Thus, hybridization between O 2p and Co 3d electrons is likely small, and the bands should be well separated. Our obtained electronic structure confirms this, but the associated crystal field is weak (Figure 4b). Inclusion of the Hubbard U parameter mixes the Co d and O 2p states. However, we found that a low value of the Hubbard U parameter does not result in significant mixing of the Co d and O 2p states (Figure S7b), and a value of Ueff = 3.0 eV provides a band gap of ∼1.7 eV, in agreement with the experimental optical band gap of ∼1.88 eV. Above this Ueff value, Co3+ transforms into a HS state, and hence, a finite magnetic moment appears on the Co3+ ion. Additionally, the electronic structure becomes increasingly complex, and for moderate Ueff values of 3.0−6.0 eV, both the Co d and O 2p states are located in the same energy window (Figure 4b, center panel). For a larger value of Ueff, the O 2p states are pushed up in energy and form states close to the Fermi level, above the Co 3d states (Figure S8c). To the best of our knowledge, there is no available experimental XPS data with which to compare our calculated electronic structure. Hence, to further validate the electronic structure obtained for Co2O3, a low value of exact HF nonlocal exchange (5%) in conjunction with the HSE06 functional was used. This approach gives an energy band gap of ∼1.4 eV, and inspection of the electronic structure suggests that 3311

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Figure 5. One-electron energy diagrams for Co2O3 (top) and Co3O4 (bottom): (a and b) octahedral Co3+ in Co2O3 and (c and d) octahedral Co3+ in Co3O4 in a LS state.

Figure 6. One-electron energy diagrams for CoO (top) and Co3O4 (bottom): (a and b) octahedral Co2+ in CoO and (c and d) tetrahedral Co2+ in Co3O4 in a HS state.

field of the Co2+ ions in Co3O4 and CoO is weaker than the Hund exchange and, hence, a HS state is observed, whereas the Co3+ ions in both Co3O4 and Co2O3 are in LS states. D. Chemical Bond Analysis Using Crystal Orbital Hamilton Population (COHP). To understand the interaction between the metal and ligand ions in these oxides, we analyze the COHP plots that provide an energy-resolved visualization of chemical bonding.60−62 On the basis of the computed results of COHP, integrated COHP (ICOHP), and the corresponding partial densities of states obtained by the

optimal functional for the specific material (i.e., the functional that provides the best electronic structure), we plot a schematic one-electron energy level diagram (Figures 5 and 6). In these figures, we show chemical bonding diagrams for Co2+ or Co3+ and nearest neighbor (NN) O2− for each cobalt oxide material in both spin channels [spin up (α), left panel; spin down (β), right panel]. The results of the computed COHP and ICOHP are shown in Figure S12 of the Supporting Information. The plotted COHP and ICOHP were averaged over the number of NN bonds. 3312

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Inorganic Chemistry Inspection of Figure 5 suggests that in both Co2O3 and Co3O4, the Co3+ ion forms strong bonding and antibonding interactions with their corresponding symmetry-allowed σ and π orbitals of the oxygen ligands. The bonding states are primarily composed of O 2p states, while the antibonding states are mostly formed from Co 3d states in both spin channels (Figure 5). The relative position of the antibonding states belonging to eg, i.e., σ*-eg, and antibonding states belonging to t2g, i.e., π*-t2g, is reversed in Co2O3 and Co3O4, and this occurs for both spin channels (Figure 5). This antibonding picture may be understood by inspecting the bonding picture as shown in panels a and b of Figure S12, as these are often near-mirror images of one another. In Co2O3, we observe that the covalent bonding between Co 3d (t2g states) and O 2p (ICOHP ∼ −0.40 eV/bond) is stronger than between Co 3d (eg states) and O 2p (ICOHP ∼ −0.01 eV/bond) (see Figure S12a). However, in Co3O4, the opposite is the case, where we find that Co 3d (eg states) and O 2p (ICOHP ∼ −0.30 eV/bond) states form stronger covalent bonds than Co 3d (t2g states) and O 2p (ICOHP ∼ −0.01 eV/bond) states (see Figure S 12b). Similar ICOHP values were also obtained in the down spin channel of these oxides. A large difference in the bonding strength of eg and t2g orbitals can be qualitatively understood on the basis of orbital symmetry and orbital overlap.65 We find that in Co3O4, the eg orbitals of the Co3+ ions point directly toward the ligands (σ-bonding), whereas the t2g orbitals point between the ligands, giving π-bonding (Figure S11a). In contrast, in Co2O3, we find that the ligands are directly facing the t2g orbitals (i.e., σbonding) and the eg orbitals are pointing in-between the ligands, giving π-bonding (Figure S11b). This may be attributed to the strong distortion of Co3+ octahedra and the existing difference between the global (a, b, and c) and local (x, y, and z) coordinate directions of the Co3+ orbitals in Co2O3 (Figure S11b). In contrast, in Co3O4, we find that the direction of the local and global coordinates is the same for the Co3+ orbitals, and the ion is located in a regular octahedra of oxygen ions (Figure S11a). Next, we discuss the chemical bonding between Co2+ (3d7) ion and O 2p in the single valence material, CoO, and mixed valence material, Co3O4. The results are shown in Figure 6. We find that the covalent bonding strength between both Co2+ (t2g) and O (2p) and Co2+ (eg) and O (2p) is weak and comparable in the up spin channel for both materials. This is expected as in both materials, Co2+ is in a HS state, and hence, the 3d orbitals are completely filled in the majority spin channel (Figure 6a,c). However, in the down spin channel, the strength of the covalent bonding in Co3O4, as well as in CoO, is stronger than in the up spin channel. In particular, we find that in Co3O4, the ICOHP for Co2+ (t2g) and O (2p) (approximately −0.40 eV/ bond) is stronger than that for Co2+ (eg) and O (2p) (−0.01 eV/bond). This is due to a large overlap between the t2g orbitals and oxygen ligands, which are directly pointing toward each other (Figure S11d). In contrast, in CoO, we find that both Co2+ (t2g) and O (2p) (ICOHP ∼ −0.22 eV/bond) and Co2+ (eg) and O (2p) (ICOHP ∼ −0.2 eV/bond) are similar and substantially stronger (Figure S12c). These findings reflect inherent differences in bonding for the down spin channel. In Co3O4, for the Co2+ (eg)−O (2p) pair, the occupied orbitals have a significant antibonding character, whereas in CoO, for both the Co2+ (t2g)−O (2p) and Co2+

(eg)−O (2p) pairs, the antibonding states are unoccupied, as they are located far above the Fermi level. In conclusion, our calculations reveal that for all the studied Co oxides, strong antibonding states between Co and oxygen ions are present at the top of the VB. This antibonding nature of the VB edge satisfies at least one criterion of materials that are defect tolerant. On the other hand, at the bottom edge of the conduction band (CB), we obtained mainly antibonding states. Surprisingly, we find smaller, yet significant, metal−metal bonding character of the CB maxima (CBM). This bonding arises from Co2+−Co2+ contacts in CoO and Co3O4 (Figure S13) and Co2+−Co3+ contacts in Co3O4 (Figure S15). We did not observe such bonding between Co3+ and Co3+ in Co2O3 or Co3O4 (Figure S14). We have summarized the bonding features associated with the VB maxima and CBM in these materials in a schematic manner in Figure S17.

IV. SUMMARY We have presented a comparative electronic structure and chemical bonding analysis of mixed valence and single valence cobalt oxides. The computed equation of state of Co2O3 using the PBE functional revealed that at high pressure, the smallervolume phase is diamagnetic, and this may be attributed to the presence of Co3+ ions in a low-spin state. Interestingly, we also observed a transformation of a low-spin state Co3+ ion to its high-spin state after a certain critical volume (ΔV/V ∼ 10%). This critical volume is in good agreement with the experimental value of 6.7%.47 Our computed phase diagrams for the single valence compounds, CoO and Co2O3, are more complex than that for the mixed valence compound, Co3O4. In Co2O3, a low-spin Co3+ ion transforms into a HS state as a function of Ueff, similar to that observed during volume change. At a larger volume, the crystal field strength is weaker than the Hund exchange, as the distances between Co and the O ligands increase. On the other hand, by inclusion of a Hubbard U parameter, the ligand field decreases due to an increase in covalency between the O 2p and Co 3d states, and therefore, a HS state is observed. Therefore, variation in the crystal field, either by thermal expansion (observed experimentally49), by changing pressure, or by including electron correlation using Hubbard U, can lead to a LS to HS transition. On the other hand, in CoO, Co2+ remains in its HS state, although a transformation from metal to insulator is observed at a critical U value of 3.0 eV. Our calculation has also revealed that the electronic structure of single, as well as mixed valence compounds, is very sensitive to the choice of functional used for the calculation. We conclude that the PBE and HSE06 (α = 5%) functionals give a reasonable electronic structure for both Co2O3 and Co3O4, and we observe that the Co 3d and O 2p states are well-separated. In contrast, these functionals are not suitable for the single valence CoO, for which they provide a metallic solution. For this material, we find that the HSE06 (α = 25%) functional is the best one in terms of both the band gap and the electronic structure. We stress that the quality of the electronic structures was compared to experimental data (CoO using XPS42 and XES-XAS64 spectra and Co3O4 using both PES10 and UPS66). For all cobalt oxides, we find that inclusion of a large Hubbard U parameter strongly influences both the band gap and the electronic structure. We conclude that even though a larger value of U might correct the band gap, such an ad-hoc correction scheme significantly perturbs the electronic structure, and therefore, great care must be taken in choosing 3313

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(7) Burschka, J.; Pellet, N.; Moon, S.-J.; Humphry-Baker, R.; Gao, P.; Nazeeruddin, M. K.; Gratzel, M. Nature 2013, 499, 316−319. (8) Anderson, A. Y.; Bouhadana, Y.; Barad, H.-N.; Kupfer, B.; RoshHodesh, E.; Aviv, H.; Tischler, Y. R.; Rühle, S.; Zaban, A. ACS Comb. Sci. 2014, 16, 53−65. (9) Rühle, S.; Anderson, A. Y.; Barad, H.-N.; Kupfer, B.; Bouhadana, Y.; Rosh-Hodesh, E.; Zaban, A. J. Phys. Chem. Lett. 2012, 3, 3755− 3764. (10) Qiao, L.; Xiao, H.; Meyer, H.; Sun, J.; Rouleau, C.; Puretzky, A.; Geohegan, D.; Ivanov, I.; Yoon, M.; Weber, W.; Biegalski, M. D. J. Mater. Chem. C 2013, 1, 4628−4633. (11) Kamimura, H. J. Phys. Soc. Jpn. 1966, 21, 484−490. (12) Roth, W. L. J. Phys. Chem. Solids 1964, 25, 1−10. (13) Scheerlinck, D.; Hautecler, S. Phys. Status Solidi B 1976, 73, 223−228. (14) Singh, V.; Kosa, M.; Majhi, K.; Major, D. T. J. Chem. Theory Comput. 2015, 11, 64−72. (15) Martens, J. W. D.; Peeters, W. L.; van Noort, H. M.; Erman, M. J. Phys. Chem. Solids 1985, 46, 411−416. (16) Kim, K. J.; Park, Y. R. Solid State Commun. 2003, 127, 25−28. (17) Walsh, A.; Wei, S.-H.; Yan, Y.; Al-Jassim, M.; Turner, J. A.; Woodhouse, M.; Parkinson, B. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 165119−165127. (18) Xu, X.-L.; Chen, Z.-H.; Li, Y.; Chen, W.-K.; Li, J.-Q. Surf. Sci. 2009, 603, 653−658. (19) Chen, J.; Wu, X.; Selloni, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 245204−245210. (20) Shockley, W.; Queisser, H. J. J. Appl. Phys. 1961, 32, 510−519. (21) Newhouse, P. F.; Parkinson, B. A. J. Mater. Chem. A 2015, 3, 5901−5907. (22) Woodhouse, M.; Parkinson, B. A. Chem. Mater. 2008, 20, 2495− 2502. (23) Cowley, R. A.; Buyers, W. J. L.; Stock, C.; Yamani, Z.; Frost, C.; Taylor, J. W.; Prabhakaran, D. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 12. (24) Doyle, W. P.; Lonergan, G. A. Discuss. Faraday Soc. 1958, 26, 27−33. (25) Forti, M.; Alonso, P.; Gargano, P.; Rubiolo, G. Procedia Mater. Sci. 2012, 1, 230−234. (26) Han, M. J.; Kim, H. S.; Kim, D. G.; Yu, J. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 5. (27) Han, M. J.; Yu, J. Journal of the Korean Physical Society 2006, 48, 1496−1500. (28) Jauch, W.; Reehuis, M.; Bleif, H. J.; Kubanek, F.; Pattison, R. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64, 3. (29) Kant, C.; Rudolf, T.; Schrettle, F.; Mayr, F.; Deisenhofer, J.; Lunkenheimer, P.; Eremin, M. V.; Loidl, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 11. (30) Powell, R. J.; Spicer, W. E. Phys. Rev. B 1970, 2, 2182. (31) Rao, K. V.; Smakula, A. J. Appl. Phys. 1965, 36, 2031−2038. (32) Shen, Z. X.; Allen, J. W.; Lindberg, P. A. P.; Dessau, D. S.; Wells, B. O.; Borg, A.; Ellis, W.; Kang, J. S.; Oh, S. J.; Lindau, I.; Spicer, W. E. Phys. Rev. B: Condens. Matter Mater. Phys. 1990, 42, 1817−1828. (33) Adler, D.; Feinleib, J. Physical Review B-Solid State 1970, 2, 3112−3134. (34) Larson, B. C.; Ku, W.; Tischler, J. Z.; Lee, C. C.; Restrepo, O. D.; Eguiluz, A. G.; Zschack, P.; Finkelstein, K. D. Phys. Rev. Lett. 2007, 99, 4. (35) Ressouche, E.; Kernavanois, N.; Regnault, L. P.; Henry, J. Y. Phys. B 2006, 385−386, 394−397. (36) Anisimov, V. I.; Aryasetiawan, F.; Lichtenstein, A. I. J. Phys.: Condens. Matter 1997, 9, 767−808. (37) Arai, M.; Fujiwara, T. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 51, 1477−1489. (38) Jiang, H.; Gomez-Abal, R. I.; Rinke, P.; Scheffler, M. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 045108. (39) Rödl, C.; Fuchs, F.; Furthmüller, J.; Bechstedt, F. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 235114.

appropriate electronic structure methods and U parameters. Importantly, these findings point to intrinsic differences in these materials: Co2O3 and Co3O4 are weakly correlated materials, whereas CoO is a strongly correlated material. Finally, our computed one-electron energy level diagrams have revealed strong antibonding states between Co and oxygen ions at the top of valence band for all the cobalt oxides, hinting at a defect tolerant capacity in these materials. Interestingly, we find that the bonding between Co3+ and O2− ions in Co2O3 and Co3O4 and that between Co2+ and O2− ions in CoO and Co3O4 are rather different. We believe that these results, which give a detailed picture of the chemical bonding in related single and mixed valence cobalt oxides, may serve as a guide to enhance the PV or PEC activity of Co3O4, by reducing its internal defect states or changing its electronic structure by doping or alloying with suitable elements.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.5b02426. Unit cells showing the possible magnetic structures for Co2O3; bar diagrams showing the variation of the total magnetic moment and the local magnetic moment of each Co3+ ion in Co2O3 for different sets of magnetic configurations; change in magnetic moment per Co3+ ion as a function of unit cell volume change for Co2O3; a comparison of phase diagrams, partial densities of states for each Co2+ and Co3+ ion for different levels of DFT, total density of states and its variation for one-electron addition and subtraction, global crystal coordinates and local coordinates of associated ligands for each metal ion, off-site COHPs and ICOHPs per bond for the nearest neighbor of Co−O and Co−Co in both spin up and spin down channels, and the defect tolerant analysis for each cobalt oxide material; and a table showing the symmetry classification of molecular orbitals for Oh symmetry (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support from the Israeli National Nanotechnology Initiative (INNI, FTA project) and also thank Stefano Curtarolo for suggesting this comparative study of single and multiple valence cobalt oxide systems.

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REFERENCES

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DOI: 10.1021/acs.inorgchem.5b02426 Inorg. Chem. 2016, 55, 3307−3315

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DOI: 10.1021/acs.inorgchem.5b02426 Inorg. Chem. 2016, 55, 3307−3315