The Effect of Degrees of Inversion on the Electronic Structure of Spinel NiCo2O4: A Density Functional Theory Study.

In this study, electronic structure calculations and Bader charge analysis have been completed on the inverse, intermediate, and normal spinel structures of NiCo2O4 in both primitive and conventional cells, using density functional theory with Hubbard U correction. Three spinel structures have been computed in the primitive cell, where the fully inverse spinel, 50% intermediate spinel, and normal spinel can be acquired by swapping Ni and Co atoms on tetrahedral and octahedral sites. Furthermore, NiCo2O4 with different degrees of inversion in the conventional cells was also investigated, along with their doping energies. Confirmed by the assigned formal charges, magnetic moments, and decomposed density of state, our results suggest that the electronic properties of Ni and Co on the tetrahedral site can be altered by swapping Ni and Co atoms, whereas both Ni and Co on the octahedral site are uninfluenced. A simple and widely used model, crystal field theory, is also compared with our calculations and shows a consistent prediction about the cation distribution in NiCo2O4. This study analyzes the correlation between cation arrangements and formal charges, which could potentially be used to predict the desired electronic properties of NiCo2O4 for various applications.

Introduction

NiCo2O4 is a widely used material, which has been studied in various fields, such as metal–air batteries,[1−5] supercapacitors,[6−8] electrochemical sensors,[9−11] water splitting,[12−14] and photocatalysis.[15−17] The presence of abundant redox couples (Ni2+/Ni3+ and Co2+/Co3+) in NiCo2O4 can provide sufficient active sites, leading to a good electrochemical/catalytic performance.[18] For example, the Co2+ and Ni3+ cations are reported to be the active sites for the oxygen reduction reaction and oxygen evolution reaction.[5,19−23] These examples indicate the importance of cations that possess the desired oxidation state and thus can serve as the active sites for electrochemical/catalytic reactions.

The origin of the oxidation states of Ni and Co cations are therefore of great interest. A simple formula supported by X-ray absorption spectroscopy describes how Ni/Co cations with different charges are distributed in the tetrahedral (Td) and octahedral (Oh) sites:[24]

In this formula, Ni cations occupy octahedral sites, and Co cations are situated in both tetrahedral sites and octahedral sites. Although Ni cations are often reported to locate in the octahedral sites, some evidences point out that the exchange between tetrahedral Co and octahedral Ni takes place easily and frequently.[25,26] Taking into account the cation exchange, the formula of NiCo2O4 can be rewritten as follows:where the fraction (x) of Ni in the octahedral site is referred to as the degree of inversion (DOI).[27] When DOI = 1 (i.e., x = 1) in formula (, NiCo2O4 is in an inverse spinel configuration (as shown in Figure a). On the other hand, when DOI = 0 (x = 0), it is in a normal spinel configuration (shown in Figure b). Except the inverse and normal structures, all other configurations are the intermediate structures that can be regarded as the combination of both inverse and normal structures with different ratios.

Figure 1

Crystal structure of (a) inverse and (b) normal spinel in a conventional unit cell. O atoms are shown in red, Ni atoms in gray, and Co atoms in blue.

In the literature, many studies focused only on a pure inverse spinel structure of NiCo2O4,[28,29] despite the fact that intermediate structures are also likely to form, due to different synthesis processes.[27,30,31] Some groups reported studies on the intermediate states of a spinel structure. For example, Ndione et al. proposed that the electrical properties of NiCo2O4 and ZnCo2O4 can be controlled by manipulating the DOI,[27] and Dileep et al. reported on various band gaps for NiCo2O4 with three different cation configurations.[32] However, these works primarily focused on physical properties such as band gaps or electrical conductivities. Accordingly, the oxidation state of cations and its relationship with the structure of NiCo2O4 have not been fully elucidated.

Taking the above into consideration, the motivation of this study is to investigate the relationship between the DOI and physical properties (i.e., oxidation state, electronic structure, and band structure). With the aid of theoretical calculations, we have systematically investigated how the site distribution (tetrahedral or octahedral) affects the cation oxidation state, magnetic moment, and electronic structure of NiCo2O4 in the spinel structure by conducting density functional theory calculations on NiCo2O4 with the Hubbard U correction (DFT + U). The results show a clear relationship between the oxidation state of Ni/Co cations and cation configuration and suggest a possibility that the NiCo2O4 with desirable properties for a specific application can be obtained by changing the spinel configuration to some extent.

Computational Details

Spin-polarized density functional theory (DFT) calculations in this work were carried out using projector augmented wave (PAW) methods to describe the ion–electron interactions as implemented in Vienna Ab initio Simulation Package (VASP).[33,34] The valence electron configuration in the calculation was 3d84s2 for Ni, 3d74s2 for Co, and 2s2p4 for O. Plane-wave expansion was truncated at a cut-off energy of 680 eV for primitive and conventional unit cells. Perdew–Burke–Ernzerhof (PBE) functional of the generalized gradient approximation (GGA) was adopted to describe the exchange and correlation effects.[35,36] Additionally, in order to correct for the strong correlation of 3d electrons in transition metals, a rotationally invariant Hubbard U correction proposed by Dudarev et al.[37] was added on Ni 3d and Co 3d electrons, where U = 6.6, 4.4, and 6.7 eV for Ni(Oh), Co(Td), and Co(Oh), respectively. The choice of U values is based on the work conducted by Shi et al.;[30] those values were determined on the basis of linear response theory and have been proved to successfully explain the magnetic and spin properties of spinel NiCo2O4, leading to adequate reproduction of experimentally measured magnetic moments of those cations.[38] As nickel at tetrahedral sites was not investigated in Shi’s work,[30] we postulated a U value for Ni(Td) according to the equation:This equation yields a value of 4.3 eV. To better understand the effect of the U term in our system, we have carried out calculations in primitive cells with selected U values from previous works.[27,39] The magnetic moments, charges, and electronic structures might vary due to different U values on Ni and Co ions. Thus, all U values equal to 3 eV were also tested to verify the overall trend and correlations of desired properties.

We have studied both NiCo2O4 primitive and conventional unit cells in this work. The primitive unit cell is composed of 14 atoms, Ni2Co4O8, which contains two formula units (f.u.). The number of possible cation arrangements in a primitive unit cell is 6!/(4!2!) = 15, whereas there are only 3 symmetrically inequivalent configurations, i.e., inverse (DOI = 1, space group: Imma), 50% intermediate (DOI = 0.5, space group: R3m), and normal (DOI = 0, space group: Fd3m).[40] In addition to the simplicity, the use of a primitive cell has been proved to sufficiently explain the properties of spinel oxide observed in experiments.[41,42] The conventional unit cell with 56 atoms allows the investigation of 9 different DOIs, which were further studied to understand more the influence of the cation distribution. For the integration of a Brillouin zone, a 3 × 3 × 3 Monkhorst-Pack[43]k-point mesh was used for both primitive and conventional unit cells. A finer k-point mesh of 14 × 14 × 14 was used for the primitive unit cell to better sample the reciprocal space for the density of state (DOS) calculations. The self-consistent calculation was converged in 10–5 eV, and structural optimization was executed by minimizing forces on all the atoms until they were smaller than 0.01 eV Å–1. Atomic charges were discussed using Bader charge analysis,[44] where the code from Henkelman et al. was applied.[45,46]

Results and Discussion

Equilibrium Structures

We first investigated the stability and geometry of the different NiCo2O4 equilibrium structures in different degrees of inversion (DOI). Table shows the computed lattice constants for both conventional and primitive unit cells and calculated relative and doping energies for corresponding DOIs.

Table 1

Calculated Lattice Constants, Relative Energies, and Doping Energies of (CoNi1–)Td(Co2–Ni)OhO4 for Different DOIs

	lattice constant (Å)
DOI (x)	conventional unit cell	primitive unit cell	relative energy (eV/f.u.)	doping energy (eV/f.u.)
1	8.178	8.16	0	–0.40
0.875	8.175		0.14	–0.26
0.75	8.160		0.28	–0.12
0.625	8.150		0.41	0.01
0.5	8.138	8.12	0.56	0.16
0.375	8.125		0.65	0.25
0.25	8.110		0.74	0.33
0.125	8.100		0.83	0.43
0	8.085	8.08	1.70	1.30

For the conventional unit cell, the computed lattice constant of inverse NiCo2O4 is 8.178 Å, which is merely 0.7% larger than the experimentally measured lattice constant 8.115 Å[47] and 0.7% smaller than the previous computational lattice constant 8.237 Å,[30] suggesting that a reliable computational setting has been used. It is clear that for both primitive and conventional cells, the lattice constant decreases continuously as NiCo2O4 transforms from an inverse to normal configuration, consistent with the previous report that lattice parameters of the spinel are dependent on DOI.[31] It is expectable to acquire slightly different lattice constants for the conventional and primitive unit cells for the same DOI after structural optimization within periodic boundary conditions. The relative energy of the structure rises steadily from 0 to 1.7 eV as DOI decreases from 1 to 0, which indicates that the inverse structure is the most thermodynamically stable, in good agreement with the experimental results seen in the literature.[48−51]

Because NiCo2O4 can be regarded as Ni-doped Co3O4, their geometry stability can be described by the doping energy, expressed as follows:[30]where ENiCo is the total energy of the NiCo2O4 in the corresponding DOI (x = 0 to 1); ECo, ENiO, and ECoO are the total energies of Co3O4 bulk, NiO bulk, and CoO bulk, respectively.

The calculated doping energy represents the stability of the NiCo2O4 structure compared to the parent compounds (i.e., Co3O4, NiO, and CoO bulks), indicating whether the formation of the structure in a certain degree of inversion is favorable or not. The high-DOI NiCo2O4 (x = 0.75 to 1) exhibits negative doping energies (under −0.12 eV/f.u.), suggesting that its formation is slightly thermodynamically favorable, whereas the structures with low DOI (x = 0 to 0.625) exhibit small positive doping energies, suggesting the formation of these DOIs are thermodynamically unfavorable. These results suggest that all NiCo2O4 in a higher DOI can be synthesised easily. Although the low-DOI NiCo2O4 seems unstable, its synthesis should still be possible under certain synthetic conditions, by taking into account the entropic effects caused by temperature.[51]

Crystal Field Stabilization Effects

For transition metal oxides with the spinel structure, crystal field theory (CFT) has been applied to predict the cation distribution and magnetic moments.[52−54] Chemical bonding has been treated as purely ionic, where each oxygen anion should be regarded as a point charge of −2. In spinel oxides, oxygen is arranged in a face-centered cubic structure, which forms tetrahedral holes and octahedral holes between oxygen atoms. The transition metal cations, which can randomly occupy both tetrahedral sites and octahedral sites, possess split d orbitals due to the electric field caused by oxygen anions. At octahedral sites, the d orbitals of each cation split into two energy levels, eg and t2g. On the other hand, at tetrahedral sites, the d orbitals split into e and t2 levels. As a result, d electrons prefer to occupy the split orbitals in the configuration, where the overall energy is the lowest. The final cation distribution is only dependent on the crystal field stabilization energy, which does not take any other effects such as cation size and covalent bonding into account. It is well known that CFT is oversimplified because of those assumptions; however, the crystal field stabilization effect is still an important factor, which affects how the cations are arranged in the spinel structure. Therefore, in this section, the crystal field stabilization energy (CFSE) and octahedral site preference energy (OSPE) derived from CFT are provided to investigate potential correlations with our DFT results. CFT predicts that the oxygen anion with a face-centered cubic structure is a relatively weak ligand and induces slight d orbital splitting.[55,56] In this case, cations that reside in tetrahedral sites have high-spin electron occupation; in comparison, those occupying octahedral sites may either have high-spin or low-spin configurations.[57] In order to describe qualitatively the crystal field stabilization effects, CFSE and OSPE for Ni2+, Ni3+, Co2+, and Co3+ are listed in Table S1.

Atomic Charges and Magnetic Moments

Understanding how DOI influences the oxidation state is the major motivation of this work. By using Bader charge analysis, a series of NiCo2O4 spinel oxides with various DOIs were computed to investigate the relationship between the oxidation state and cation distribution. The obtained charges and magnetic moments of Ni and Co cations in primitive cells are listed in Table . In the literature, Ni and Co have been reported to possess various oxidation states, ranging from +2 to +3.[58−60] This phenomenon may result from the complex cation distribution in spinel oxides because the cation, which has a certain oxidation state, can be stabilized more in a specific position, as predicted by CFT.[40] In this section, three structures (inverse, 50% intermediate, and normal) in primitive cells are considered preliminarily, in order to assess the variation of oxidation states and magnetic moments in different cation arrangements. Note that all calculated cation charges are underestimated compared to their formal oxidation state, which is common for the GGA functional and Bader analysis.[61−63] In the fully inverse spinel, the charge of octahedrally coordinated Ni(Oh) is +1.20 |e|, while Co(Td) and Co(Oh) possess charges of +1.49 and +1.38 |e|, respectively. On the other hand, Ni occupies tetrahedral sites in the normal spinel, with all Co cations in octahedral positions. In such configuration, Ni is calculated to be +1.21 |e|, whereas Co has a charge of +1.32 |e|. By making the assumption that the Bader charge of the atom is correlated to the atom’s oxidation state, it is expected that the valence electrons of cations may experience a significant change while being swapped to different positions. Comparing the 50% intermediate structure to the inverse and normal structures, Ni(Td) exhibits a higher oxidation state compared with the normal spinel (+1.33 versus +1.21 |e|), whereas Co(Td) shows an obvious decrease in the oxidation state compared to the inverse structure (+1.33 versus +1.49 |e|). All minor changes in charges, which occur in Ni(Oh) and Co(Oh), may be ascribed to the balance of total charge in order to maintain the charge neutrality. In order to compare the effects of different U values, a set of U values (3 eV for all cations, reported by Stevanović et al.[39]) are computed as well, and the Bader charge analysis and magnetic moments are shown in Table S2. The trend observed is similar for all DOIs, with slightly different charges and magnetic moments.

Table 2

Bader Charges (Q, in |e|), Assigned Formal Charges, and the Numbers of Projected Unpaired Electron (Nα–Nβ) of Ni and Co at Tetrahedral and Octahedral Sites and the Total Magnetization per Formula Unit (Nα–Nβ, total) of the Inverse, 50% Intermediate, and Normal NiCo2O4 in a Primitive Unit Cell

cations	properties	inverse	50% intermediate	normal
Ni(Td)	Q		+1.33	+1.21
	formal charge		+2 to +3	∼+2
	Nα–Nβ		1.998	1.791
Ni(Oh)	Q	+1.20	+1.19
	formal charge	∼+2	∼+2
	Nα–Nβ	–1.670	–1.661
Co(Td)	Q	+1.49	+1.33
	formal charge	∼+3	+2 to +3
	Nα–Nβ	3.022	2.696
Co(Oh)	Q	+1.38	+1.35	+1.32
	formal charge	+3	+3	+3
	Nα–Nβ	0.060	0.070	–0.260
	Nα–Nβ, total	2	2	2

The Bader charge results exhibit a relationship between the oxidation state of cations and DOI. However, a further explanation of the Bader analysis is required to correlate the obtained Bader charge with the formal charge of cations in real NiCo2O4. Although the magnetic moment is not typically reported to affect the catalytic activities of NiCo2O4, it can help to understand the occupation of d orbitals of Ni and Co, and thus the formal charge of each cation. When considering the magnetic moments along with the charges obtained in the DFT calculations, formal charges (Table ) and electronic configurations (in Figure a–c) of NiCo2O4 at corresponding DOIs (inverse, normal, and 50% intermediate) can be estimated. Two important assumptions should be made prior to the assignment of formal charges. First, the Bader charges can only be compared between the same atoms at the same sites in various DOIs; i.e., Co(Td) with a charge of +1.49 is not necessary to be more positive than Co(Oh) of +1.38. The comparison between two Bader charges is only made when the cations are in similar environments (i.e., tetrahedral or octahedral sites). Second, the formal charges are rounded to an integer, due to known underestimates by GGA and Bader analysis; i.e., all charges are rounded up based on comparisons between the calculated results and known experimental results, making the assumption that there is a correlation between the calculated Bader charge and formal oxidation charge on the atom. Note that some formal charges with a tilde mark means that they are close to an integer (e.g., ∼+3 represents that the charge is close to +3), which is reasonable owing to the partial occupation of d orbitals.[30] The assignment of the electronic configuration starts from the fact that Co(Oh) has been commonly reported to possess a charge of +3 and is nonmagnetic,[30,64,65] which is also confirmed by our calculated magnetic moment (see Table ). In the inverse structure, Co(Td) is assigned a formal charge near +3 by referring to the obtained magnetic moment. The formal charge of Ni(Oh) is assigned to be close to +2, considering the calculated magnetic moment (−1.67 μB) and the overall formal charge is close to +8. Figure a shows the predicted electron occupation in d orbitals for the inverse NiCo2O4 based on the oxidation states and magnetic moments in Table . Regarding the normal spinel structure, the Ni(Td) should be near +2 to fulfil the overall +8 formal charge because each Co(Oh) possesses a +3 charge. The proposed electronic configuration of the normal spinel based on Table is shown in Figure b. As a more complex system, 50% intermediate NiCo2O4 is of great interest and worth researching. In 50% intermediate NiCo2O4, Co(Oh) remains +3 in this structure, while Co(Td) has been assigned a formal charge between +2 and +3 according to the Bader charge and magnetic moment, which is also in line with the literature reporting that Co(Td) can be a mix of +2 and +3 cations.[24,26,60] Ni(Oh) displays a similar Bader charge to the one in inverse NiCo2O4, so the proposed oxidation state for Ni(Oh) is +2 as well. However, Ni(Td) exhibits a more positive Bader charge compared to that of normal NiCo2O4, resulting in a higher formal charge than that of the normal NiCo2O4. Therefore, Ni(Td) in the 50% intermediate is assigned to range from +2 to +3.

Figure 2

Proposed electronic configurations of the 3d orbitals of Ni and Co ions at octahedral and tetrahedral sites of (a) inverse, (b) normal, and (c) 50% intermediate structures. Black arrows indicate full occupation of electrons, and red arrows represent partial occupation.

To further probe the relationship between the oxidation state and DOI, more DOIs were taken into account in conventional cells, and the results are shown in Figure . All cations maintain almost an unchanged oxidation state at octahedral sites regardless of whether the sites are occupied by Ni or Co. By contrast, both Ni(Td) and Co(Td) generally experience an increase in the charge. This result indicates that Ni(Td) and Co(Td) are cations that are more likely to be altered/optimized in the synthesis of NiCo2O4 because they experience large changes in oxidation states as DOI changes. Note that when the DOI is 0.5, there is a deviation from the general trend of increasing oxidation states for Co(Td) and Ni(Td). The reason remains unclear at the current stage and may need future investigations. Despite the deviation observed for 50% intermediate spinel, a general relationship between the oxidation state and DOI is clearly illustrated.

Figure 3

Average Bader charges of all the Ni and Co atoms at both tetrahedral and octahedral sites in a NiCo2O4 conventional unit cell.

The CFT predictions and experimental results in the literature are compared carefully with our DFT results. First, the CFT and OSPE expect that Ni2+ prefers octahedral sites, which matches our calculations and experimental results in the literature (see Table and Table S1).[24,66−71] For Ni3+ cations, CFT also predicts that Ni3+ with a low-spin state favors the occupation of octahedral sites (see Table S1), which is not in agreement with our calculations. Nevertheless, it is common to observe tetrahedrally coordinated Ni3+ in synthesized NiCo2O4 spinel,[22,58,66] which is consistent with our results. This discrepancy between CFT and experimental results may be ascribed to the oversimplified crystal field theory. Ni3+ with a high-spin state, which has a less negative OSPE value, is theoretically more likely to stay in tetrahedral sites. On the other hand, CFT expects that Co3+ with a low-spin state substantially tends to reside in octahedral sites, which agrees with the results from our calculations and in the literature.[66,69] Therefore, a high-spin Co3+ cation is less possible to exist in octahedral positions.[71] Though the Co2+ is predicted by CFT to prefer octahedral sites as well, the affinity is not as strong as Co3+. Therefore, Co2+ is observed mainly in tetrahedral holes. The assignment of Co2+ and Co3+ is in good consistency with NiCo2O4 synthesized by different methods, studied by Marco et al. and Kim et al.[59,71] Although CFT is a simple model that only considers the electrostatic forces between cations and anions, surprisingly, it performs well in predicting the cation distribution in the case of NiCo2O4, which validates the application of the OSPE model to simply and quickly explain the different cation arrangements and electronic structures of NiCo2O4 in the literature.

Density of States

Density of state (DOS) calculations were used to analyze how DOI of NiCo2O4 affects its corresponding electronic structure. The projected DOS in Figure a shows that the inverse NiCo2O4 has a band gap of 0.9 eV, consistent with the previous study, which used similar U terms.[72] Also, an integer magnetic moment of the entire system was set as 2 μB per formula unit based on the previous work.[73,74] If there is a band gap in at least one spin channel, the number of electrons in that channel(s) should be an integer. The number of electrons with the opposite spin is also an integer, so the total magnetization per formula unit is an integer as well. The integer magnetic moment criterion can be used to distinguish half metals and insulators from metals.[75] This methodology is applied here because NiCo2O4 is a semiconductor.

Figure 4

Projected density of state (PDOS) of (a) inverse (b) 50% intermediate, and (c) normal NiCo2O4.

In the inverse structure, the main contribution to the states around the Fermi level is strongly hybridized O 2p, Ni(Oh), and Co(Td) 3d orbitals in the minority spin, shown in Figure a. Moreover, at all energy levels in both spin channels, hybridization is significant between cation 3d and O 2p orbitals, which may lead to different crystal field splitting effects of cation 3d orbitals and thus influence the electron occupancy. For example, the occupancies of Co(Oh) in the inverse structure in Table S3 show that Co(Oh) has 71 and 72% occupancies for the spin up and spin down, respectively. The occupancies estimated by DOS are not exactly the same as our proposed electronic structure (60% for both spin up and spin down, see Figure a) based on our assigned formal charge +3 in Table , which may be owing to the hybridization of d and p orbitals. Despite the small difference in the electron occupancy, the DOS results still suggest that Co(Oh) is nonmagnetic, supporting our assumption in Section again. Generally speaking, the d orbital occupancy obtained from the DOS fits well with our proposed electronic configurations in the previous section, which confirms that our assignments for oxidation states of cations are reasonable.

For the 50% intermediate structure (see Figure b), NiCo2O4 has a smaller band gap of 0.36 eV and is insulating, which follows again its integer criterion of magnetic moment (Table ). This band gap is quite close to what Ndione et al. reported (approximately 0.3 eV).[27] In this cation configuration, O 2p is still highly hybridized with cation 3d orbitals in both valence and conduction bands. Again, the d orbital occupancy acquired from the DOS results is given in Table S4, which is very close to our prediction of electronic configurations. The difference between Bader charge analysis and DOS may be attributed to the partially localized d orbitals and the hybridization effects. Note that there is tiny magnetization for Co(Oh) from DOS calculation (74 and 69% occupancy for up and down spins, respectively); however, this magnetic moment is negligible when the electronic configuration is assigned in the previous section, suggesting that we can follow the assumption of zero magnetization for Co(Oh), based on the literature data.

For the normal spinel structure (see Figure c), half-metallicity, which is contributed by O 2p, Co(Oh), and Ni(Td) orbitals, is shown in our DOS calculation with an integer magnetic moment (Table ), which obeys the integer magnetic moment criterion. The resultant DOS resembles the result using similar U terms completed by Pandey et al., which exhibits great consistency, compared to our calculations.[72] O 2p is also strongly hybridized with Co(Oh) and Ni(Td) for all energy levels. The d orbital occupancy integrated from the DOS results is provided in Table S5, which is close to our prediction of electronic configurations, apart from the little discrepancy between the Co(Oh) occupancy of DOS (Table S5) and proposed electronic configuration (Figure b). Note that the discrepancy between our proposed electronic configurations and the orbital occupancy is expected to occur because we apply the nonmagnetic Co(Oh) assumption for all spinel structures when assigning the occupancy.

Overall, the projected DOS results (Figure a–c) demonstrate that our proposed electronic configurations for the inverse, 50% intermediate, and normal NiCo2O4 are valid and exhibit a good agreement with the DOS presented in the literature. In all DOS calculations, hybridization of O 2p and metal cation 3d orbitals is observed, implying the possible covalent effect on the cation distribution and electronic structure, but the crystal field splitting effect is still the dominant factor for the NiCo2O4, confirmed by our calculation and OSPE model.

Conclusions

We investigated the equilibrium structures and relative stabilities of NiCo2O4 with various degrees of inversion (DOIs). The high-DOI NiCo2O4 is computed to be energetically favorable, and low-DOI ones have tiny positive doping energies, suggesting that it is still possible to produce lower DOI NiCo2O4 via some synthesis routes. In our DFT calculations, Ni(Td) and Co(Td) are found to undergo significant changes in the oxidation state, suggesting that the desired oxidation state may be modulated by altering the DOI. In comparison, Ni(Oh) and Co(Oh) remain almost unchanged as the DOI changes. The crystal field theory and the consequent crystal field stabilization energy are also compared in this work, supporting the trends we found for the cation distribution in all NiCo2O4 crystal models. The DOS results also confirm that the predicted d-band occupancy agrees with the formal charges assigned to the Ni and Co cations.

In summary, by combining the Bader charge analysis and magnetic moments of cations, the formal charges and electronic structures of NiCo2O4 can be evaluated systematically, and the results are in good agreement with the widely used crystal field theory. The confirmation of Ni/Co oxidation states via different analyses could be essential for further understanding of electrochemical/catalytic performance.