Structural and Electronic Features of Î²-Ni(OH)2 and Î²-NiOOH from

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Structural and Electronic Features of #Ni(OH) and #-NiOOH from First Principles 2

Alexander J. Tkalych, Kuang Yu, and Emily A. Carter J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b08481 • Publication Date (Web): 07 Oct 2015 Downloaded from http://pubs.acs.org on October 12, 2015

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The Journal of Physical Chemistry

Structural and Electronic Features of β-Ni(OH)2 and β-NiOOH from First Principles Alexander J. Tkalych,† Kuang Yu,‡ and Emily A. Carter*,§ †

Department of Chemistry, Princeton University, Princeton, NJ 08544, USA

‡

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ

08544-5263, USA §

Department of Mechanical and Aerospace Engineering, Program in Applied and Computational

Mathematics, and Andlinger Center for Energy and the Environment, Princeton University, Princeton, NJ 08544-5263, USA

Supporting Information

1 ACS Paragon Plus Environment


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ABSTRACT NiOx, long studied for its use in nickel-based secondary batteries, has been the subject of much recent interest due to its efficacy as an oxygen evolution catalyst. Despite extensive study over more than a century, however, many outstanding questions remain surrounding both the structure and the activity of NiOx. Further compounding this ambiguity is the recent finding that much of the previous experimental work on NiOx may have been influenced by incidental doping. Here, we report a computational study of the two simplest members of the NiOx family: β-Ni(OH)2 and β-NiOOH. Using DFT+U calculations, we first identify a β-NiOOH structure with a staggered arrangement of intercalated protons that is more consistent with experimental crystal structures of β-NiOOH than previously proposed geometries. Next, by conducting a thorough study of various initial spin configurations of this β-NiOOH structure, we found that a low-spin d7 Ni3+ configuration is always favored, which suggests a Jahn-Teller distortion, rather than disproportionation, explains the different Ni-O bond distances found in experiment. G0W0 calculations performed on β-Ni(OH)2 and β-NiOOH reveal electronic structures consistent with previous experimental results. Lastly, calculations of various low-index surface energies of both β-Ni(OH)2 and β-NiOOH demonstrate that the (0 0 1) surface is the most thermodynamically stable surface, in keeping with numerous experimental results but in contrast to recent computational models.

INTRODUCTION Interest in the nickel hydroxide (Ni(OH)2) and nickel oxyhydroxide (NiOOH) redox pair (henceforth collectively termed NiOx) dates back to the turn of the last century. Patents by 2 ACS Paragon Plus Environment

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Thomas Edison1-2 in the U.S. and Waldemar Jungner3-5 in Sweden describe Ni-based alkaline batteries using NiOx as the cathode material. A flurry of subsequent work established NiOx as one of the most important battery materials of the 20th century. NiOx serves as the cathode material for all nickel-based secondary batteries, including Ni–Cd, Ni–Fe, Ni–Zn, Ni–H2 and Ni– MH (metal hydride) batteries.6-8 In addition to batteries, the electrocatalytic properties of NiOx have been studied in myriad areas: fuel cell electrodes,9 oxidation of alcohols,10 carbohydrates,11 and urea,12 oxidation of sulfide ions,13 and electrochromic devices.14-16 Perhaps the most important of all of these applications is the use of NiOx as an alkaline electrolyzer. Work by Trotochaud et al. in 2012,17 extending on work by Corrigan et al. in the 1980s,18-20 has shown that NiOx is one of the most promising materials for water splitting available today. Indeed, NiOx has been shown to be as active, or even more active, than the previous state-of-the-art alkaline water electrolyzer materials RuO2 and IrO2.21-23 The finding that a nickel-based oxide is more active than even precious metal catalysts has sparked intense interest in understanding and improving this material.

Despite many outstanding questions related to the study of NiOx, much of the fundamental work relating to its structure was done almost half a century ago. Seminal work by Bode et al.24-25 showed, using X-ray diffraction, that NiOx consists of four main phases: βNi(OH)2, α-Ni(OH)2, β-NiOOH, and γ-NiOOH. The main feature of these phases is that each consists of NiO2 slabs with tetrahedrally-coordinated hydrogen atoms in the interslab space. αNi(OH)2 and γ-NiOOH differ from β-Ni(OH)2 and β-NiOOH, respectively, in that they are intercalated by species such as H2O, OH−, SO42-, CO32-, and others.26-31 These intercalated species make the study of α-Ni(OH)2 and γ-NiOOH relatively difficult as both phases are poorlycrystallized, turbostratic structures. Nevertheless, the α/γ redox cycle has attracted considerable 3 ACS Paragon Plus Environment


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interest. This is because the cycle involves little mechanical deformation32 and because of persistent evidence of the existence of tetravalent metallic species in γ-NiOOH phases.20, 23, 33-35 Both findings suggest that the α/γ cycle could find considerable application in battery technologies due to its high specific capacity.36-38 Additionally, recent work suggests that γNiOOH, rather than β-NiOOH, is the more active phase for the oxygen evolution reaction (OER).21, 23, 39-40 However, it is difficult to generate general model systems to study α-Ni(OH)2 and γ-NiOOH computationally. This is due to the numerous possible species that can intercalate these structures and the turbostratic stacking of the NiO2 sheets. Additionally, because αNi(OH)2 and γ-NiOOH are based on β-Ni(OH)2 and β-NiOOH, it is important to first understand the features that characterize the more fundamental β phases. The understanding obtained from this research will be useful for studying α-Ni(OH)2 and γ-NiOOH in future work. Therefore, this work focuses on the properties of β-Ni(OH)2 and β-NiOOH.

Of the four phases of NiOx, only the structure of β-Ni(OH)2 is known with a high degree of confidence.41 Its space group is 31 (brucite),42-43 and its experimental lattice parameters are: a = b = 3.12 Å and c = 4.66 Å.44 β-Ni(OH)2 is a compact, layered structure with a c parameter that does not permit intercalation of any guest moieties.45 Thermogravimetric studies show that β-Ni(OH)2 loses only about 1% of its weight on drying at 100°C.38,

46-47

The same

study shows a corresponding loss of about 30% for α-Ni(OH)2, reflecting the large number of intercalated species present in the structure. Information about the structure of β-Ni(OH)2 can also be extracted from infrared spectroscopy studies.48-50 The sharp non-hydrogen bonded OH stretch at 3650 cm−1 is due to the ν(OH) stretching vibration, which indicates free OH groups and a lack of hydrogen bonds. Further structural information can be extracted from Extended X-ray


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Absorption Fine Structure (EXAFS) studies. One study conducted at 77 K showed coordination shells with 6.2 nickel ions at 3.13 Å, and 6.0 oxygen ions at 2.07 Å.51 Similar results were obtained at room temperature. The EXAFS data can be explained in terms of the ionic radii of Ni2+ and O2-. The ionic radius of Ni2+ with six neighbors is 0.69 ± 0.01 Å, while the ionic radius of oxygen is 1.35-1.40 Å.52 Taking the ionic radius of O2- to be 1.37 Å, the sum of the two radii is 2.07 Å. X-ray diffraction (XRD) studies show that the (0 0 1) reflection is most intense.53-54 The strength of the (0 0 1) signal increases with increasing pH, as does the crystallinity of βNi(OH)2. Turning to electronic properties, β-Ni(OH)2 has been reported to be a p-type semiconductor with a band gap of about 4 eV.8, 16

The structure of β-NiOOH is considerably more complicated than that of β-Ni(OH)2. One investigation determined that the oxygen stacking sequence in β-Ni(OH)2 changes from ABAB to ABCA upon oxidation to β-NiOOH.43 This is the same oxygen stacking sequence as is found for γ-NiOOH.55 It has been suggested that deviations in the β-NiOOH structure from the brucite lattice structure are due either to incomplete oxidation (leaving residual β-Ni(OH)2) or overoxidation (leading to the formation of γ-NiOOH).56 Other studies indicate that oxidation of βNi(OH)2 to form β-NiOOH proceeds without major structural changes.47, 55, 57 The space group of β-NiOOH, like β-Ni(OH)2, is 31.44,

55

Infrared spectroscopy measurements suggest that β-

NiOOH is a hydrogen-bonded structure with no free hydroxyl groups.48, 55 EXAFS analysis of the β-NiOOH data yields two Ni-O distances: 1.88 and 2.07 Å.58 The two Ni-Ni distances are 2.82 and 3.13 Å. These data suggest two possibilities for the nickel ions in β-NiOOH: Ni3+ in distorted octahedra, or a mixture of Ni2+ and Ni4+. Recent evidence suggests that disproportionation into Ni2+ and Ni4+ is possible in β-NiOOH,59 while other data support a Jahn-



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Teller distortion as a more likely explanation for the different Ni-O bond distances.21,

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39

The

experimental band gap for β-NiOOH was estimated to be 1.7 - 1.8 eV, although the authors emphasized that this value was merely an estimate.16 Most studies conclude that β-NiOOH is an n-type semiconductor.60-61 However, it has also been reported that β-NiOOH is a p-type semiconductor.62 Thus, there are still many unanswered questions concerning the properties of βNiOOH.

Given the sustained interest in the nickel oxyhydroxides, it might come as a surprise to note the relative paucity of theoretical studies of this material. This is attributable to many causes, but perhaps none as important as the difficulty in establishing the structures of the various phases involved. The structures of α-Ni(OH)2 and γ-NiOOH, with their turbostratic layered structures and uncertain nickel oxidation states, are the subject of persistent debate. Even β-NiOOH, with its many possible stacking orders and nickel oxidation states, presents non-trivial difficulties for those hoping to model its properties. Nevertheless, two recent studies by Li and Selloni have sought to unravel some of the mystery surrounding NiOx. Their first work studied the mechanism of the OER on various nickel oxyhydroxide surfaces.63 They found that the overpotential for this reaction is lowest on Fe-doped β-NiOOH. In fact, the calculated overpotential for the OER on this surface was predicted to be even lower than the one on RuO2. They also concluded that the (0 1 1 5) β-NiOOH surface is more active than the (101) γ-NiOOH surface. The choice of the (0 1 1 5) surface was justified by the results of previous work on CoOx.64 It was found that the high-index surfaces (0 1 1 2) and (0 1 1 4) were most active for the OER on CoOx. This was rationalized by noting that surface Co ions on these surfaces are under-coordinated.


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In subsequent work, Li and Selloni studied various aspects of the β-NiOOH phase.

59

Much of the motivation of this work was to explain the occurrence of an irreversible microstructural transformation that produces mosaic textures during the first oxidation of βNi(OH)2. In this case, they studied the doubled c-axis β-NiOOH phase proposed by CasasCabanas et al.43 Using a genetic algorithm approach, they found that structures composed of alternating layers of NiO2 and Ni(OH)2 were most favorable. It was found that Ni3+ dissociated into Ni2+ and Ni4+. This structure justified the use of a doubled unit cell of β-NiOOH. It was hypothesized that the instability of the layered structure versus the disproportionated structure was due to strains in the hydrogen bond network between sheets. This strain was hypothesized to result from the Jahn-Teller effect of low-spin Ni3+.

There is clearly a great deal of ambiguity surrounding the properties of even the relatively simple β phases of NiOx. This ambiguity has been further compounded by a striking recent result from Trotochaud et al. that showed that even trace amounts of Fe in the electrolyte are scavenged by the NiOx film.23 This effect was previously noted by Corrigan, who found that incidental iron incorporation could lead to improved activity towards the OER.18 Indeed, Trotochaud et al. showed that, upon ensuring strict exclusion of Fe from the electrocatalytic film, the activity towards the OER was dramatically reduced. This scavenging of metal ions from solution has also been shown for NiOx films in the presence of Al ions.6 These results suggest that part of the difficulty in studying these materials has been at least partly due to incidental doping by metal impurities in the electrochemical apparatus. This could explain why it has been difficult to measure accurate band gaps, to determine the nature of the semiconductor, and why



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so many different structures have been observed. Given this possibility, it seems that many fundamental properties of the pure NiOx system may have to be re-examined. Thus, a means of understanding the properties of the pure materials could be of great utility. Computational studies of these materials are therefore of great interest as simulations can control whether or not a dopant/impurity is present. This paper will seek to answer some basic questions about β-Ni(OH)2 and β-NiOOH. After outlining the computational details of the work, the results will focus on determining the structure of both materials, the spin state of β-NiOOH, the electronic structure of β-Ni(OH)2 and β-NiOOH, and the most stable surfaces of β-Ni(OH)2 and β-NiOOH.

METHODOLOGY AND COMPUTATIONAL DETAILS The initial β-Ni(OH)2 structure (that was subsequently optimized) was taken from the literature.44 Numerous experimental studies have found essentially the same structure.24, 47, 65 The choice of an initial β-NiOOH structure is less obvious. As stated earlier, it has been suggested that deviations in the β-NiOOH structure from the brucite lattice structure are due to either incomplete oxidation (leaving residual β-Ni(OH)2) or over-oxidation (leading to the formation of γ-NiOOH).56 This could provide an explanation as to why a doubled unit cell was required in earlier studies to capture the structure of β-NiOOH. Because of this fact, and because of the numerous previous studies suggesting that the oxidation of β-Ni(OH)2 proceeds without major structural modifications,47, 66-67 we chose a representative 31 (brucite) structure to model βNiOOH.44


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All calculations were performed within the Vienna Ab-initio Simulation Package (VASP) version 5.3.3.68-71 Known failures in density functional theory (DFT) descriptions of transition metal oxides result from spurious self-repulsion and the missing derivative discontinuity in the exchange-correlation functional that lead to over-delocalization of electrons.72 Therefore, the spin-polarized, DFT+U approach of Dudarev et al. was employed to ameliorate these errors.73 A U−J correction of 5.5 eV was added via the Dudarev functional in combination with the PerdewBurke-Ernzerhof (PBE) exchange-correlation functional.74 This value was taken from Li and Selloni’s work on β-NiOOH,63 which was calculated using linear response theory. Other U−J values were not found to affect the qualitative results (see Supporting Information). Blöchl’s allelectron, frozen-core, projector augmented wave (PAW) method was used.76,78 PAW potentials acted on the 4s/3d electrons of Ni, and the 2s/2p electrons of O, while all other (core) electrons were kept frozen. The total energy was converged to less than 1 meV / atom using a plane wave kinetic energy cutoff of 750 eV and Γ-point-centered Monkhorst-Pack k-point meshes75 of 6 × 6 × 4 for β-Ni(OH)2 and 5 × 5 × 3 for β-NiOOH; see Supporting Information for structural parameters. Structures were considered converged upon reaching a force threshold of 0.01 eV Å1

. For the geometry optimizations, the Brillouin zone was integrated using Gaussian smearing

with a smearing width of 0.01 eV, while the tetrahedron method was used for evaluating total energies.77 For densities of states, PBE+U calculations with a 30 x 30 x 20 Γ-point-centered kpoint mesh for β-Ni(OH)2 and a 24 x 24 x 14 Γ-point-centered k-point mesh for β-NiOOH were performed.

It was shown previously that G0W0 calculations performed as a perturbation on DFT+U eigenvalues and eigenfunctions with the Perdew–Burke–Ernzerhof (PBE) exchange-correlation



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functional result in excellent agreement with experiment for pure NiO.79 Therefore, the PBE+U wavefunctions and eigenvalues of both β-Ni(OH)2 and β-NiOOH were used as the input for the G0W0 calculations. Three separate G0W0 calculations were performed. The first was performed on structurally optimized β-Ni(OH)2 (see Supporting Information for structure). This calculation used a 3 x 3 x 2 Γ-point-centered k-point mesh and a Γ-point-only q-point mesh, with 80 empty bands and 96 frequency points for the evaluation of the response function. At these values, the quasi-particle (ionization potential minus electron affinity) gap was converged to within 0.1 eV. Denser q-point meshes added to the computational expense, but did not significantly affect the results. The next two calculations were performed on two different β-NiOOH structures (vida infra; see Supporting Information for structures). Both sets of calculations used a 3 x 3 x 2 Γpoint-centered k-point mesh and a Γ-point-only q-point mesh. Both calculations used 80 empty bands and 96 frequency points for the evaluation of the response function. At these values, the quasi-particle gap was converged to within 0.1 eV.

To calculate the most stable surfaces of β-Ni(OH)2 and β-NiOOH, numerous low-index surfaces were considered. Therefore, initial structures were cleaved along (1 0 0), (0 1 0), (0 0 1), (1 0 1), and (1 1 1) planes in order to generate slabs. The unique cleavage surface was selected such that there were no dangling bonds. A vacuum layer of 15 Å was introduced between the slabs, which was sufficient to prevent interactions between periodic images of the slabs. Dipole interactions between slabs were addressed by introducing a priori dipole field and energy corrections in the direction perpendicular to the surface. The dipole correction was always less than 0.04 eV. For all surface calculations, slabs of five layers were used. Optimizations were performed with fixed lattice parameters taken from the optimized bulk material whereas the ionic


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positions were allowed to relax. This thickness was found to accurately replicate the bulk density of states in the middle layer, thereby suggesting that the surface layers experience a bulk-like electronic structure of the subsurface, which sets a physically appropriate boundary condition for the surface model. Further computational details are included in the Supporting Information. The surface energy was calculated according to:

=

! ; " #

where is the surface energy, $% is the slab energy, &'() is the number of atoms in the slab cell, %$* is the energy per atom of the bulk structure, and +$% is the surface area of the slab.

RESULTS AND DISCUSSION

β-NiOOH structure The geometry optimization beginning with the experimental β-Ni(OH)2 structure led to an optimized structure with almost identical lattice parameters to the experimental structure (see Supporting Information). Surprisingly, the geometrical refinement of the experimental structure of β-NiOOH using DFT+U leads to inaccurate lattice parameters compared to experiment (see Supporting Information). In particular, calculations using PBE+U underestimate the value of the c parameter by about 0.3 Å, which is higher than the typical error in structural parameters found 11 ACS Paragon Plus Environment


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using DFT. A similar underestimation of the c parameter was found for the β-NiOOH structure determined in a previous DFT study.63 As presented next, we eventually determined that a structural effect explains this discrepancy.

Because of the inability of XRD to resolve hydrogen atom positions, differences in hydrogen positions would not be noticeable in those experiments. Therefore, this led to our hypothesis that the proton arrangement between the NiO2 sheets may explain the discrepancy between the computational and experimental lattice parameters. In the structure obtained by repeating the primitive unit cell found experimentally, all of the protons lie on the same side of the NiO2 sheet. To test the effect of placing protons different sides of the NiO2 sheets, five supercells were constructed based on the experimental primitive cell. Figure 1 shows the primitive cell and two of these supercells (the others are shown in Supporting Information). All protons in the 1 × 1 × 1 structure are on the same side; this corresponds to the original structure from experiment. This structure will henceforth be called the unstaggered structure. The 1 × 2 × 1 structure is a supercell (doubled in the a direction; see Figure 1) of the 1 × 1 × 1 structure; every second proton in this structure is on the opposite side of the NiO2 sheet. This structure will henceforth be called the staggered structure.

The 1 × 6 × 1 structure is also a supercell

(sextupled in the a direction) of the 1 × 1 × 1 structure; every sixth proton in this structure is on the opposite side of the NiO2 sheet. The other supercells constructed for these calculations were the 1 × 3 × 1, 1 × 4 × 1, and 1 × 5 × 1 structures, following the same naming convention.

As shown in Table 1, the structural parameters for the staggered structure are in far better agreement with experiment than the initial results. Furthermore, the staggered structure is also


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lower in energy than the unstaggered structure; indeed, the staggered structure is more stable than all other structures considered. Analysis of the dipole moment per NiO2 sheet shows that the parameter c is strongly influenced by dipole interactions between the NiO2 sheets (Table 2). When the protons are staggered, the dipole moment is effectively cancelled. The unstaggered structure, on the other hand, has a significant dipole moment that causes the sheets to be much closer to one another. In summary, this work shows that the staggered hydrogen arrangement leads to the best agreement of the lattice parameters with the experimental structure. This arrangement decreases the inter-sheet dipole interactions, while also decreasing the intra-sheet dipole repulsions. The overall effect of this arrangement leads to the most thermodynamicallystable structure. This structure is therefore the most likely β-NiOOH structure formed upon the complete oxidation of β-Ni(OH)2. Because the staggered structure is most stable and its lattice parameters agree most closely with experiment, we suggest this structure as an effective model for further computational study of β-NiOOH.

Figure 1: Unit cells used to test effect of staggering protons in β-NiOOH.



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Table 1: Comparison of staggered-proton structures of β-NiOOH. The total energy for each system is divided by the number of unit cells in the supercell to allow for comparison with the single unit cell structure (1 × 1 × 1).

Lattice Parameters

Normalized Energy System (eV / NiOOH cell)

a (Å)

b (Å)

c (Å)

1×1×1

-19.01

2.97

2.97

4.54

1×2×1

-19.21

2.95

2.96

4.84

1×3×1

-19.13

2.95

2.95

4.74

1×4×1

-19.11

2.93

2.96

4.71

1×5×1

-19.09

2.95

2.95

4.69

1×6×1

-19.09

2.96

2.95

4.68

Experiment44

—

2.82

2.82

4.84

Table 2: Comparison of dipole moments (µ) per NiO2 sheet for the β-NiOOH structures with different proton arrangements

Dipole moment System µ (e Å)


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1×1×1

0.32

1×2×1

0.00

1×3×1

0.11

1×4×1

0.16

1×5×1

0.19

1×6×1

0.20

β-NiOOH Spin As stated in the introduction, EXAFS studies on β-NiOOH reveal two different Ni-O bond lengths. Whether this is due to the presence of multiple nickel valencies, or a Jahn-Teller distortion, is a subject of debate. The cause is not only important for understanding the structure of β-NiOOH; it has implications for the catalytic activity of β-NiOOH towards the OER. One of the explanations posited for the high activities of these catalysts is that overcharging leads to local domains containing Ni4+ centers,20, 35, 80 which are hypothesized to serve as the active sites for the OER.39 There is ambiguity as to whether it is the β-NiOOH or γ-NiOOH phase that is the more active oxygen evolution catalyst. Several authors have concluded that it is the β-NiOOH phase that is the more active phase,63, 81-82 and that the high activity of these catalysts is due to the presence of local domains of Ni4+ in β-NiOOH. One hypothesis is that this valency above +3 is a result of a mixture of integer oxidation states (i.e. +2, +3, +4).59, 67 Previous computational work suggested that the formation of Ni4+ is indeed possible in β-NiOOH via disproportionation.59 Alternatively, the two Ni-O bond lengths observed in the EXAFS spectra have been attributed to 15 ACS Paragon Plus Environment


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a Jahn-Teller distortion of low-spin Ni3+ in β-NiOOH.21,

83

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A Jahn-Teller distortion is

characteristic of low-spin, d7 Ni3+ systems.

To investigate the cause of this phenomenon, extensive tests were done to determine the most likely spin configuration of β-NiOOH. The unit cell for β-NiOOH suggested in the previous section (i.e., the staggered structure) was doubled in the b- and c-directions to generate a supercell with eight nickel ions. The initial magnetic configurations studied included ferromagnetic (FM), antiferromagnetic (AFM), and parallel spin (PS; spins ferromagnetic within the NiO2 sheets but antiferromagnetic between them) configurations (see Figure 2). The initial spin states on each Ni ion were either low-spin (LS) or high-spin (HS). A low-spin initial configuration corresponds to a magnetic moment of approximately ±1.5 µB on each of the nickel ions; a high-spin initial configuration corresponds to a magnetic moment of approximately ±4.5 on each of the nickel ions. In all cases, the high-spin structures relaxed to low-spin configurations, indicating that the latter represents the preferred spin arrangement (see Table 3). This work concluded that a low-spin configuration for β-NiOOH is always more favorable than a high-spin arrangement (see Table 3 for a representative sample of these data; see Supporting Information for further tests).

As seen in Table 3, the lowest-energy state is a low-spin, antiferromagnetic configuration. According to ligand field theory, octahedrally coordinated, low spin d7 Ni(III) is characterized by a Jahn-Teller distortion. As expected, this distortion was observed: two Ni-O bond lengths exist in the optimized staggered structure (1.93 Å and 2.09 Å, which compare well with experimentally measured bond lengths of 1.88 Å and 2.07 Å58). Therefore, these results


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support the hypothesis that the multiple bond lengths seen in the EXAFS spectra are simply due to a Jahn-Teller distortion, rather than disproportionation.

Figure 2: Spin configurations for β-NiOOH; from left to right: ferromagnetic (FM), antiferromagnetic (AFM), and parallel spin (PS).

Table 3: Initial and final spin configurations of staggered β-NiOOH. Initial

Initial

Final

Final

Energy

spin configuration

spin state

spin configuration

spin state

(eV)

FM

LS

FM

LS

-19.21

FM

HS

FM

LS

-19.21

AFM

LS

AFM

LS

-19.38

AFM

HS

AFM

LS

-19.38



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PS

LS

PS

LS

-19.21

PS

HS

PS

LS

-19.21

Band Gap Calculations To further understand the electronic structures of β-Ni(OH)2 and β-NiOOH, projected density of state calculations were performed. As stated earlier, previous experiments derived band gaps for β-Ni(OH)2 and β-NiOOH of approximately 4.0 eV and 1.7 - 1.8 eV, respectively.16 We first calculated PBE+U projected densities of states for both β-Ni(OH)2 and low-spin, antiferromagnetic β-NiOOH. The band gap of β-Ni(OH)2 predicted by PBE+U is 2.98 eV (see Figure 3). β-NiOOH, on the other hand, is not even predicted to have a band gap (see Figure 4). This underestimation of the band gaps is reflective of well-known flaws within DFT exchangecorrelation resulting from the self-interaction and derivative discontinuity error.72 Moreover, these predicted band gaps are not actually directly comparable to an experiment, as they are actually just the DFT eigenvalue gaps rather than comparable to an optical band gap (which would involve computing excited states) or a photoemission/inverse photoemission band gap (which would involve computing ionized states). Thus, to improve the accuracy of our results, we performed G0W0 calculations on both structures, which are directly comparable to photoemission/inverse photoemission (quasiparticle) band gaps.

Different k-point meshes are used for the PBE+U and G0W0 computations because the latter are substantially more expensive than the former. The k-point mesh settings for the G0W0 18 ACS Paragon Plus Environment

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calculations represent the most expensive calculations that we could afford; finer k-point settings would, of course, lead to more accurate results. Using the settings described in the computational details section, β-Ni(OH)2 is predicted to be an indirect gap semiconductor with a band gap of 5.83 eV (see Figure 5). This value is significantly higher than the experimental result reported. We propose two possible explanations for this observation. First, finer k-point settings could lead to a lower band gap; because the material is an indirect gap semiconductor, relatively fine k-point meshes are required to find the precise band edges. Second, incidental doping of the material that was measured could have led to a lower band gap than is actually the case for pure β-Ni(OH)2. Nevertheless, both experiments and calculations demonstrate that β-Ni(OH)2 is a wide-gap insulator.

Our calculations predict that β-NiOOH is an indirect gap semiconductor with a band gap of 1.96 eV (see Figure 6). This bandgap is only slightly higher than the experimentally determined band gap, although the margin of error implied in the experimental paper suggests that the calculated value is well within range of the experimental value. This band gap also lies closer to the experiment than other theoretical values obtained in a previous study: 2.5 eV for PBE0 calculations and 1.5 eV for HSE06 calculations.59 These results will provide a useful starting point for the effect of doping on the electronic structure of β-NiOOH, which is the subject of our future work.



6 Ni d Ni d Op Op

4

DOS (arb. units)

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2

0

-2

-4

-6 -10

-8

-6

-4

-2

0

2

Energy (eV)

4

6

8

10

Figure 3: β-Ni(OH)2 PBE+U projected density of states (PDOS). The Fermi level is at zero. Majority spin states are depicted with positive PDOS, minority spin with negative. The same convention is used in all plots.


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3 Ni d Ni d Op Op

DOS (arb. units)

2

1

0

-1

-2

-3 -10

-8

-6

-4

-2

0

2

Energy (eV)

4

6

Figure 4: β-NiOOH PBE+U projected density of states.

6 Ni d Ni d Op Op

5 4

DOS (arb. units)

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3 2 1 0

-1 -2 -3 -4 -5 -6 -10

-8

-6

-4

-2

0

2

Energy (eV)

4

6

8

10

Figure 5: β-Ni(OH)2 G0W0 projected density of states.



7 Ni d Ni d Op Op

6 5 4

DOS (arb. units)

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3 2 1 0

-1 -2 -3 -4 -5 -6 -7 -10

-8

-6

-4

-2

0

Energy (eV)

2

4

6

Figure 6: β-NiOOH G0W0 projected density of states.

Surface Calculations Recent computational work on the OER on β-NiOOH focused on the (0 1 1 5) surface and similar high-index surfaces.40,

63

This was justified by noting that these surfaces lead to

coordinatively unsaturated nickel ions at the surface, which should hypothetically lead to higher activities. It was further justified by noting the (0 1 1 2) and (0 1 1 4) surfaces of CoOx, an analogous material to NiOx, are theoretically predicted to be the most active towards the OER. However, an interesting finding regarding NiOx is that its activity towards the OER is practically independent of the synthesis method and electrocatalytic surface area.84 The authors of Ref. 84 concluded that the observed oxygen evolution activity cannot be explained by variations in electrocatalytic surface area. This suggests that NiOx is robust towards the OER for a variety of surfaces. Therefore, rather than focusing on the surface with the lowest overpotential for the


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OER, it might be better to consider the surface most likely to be exposed under electrochemical conditions.

To determine which surface is most likely to be exposed, the energies were calculated for a variety of low-index surfaces. Because we used a brucite stacking pattern for β-NiOOH, the high-index (0 1 1 5) surface studied in the work by Li and Selloni was inaccessible to us.63 Cleavage along the (0 1 1 5) plane in staggered β-NiOOH creates multiple dangling bonds that lead to an unphysical structure. Therefore, we calculated the surface energies for the (1 0 0), (0 1 0), (0 0 1), (1 0 1), and (1 1 1) surfaces for both β-Ni(OH)2 and β-NiOOH (see Supporting Information for structures).

Our results are in agreement with numerous XRD studies that conclude that the (0 0 1) surface is the most stable for both materials (see Tables 4 and 5). Our staggered structural model for β-NiOOH was further validated in this regard. We note here that we were unable to converge the (0 0 1) surface for the unstaggered β-NiOOH unit cell taken from experiment. The intrinsic dipole within each individual sheet leads to huge dipole moments for the entire slab. This increases linearly with slab thickness and is undoubtedly responsible for the difficulties in convergence. The (0 0 1) surface of unstaggered β-NiOOH is also an unphysical model due to the large concentration of surface oxygen ions. In an aqueous environment, surface oxygen ions would be quickly protonated. Because the surface oxygen ions are partially capped, the staggered β-NiOOH structure identified in this study readily converges. Therefore, the staggered β-NiOOH structure is also well-suited for further study involving the OER at the (0 0 1) surface.



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Table 4: Surface energies for β-Ni(OH)2 Total energy

Surface energy

(eV)

(J m-2)

(1 0 0)

-121.616

0.448

(0 1 0)

-121.620

0.445

(0 0 1)

-122.190

0.201

(1 0 1)

-121.412

0.461

(1 1 1)

-120.502

0.502

Surface

Table 5: Surface energies for staggered, antiferromagnetic β-NiOOH Total energy

Surface energy

(eV)

(J m-2)

(1 0 0)

-186.562

1.540

(0 1 0)

-185.548

1.918

(0 0 1)

-191.858

0.094

(1 0 1)

-186.295

1.382

(1 1 1)

-187.853

0.857

Surface


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CONCLUSIONS In this work, we reported a computational study of numerous features of β-Ni(OH)2 and β-NiOOH. We first demonstrated, using PBE+U calculations, that optimization of the experimental crystal structure of β-NiOOH fails to replicate the c-axis lattice parameter. A simple structural modification in which the unit cell is doubled and the protons are staggered correctly replicates the experimental c-axis parameter. This was found to result from the effective cancellation of the dipolar interaction between adjacent sheets. Neutron diffraction experiments on a well-crystallized β-NiOOH structure are needed to confirm our predictions. We then proved that a low-spin d7 Ni3+ configuration is always favorable for β-NiOOH, which suggests a Jahn-Teller distortion, rather than oxidation state disproportionation, is responsible for the two different Ni-O bond distances found in experiment. Our G0W0 calculations on β-Ni(OH)2 and β-NiOOH yield band gaps consistent with previous experimental data. These results suggest that incidental doping may have lowered the measured band gap of β-Ni(OH)2 and also indicate the reason for the difficulty in determining an accurate value for the band gap of β-NiOOH. Lastly, calculations of various low-index surface energies of β-Ni(OH)2 and β-NiOOH showed that the (0 0 1) surface is the most thermodynamically stable surface. This was to be expected from previous XRD data, but could only be replicated upon use of the newly-proposed structural model for β-NiOOH. Thus, based on the combined results of this work, we propose the protonstaggered, antiferromagnetic, low-spin structure as the most probable stable state of pure βNiOOH, with the (0 0 1) surface as the most stable surface, at least under ultrahigh vacuum conditions. The influence of an aqueous environment on the surface is the subject of future work.



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￭ ASSOCIATED CONTENT Supporting Information Optimized geometries, further data for structural, spin, and surface calculations are all provided in supporting information. This material is available free of charge via the Internet at http://pubs.acs.org.

￭ AUTHOR INFORMATION Corresponding Author * e-mail: [email protected] Notes The authors declare no competing financial interest.

￭ ACKNOWLEDGMENTS We are grateful to the Air Force Office of Scientific Research for funding (Grant No. FA955014-1-0254). We acknowledge use of the TIGRESS high performance computer center at Princeton University. We also acknowledge use of the COPPER high performance computer center at the Air Force Office of Scientific Research High Performance Computing Center.


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-H+ -e-

β-Ni(OH)2

β-NiOOH

TOC graphic


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Structural and Electronic Features of Î²-Ni(OH)2 and Î²-NiOOH from

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