Energy &Environmental
Science
View Article Online

Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

PAPER

Cite this: Energy Environ. Sci.,
2020, 13, 1492

View Journal | View Issue

Multiorbital bond formation for stable oxygenredox reaction in battery electrodes†
Takaaki Sudayama,a Kazuki Uehara,b Takahiro Mukai,c Daisuke Asakura, aXiang-Mei Shi,b Akihisa Tsuchimoto,b Benoit Mortemard de Boisse,bd
Tatau Shimada,b Eriko Watanabe,b Yoshihisa Harada, e Masanobu Nakayama,
Masashi Okubobd and Atsuo Yamada *bd

cdf

High-energy-density batteries have been a long-standing target toward sustainability, but the energy
density of state-of-the-art lithium-ion batteries is limited in part by the small capacity of the positiveelectrode materials. Although employing the additional oxygen-redox reaction of Li-excess transitionmetal oxides is an attractive approach to increase the capacity, an atomic-level understanding of thereaction mechanism has not been established so far. Here, using bulk-sensitive resonant inelastic X-ray
scattering spectroscopy combined with ab initio computations, we demonstrate the presence of a
Received 30th December 2019,
Accepted 10th March 2020
DOI: 10.1039/c9ee04197d

localized oxygen 2p orbital weakly hybridized with transition metal t2g orbitals that was theoretically
predicted to play a key role in oxygen-redox reactions. After oxygen oxidation, the hole in the oxygen
2p orbital is stabilized by the generation of either a (s + p) multiorbital bond through strong p backdonation or peroxide O22 through oxygen dimerization. The multiorbital bond formation with s-accepting

rsc.li/ees

and p-donating transition metals can thus lead to reversible oxygen-redox reaction.

Broader context
Increasing the energy density of lithium-ion batteries is an urgent task toward achieving a sustainable society. However, the limited capacities of cathodes
render lithium-ion batteries unsuitable for electric transport or grid-scale applications. As an eﬀective way to increase the capacity of cathodes, additional
oxygen-redox reactions have attracted much attention. Although the presence of ‘‘orphaned’’ oxygen 2p orbitals that are responsible for additional oxygen-redox
reactions was theoretically proposed in 2016, no experimental verification has been reported to date. In this work, we experimentally verify the presence of a
localized oxygen 2p orbital weakly hybridized with transition metal t2g orbitals in oxygen-redox battery cathodes using resonant inelastic X-ray scattering. We
also clarify the stabilization mechanism of the oxidized phase through multiorbital bond formation of oxidized oxygen 2p orbitals.

Introduction
The development of advanced electrochemical energy storage
devices has been a topic of intensive research because it oﬀers
aResearch Institute for Energy Conservation, National Institute of Advanced
Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japanb
Department of Chemical System Engineering, School of Engineering,
The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan.
E-mail: yamada@chemsys.t.u-tokyo.ac.jpcFrontier Research Institute for Materials Science (FRIMS), Nagoya Institute ofTechnology, Showa-ku, Nagoya, Aichi 466-8555, Japand
Elements Strategy Initiative for Catalysts & Batteries (ESICB), Kyoto University,
Nishikyo-ku, Kyoto 615-8245, Japane
Institute for Solid State Physics, The University of Tokyo, Kashiwa,
Chiba 277-8581, Japanf
Mi2i GREEN, National Institute of Materials Science (NIMS), Tsukuba, Ibaraki,305-0047, Japan† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9ee04197d

1492 | Energy Environ. Sci., 2020, 13, 1492--1500

prospects of sustainability, for instance, reduction of fossil fuelreliance by realizing an electric vehicle range of 500 km per
charge or integrating renewable energy sources to an electricalgrid.1–3 Market-leading lithium-ion batteries (LIBs) efficiently
store energy by lithium-ion (de)intercalation associated with
redox reactions.4,5 However, their energy density has approached
the theoretical limit, in part owing to the small capacity of thepositive electrode materials, which severely hinders the wide
deployment of LIBs.6 Therefore, it is important to find analternative battery chemistry that can exceed the existing
positive-electrode capacity limits.
The use of redox reactions of oxygen in addition to conventional transition-metal redox reactions is an attractive way toincrease the capacity of transition-metal oxides.7 In general,most oxygen 2p orbitals in conventional electrode materials
LiMO2 (M: transition metal) form s-type bonds with axial M 3d
orbitals (eg orbitals in an Oh symmetry). As the atomic energy

This journal is © The Royal Society of Chemistry 2020

View Article Online

Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Paper

Energy & Environmental ScienceFig. 1 Resonant inelastic X-ray scattering (RIXS) spectra for delocalized and localized oxygen 2p orbitals. (a) Crystal structure of Li-excess layeredtransition-metal oxides Li[LixM1 x]O2 (M: transition metal). (b) p-type localized occupied/unoccupied states consisting of oxygen 2p and M t2g orbitals(b1/b1* bands in a C2v-symmetry OM2Li4 cluster) give a Raman-like RIXS peak with constant energy loss regardless of the excitation energy. (c) s-type
delocalized occupied/unoccupied states consisting of oxygen 2p and M eg orbitals (3a1/3a1* and 3b2/3b2* bands in a C2v-symmetry OM2Li4 cluster) give afluorescence-like RIXS peak with variable energy loss depending on the excitation energy.

level of oxygen 2p orbitals is usually lower than that ofM eg orbitals, the s-type bonding orbitals are predominantly
from oxygen 2p orbitals.8,9 Therefore, it is diﬃcult to oxidize
oxygen 2p orbitals that have a s-type bonding character.10
However, research groups led by Bruce and Ceder postulated
that oxygen in Li-excess transition-metal oxides Li1+xM1 xO2(Fig. 1a) intrinsically have localized (‘‘orphaned’’) 2p orbital
along the Li–O–Li axis without s-type bonding characteristics,
which can contribute to an additional oxygen-redox capacity.10,11
Indeed, large capacities exceeding the capacity limit of M redox
reactions have been reported for many Li-excess transition-metaloxides including Li2MnO3–LiMO2 solid solutions,12,13 layered
honeycomb Li2IrO3,14 random rock salt Li1.2Ti0.4Mn0.4O2,15
three-dimensional b-Li2IrO3,16 and anti-fluorite Li5FeO4.17 In
addition, the electronic states of various oxygen-redox electrodematerials have been intensively investigated using analyticalmethods such as X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, X-ray emission spectroscopy (or resonant
inelastic X-ray scattering (RIXS)), or density functional theory(DFT) calculations.18–22
However, despite the theoretical adequacy of the proposed‘‘orphaned’’ oxygen 2p orbital hypothesis, the presence of thelocalized oxygen 2p orbitals in Li-excess transition-metal oxides
has not been verified experimentally. Furthermore, although
localized, the oxygen 2p orbital along the Li–O–Li axis still
exhibits p-type interactions with the M t2g orbital, which shouldplay an essential role in oxygen-redox reactions.23 It is important toemphasize that the rigid-band model, which has been frequently
used for consideration of oxygen-redox electrodes,15,24 cannot
qualitatively discuss M–O interaction (e.g., covalency), because it
only considers a bandwidth and the band-center energy of eachband. Therefore, for a thorough understanding of the reversible
oxygen-redox reactions occurring in Li-excess transition-metaloxides, it is necessary to clarify the nature of the M–O bonds
during the oxygen-redox reactions.25

This journal is © The Royal Society of Chemistry 2020

In this work, we used oxygen K-edge resonant inelastic X-ray
scattering (RIXS) spectroscopy combined with ab initio computations to demonstrate a criterion for stable oxygen-redox reactions.

Results and discussion
RIXS to detect localized orbitals
Oxygen K-edge RIXS spectroscopy was used to examine theexistence of p-type localized oxygen 2p orbitals in Li2MnO3, a
standard Li-excess layered transition-metal oxide. Li2MnO3 wassynthesized by a conventional solid-state method, and thepowder X-ray diﬀraction pattern and Rietveld refinement confirmed its successful synthesis (Fig. S1 and Table S1, ESI†).
Li2MnO3 that contains only Mn4+ enables obtaining a simple
RIXS spectrum, allowing for direct comparison with DFT calculations. Oxygen K-edge RIXS spectroscopy records the inelastic
scattering during core excitation–relaxation (1s - 2p - 1s), in
which the energy loss corresponds to valence excitation between
occupied and unoccupied 2p bands.26 RIXS spectroscopy has
a probing depth of approximately 100 nm (bulk-sensitive).
Importantly, when occupied/unoccupied oxygen 2p bands
show a localized character with weak orbital hybridization, theinelastic scattering becomes Raman-like and leads to constantenergy loss regardless of the incident photon energy (Fig. 1b andFig. S2a, ESI†).27 Conversely, delocalized occupied/unoccupied
oxygen 2p bands with a large orbital hybridization give fluorescencelike inelastic scattering with variable energy loss depending on theincident photon energy (Fig. 1c and Fig. S2b, ESI†).27 Therefore,
oxygen K-edge RIXS spectroscopy allows us to diagnose localized
or delocalized oxygen 2p bands.
Before obtaining the RIXS spectra, we conducted ab initio
calculations using the HSE06 hybrid functional28 for Li2MnO3.
Fig. 2a shows that a localized oxygen 2p orbital exists along
the Li–O–Li axis with an orbital energy of approximately 0.9 toEnergy Environ. Sci., 2020, 13, 1492--1500 | 1493

View Article Online

Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Energy & Environmental Science

Paper

Fig. 2 Direct observation of a localized oxygen 2p orbital hybridized with Mn t2g orbitals in Li2MnO3. (a) Calculated partial density of states for oxygenand manganese in Li2MnO3. The inset shows the spatial electron density at the energy range from 0.9 to 0 eV versus the Fermi energy. (b) Oxygen
K-edge RIXS spectra, and (c) second diﬀerential RIXS map for Li2MnO3 with excitation photon energy from 527 to 533.75 eV. The Raman-like RIXS peakwith constant energy loss of approximately 2.5 eV indicates the existence of a localized oxygen 2p orbital that is weakly hybridized with Mn t2g orbitals.

0.0 eV against the Fermi energy. The RIXS spectra and thecorresponding second differential RIXS map (Fig. 2b and c)
exhibit two broad fluorescence-like peaks (the energy loss
ranging from 3.5 to 8.0 eV), which could be related to thevalence excitation between the s-type wide oxygen 2p bands
strongly hybridized with axial Mn eg orbitals (Fig. 1c). Based on
the C2v symmetry of an OMn2Li4 cluster, these bands are labelled
as 3a1/3b2 bands.8,23 More importantly, the RIXS spectra show anintense Raman-like peak with constant energy loss of approximately 2.5 eV. This Raman-like peak clearly indicates the existenceof the p-type narrow oxygen 2p bands weakly hybridized with
Mn t2g orbitals (b1/b1* bands based on the C2v-symmetry labelling,
Fig. 1b). It is important to note that the Raman-like feature is not
the simple projection of the d–d excitation of Mn L-edge, because
O K-edge XAS and RIXS always involve charge-transfer processes
through O–Mn interactions (Fig. S3, ESI†). Therefore, whether
Raman- or fluorescence-like RIXS is observed depends primarilyon the strength of the O–Mn interactions.
In contrast, for a non-Li-excess layered oxide LiNi1/3Co1/3Mn1/3O2, the RIXS spectra show only fluorescence-like peaks
with variable energy loss depending on the incident photon
energy (Fig. S4, ESI†) because most oxygen 2p orbitals forms-type wide bands with axial M 3d orbitals. Therefore, thisis the first experimental verification of the localized oxygen
2p orbital weakly hybridized with M t2g orbitals in Li-excesstransition-metal oxides, and oxygen K-edge RIXS spectroscopy
can, thus, be considered as an eﬀective diagnostic tool to detect
electrochemically active oxygen states.
Oxidation of localized oxygen 2p orbital
Having experimentally confirmed the existence of the p-type
narrow oxygen 2p bands, the contribution of the localizedstates to the oxygen-redox reactions was examined using ex situ
oxygen K-edge RIXS spectroscopy. As a target Li-excess layeredtransition metal oxide, Li1.2Ni0.13Co0.13Mn0.54O2 was used as anoxygen-redox electrode material. Li1.2Ni0.13Co0.13Mn0.54O2 wassynthesized by a conventional solid-state method, and the1494 | Energy Environ. Sci., 2020, 13, 1492--1500

powder X-ray diﬀraction pattern and Rietveld refinement
confirmed its successful synthesis (Fig. S5 and Table S2, ESI†).
Before acquiring the RIXS spectra, ab initio calculations
using the HSE06 hybrid functional were carried out forLi1.2 xNi0.13Co0.13Mn0.54O2 (Fig. 3a). The structural configuration of Li1.2Ni0.13Co0.13Mn0.54O2 was determined by a genetic
algorithm (GA) approach that optimizes Li/Ni/Co/Mn arrangement (Fig. S6a and b, ESI†). For the delithiated states, Li andthe vacancy configuration in Li1.2 xNi0.13Co0.13Mn0.54O2 wasalso determined by the GA approach (Fig. S6c, ESI†). The
optimized structures for x = 0 and 1.2 are shown in the inset
of Fig. 3b. The analysis of partial density of states (pDOS) for
pristine Li1.2Ni0.13Co0.13Mn0.54O2 shows that Co and Ni 3d bands
dominate the top of the valence band ( 1 eV o E EF o 0 eV),accompanied by a localized oxide band due to Li–O–Li at aslightly lower energy region ( 2 eV o E EF o 1 eV) (Fig. S7,
ESI†). The averaged Bader charges of Ni and Co decrease only
during the early stage of Li+ extraction (x o 0.4), whereas that ofoxygen decreases continuously during the entire delithiation
process, suggesting the occurrence of additional oxygen-redox
reactions for x 4 0.4 (Fig. 3a). This trend is also confirmed by thespin integration (SI) analysis, where the change of spin densityof O (O oxidation) occurs at the delithiation process of x 4 0.4(Fig. S8, ESI†).29 Ni2+ and Co3+ ions are oxidized to Ni4+ andCo4+ respectively in the early stage of delithiation (x o 0.4),
followed by oxidation of oxide ions (x 4 0.4). The oxidation stateof Mn4+ ions remains unchanged in the entire compositional
range. Indeed, using the predicted oxygen-redox reactions,Li1.2Ni0.13Co0.13Mn0.54O2 delivers a large reversible capacity of
approximately 250 mA h g 1, which exceeds the theoretical
capacity (123 mA h g 1) of the Ni4+/Ni2+ and Co4+/Co3+ redox
reactions (Fig. 3b).11,30
The oxygen K-edge X-ray absorption spectrum (XAS)
obtained in the bulk-sensitive partial fluorescence yield mode
for the pristine Li1.2Ni0.13Co0.13Mn0.54O2 (Fig. 3c) shows two
absorption peaks (528.5 and 531 eV) for the 1s core-electronm
excitation to unoccupied s-type bands (oxygen 2p-Mn ek
g /eg )

This journal is © The Royal Society of Chemistry 2020

View Article Online

Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Paper

Fig. 3 Oxygen-redox reaction in Li1.2 xNi0.13Co0.13Mn0.54O2. (a) The average
Bader charge changes of Mn, Co, Ni, and O in Li1.2 xNi0.13Co0.13Mn0.54O2.
(b) Charge–discharge curves for Li1.2Ni0.13Co0.13Mn0.54O2. The inset shows
optimized Li/Ni/Co/Mn arrangements for Li1.20Ni0.13Co0.13Mn0.54O2, andLi0Ni0.13Co0.13Mn0.54O2. Green, grey, deep blue, and purple-colored octahedra correspond to LiO6, NiO6, CoO6, and MnO6 octahedra, respectively.
(c) Oxygen K-edge X-ray absorption spectra in a bulk sensitive partial
fluorescence yield mode for Li1.2 xNi0.13Co0.13Mn0.54O2 during the first cycle.
The pre-edge region is enlarged for comparison.

and an unoccupied p-type band (oxygen 2p-Mn tk
2g). Uponcharging to 4.4 V vs. Li/Li+ (A - B in Fig. 3b), a new XAS
shoulder emerged at 527 eV owing to hole generation in s-type(oxygen 2p-Ni eg) and p-type (oxygen 2p-Co t2g) bands. After
further charging to 4.8 V vs. Li/Li+ (B - C in Fig. 3b), a newabsorption peak emerged at a relatively high absorption-energy
region of approximately 530.5 eV. Similar spectral changes
were also observed during the second cycle (Fig. S9, ESI†).
The XAS signal at 530.5 eV can be ascribed to a 1s core electronThis journal is © The Royal Society of Chemistry 2020

Energy & Environmental Science
excitation to an unoccupied p-type band (oxygen 2p-Mn tm
2g).
Emergence of the absorption peak at a relatively high energy
region is reasonable because oxygen oxidation increases theeﬀective nuclear charge, which lowers the initial energy level of an
oxygen 1s core electron and hence raises the excitation energy.23
Similar changes in the XAS signals by oxidation (the emergence of
new absorption peaks at a high energy region) are often observedin transition-metal K-edge absorption spectra.11,15,31 Anotherexplanation for this new absorption is a 1s core electron excitation
to an unoccupied s* molecular orbital of peroxide O22 resulting
from the dimerization of oxidized oxide ions, which will be
discussed later. In either case, the emergence of the XAS signal
at 530.5 eV is an experimental indicator for the occurrence ofoxygen oxidation.
The RIXS spectra of pristine Li1.2Ni0.13Co0.13Mn0.54O2(Fig. 4a) exhibit a Raman-like peak with constant energy loss
corresponding to a p-type narrow oxygen 2p band (p - p*), in
addition to the fluorescence-like peaks (s - s*). The ab initio
calculations for pristine Li1.2Ni0.13Co0.13Mn0.54O2 supports theexistence of localized oxygen 2p orbitals along the Li–O–Li axes
with an orbital energy near the Fermi level (Fig. S7, ESI†). Thep - p* RIXS peak intensified after charging to 4.4 V vs. Li/Li+(transition-metal oxidation, Fig. 4b), which indicates accumulation of the localized oxygen 2p states to the Fermi level.
The initial Li+ extraction associated with Co and Ni oxidation
gives an oxygen coordination environment with a &–O–Li+ or&–O–& axis (&: Li+ vacancy), which electrostatically raises theenergy level of the localized oxygen 2p orbitals. Indeed, the factthat the energy loss of the Raman-like RIXS peak decreased
from 2.5 to 2.0 eV supports a rise in the energy level of thelocalized oxygen 2p orbitals. We presume that accumulationof the localized oxygen 2p states to the Fermi level should
be an essential preceding process that triggers oxygen-redox
reactions. For example, it is well known that the electrochemical activity of Li2MnO3 is poor32 even though oxygen
has a Li+–O–Li+ axis and hence a localized oxygen 2p orbital(Fig. 2a).10 Most likely, as Li2MnO3 cannot exhibit initial Li+
extraction owing to the electrochemically inactive Mn4+, it isdifficult to generate the &–O–Li+ and &–O–& axes, and theenergy level of the localized oxygen 2p orbital remains too low toundergo oxidation within the liquid electrolyte stability window.
Indeed, Li2MnO3 delivers large reversible capacities when cycledwith a solid electrolyte that possesses a large electrochemical
stability window.33 Conversely, when redox-active transition
metals are present, such as in Li2MnO3–LiMO2 solid solution,&–O–Li+ and &–O–& axes are easily formed by the initial Li+
extraction to raise the energy level of the localized oxygen 2p
orbital, unlocking the redox activity of oxygen. Once the oxygenredox reaction is triggered, the &–O–Li+ and &–O–& axes arecontinuously generated to achieve a large oxygen-redox capacity.
After charging to 4.8 V vs. Li/Li+ (oxygen oxidation, Fig. 4c),the Raman-like p - p* RIXS peaks disappear, and all the RIXS
peaks become fluorescence-like. Importantly, a new intense
fluorescence-like peak emerges at an energy loss of approximately 7.5 eV with an incident photon energy of 530.5 eV.
Assuming an incident photon of 530.5 eV excites a 1s core

Energy Environ. Sci., 2020, 13, 1492--1500 | 1495

View Article Online

Energy & Environmental Science

Paper

Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

environment of oxide ions, making the RIXS peak weakly
fluorescence-like. The irreversible structural change during
the 1st charge could explain the experimental observation thatthe potential profile of the 2nd charge diﬀers from that of the
1st charge (Fig. 3b). Nevertheless, in the 2nd cycle, the spectral
shape change is reversible (Fig. S11, ESI†), suggesting stableoccurrence of the oxygen-redox reactions.
Possible O–O bond formation in oxygen redox electrodes

Fig. 4 Monitoring oxygen 2p orbitals during oxygen-redox reaction of
Li1.2Ni0.13Co0.13Mn0.54O2. Oxygen K-edge second diﬀerential RIXS map forthe samples (a) before charge (sample A in Fig. 3b), (b) after transitionmetal oxidation (sample B in Fig. 3b), (c) after oxygen oxidation (sample C
in Fig. 3b), and (d) after discharge (sample D in Fig. 3b), with excitation
photon energy from 527 to 533.75 eV. The corresponding RIXS spectra areshown in Fig. S10 (ESI†).

electron to an unoccupied p-type band (oxygen 2p-Mn tm
2g),
resonant inelastic scattering with the 530.5 eV incident photon
includes valence excitation between the p-type bands (p - p*).
Therefore, a large energy loss of approximately 7.5 eV for thisRIXS peak should correspond to p-type splitting. This large
p-type splitting should be induced by hole generation in the
antibonding p-type band which makes the Mn–O bonds morebonding (more delocalization/larger orbital hybridization).
Therefore, the RIXS peak is observed as fluorescence-like. The
enhanced p-type interaction stabilizes the oxidized oxygen,leading to reversible oxygen-redox reactions.
It is also important to note that the Raman-like RIXS peak of
the localized oxygen 2p orbitals was not fully recovered after fulldischarge (Fig. 4d). The emission at the energy loss region of
approximately 2 eV becomes weakly fluorescence-like after the
1st cycle. Presumably, structural degradation such as cation
migration during the 1st charge modulates the coordination

1496 | Energy Environ. Sci., 2020, 13, 1492--1500

Gent and Hong et al. also observed similar intense RIXS peaks
for Li1.17 xNi0.21Co0.08Mn0.54O2 and Li2Ir0.75Sn0.25O3 after oxygen
oxidation,34,35 and transition-metal migration and subsequent
O–O bond formation were proposed to explain the emergence ofthe new XAS and RIXS peaks after oxygen oxidation. To examine
this hypothesis, we acquired O K-edge XAS and RIXS spectra
for WO2(O2)(H2O), which contains peroxide O22 coordinatedto W6+.36 Based on the DFT calculations (Fig. 5a and b),
WO2(O2)(H2O) possesses (i) a strong p-type LUMO bandconsisting of O 2p and large W 5d (t2g) (3.5 o E EF o 4.3 eV)and (ii) an unoccupied s* band of peroxide (6.1 o E EF o 7.1 eV).
The XAS spectrum shows a broad absorption arising from coreelectron excitations to these unoccupied p-type and s-type bandsof W–O and peroxide (Fig. 5c). Importantly, two intense
fluorescence-like emissions were observed in the RIXS map(Fig. 5d), which can be ascribed to valence excitations between
the p-type bands of W–O and between the s-type bands of O–O,
respectively. The fluorescence-like feature of the emission fromthe p-type bands of W–O is explained by electron delocalization
through strong p-type W t2g–O 2p interactions. The fluorescencelike emission between the s-type bands of O–O takes placeapproximately with an energy loss of 6 eV at hvin = 530 eV,
which differs slightly from that observed for fully charged
Li1.2Ni0.13Co0.13Mn0.54O2 (the energy loss of 7.5 eV at hvin =530.5 eV). Furthermore, the transition-metal migration andperoxide formation are one of possible explanations for the RIXS
spectral changes for lithium-rich layered oxides, but cannot
explain the almost identical RIXS spectral changes during
the oxygen-redox reactions of many other sodium-based layeredoxides (e.g., Na2/3[Mg0.28Mn0.72]O2)37 and Na2Mn3O7,38 where thetransition-metal migration is known to be negligible due to large
Na+ slabs. In fact, neither a short O–O distance below 2.2 Å nor
significant MO6 distortion was found in the relaxed structures ofdelithiated phases (Fig. S12, ESI†). Although the possibility of the
O–O bond formation cannot be excluded, another possible
but less argued mechanism of hole generation in the antibonding
p-type band will be discussed below.
Multiorbital bond formation in oxygen redox electrodes
Crystal orbital overlap population (COOP) diagrams for selected
Mn–O bonds from ab initio calculations for Li1.2Ni0.13Co0.13Mn0.54O2 (Fig. 6) quantify the reversible transformationof an oxygen 2p orbital characteristics during the oxygen-redox
reaction. The COOP is an overlap-population-weighted densityof states that serves as a bonding descriptor.39 The sign of
COOP indicates bonding (positive), non-bonding (zero), or antibonding (negative) contributions between two selected atoms.

This journal is © The Royal Society of Chemistry 2020

View Article Online

Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Paper

Energy & Environmental ScienceFig. 5 Electronic structure and XAS/RIXS spectra for WO2(O2)(H2O). (a) Partial density of states (pDOS) for W and O, and crystal orbital overlap
population (COOP) diagrams for W–O and O–O bonds. (b) Spatial hole densities with the selected orbital energies (i) from 3.5 to 4.3 eV, and (ii) from 6.1
to 7.1 eV against the Fermi energy (dotted areas in pDOS). (c) O K-edge X-ray absorption (XAS) spectrum. (d) O K-edge differential RIXS map. While the
RIXS peak for O22 can be referred to explain a mechanism of O redox cathodes, a care should be taken that the similar signal is also induced by M–O
multi-orbital bond formation (see text).

Before charging, the spatial distribution of the electron at theenergy range of 2.0 to 1.0 eV against the Fermi energy (Fig. 6a)Fig. 6 Enhancement of p-type interaction after oxygen oxidation. Partial
density of states (pDOS) for oxygen and manganese, and crystal orbital
overlap population (COOP) diagrams for Mn–O bonds in Li1.2 xNi0.13Co0.13Mn0.54O2 (a) before charge (x = 0) and (b) after oxygen oxidation(x = 1.2). The dotted areas denote states mainly consisting of oxygen 2p
orbitals responsible for oxygen-redox reactions. The spatial electron orhole density with the selected orbital energy (dotted areas in pDOS) is
depicted.

This journal is © The Royal Society of Chemistry 2020

takes up a p-type orbital shape consisting of oxygen 2p and
Mn t2g orbitals (b1* in C2v). However, the oxygen 2p orbitals haveno significant COOP with Mn t2g orbitals (black arrow, Fig. 6a),indicating a localized nature of the oxygen 2p orbitals. Afteroxygen oxidation, the spatial distribution of a hole at the energy
range from +1.0 to +2.0 eV versus the Fermi energy also has ap-type orbital shape (Fig. 6b). On increasing the number of holes
in the antibonding p-type orbital, Mn–O bonds show morebonding characteristics with a considerable COOP between theoxygen 2p and Mn t2m
g orbitals (Fig. S13, ESI†). The COOP diagram
also indicates that the bonding states reside at the energy range of
7.0 to 6.0 eV against the Fermi energy (red arrows, Fig. 6b),which may correspond to the occupied p-type bonding b1 orbital.
The calculated b1/b1* splitting (ca. 7.0 eV) agrees well with theenergy loss of the intense fluorescence-like peak observed in the
RIXS spectra (Fig. 4c).
To summarize the reaction mechanism, the Li+–O–Li+ coordination in the pristine state forms localized oxygen 2p orbital weakly
hybridized with the Mn t2g orbital. When the initial Li+ extraction
occurs in association with M redox reactions, the &–O–Li+ and&–O–& coordination axes are generated, which raises the energy
level of the localized oxygen 2p states to the Fermi level. After thisaccumulation, exclusive oxygen oxidation occurs; a hole is generated
in the antibonding p-type orbital and orbital hybridization isenhanced to delocalize the hole within a Mn–O–Mn bond. Alternatively, or in parallel, unstable oxidized oxide ions dimerize to form
peroxide O22 . The resulting either b1/b1* splitting of the Mn–O–Mnbond or s/s* splitting of the O–O bond stabilizes the oxidized
oxygen, enabling a reversible oxygen-redox reaction.

Energy Environ. Sci., 2020, 13, 1492--1500 | 1497

View Article Online

Energy & Environmental Science

Paper
em
g to O 2p). The exploration of Li-excess oxides includingtransition metals that satisfy these criteria could help surpassthe existing LIB performance limits.

Methods
Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Synthesis

Fig. 7 Multiorbital bond formation upon oxygen oxidation. (a) s bond inconventional metal oxides. (b) (s + p) multiorbital bond in oxygen-oxidized
states.

From a conventional viewpoint of an electronic structure intransition-metal oxides, an M–O bond is formed mainly bys donation from oxygen (s bond), as the 2p orbitals of O2 arefilled completely (Fig. 7a).9 However, hole generation on theouter sphere 2p orbital of oxygen is intrinsically unstable, andp back-donation from M occurs to stabilize the oxygen hole,giving rise to (s + p) multiorbital bonds (Fig. 7b).8 Therefore,
the reversible oxygen-redox reaction requires M to possess boths-accepting and p-donating abilities for oxidized oxygen. For
example, Ti4+ with a vacant t2g configuration has no p-donating
ability whereas Sn4+ with a filled eg configuration has nos-accepting ability. Therefore, Li2TiO3 and Li2SnO3 are notoxygen-redox active,40,41 and replacing transition metals with
Ti4+ or Sn4+ could promote stabilizing oxidized oxygen, forinstance, by peroxide formation.35 Conversely, Mn4+, Co4+, andNi4+ with (partially) filled t2g and vacant eg configurations satisfy
the requirement for (s + p) multiorbital bond formation, leading
to the high oxygen-redox activity of the Li2MnO3–LiMO2 solid
solution such as Li1.2Ni0.13Co0.13Mn0.54O2. Large overlap between
O 2p and M 4d/5d orbitals should give more stable (s + p)
multiorbital bonds. Indeed, a short Ru(V)–O distance of 1.85 Å(relative to the conventional Ru(V)–O distance of 2.0 Å) was
observed for Li2Ru0.75Sn0.25O3 after oxygen oxidation.42 Owing to
the enhanced multiorbital bonding, Li-excess 4d/5d transitionmetal oxides exhibit highly reversible oxygen-redox reactions
without oxygen gas release or surface side reactions.

Conclusions
In this work, using oxygen K-edge RIXS spectroscopy, we investigated oxygen-redox battery electrodes, demonstrating theimportance of the combined control of the (s + p) interaction
between transition metals and oxygen. In addition to the previously reported criteria,10,11,15 we have discussed a novel andcrucial criterion related to the electronic configuration: transition metal ions with simultaneous s-accepting and p-donating
abilities can realize stable oxygen redox reaction toward highercapacity, higher-energy-density cathode materials. Typicaltransition metals that satisfy these requirements are Mn4+
k0 m0 k0mm
(t2m3
g t2g eg eg ; p-donating t2g and s-accepting eg to O 2p) and5+ m3 k0 m0 k0mRu (t2g t2g eg eg ; significantly p-donating t2g and s-accepting

1498 | Energy Environ. Sci., 2020, 13, 1492--1500

Li2MnO3, LiNi1/3Co1/3Mn1/3O2, and Li1.2Ni0.13Co0.13Mn0.54O2
were prepared using stoichiometric amounts of Li2CO3 (Wako,99%), NiO (Wako, 99%), Co3O4 (Kanto chemicals, 99%) and
MnO2 (Wako, 99.5%). The precursors were ball-milled at
400 rpm for 6 h (cycles of 5 min ball milling followed by
5 min of resting) using a FRITSCH P-7. After recovery, the powders
were pelletized and fired at 900 1C (heating rate of 5 1C min 1) for
12 h under an O2 atmosphere (ASAHI RIKA, ARF-MC). WO2(O2)(H2O)
was synthesized by a procedure reported in literature.30 The resulting
powder compounds were characterized by X-ray diﬀraction recorded
using a Rigaku RINT TTR-III (Cu Ka radiation), and Rietveld
refinements were performed using Jana 2006 software.43 The
crystal structures were drawn using VESTA.44
ElectrochemistryElectrochemical measurements were carried out in Li/LiPF6 in
PC (1 mol L 1, Kishida Chemical)/positive electrode batteries
assembled in 2032-type coin cells. The positive electrodes wereprepared by mixing 80 wt% active material with 10 wt%
acetylene black (Denka) and 10 wt% polyvinylidene difluoride(Sigma-Aldrich) in N-methyl pyrrolidone (Kanto Chemical) toform a slurry, which was then coated onto Al foil (mass loadingof ca. 1 mg cm 2). The obtained films were dried at 70 1C for
several hours before punching the electrodes (diameter:
16 mm), which were then further dried under vacuum at
120 1C overnight before placing them into a glovebox. The
positive and negative electrodes (Li foils) were separated by aglass fiber separator soaked with the electrolyte. All electrochemical measurements were controlled and recorded using a
TOSCAT-3100 battery tester.
Sample preparation for X-ray absorption/emission spectroscopy
Samples for the X-ray absorption and emission spectroscopy
experiments were prepared in 2032-type coin cells. The
batteries were galvanostatically charged/discharged until agiven voltage, and then the voltage was maintained until theresidual current dropped to 0 mA. The batteries were recoveredand disassembled in an Ar-filled glovebox and the electrodes
were washed three to five times with anhydrous dimethylcarbonate and dried before being stored in air-tight containers.
The samples were then transported to the synchrotron facility
without exposure to air.
X-ray absorption/emission spectroscopy
The XAS and RIXS experiments were performed at BL07LSU,
SPring-8.45 For the oxygen K-edge XAS, the bulk-sensitive
partial-fluorescence-yield (PFY) detection mode was employed.
Flat-field type grazing incidence spectrometers were used forThis journal is © The Royal Society of Chemistry 2020

View Article Online

Paper
the oxygen K-edge RIXS. All the measurements were performedat room temperature. The samples were taken out from thecell in the glove box filled with Ar gas, and then they weretransferred into a vacuum chamber without exposure to air
using a transfer vessel.

Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Ab initio calculations
Ab initio calculations were performed using the Vienna ab initio
simulation package (VASP)46 using the projector-augmentedwave (PAW) method.47,48 For Li2MnO3, the range-separated
hybrid functional introduced by Heyd, Scuseria, and Ernzerhof(HSE) was used throughout the calculations.28 The exact exchange
fraction in the Hartree–Fock/density functional theory (DFT)hybrid functional and range-separation parameter are set at 0.25
and 0.2, respectively (HSE06). The DFT part of HSE06 employed amodified version of the Perdew–Burke–Ernzerhof functional(PBEsol)49 according to literature. The kinetic energy cutoff was
set to 520 eV and the k-point was sampled on a (5  3  5) grid.
The lattice parameters and atomic positions were relaxed until
the forces on each atomic site were less than 0.01 eV Å 1. To
model Li1.2Ni0.13Co0.13Mn0.54O2, Li29/24Ni3/24Co3/24Mn13/24O2 wasconsidered and the structural configurations were determined by
the genetic algorithm (GA) approach that optimizes the Li/Ni/Co/
Mn arrangement. The on-site Coulomb correction (GGA+U) was
included for localized electronic states, and the U value waschosen to be 6.0, 3.4 and 3.9 eV for the 3d states of Ni, Co
and Mn, respectively, according to literature.50 During the
GA procedure, we obtained the total energies using modified
Perdew–Burke–Ernzerhof generalized gradient approximation(PBEsol–GGA)49 by reducing the energy cutoff and the numberof k points in the reciprocal cell to 360 eV and unity (G point
sampling), respectively. After the GA cycles, the obtained fivelowest energy configurations were recalculated with a sufficientenergy cutoff (500 eV) and k point mesh (2  2  2 k-point
meshes) using the HSE06 hybrid functional. U was not employedin the HSE calculations. The lowest energy configuration among
the five configurations was chosen for Li29/24Ni3/24Co3/24Mn13/24O2.
Similarly, the Li and vacancy configurations for delithiatedLi29/24(1 x)Ni3/24Co3/24Mn13/24O2 were also determined by optimizing the Li/vacancy arrangement using the GA approach, andrecalculated using the HSE06 functional for selected configurations. The calculated formation energies correspond to zeroKelvin conditions. The GA approach was detailed in the ESI.†
For WO2(O2)(H2O), HSE06 hybrid functional was employed with
the Grimme dispersion correction (DFT-D3)51 for hydrogenbonds. The energy cutoff was set to 520 eV with the k-point of
4  6  4. The COOP was calculated by LOBSTER software.52

Author contribution
M. O. and A. Y. conceived and directed the project. K. U.
and B. M. B. synthesized and characterized Li2MnO3,
Li1.2Ni0.13Co0.13Mn0.54O2 and Na2Ru0.5Sn0.5O3. A. T. synthesized
WO2(O2)(H2O). T. S., K. U., A. T., D. A., T. S., Y. H. and M. O.
measured and analysed the XAS, XES, and RIXS spectra.

This journal is © The Royal Society of Chemistry 2020

Energy & Environmental Science
T. M., X. M. S., T. S., E. W., and M. N. conducted the ab initio
calculation. All authors wrote the manuscript.

Conflicts of interest
There are no conflicts to declare.

Acknowledgements
This work was financially supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan;
Grant-in-Aid for Specially Promoted Research No. 15H05701 andthe ‘‘Elemental Strategy Initiative for Catalysis and Batteries’’(ESICB). M. O. was financially supported by JSPS KAKENHI Grant
Number 19H05816, 18K19124, and the Iketani Science and Technology Foundation. The RIXS spectroscopy was performed by thejoint research in Synchrotron Radiation Research Organizationand the Institute for Solid State Physics, the University of Tokyo(Proposal No. 2019B7456, 2019A7452, 2018B7590, 2018A7560,
2017B7540, 2017A7525, 2016B7516 and 2015B7500). We also
thank the Information Technology Center of Nagoya University
for providing computing resources (CX400 and FX400). M. N. was
supported by ‘‘Materials Research by Information Integration’’Initiative (MI2I) project of the Support Program for Starting Up
Innovation Hub from Japan Science and Technology Agency (JST),and JSPS KAKENHI Grant Number 19H05815. We are grateful to
J. Miyawaki at the University of Tokyo for his support to the RIXS
measurements.

References
1 R. V. Noorden, Nature, 2014, 507, 26–28.
2 B. Dunn, H. Kamath and J. M. Tarascon, Science, 2011, 334,
928–935.
3 D. Larcher and J. M. Tarascon, Nat. Chem., 2015, 7, 19–29.
4 M. S. Whittingham, Chem. Rev., 2014, 114, 11414–11443.
5 R. A. Huggins, Advanced Batteries, Springer, New York, 2009.
6 J. B. Goodenough and Y. Kim, Chem. Mater., 2010, 22,
587–603.
7 A. Grimaud, W. T. Hong, Y. Shao-Horn and J. M. Tarascon,Nat. Mater., 2016, 15, 121–126.
8 I. B. Bersuker, Electronic Structure and Properties of Transition Metal Compounds, John Wily & Sons, New York, 1995.
9 P. A. Cox, Transition Metal Oxides, Oxford Press, New York,1992.
10 D.-H. Seo, J. Lee, A. Urban, R. Malik, S. Y. Kang and
G. Ceder, Nat. Chem., 2016, 8, 692–697.
11 K. Luo, M. R. Roberts, R. Hao, N. Guerrini, D. M. Pickup,
Y.-S. Liu, K. Edström., J.-H. Guo, A. V. Chadwick, L. C. Duda
and P. G. Bruce, Nat. Chem., 2016, 8, 684–691.
12 Z. Lu, D. D. MacNeil and J. Dahn, ECS Solid State Lett., 2001,
4, A191–A194.
13 Z. Lu and J. Dahn, J. Electrochem. Soc., 2002, 149, A815–A822.
14 E. McCalla, A. M. Abakumov, M. Saubanère, D. Foix, E. J.
Berg, G. Rousse, M.-L. Doublet, D. Gonbeau, P. Novák,

Energy Environ. Sci., 2020, 13, 1492--1500 | 1499

View Article Online

Open Access Article. Published on 12 March 2020. Downloaded on 10/6/2024 5:06:11 PM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Energy & Environmental Science
G. Van Tendeloo, R. Dominko and J.-M. Tarascon, Science,
2015, 350, 1516–1521.
15 N. Yabuuchi, M. Nakayama, M. Takeuchi, S. Komaba,
Y. Hashimoto, T. Mukai, H. Shiiba, K. Sato, Y. Kobayashi,
A. Nakao, M. Yonemura, K. Yamanaka, K. Mitsuhara and
T. Ohta, Nat. Commun., 2016, 7, 13814.
16 P. E. Pearce, A. J. Perez, G. Rousse, M. Saubanère, D. Batuk,
D. Foix, E. McCalla, A. M. Abakumov, G. Van Tendeloo, M. L.
Doublet and J. M. Tarascon, Nat. Mater., 2017, 16, 580–586.
17 C. Zhan, Z. P. Yao, J. Lu, L. Ma, V. A. Maroni, L. Li, E. Lee,E. E. Alp, T. P. Wu, J. G. Wen, Y. Ren, C. Johnoson, M. M.
Thackeray, M. K. Y. Chan, C. Wolverton and K. Amine, Nat.
Energy, 2017, 2, 963–971.
18 G. Assat, D. Foix, C. Delacourt, A. Ladecola, R. Dedryvere
and J. M. Tarascon, Nat. Commun., 2017, 8, 2219.
19 D. Eum, B. Kim, S. J. Kim, H. Park, J. Wu, S. P. Cho, G. Yoon,
M. H. Lee, S. K. Jung, W. Yang, W. M. Seong, K. Ku,
O. Tamwattana, S. K. Park, I. Hwang and K. Kang, Nat.
Mater., 2020, DOI: 10.1038/s41563-019-0572-4.
20 R. A. House, U. Maitra, M. A. Perez-Osorio, J. G. Lozano,
L. Jin, J. W. Somerville, L. C. Dude, A. Nag, A. Walters,
K. J. Zhou, M. R. Roberts and P. G. Bruce, Nature, 2020, 577,
502–508.
21 M. B. Yahia, J. Vergnet, M. Saubanere and M. L. Doublet,
Nat. Mater., 2019, 18, 496–502.
22 J. Xu, M. Sun, R. Qiao, S. E. Renfrew, L. Ma, T. Wu, S. Hwang,
D. Nordlund, D. Su, K. Amine, J. Lu, B. D. McCloskey,
W. Yang and W. Tong, Nat. Commun., 2018, 9, 947.
23 M. Okubo and A. Yamada, ACS Appl. Mater. Interfaces, 2017,9, 36463–36472.
24 Y. Xie, M. Saubanere and M. L. Doublet, Energy Environ. Sci.,
2017, 10, 266–274.
25 G. Assat and J. M. Tarascon, Nat. Energy, 2018, 3, 373–386.
26 F. de Groot and A. Kotani, Core level spectroscopy of solids,
CRC Press, Boca Raton, 2008.
27 V. Bisogni, S. Catalano, R. J. Green, M. Gilbert, R. Scherwitzl,
Y. B. Huang, V. N. Strocov, P. Zubko, S. Balandeh, J. M. Triscone,
G. Sawatzky and T. Schmitt, Nat. Commun., 2016, 7, 13017.
28 J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys.,
2003, 118, 8207–8215.
29 J. Reed and G. Ceder, Electrochem. Solid-State Lett., 2002, 5,
A145–A148.
30 H. Koga, L. Croguennec, M. Menetrier, K. Douhil, S. Belin,
L. Bourgeois, E. Suard, F. Weill and C. Delmas,
J. Electrochem. Soc., 2013, 160, A786–A792.
31 B. Mortemard de Boisse, G. D. Liu, J. T. Ma, S. Nishimura,
S. C. Chung, H. Kiuchi, Y. Harada, J. Kikkawa, Y. Kobayashi,
M. Okubo and A. Yamada, Nat. Commun., 2016, 7, 11397.
32 A. D. Robertson and P. G. Bruce, Chem. Commun., 2002,
2790–2791.
33 K. Hikima, K. Suzuki, S. Taminato, M. Hirayama, S. Yasuno
and R. Kanno, Chem. Lett., 2019, 48, 192–195.

1500 | Energy Environ. Sci., 2020, 13, 1492--1500

Paper
34 W. E. Gent, K. Lim, Y. F. Liang, Q. H. Li, T. Barnes, S.-J. Ahn,
K. H. Stone, M. Mclntire, J. Y. Hong, J. H. Song, Y. Y. Li,
A. Mehta, S. Ermon, T. Tyliszczak, D. Kilcoyne, D. Vine, J.-H.
Park, S.-K. Doo, M. F. Toney, W. L. Yang, D. Prendergast andW. C. Chueh, Nat. Commun., 2017, 8, 2091.
35 J. Hong, W. E. Gent, P. Xiao, K. Lim, D.-H. Seo, J. Wu,
P. M. Csernica, C. J. Takacs, D. Nordlund, C. J. Sun, K. H.
Stone, D. Passarello, W. L. Yang, D. Prendergast, G. Ceder,
M. F. Toney and W. C. Chueh, Nat. Mater., 2019, 8, 256–265.
36 B. Pecquenard, S. Castro-Garcia, J. Livage, P. Y. Zavalij,
M. S. Whittingham and R. Thouvenot, Chem. Mater., 1998,
10, 1882–1888.
37 U. Maitra, R. A. House, J. Somerville, N. Tapia-Ruiz,
J. G. Lozano, N. Guerrini, R. Hao, K. Luo, L. Y. Jin,
M. A. Perez-Osorio, F. Massel, D. M. Pickup, S. Ramos,
X. Y. Lu, D. E. McNally, M. R. Roberts and P. G. Bruce,
Nat. Chem., 2018, 10, 288–295.
38 B. Mortemard de Boisse, S. Nishimura, E. Watanabe,
L. Lander, A. Tsuchimoto, J. Kikkawa, E. Kobayashi,
D. Asakura, M. Okubo and A. Yamada, Adv. Energy Mater.,
2018, 8, 1800409.
39 T. Hughbanks and R. Hoﬀmann, J. Am. Chem. Soc., 1983,
105, 3528–3537.
40 H. Shigemura, M. Tabuchi, H. Sakaebe, H. Kobayashi and
H. Kageyama, J. Electrochem. Soc., 2003, 150, A638–A644.
41 M. Sathiya, G. Rousse, K. Ramesha, C. P. Laisa, H. Vezin,
M. T. Sougrati, M. L. Doublet, D. Foix, D. Gonbeau,
W. Walker, A. S. Prakash, M. Ben Hassine, L. Dupont andJ. M. Tarascon, Nat. Mater., 2013, 12, 827–835.
42 G. Assat, A. Iadecola, C. Delacourt, R. Dedryvere andJ. M. Tarascon, Chem. Mater., 2017, 29, 9714–9724.
43 V. Petricek, M. Dusek and L. Palatinus, Z. Kristallogr., 2014,
229, 345–352.
44 F. Monma and F. Izumi, J. Appl. Crystallogr., 2011, 44,
1272–1276.
45 Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi,
T. Tokushima, Y. Horikawa, S. Shin and M. Oshima, Rev.
Sci. Instrum., 2012, 83, 013116.
46 G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter
Mater. Phys., 1996, 54, 11169–11186.
47 G. Kresse and J. Furthmüller, Comput. Mater. Sci., 1996, 6,
15–50.
48 P. E. Blöchl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994,
50, 17953–17979.
49 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett.,
1996, 77, 3865.
50 G. Hautier, S. P. Ong, A. Jain, C. J. Moore and G. Ceder, Phys.
Rev. B: Condens. Matter Mater. Phys., 2012, 85, 155208.
51 S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys.,
2010, 132, 154104.
52 S. Maintz, V. L. Deringer, A. L. Tchougréeﬀ and R. Dronskowski,
J. Comput. Chem., 2016, 37, 1030–1035.

This journal is © The Royal Society of Chemistry 2020