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Vision for Designing High-Energy, Hybrid Li Ion/LiO 2 Cells Michael M. Thackeray,* ,Maria K. Y. Chan, Lynn Trahey, Scott Kirklin, § and Christopher Wolverton § Chemical Sciences and Engineering Division and Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States § Materials Science and Engineering, Northwestern University, Evanston, Illinois 60202, United States ABSTRACT: A new concept to design hybrid Li ion/LiO 2 cells employing dual-functioning metal oxide electrodes/electrocatalysts that have an anity for releasing lithium and oxygen during charge and producing Li 2 Ometal oxide compounds during discharge, at voltages at or above the theoretical potential for Li 2 O 2 and Li 2 O formation, is discussed. First-principles density functional theory calculations lend support to previously-reported experimental data and the concept that a LiFeO/FeO charge product derived electrochemically from a parent Li 5 FeO 4 crystalline structure can react, at thermodynamic equilibrium, with lithium and oxygen at or above the potential for LiO 2 reactions to regenerate the Li 5 FeO 4 composition, presumably with concomitant redox of the iron ions to assist the catalytic process. Because all of the lithium, iron, and oxygen required for the electrochemical reaction are, in principle, contained in the parent Li 5 FeO 4 structure, these results have exciting implications for designing an all-in-oneelectrode for a hybrid Li ion/LiO 2 cell that can provide a specic energy and an energy density that far exceeds the practical energy of conventional lithium ion batteries. SECTION: Energy Conversion and Storage; Energy and Charge Transport The Vision: An Alternative to Li 2 O 2 in LiO 2 Batteries. Lithiumoxygen reactions currently receive widespread attention because, in principle, they provide signicantly higher energy than conventional lithium ion insertion reactions. 13 Most research eorts 3 have focused on exploiting the Li + O 2 Li 2 O 2 reaction because lithium peroxide formation does not completely sever the oxygenoxygen bond, thereby oering greater reversibility than is the case if the ultimate discharge reaction product, Li 2 O, 4 with a cubic close-packed oxygen array, is formed. Lithiumoxygen electrochemistry is fraught with diculties, (1) a metallic lithium anode that is prone to dendrite formation and short circuiting, (2) high polarization at the oxygen electrode, particularly during charge, (3) electrolyte instability and undesirable side reactions, and (4) low reaction rate and poor cycle life. These limitations are severely hampering progress in advancing LiO 2 technology. We have adopted a dierent approach to exploit LiO 2 electrochemistry, based on structural and thermodynamic considerations. We have been inspired by the electrochemical behavior of structurally integrated Li 2 MnO 3 ·LiMO 2 compo- siteelectrodes (M = Mn, Ni, Co) that can deliver an extremely high capacity (250 mA h/g), relative to other lithiumtransition metal oxide cathodes, if they are electrochemically activated at a high potential (>4.5 V). 5,6 The activation process, which removes both lithium and oxygen from the Li 2 MnO 3 component (net loss Li 2 O), is irreversible; it yields an active MnO 2 component into which lithium can be inserted with a concomitant reduction of the manganese ions upon subsequent discharge cycles, thereby signicantly enhancing the capacity of the electrode. However, because Li 2 O is the ultimate discharge product of a lithiumoxygen cell, we are exploring the possibility of reversing the Li 2 O reactionby providing an oxygen environment to the cathode during the discharge reaction, to reaccommodate Li 2 O around electrochemically activated metal oxide products that have an anity to form compounds with lithium and oxygen. In this respect, lithium metal oxides with a high Li 2 O content, such as those with a defect antiuorite-type structure, are of particular interest, for example, Li 5 FeO 4 (5Li 2 O·Fe 2 O 3 ) 7,8 and Li 6 MO 4 compounds (3Li 2 O·MO, M = Mn, Co). 7,8 From a physical chemistry standpoint, this Letter addresses the structural, electrochemical, and thermodynamic aspects of a novel approach for designing dual-functioning electrode/electrocatalyst materials for hybrid Li ion/LiO 2 cells. The Prototype: Li 5 FeO 4 , an All-in-OneElectrode/Electro- catalyst. We have focused our initial studies on Li 5 FeO 4 , which lies on the Li 2 OFe 2 O 3 tie-line of the LiFeO phase diagram along with two other compounds, namely, rocksalt LiFeO 2 9,10 (Li 2 O·Fe 2 O 3 ) and spinel LiFe 5 O 8 11 (Li 2 O·5Fe 2 O 3 ) and the end members Fe 2 O 3 (defect spinel or corundum) and Li 2 O (antiuorite). 12,13 These preliminary investigations have yielded intriguing results that suggest that 80% of the Li 2 O component in Li 5 FeO 4 (5Li 2 O·Fe 2 O 3 ) can be extracted (as Li and O 2 ) during charge 12 and reaccommodated in a Li/Li 5 FeO 4 O 2 cell around the residual LiFeO component during discharge between 3.2 and 2.8 V. 13 It has been demonstrated previously that it is possible to extract four lithium ions from Li 5 FeO 4 , both chemically with NO 2 BF 4 and electrochemically in a standard Li/Li 5 FeO 4 button cell between 3.5 and 4.2 V at a very slow rate (0.05 mA/cm 2 ), Received: August 30, 2013 Accepted: September 30, 2013 Letter pubs.acs.org/JPCL © XXXX American Chemical Society 3607 dx.doi.org/10.1021/jz4018464 | J. Phys. Chem. Lett. 2013, 4, 36073611

Vision for Designing High-Energy, Hybrid Li Ion/Li–O 2 Cells

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Page 1: Vision for Designing High-Energy, Hybrid Li Ion/Li–O               2               Cells

Vision for Designing High-Energy, Hybrid Li Ion/Li−O2 CellsMichael M. Thackeray,*,† Maria K. Y. Chan,‡ Lynn Trahey,† Scott Kirklin,§ and Christopher Wolverton§

†Chemical Sciences and Engineering Division and ‡Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois60439, United States§Materials Science and Engineering, Northwestern University, Evanston, Illinois 60202, United States

ABSTRACT: A new concept to design hybrid Li ion/Li−O2 cells employing dual-functioningmetal oxide electrodes/electrocatalysts that have an affinity for releasing lithium and oxygenduring charge and producing Li2O−metal oxide compounds during discharge, at voltages at orabove the theoretical potential for Li2O2 and Li2O formation, is discussed. First-principlesdensity functional theory calculations lend support to previously-reported experimental data andthe concept that a Li−Fe−O/Fe−O charge product derived electrochemically from a parentLi5FeO4 crystalline structure can react, at thermodynamic equilibrium, with lithium and oxygenat or above the potential for Li−O2 reactions to regenerate the Li5FeO4 composition,presumably with concomitant redox of the iron ions to assist the catalytic process. Because all ofthe lithium, iron, and oxygen required for the electrochemical reaction are, in principle,contained in the parent Li5FeO4 structure, these results have exciting implications for designingan “all-in-one” electrode for a hybrid Li ion/Li−O2 cell that can provide a specific energy and anenergy density that far exceeds the practical energy of conventional lithium ion batteries.

SECTION: Energy Conversion and Storage; Energy and Charge Transport

The Vision: An Alternative to Li2O2 in Li−O2 Batteries. Lithium−oxygen reactions currently receive widespread attentionbecause, in principle, they provide significantly higher energythan conventional lithium ion insertion reactions.1−3 Mostresearch efforts3 have focused on exploiting the Li + O2 →Li2O2 reaction because lithium peroxide formation does notcompletely sever the oxygen−oxygen bond, thereby offeringgreater reversibility than is the case if the ultimate dischargereaction product, Li2O,

4 with a cubic close-packed oxygen array,is formed. Lithium−oxygen electrochemistry is fraught withdifficulties, (1) a metallic lithium anode that is prone todendrite formation and short circuiting, (2) high polarization atthe oxygen electrode, particularly during charge, (3) electrolyteinstability and undesirable side reactions, and (4) low reactionrate and poor cycle life. These limitations are severelyhampering progress in advancing Li−O2 technology.We have adopted a different approach to exploit Li−O2

electrochemistry, based on structural and thermodynamicconsiderations. We have been inspired by the electrochemicalbehavior of structurally integrated Li2MnO3·LiMO2 “compo-site” electrodes (M = Mn, Ni, Co) that can deliver an extremelyhigh capacity (∼250 mA h/g), relative to other lithium−transition metal oxide cathodes, if they are electrochemicallyactivated at a high potential (>4.5 V).5,6 The activation process,which removes both lithium and oxygen from the Li2MnO3component (net loss Li2O), is irreversible; it yields an activeMnO2 component into which lithium can be inserted with aconcomitant reduction of the manganese ions upon subsequentdischarge cycles, thereby significantly enhancing the capacity ofthe electrode. However, because Li2O is the ultimate dischargeproduct of a lithium−oxygen cell, we are exploring thepossibility of reversing the “Li2O reaction” by providing an

oxygen environment to the cathode during the dischargereaction, to reaccommodate Li2O around electrochemicallyactivated metal oxide products that have an affinity to formcompounds with lithium and oxygen. In this respect, lithiummetal oxides with a high Li2O content, such as those with adefect antifluorite-type structure, are of particular interest, forexample, Li5FeO4 (5Li2O·Fe2O3)

7,8 and Li6MO4 compounds(3Li2O·MO, M = Mn, Co).7,8 From a physical chemistrystandpoint, this Letter addresses the structural, electrochemical,and thermodynamic aspects of a novel approach for designingdual-functioning electrode/electrocatalyst materials for hybridLi ion/Li−O2 cells.The Prototype: Li5FeO4, an “All-in-One” Electrode/Electro-

catalyst. We have focused our initial studies on Li5FeO4, whichlies on the Li2O−Fe2O3 tie-line of the Li−Fe−O phase diagramalong with two other compounds, namely, rocksalt LiFeO2

9,10

(Li2O·Fe2O3) and spinel LiFe5O811 (Li2O·5Fe2O3) and the end

members Fe2O3 (defect spinel or corundum) and Li2O(antifluorite).12,13 These preliminary investigations have yieldedintriguing results that suggest that 80% of the Li2O componentin Li5FeO4 (5Li2O·Fe2O3) can be extracted (as Li and O2)during charge12 and reaccommodated in a Li/Li5FeO4−O2 cellaround the residual Li−Fe−O component during dischargebetween 3.2 and 2.8 V.13

It has been demonstrated previously that it is possible toextract four lithium ions from Li5FeO4, both chemically withNO2BF4 and electrochemically in a standard Li/Li5FeO4 buttoncell between 3.5 and 4.2 V at a very slow rate (0.05 mA/cm2),

Received: August 30, 2013Accepted: September 30, 2013

Letter

pubs.acs.org/JPCL

© XXXX American Chemical Society 3607 dx.doi.org/10.1021/jz4018464 | J. Phys. Chem. Lett. 2013, 4, 3607−3611

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with a concomitant loss of oxygen (Figure 1a8,12); the reactiongenerates an amorphous LiFeO2 (Li2O·Fe2O3) product. Thecharge capacity for the extraction of four Li per Li5FeO4 isextremely high (694 mA h/g). In the Li/Li5FeO4 cell (withoutO2), this reaction is irreversible. In a Li/Li5FeO4−O2 cell, thecharge capacity, delivered between 3.7 and 4.6 V, is 475 mA h/g of Li5FeO4 (Figure 1b

13). Remarkably, the reaction in the Li/Li5FeO4−O2 cell appears to be reversible, delivering essentiallythe same capacity during discharge on a sloping plateaubetween 3.2 and 2.9 V before the expected reaction betweenlithium and oxygen occurs at a lower voltage, ∼2.6 V (Figure1b). The capacity between 2.9 and ∼2.6 V is tentativelyattributed to the reduction of some Fe3+ to Fe2+.

These findings have exciting implications for furtherexploitation. If 80% of the Li2O content in Li5FeO4 (i.e., 4Li) can be extracted (with oxygen loss), as indicated in Figure1a, and reaccommodated during discharge, as suggested byFigure 1b, at an average of ∼3 V, then this would lead to apractical cell with a specific energy of more than 2000 W h/kg(based on the mass of the active electrode materials only).What is more remarkable is that all of the lithium, iron, andoxygen required for this reaction are initially contained in theparent Li5FeO4 electrode structure, thereby presenting thenotion of an “all-in-one” parent electrode for a Li−O2 cell.We have presented this concept cursorily in a recent

publication on dual-functioning MnO2 electrode/electrocata-lysts for Li−O2 cells14 and with reference to lithium−ironoxides in the Li−Fe−O phase diagram, which is provided againin Figure 2, for convenience. The Fe2O3−Li2O tie-line containsseveral “xLi2O·Fe2O3” compounds, in which 0 < x ≤ 5, such asspinel LiFe5O8 (0.2Li2O·Fe2O3), rocksalt LiFeO2 (Li2O·Fe2O3), and defect antifluorite Li5FeO4 (5Li2O·Fe2O3). It isconceivable that highly porous iron oxide or lithium−iron oxidenanoparticles derived from charged Li5FeO4 electrodes mayrecombine with lithium and oxygen during discharge to formthe above-mentioned compositions. Furthermore, it is knownthat lithium can be inserted into Fe2O3 at room temperature atapproximately the same potential that Li2O2 and Li2O aregenerated, at least during the early stages of discharge (∼2.9−3.0 V).15 In these cells, oxygen is absent; therefore, lithiuminsertion will be accompanied by Fe reduction, therebyproviding mixed Fe3+/Fe2+ valence states at the electrodesurface. A previous report has also indicated that some lithiumcan be extracted from a corrugated layered LiFeO2 (Li2O·Fe2O3) structure without oxygen loss, suggesting mixed Fe4+/Fe3+ character at about 4 V.16 We hypothesize that iron redoxreactions during the charge/discharge of Li/Li5FeO4 cells maycatalyze the reactions that involve lithium and oxygen. In thisrespect, iron oxide and lithium−iron oxides would act as dual-functioning electrode/electrocatalysts by providing electro-chemical redox capacity to the electrode and facilitatingelectron transfer for Li−O2 reactions.

11

The Numbers: Calculated Voltages and Capacities. In order toprobe and accelerate our understanding of this concept, wehave used first-principles density functional theory (DFT)calculations to determine the electrochemical potentials of

Figure 1. Electrochemical reactions for (a) the extraction of lithium(and oxygen) from a Li/Li5FeO4 cell (adapted from ref 12) and (b)the initial charge and discharge of a Li/Li5FeO4−O2 cell (adapted fromref 13). Capacities are given in mA h per gram of Li5FeO4.

Figure 2. A Li−Fe−O phase diagram indicating tie-lines for the reaction of Fe2O3 with Li and Li2O.14

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reactions that produce compounds along the Li2O−Fe2O3 tie-line and to investigate the electrochemical parameters of otherLi2O-containing materials, particularly those with defectantifluorite structures, namely, Li6CoO4, Li6MnO4, andLi5AlO4. Table 1 shows the voltages for the various electro-chemical reactions calculated from DFT. Calculated voltages(2.94 and 2.85 V) for the electrochemical reactions of lithiumwith O2 to form Li2O2 and Li2O, that is, reactions 1 and 2, areconsistent, within uncertainties, with previously reportedcalculated values (3.00 and 2.87 V)14 and values derived fromexperimental formation enthalpies (2.96 and 2.91 V).17 Table 1also provides corresponding gravimetric (Cg) and volumetric(Cv) capacities and gravimetric (Eg) and volumetric (Ev) energydensities for the various reactions involving Li, O2, and metaloxides or lithium−metal oxides. The theoretical gravimetric andvolumetric capacities for both Li2O2 (Eg = 3440 W h/kg; Ev =8790 W h/L) and Li2O electrodes (Eg = 5110 W h/kg; 10700W h/L) are impressive. The significantly lower band gap18 forLi2O2 (2.4 eV) significantly favors electron transfer and plays apossible role in the electrochemical reversibility of the Li2O2reaction relative to the Li2O reaction (Li2O band gap = 5.1 eV).Note that the electrochemical reaction of lithium with solidLi2O2 to form Li2O (reaction 3) is predicted to occur at a lowerpotential (than reactions 1 and 2) of 2.76 V, with expectedlylower Eg (2480 W h/kg) and Ev (5180 W h/L) values.Reactions 4−6 of Table 1 show the calculated voltages,

capacities, and energy densities for the reaction of variouscompounds on the Fe2O3−Li2O tie-line with lithium andoxygen and the calculated band gap of the discharge product.The reaction of lithium and oxygen with Fe2O3 to formLiFe5O8 (0.2Li2O·Fe2O3) and, thereafter, LiFeO2 (Li2O·Fe2O3)and Li5FeO4 (5Li2O·Fe2O3) occur at 3.54, 3.48, and 2.93 V,respectively. This is a significant finding because all threereactions occur at or above the calculated potential for Li2O2and Li2O formation (2.94 and 2.85 V, respectively), therebygiving credence to our hypothesis that metal oxides with anaffinity for accommodating Li2O may be of interest fordesigning highly porous, nanoparticulate electrodes thatoperate by “Li2O” extraction/reaccommodation reactions witha host oxide framework.The reaction (6) of Li5FeO4 to LiFeO2 (and vice versa) is

particularly significant; it is consistent with the experimentaldata that we have obtained thus far in our studies ofLi5FeO4.

12,13 Under thermodynamic equilibrium, Li2O removal(i.e., Li + O2 extraction) and reaccommodation reactions occurat 2.93 V, delivering very high gravimetric and volumetricenergy densities of 2030 W h/kg and 5700 W h/L, respectively,

based on the mass and density of Li5FeO4 (Table 1). Inpractice, the charge reaction is observed to occur between 3.7and 4.6 V,12,13 and the discharge reaction occurs between 3.2and 2.9 V,13 reflecting considerable polarization, particularlyduring the charge process. While the calculated voltage forreaction 6 is close to the predicted voltage for lithium peroxideformation, the experimental discharge voltages indicate thatcrystalline Li2O2 formation is unlikely; however, the possiblerole of superoxide O2

− and peroxide O22− species during the

charge and discharge reactions should not be overlooked anddeserve investigation.These experimental and theoretical results open the door to

many other interesting Li2O-containing materials, such as thefamily of Li6MO4 compounds (M = Co, Mn), which, likeLi5FeO4, have a defect antifluorite structure in which the Mcations are divalent rather than trivalent. For example, the Li2Oextraction/reaccommodation reactions associated with theLi6CoO4 to CoO and Li6MnO4 to MnO transformations arepredicted to occur at ∼2.9 V versus Li0 and to offer gravimetricand volumetric energy densities of 2880(Co)/2820(Mn) W h/kg and 7580(Co)/8120(Mn) W h/L. In addition, the LiAlO2 toLi5AlO4 reaction, which offers gravimetric and volumetricenergy densities of 2480 W h/kg and 5870 W h/L, respectively,warrants attention, despite the high band gap of Li5AlO4 (5.4eV). To solve the possible electron-transfer problemsassociated with the high band gap of Li5AlO4, we speculatethat it may be possible to use carbon as the electrocatalyst incarbon-coated lithium aluminates and to use porous, nano-particulate alumina/aluminate architectures to facilitate chargetransfer on the surface. The approach also opens the door tothe exploitation of charged electrode/electrocatalytic materials,such as Fe2O3, in the absence of the Li2O component; in thiscase, a lithium-containing anode and an external source ofoxygen at the cathode would have to be provided to generatethe all-in-one Li5FeO4 discharge product.In conclusion, we have described an unconventional

approach to exploiting Li−O2 electrochemistry in terms ofthe ability of metal oxides, particularly iron oxides, to react withlithium and oxygen to produce compounds that contain a Li2Ocomponent, at or above the potentials of Li2O2 and Li2Oformation. We have presented a structural motivation for thisnew approach; electrochemical and thermodynamic datasupport our hypothesis. These reactions can provide an energydensity that is at least 50% of the theoretical value for the Li +O2 → Li2O2 reaction. Such high capacities and potentials mayconceivably allow the use of materials such as Li5FeO4 as anelectrode/electrocatalyst in a hybrid Li ion/Li−O2 cell with a

Table 1. Calculated Voltages, Gravimetric Capacity (Cg), Volumetric Capacity (Cv), Gravimetric Energy Density (Eg), andVolumetric Energy Density (Ev) for Various Reactions Involving Lithium and Oxygen and Band Gaps of Productsa

reaction reactants productsvoltage (V)± 0.1 V

Cg (mA h/g)± 0.1%

Cv (mA h/mL)± 4%19

Eg (W h/kg)± 3%

Ev (W h/L)± 7%

band gap (eV)+ 20−100%

1 Li, O2 Li2O2 2.94 1168 2990 3440 8790 2.42 Li, O2 Li2O 2.85 1794 3750 5110 10700 5.13 Li, Li2O2 Li2O 2.76 897 1870 2480 5180 5.14 Li, O2, Fe2O3 LiFe5O8 3.54 65 311 229 1100 1.25 Li, O2, LiFe5O8 LiFeO2 3.48 226 1020 787 3550 1.56 Li, O2, LiFeO2 Li5FeO4 2.93 694 1940 2030 5700 2.87 Li, O2, CoO Li6CoO4 2.89 977 2810 2820 8120 2.78 Li, O2, MnO Li6MnO4 2.88 1001 2640 2880 7580 2.79 Li, O2, LiAlO2 Li5AlO4 2.90 853 2020 2480 5870 5.4

aSee the Computational Methods section for details.

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carbon or lithum−metal alloy anode rather than a metalliclithium anode but only if a kinetically fast process can bedevised to capture and release the oxygen within the cathodecompartment during charge and discharge.

■ COMPUTATIONAL METHODSDFT calculations were carried out as a part of the openquantum materials database (OQMD).20 All calculations wereperformed using the Vienna ab initio software package(VASP)21 at a plane wave cutoff of 520 eV using projectoraugmented wave potentials.22 We use the generalized gradientapproximation (GGA) for the exchange−correlation functionalas parametrized by Perdew, Burke, and Enzerhoff.23 The k-point mesh was constructed such that Natoms × Nkpts ≈ 8000 ina gamma centered mesh. Any species with a partially filled dshell was given an initial magnetic moment of 5 μb in aferromagnetic structure and then allowed to relax self-consistently. The Kohn−Sham gap, that is, the differencebetween the highest occupied and lowest unoccupiedeigenvalues, of each compound is reported as the band gap.For the metal oxide compositions, DFT+U was applied using

U values fitted to reproduce oxidation energies obtained fromexperimental formation enthalpies, as found by Wang et al.24

For gaseous oxygen, the chemical potential was fit toexperimental data collected from the SGTE substances database(SSUB).25,26

The voltage of each reaction is calculated as the negativechange in Gibbs free energy per electron transferred (V =−ΔG/Ne, where N is the number of electrons transferred inthe reaction).27,28 In the free energy, we take into account theentropy for gaseous O2 at 300 K and 1 atm. The contributionsof solid-state vibrations to ΔG, which are expected to be small(∼0.05−0.1 eV per electron), are neglected.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank Michael Krumpelt for helpful discussions. This workwas supported by the Center for Electrical Energy Storage:Tailored Interfaces, an Energy Frontier Research Center fundedby the U.S. Department of Energy, Office of Science, Office ofBasic Energy Sciences. Use of the Center for NanoscaleMaterials was supported by the U.S. Department of Energy,Office of Science, Office of Basic Energy Sciences, underContract No. DE-AC02-06CH11357.

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(0 < x < 2). Mater. Res. Bull. 1982, 17, 785−793.(16) Kanno, R.; Shirane, T.; Kawamoto, Y.; Takeda, Y.; Takano, M.;Ohashi, M.; Yamaguchi, Y. Synthesis, Structure, and ElectrochemicalProperties of a New Lithium Iron Oxide, LiFeO2, with a CorrugatedLayer Structure. J. Electrochem. Soc. 1996, 143, 2435−2442.(17) Kubaschewski, O.; Alcock, C. B.; Spencer, P. J. MaterialsThermochemistry; Pergamom Press: Oxford, U.K., 1993.(18) Note that the band gap values reported are Kohn−Shameigenvalue gaps in density functional theory, which are well-known tosignificantly underestimate experimental gaps and hence are providedfor trends only.(19) Haas, P.; Tran, F.; Blaha, P. Calculation of the Lattice Constantof Solids with Semilocal Functionals. Phys. Rev. B 2009, 79, 085104.(20) Saal, J.; Kirklin, S.; Aykol, M.; Meredig, B. M.; Wolverton, C.Materials Design and Discovery with High-Throughput DensityFunctional Theory: The Open Quantum Materials Database(OQMD). JOM 2013, DOI: 10.1007/s11837-013-0755-4.(21) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for AbInitio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys.Rev. B 1996, 54, 11169−11186.(22) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to theProjector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758−1775.(23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized GradientApproximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868.

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