Structure and Stability of Lithium Superoxide Clusters and Relevance

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Letter pubs.acs.org/JPCL

Structure and Stability of Lithium Superoxide Clusters and Relevance to Li−O2 Batteries Ujjal Das,*,† Kah Chun Lau,† Paul C. Redfern,‡ and Larry A. Curtiss*,†,§ †

Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States § Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States ‡

S Supporting Information *

ABSTRACT: The discharge mechanism of a Li−O2 battery involves lithium superoxide (LiO2) radicals. In this Letter, we have performed highlevel quantum chemical calculations (G4MP2) to investigate the structure and stability of LiO2 clusters. The clusters have planar ring-shaped structures, high spins, and are thermodynamically more stable than LiO2 dimer. The computed energy barrier for disproportionation of the larger clusters is also significantly higher than the corresponding barrier in the LiO2 dimer (1.0 eV vs 0.5 eV). This means that disproportionation rate should be much slower if the reaction involves LiO2 clusters other than the dimer. As a result, the clusters may survive long enough to be incorporated into the growing discharge product. These results are discussed in terms of recent experimental studies of the electronic structure and morphology of the discharge products in Li−air batteries. SECTION: Energy Conversion and Storage; Energy and Charge Transport

R

echargeable lithium−oxygen batteries have drawn considerable interest in recent years due to their high gravimetric energy density, which is potentially 10 times higher than Li-ion batteries, and comparable to the gasoline-run internal combustion engine.1−5 However, lack of fundamental understanding of the reaction mechanisms involved in the charge and discharge chemistries severely limits the progress of Li−O2 battery research.6−8 To develop Li−O2 batteries for practical applications, it is critical to understand the mechanism of the charge−discharge cycle in the cell, including such processes as nucleation and growth,9−11 electronic transport,12−14 electrocatalysis,15−19 and electrolyte stability.20−26 O2 + e + Li+ = LiO2

(1)

2LiO2 = Li 2O2 + O2

(2)

monomers as shown in Reaction 2. They reported the existence of an oxygen-rich component with superoxide-like character and a Li2O2 component in the discharge product. Their charge profile contains two plateaus which were attributed to O-rich Li2O2 and stoichiometric Li2O2. Shao Horn and co-workers have also reported discharge products with a superoxide-like component.28 Thus, recent studies indicate that LiO2 in some cases may play a deeper role in Li−O2 discharge chemistry than what has been known so far. It is, therefore, of interest to investigate the structure and stabilities of small LiO2 clusters as they may be involved in the nucleation and growth of the initial discharge product as some experimental results suggest.27−30 The (LiO2)n cluster (n = 1−12) geometries were optimized using the B3LYP density functional and the 6-31G(2df) basis set.31−33 To assess the B3LYP energies, calculations were also performed using the MP234 and G4MP235 theories at the B3LYP optimized geometries with zero-point and thermal corrections taken from B3LYP calculations. The gas phase formation energies of LiO2 clusters (ΔEf and ΔGf) are computed according to the reaction shown in eq 3 and using the expressions shown in eqs 4 and 5.

Lithium superoxide radical (LiO2) is initially formed via Reaction 1 during discharge following a one-electron oxygen reduction reaction (ORR) at the cathode. One of the unresolved problems involving a Li−O2 battery is the mechanism for the conversion of LiO2 into Li2O2 discharge product. The conversion mechanism may have a significant impact on the electronic properties and morphology of the discharge product, as well as the charge chemistry. Recent kinetic studies for a Li−O2 cell based on an activated carbon cathode by Zhai et al.27 have revealed a first-order reaction during discharge that can be correlated to a disproportionation reaction of LiO2 in the bulk discharge product, thus indicating that the reaction may not necessarily involve two LiO2 © 2014 American Chemical Society

nLiO2 = (LiO2 )n

(3)

ΔEf = En /n − E1

(4)

Received: January 13, 2014 Accepted: February 10, 2014 Published: February 10, 2014 813

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Figure 1. LiO2 clusters with planar-ring shape optimized at the B3LYP/6-31G(2df) level of theory. Their relative stabilities are compared using ΔGf (eV/LiO2).

Figure 2. (a) Formation free energy of planar-ring (LiO2)n clusters for n = 2−12 at different levels of theory. Note that G4MP2 calculations are performed for cluster size up to n = 7. (b) Comparison of formation free energies between planar and nonplanar structures of LiO2 clusters at B3LYP and MP2 levels of theory using the 6-31G(2df) basis set.

ΔGf = Gn /n − G1

(5)

Gn = En + Etr + Erot + Evib + pV − TS

(6)

and 18) were also performed using the gradient corrected PBE functional39 with the projector augmented wave (PAW)40 method, and plane wave basis sets up to a kinetic energy cutoff of 400 eV. The convergence criterion of the total energy was set to be 1 × 10−5 eV within the k-point integration at Γ-point, and all the geometries were optimized until the residual forces became less than 1 × 10−2 eV/Å. Structure and Energy of (LiO2)n Clusters, n = 2−12, 16, 18. The optimized lowest energy structure of (LiO2)n clusters for n = 2−12 is shown in Figure 1. For all cluster sizes, the lowest energy isomer exhibits a planar ring configuration. For (LiO2)3, (LiO2)4, and (LiO2)9 clusters, multiple ring structures with different point group symmetries were located. For example, (LiO2)3 ring has both C2v and D3h symmetries with the former

Here, En is zero-point corrected electronic energy and Gn is the Gibbs free energy of gas phase LiO2 clusters, and n represents the number of LiO2 units in each cluster. To uniformly assess the stability of the clusters as a function of cluster size, the formation energies are reported on the basis of per LiO2 unit. The SMD36 solvation model was used to compute the solvation free energies of the clusters in acetone at the B3LYP/631G(2df) level of theory, while, for nonpolar oxygen molecule, the PCM37 solvation model was used. All calculations were performed using the Gaussian-09 quantum chemistry software version D.01.38 The calculations of LiO2 clusters (n = 1−12, 16, 814

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being slightly more stable (ΔGf = −0.55 eV/LiO2 and −0.21 eV/LiO2, respectively at the B3LYP/6-31G(d) level of theory). A full list of the different ring isomers and their energies are provided in the Supporting Information, and only the lowest energy isomers are reported and discussed in the paper. The O−O bond distance in (LiO2)n rings is almost invariably 1.35 Å, similar to the typical O−O distance in the superoxide anion (O2−) of LiO2 monomer. The Li−O bond distance, however, depends on the size of the rings, and, in general, the smaller rings have longer Li−O bonds. Overall, the Li−O distance varies between 1.88 and 1.93 Å. The formation free energies (ΔGf) of the LiO2 rings, starting from the dimer, are plotted against the size of the rings in Figure 2a at different levels of theory (G4MP2, MP2, B3LYP, and PBE). For all cluster sizes, the ring formation from LiO2 monomer is a thermodynamically downhill process. When compared on the basis of per LiO2 unit, it appears that the stability of the rings increases with size, although there is little or almost no change in ΔGf for n = 10 and onward. The energies are slightly different at different levels of theory. Nevertheless, they all support the general observation that the larger LiO2 clusters are more stable than the LiO2 dimer, and cluster stability reaches a limiting value. Several alternative structures of the LiO2 clusters were calculated to compare their stability against the ring structures. These structures were generated by (1) linearly stacking LiO2 monomers in head-to-tail fashion (“linear−chain”) and (2) vertically stacking two or more small rings (“stacked ring”) as shown in Scheme 1. The planar rings in Figure 1 are always

the ring size is small, this also introduces additional strain. The strain is reduced gradually as the ring size increases and after a certain size limit, it becomes insignificant (vide infra). This not only explains why the rings are more stable, but also shows why after a certain size limit, there is little or almost no change in net stability. The optimized nonplanar structures obtained from vertically stacking two or more small rings are shown in Figure 3 (see Tables S1 and S2 for additional structures considered). The (m × n) convention used to represent the stacked-ring structures indicates that two rings were used each carrying m and n number of LiO2 units, respectively. The formation free energies of the most stable planar-ring and stacked-ring clusters are compared in Figure 2b. Both B3LYP and MP2 calculations indicate that the planar ring structures are more stable at all cluster sizes. However, as size increases, the relative stability of the planar rings against stacked ring structures become less prominent, and at n = 12, they become almost equally stable. The comparison of ΔEf instead of ΔGf indicates a slightly different trend (Figure S2), and the stacked-ring structures become more stable at n = 10. While the exact location of the crossover point is of little significance, it indicates that the LiO2 rings are stable initially (up to about n = 12), after which the nonplanar structures are expected to be the dominant configurations. To verify the predictions based on clusters up to n = 12, we have performed geometry optimizations on (LiO2)16 and (LiO2)18 clusters. These calculations were done with the PBE functional and a plane wave basis function, which agrees with the energy trends for smaller clusters, n = 2−12, from the other methods as shown in Figure 2a. In addition to the planar-ring and different vertically stacked-rings, the starting geometries also included several 3-D structures mimicking the pattern in LiO2 bulk.41 The optimized structures are shown in Figure S3. For (LiO2)16, a 3-D structure resembling LiO2 bulk is slightly more stable (0.01 eV/LiO2) than a single ring structure. For (LiO2)18, again a 3-D structure, in this case obtained from 8 × 6 × 4 stacked-rings, is 0.05 eV/LiO2 more stable than the single (LiO2)18 ring. Note that these comparisons are made using energies without including the thermal corrections. The increasing stability of the 3-D structures, especially for large clusters, can be understood by comparing them with the

Scheme 1. Alternative Starting Geometries of LiO2 Clusters

more stable than linear-chain LiO2 clusters (see Figure S1). The ring may be considered as a special case in which the two ends of the linear structure are folded and joined together. This introduces additional stability coming from interactions between Li+ and O2− ions at the two ends. However, when

Figure 3. Nonplanar LiO2 clusters optimized at the B3LYP/6-31G(2df) level of theory and the corresponding ΔGf (eV/LiO2). 815

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Figure 4. Disproportionation mechanism of the (LiO2)7 cluster and corresponding free energy profile computed using the G4MP2 theory. The dashed line represents the free energy profile in solution (acetone).

by only 0.05 eV. The existence of multiple spin states within such a narrow energy gap may be called “spin fluxionality”, along the line of molecular fluxionality43 seen in molecules with different spatial configurations, but identical energies. Note that at the B3LYP level, there are spin contaminations for some of the low spin states, which is due to the overlap with the more stable high spin states. For the LiO2 trimer, both doublet and quartet states are optimized, and it is found that the quartet is approximately 0.3 eV less stable than the doublet. The high spins are also observed in the 3-D clusters (LiO2)16 and (LiO2)18. Disproportionation Energetics of LiO2 Clusters. We have investigated barriers and reaction energies to gain insight into the disproportionation mechanism of LiO2 clusters. The first step toward formation of lithium peroxide from lithium superoxide cluster is the removal of O2 molecule. The evolution of oxygen from (LiO2)n, n = 2−6, clusters is a single step process, while the evolution of oxygen from (LiO2)7 and larger clusters involves several steps. We have found that the ring strain energy (GRS) in the cyclic LiO2 clusters may influence the O2 evolution process. GRS is calculated following a procedure described elsewhere,44 and the details of the calculations are provided in the Supporting Information (Table S5). As expected, the smaller clusters possess more strain. For example, the LiO2 dimer ring is the most strained structure (GRS = 1.0 eV) and the strain energies in other small clusters (n = 3, 4, 5) are 0.7, 0.5, and 0.4 eV, respectively. In comparison, the strain in larger LiO2 rings (n ≥ 7) is less than 0.1 eV. The higher strain in the small clusters favors the release of oxygen without requiring a significant structural rearrangement. As an example, the multistep mechanism of O2 evolution from the (LiO2)7 cluster is shown in Figure 4. The first step involves deformation of the ring (TS1) that projects two LiO2 units out of the circle (IM1). The barrier for ring deformation is 0.52 eV. The subsequent step facilitates the release of O2 by making a new Li−O bond, and shows only a small change in energy. The rate-determining transition state (TS3) appears late in the mechanism, which involves breaking of Li−O2 bonds. This is confirmed from the significantly long Li−O distance, more than 2.0 Å as opposed to 1.9 Å in the parent cluster, and shorter O−O distance (1.25 Å) in the dissociating oxygen. Once O2 is released, the ring is reformed with six LiO2 units and an additional Li atom sitting like a jewel on top of the ring. Interestingly, the O−O distance in the vicinity of three Li atoms in Li7O12 is 1.55 Å, close to the typical O−O distance in

structure of lithium superoxide bulk. Though the structure of crystalline LiO2 is not yet resolved, several theoretical studies41,42 suggest an orthorhombic phase (Pnnm) in which each Li+ ion is surrounded by six superoxide anions (O2−). The Li+ ions in the LiO2 rings are surrounded by two O2− anions, and this does not change even when the ring size increases. In comparison, the Li+ ions in the 3-D clusters have more than two O2− ions surrounding them, and as the cluster size increases, the Li+ ions may have bulk-like coordination. The ΔEf for three-dimensional (LiO2)16 and (LiO2)18 clusters are −1.36 eV/LiO2 and −1.44 eV/LiO2, respectively as compared to −1.85 eV/LiO2 for LiO2 solid. This energy trend also supports the explanation provided here. While our calculations predict planar ring-shaped structures as the lowest energy isomer for (LiO2)n clusters, n = 2−12, the number of possible alternative structures, especially for the large clusters, are very high. It might be possible that the planar rings are not the true global minimum, but represent a very stable local minimum on the potential energy surface. Optimization methods involving genetic algorithms or simulated annealing might be employed in the search of global minimum structures. However, in this study, we have relied upon an extensive search of possible alternative structures, consisting of both planar and nonplanar geometries, some of which are reported in the Supporting Information. Spin in LiO2 Clusters. Another important finding from these calculations is that the LiO2 clusters have high spin states. The amount of spin directly correlates to the size of the clusters. The origin of such high spin can be understood from the electronic structure of LiO2 monomer, which is a doublet with an unpaired electron located in the singly occupied π* antibonding orbital on oxygens. Theoretically, the maximum number of unpaired electrons in LiO2 clusters is equal to the number of LiO2 units present in them, if all unpaired electrons are ferromagnetically coupled. On the other hand, the minimum number of unpaired electrons is either 0 or 1 depending on an even or odd number of LiO2 units in the cluster. For the LiO2 clusters, we have optimized ring structures at the B3LYP level with highest, lowest, and all possible intermediate spin states and found that, with the exception of n = 3, the lowest energy structure always has highest spin, although the energy differences with intermediate spin states can be very small or even zero. The results are summarized in Table S4. The (LiO2)11 cluster provides an example of multiple low energy spin states as six different spin states are separated 816

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Table 1. Gas Phase Reaction Energy (ΔE) and Free Energy (ΔG) As Well As Reaction Free Energy in Solution (ΔGsol) for the Removal of an Oxygen Molecule from LiO2 Clusters Computed at Three Different Levels of Theory ΔE (eV) reaction (LiO2)2 (LiO2)3 (LiO2)4 (LiO2)5 (LiO2)6 (LiO2)7 (LiO2)8

= = = = = = =

Li2O2 + O2 Li3O4 + O2 Li4O6 + O2 Li5O8 + O2 Li6O10 + O2 Li7O12 + O2 Li8O14 + O2

ΔG (eV)

ΔGsol (eV)

B3LYP

MP2

G4MP2

B3LYP

MP2

G4MP2

B3LYP

MP2

G4MP2

0.94 0.85 0.91 0.84 0.82 0.77 0.79

0.72 0.81 0.67 0.62 0.56 0.52 0.54

0.67 0.68 0.73 0.62 0.58 0.53

0.61 0.40 0.51 0.43 0.46 0.46 0.42

0.39 0.36 0.27 0.21 0.20 0.21 0.18

0.34 0.23 0.33 0.30 0.20 0.22

0.55 0.15 0.30 0.23 0.26 0.27 0.22

0.33 0.11 0.06 0.01 0.00 0.02 −0.02

0.29 −0.02 0.12 0.10 0.00 0.03

Table 2. Gas Phase Activation Energy (ΔE‡) and Free Energy (ΔG‡) As Well As Free Energy of Activation in Solution (ΔG‡sol) for the Removal of an Oxygen Molecule from LiO2 Clusters Computed at Three Different Levels of Theory ΔE‡ (eV) reaction (LiO2)2 (LiO2)3 (LiO2)4 (LiO2)5 (LiO2)6 (LiO2)7 (LiO2)8

= = = = = = =

Li2O2 + O2 Li3O4 + O2 Li4O6 + O2 Li5O8 + O2 Li6O10 + O2 Li7O12 + O2 Li8O14 + O2

ΔG‡ (eV)

ΔG‡sol (eV)

B3LYP

MP2

G4MP2

B3LYP

MP2

G4MP2

B3LYP

MP2

G4MP2

0.57 0.62 0.81 0.74 0.75 0.58 0.61

0.53 0.85 1.43 1.65 1.61 1.12 1.27

0.53 0.61 1.00 1.15 1.14 0.75

0.58 0.54 0.73 0.70 0.77 0.68 0.70

0.54 0.77 1.36 1.61 1.63 1.22 1.37

0.54 0.53 0.92 1.21 1.13 0.84

0.20 0.32 0.71 0.59 0.64 0.56 0.58

0.15 0.55 1.33 1.51 1.49 1.11 1.25

0.16 0.32 0.90 1.10 1.00 0.73

lithium peroxide while the remaining O−O distances are 1.35 Å. Mulliken population analysis shows that charges on these two oxygen atoms are 2 times higher than the charges on other oxygen atoms in the cluster (−0.55e versus −0.26e). In addition, these two O atoms do not carry any electron spin, while the rest of the O atoms have 0.5 electron spin as expected in the superoxide units. While the rest of the cluster is still superoxide-like, the evidence provided above clearly shows that the part of the cluster from which O2 is released has become peroxide. Thus, sequential release of O2 molecules will complete the transformation of lithium superoxide clusters into lithium peroxide. The reaction free energies (ΔG) for the removal of O2 from (LiO2)n, n = 2−8, clusters are shown Table 1. For comparison, free energies at T = 0 K (i.e., ΔE), and in solution (ΔGsol) are also included in the table. While ΔG values are computed using B3LYP, MP2, and G4MP2 model chemistries, the G4MP2 results are used for discussions as they are expected to be the most accurate. The calculations suggest that O2 removal from LiO2 clusters is an endergonic process (ΔG > 0). The ΔG is maximum for the LiO2 dimer (0.34 eV), and stays around 0.2− 0.3 eV for LiO2 clusters between n = 2−8. While the trend remains the same, the B3LYP predictions of ΔG are more positive than G4MP2. MP2 numbers are closer to G4MP2 than B3LYP. Nevertheless, they all suggest that O2 removal from the gas phase LiO2 clusters is not a thermodynamically favorable process. In comparison, ΔGsol for the removal of O2 from LiO2 clusters in acetone, with the exception of LiO2 dimer, is marginally positive, suggesting that disproportionation might actually be favorable in solution. The disproportionation of solid LiO2 to Li2O2 is thermodynamically favorable in ambient conditions.41 The activation free energies (ΔG‡) for the removal of O2 molecules from LiO2 clusters are listed in Table 2. The barrier is smallest for the LiO2 dimer (0.54 eV) and gradually increases until it reaches a maximum at n = 5. The maximum barrier is 1.2 eV while the average barrier for O2 removal from large LiO2

clusters is close to 1 eV. The B3LYP theory significantly underestimates the barrier calculations while MP2 theory overestimates them. For example, the average barrier predicted by B3LYP is 0.7 eV and for MP2 it is 1.4 eV. With the exception of the LiO2 dimer, the change in ΔG‡ from gas phase to solution is small. For the LiO2 dimer, however, the activation energy changes significantly from 0.54 eV in the gas phase to 0.16 eV in solution. The mechanisms and energetics of the O2 evolution from LiO2 dimer and some of the larger LiO2 clusters are compared in Figure 5. Three important conclusions can be drawn from

Figure 5. Disproportionation mechanisms and energetics of (LiO2)2 (gray), (LiO2)5 (green), and (LiO2)6 (red) clusters in gas phase using the G4MP2 theory. (LiO2)5 and (LiO2)6 have similar mechanisms, and, therefore, only (LiO2)6 has been shown.

the trends shown in this figure as well as in Figure 2a. First, the comparison of ΔGf in Figure 2a indicates that the formation of larger clusters from LiO2 monomer is thermodynamically more favorable than the formation of LiO2 dimer. Second, the thermodynamics of the O2 evolution are different in larger LiO2 clusters than in the dimer, especially in the presence of a solvent. The reaction free energy (ΔGsol) for the disproportio817

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nation of LiO2 dimer in acetone is significantly positive (0.3 eV) in comparison to the average ΔGsol for the disproportionation of larger LiO2 clusters (≈ 0.1 eV or less). Finally, the kinetics of O2 removal is significantly different. The activation barrier for the O2 evolution is significantly higher in larger clusters than in the LiO2 dimer (1.0 eV vs 0.5 eV). The difference is even more noticeable in solution (1.0 eV vs 0.2 eV). The slow kinetics of the O2 dissociation and enhanced stability perhaps indicate that LiO2 clusters are not just transient intermediates, but they may have long enough lifetime to form larger superoxide agglomerates, say, (LiO2)N, which will then disproportionate into lithium peroxide over time. Our calculated gas phase activation barrier for the dimer is consistent with what Bryantsev et al. have reported45 and their conclusion that the dimer will have a very short lifetime. The dimer seems to be an exception, perhaps due to its low stability compared to the larger clusters. In Scheme 2, we have shown two possible mechanisms of how Li2O2 could be formed from LiO2. The first involves early

For some clusters, several spin states coexist within a very small energy gap even at room temperature. 3. The LiO2 dimer has a disproportionation barrier of ∼0.5 eV, in agreement with previous calculations. However, the barriers for the disproportionation of the larger clusters can be much higher than the dimer, with some of the ring structures having barriers of ∼1 eV. This means that if disproportionation goes through clusters other than the dimer, it may be much slower, and LiO2 in some form may survive long enough to be incorporated into the growing discharge product. While more exploration of the disproportionation kinetics of bulk LiO2 is needed, these results can explain how LiO2 in some form could get incorporated into the discharge product as evidenced by several recent experimental studies.9,10,27,46,48

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ASSOCIATED CONTENT

S Supporting Information *

Energies of alternative planar-ring, stacked-ring, and linearchain isomers are listed and compared at different levels of theory. This material is available free of charge via the Internet at http://pubs.acs.org.

Scheme 2. Possible Mechanisms of Li2O2 Formation from Disproportionation of LiO2

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] *E-mail: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support for this work came from the U.S. Department of Energy, Basic Energy Science, Joint Center for Energy Storage Research under Contract No. DE-AC02-06CH11357. The calculations were performed using the computational resources available at the Argonne National Laboratory Center for Nanoscale Materials (CNM) and the computing resources provided on Fusion and Blues, high-performance computing clusters operated by the Laboratory Computing Resource Center at Argonne National Laboratory.

disproportionation of LiO2 dimer leading to the formation of Li2O2 (in red). The second involves late disproportionation of (LiO2)N particles into Li2O2 (in blue). The (LiO2)N particles are formed as metastable intermediates due to the aggregation of small LiO2 prenucleation clusters. The discharge product formed in the early and late disproportionation mechanisms could have different electronic properties and perhaps morphologies. There are several recent studies that report evidence for lithium superoxide-like species in the discharge product of a Li−O2 cell. Shao-Horn and co-workers reported46 evidence from X-ray absorption near edge structure (XANES) for surface superoxide species. Amine and co-workers have reported Raman and magnetic measurements and kinetics experiments indicating that the discharge product under some conditions can have an O-rich component with superoxide-like character and a Li2O2 component.27,47 In summary, we have reported calculations of the structures and energies of (LiO2)n clusters for n = 2−12, 16, 18 using density functional theory, along with higher level G4MP2 calculations of some of the clusters for validation. The main conclusions from this study are as follows: 1. The lowest energy (LiO2)n clusters exhibit planar ring structures for up to n = 12 and the stability of the rings increases with the size of the clusters. After n = 12, threedimensional stacked-ring structures become energetically more stable. 2. The clusters have high electronic spin states, with the spin multiplicity increasing with the size of the clusters.

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REFERENCES

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The Journal of Physical Chemistry Letters

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