Electronic Structure of Lithium Peroxide Clusters and Relevance to

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Electronic Structure of Lithium Peroxide Clusters and Relevance to Lithium−Air Batteries Kah Chun Lau,† Rajeev S. Assary,†,‡ Paul Redfern,§ Jeffrey Greeley,∥ and Larry A. Curtiss*,†,∥ †

Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States Chemical & Biological Engineering, Northwestern University, Evanston, Illinois 60208, 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 prospect of Li−air(oxygen) batteries has generated much interest because of the possibility of extending the range of electric vehicles due to their potentially high gravimetric density. The exact morphology of the lithium peroxide formed during discharge has not been determined yet, but the growth likely involves nanoparticles and possibly agglomerates of nanoparticles. In this article, we report on density functional calculations of stoichiometric lithium peroxide clusters that provide evidence for the stabilization of high spin states relative to the closed shell state in the clusters. The density functional calculations indicate that a triplet state is favored over a closed shell singlet state for a dimer, trimer, and tetramer of lithium peroxide, whereas in the lithium peroxide monomer, the closed shell singlet is strongly favored. Density functional calculations on a much larger cluster, (Li2O2)16, also indicate that it similarly has a high spin state with four unpaired electrons located on the surface. These results have been confirmed by higher level G4 theory calculations that indicate that the singlet and triplet states of the dimer are nearly equal in energy and that the triplet state is more stable than the singlet for clusters larger than the dimer. The high spin states of the clusters are characterized by O−O moieties protruding from the surface, which have superoxide-like characteristics in terms of bond distances and spin. The existence of these superoxide-like surface structures on stoichiometric lithium peroxide clusters may have implications for the electrochemistry of formation and decomposition of lithium peroxide in Li−air batteries including electronic conductivity and charge overpotentials.

1. INTRODUCTION The rechargeable Li−air (or Li−O2) battery is receiving a great deal of interest because, theoretically, it can store significantly more energy than the conventional lithium ion batteries.1−3 Since it was first introduced,4 much interest has been focused on the discharge and charge processes occurring in the Li−O2 system. In contrast to the conventional lithium ion batteries, the main discharge product of the Li−air cell is supposed to be lithium oxide. During electrochemical discharge, the lithium anode is oxidized by releasing an electron to the external circuit to produce lithium ions in the electrolyte, whereas the oxygen is reduced at a cathode surface to form, in the case of nonaqueous electrolytes, lithium peroxide (Li2O2) or lithium oxide (Li2O). During recharge, the lithium oxide discharge products should be reconverted to lithium and oxygen. Electrolyte decomposition can also occur during discharge and charge, which will cause eventual cell failure. In order to understand the charge and discharge chemistries taking place in the Li−air battery, it is necessary to have a fundamental knowledge of the electronic and structural properties of lithium oxides. So far, the phase diagram of the © 2012 American Chemical Society

Li−O2 system remains elusive and far from complete. In the condensed phase, the most commonly known stoichiometric LixOy compound is the thermodynamically stable Li2O (i.e., lithia) and a Li2O2 crystalline phase.5 Similar to Li2O, the Li2O2 crystalline bulk is known to be a semiconductor with an electronic band gap of ∼4.9 eV from theoretical predictions.6−9 In order to explain the electronic conductivity and charge transfer required in the redox chemistry of an operating Li−O2 cell cathode electrode, a Li-vacancy induced metallicity in bulk Li2O2 has recently been proposed.6,10 The formation energy of a Li-vacancy in bulk crystal is predicted to be ∼3.0 eV and depends on the vacancy concentration. The Li2O2 formation observed as the discharge product of a Li−O2 cell is generally found to be as nanoparticles.8,11 Since the formation and growth of Li2O2 products in Li−air batteries is currently not well-understood, it is of much interest to investigate computationally the structural and electronic Received: June 19, 2012 Revised: August 9, 2012 Published: September 26, 2012 23890

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Figure 1. Lowest energy structures (singlet and triplet) for the lithium peroxide monomer, dimer, trimer, and tetramer at the B3LYP/6-31G(2df) level of theory. Selected O−O bond distances are given along with Mulliken charge on those O−O moieties in parentheses. The Mulliken spin is also given for the triplet states (first number in parentheses for the triplets). Note that, for the triplet dimer, the second unpaired electron is delocalized over the other oxygens.

out geometry optimization of a large number of possible structures to locate the most stable ones. The lowest energy structures were further refined by subsequent geometry optimization using the B3LYP/6-31G(2df) level of theory. A (Li2O2)16 cluster was also optimized at the B3LYP/6-31G(d) level, but without the refinement with the larger basis set. We also used the PBE functional,16 as implemented in the Vienna ab initio simulation package (VASP),17,18 to assess the effect of a different functional and a plane wave basis set on the results. Both nonspin-polarized and spin-polarized calculations were carried out. The projector augmented wave (PAW)19 method was used to represent the interaction between the core electrons and valence electrons, and the Kohn−Sham valence states (2s for Li; 2s2p for O) were expanded in plane wave basis sets up to a kinetic energy cutoff of 400 eV. For the (Li2O2)16 cluster, the system was computed in 30 × 30 × 30 Ǻ 3 simulation cells. For comparison with the B3LYP results, plane wave calculations were also carried out on the smaller clusters, n = 1−4, using a 16 × 16 × 16 supercell. The convergence criterion of the total energy was set to be within 1 × 10−5 eV within the Γ-point integration, and all the geometries were optimized until the residual forces became less than 1 × 10−2 eV/Ǻ .

properties of small Li2O2 clusters as they may provide insight into the nucleation of Li2O2 during battery discharge as well as the properties of larger nanoparticles. In this article, we report on a density functional study of the structure of (Li2O2)n clusters with n = 1−4. We have investigated many possible structures of the clusters and also considered their electronic states. Surprisingly, our calculations show that, with increase in size, the triplet state becomes stabilized relative to the singlet state. We have confirmed these results using high level G4 calculations.12,13 Finally, in order to investigate this further on larger clusters, we have carried out density functional calculations on a 64 atom Li2O2 cluster to determine its spin state and structure. The computational methods used on the clusters are described in section 2. The structural and electronic states of the Li2O2 clusters are presented in section 3 along with an analysis of the electronic structure of the clusters. Conclusions and possible implications for Li−air batteries are presented in section 4.

2. COMPUTATIONAL METHODS Two density functional methods were used in this study. The first is the B3LYP density functional method14 as implemented in the Gaussian09 code.15 The smaller clusters (Li2O2)n, n = 1− 4, were initially studied using the 6-31G(d) basis set to carry 23891

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Table 1. Energies of Triplet State Relative to Singlet State (in eV) of (Li2O2)n Clusters, n = 1−4, at Various Levels of Theory; Also Given in the Table Is the Energy of the Quintet State Relative to the Singlet for the (Li2O2)16 Cluster B3LYP/6-31G(2df)//B3LYP/631G(2df) b

N

state

1

singlet (1) triplet (1) singlet (4) triplet (4) singlet (11) triplet (11) singlet (22) triplet (22) singlet (1) quintet (1)

2 3 4 16

PBE/PW//PBE/PWa

G4 theory

Ee

G298

Ee

Ee

G298

0.00 0.96 0.0 −0.04 0.0 −0.48 0.0 −0.45 0.0d −1.09d

0.0 0.86 0.0 −0.21 0.0 −0.72 0.0 −0.64 0.0d −1.39d

0.0 0.88 0.0 −0.02 0.0 −0.49 0.0 −0.55 0.0 −1.03

0.0 1.27 0.0 0.55 0.0 −0.08 0.0c −0.17c

0.0 1.17 0.0 0.36 0.0 −0.32 0.0c −0.35c

a

PBE functional with plane wave (PW) basis set (see text). bThe number of structures investigated for each state is given in parentheses. In some cases, these structures were investigated at the B3LYP/6-31G* level, and only the most stable were refined at the larger basis set level. The initial guess for the triplet state was usually the singlet state geometry. cG4MP2 theory. dB3LYP/6-31G(d)//B3LYP/6-31G(d) level of theory. The unrestricted triplet converges to the quintet due to spin contamination. There is no significant spin contamination present in the triplet states of the smaller clusters (n = 1−4), which were done using unrestricted B3LYP wave functions.

Figure 2. Energies of triplet state relative to singlet state (in eV) of (Li2O2)n clusters, n = 1−4, at various levels of theory.

Figure 3. Energies of all 42 tetramer (Li2O2)4 structures relative to the lowest energy (Li2O2)4 triplet configuration (structure 14, triplet in Figure 1) based on the B3LYP/6-31G(d) level of calculation. Note that structure 19 (triplet) has the same energy and geometry as that of structure 14. 23892

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Figure 4. G4(MP2) free energies (in eV) of nine (Li2O2)3 singlet structures relative to the lowest energy (Li2O2)3 triplet structure (corresponding to the B3LYP triplet structure in Figure 1).

The G4 method,13 which is based on CCSD(T) theory, was used to obtain accurate energies for the singlet−triplet energy differences of the smaller clusters (Li2O2)n, n = 1−4. This method was used to assess the predictions of the density functional methods for the singlet−triplet energy differences of the clusters.

normal peroxide O−O distance of about 1.55 Å (Figure 1). These O2 moieties have bonds to two Li atoms in the cluster as seen in Figure 1. More accurate G4 theory was used to check on the validity of the density functional results for the singlet−triplet energy differences as there may be some question of reliability of density functional methods for excited state energies. G4 theory, which is based on coupled cluster (CCSD(T)) energies, gives similar trends for the singlet−triplet energy differences as the B3LYP and PBE functionals, although the energy differences are somewhat smaller (Figure 2). In contrast to the density functional results, G4 theory indicates that, for the dimer, the singlet is still more stable than the triplet, although it does indicate that the triplet singlet gap decreases from monomer to the dimer, in agreement with the trend found from the density functional results. In the case of G4 theory, it is not until the cluster size is n = 3 that the triplet becomes more stable than the singlet. In terms of free energy, the triplet trimer is more stable than the trimer singlet by 0.32 eV (Table 1) compared to 0.78 eV predicted by the B3LYP/6-31G(2df) level of theory. Further, we have performed G4MP2 calculations for the nine lowest energy singlet conformers, and the computed free energy was compared against the free energy of lowest energy triplet trimer in Figure 4. As shown, the trend of singlet−triplet free energy differences remains consistent with the results of B3LYP/6-31G(2df). The triplet state remains energetically more favorable than the closed shell singlet. The triplet tetramer is more stable by 0.17 eV than the singlet tetramer at the G4 level (0.35 eV for the free energy comparison). Thus, the increased stability of the triplet state over the singlet state for small lithium peroxide clusters is confirmed by high level theory. 3.2. Energy and Structure of (Li2O2)n, n = 16. The structure and electronic state of a much larger cluster with 16 Li2O2 monomers was investigated using density functional methods and found to have a quintet ground state for the structures investigated. The structures were obtained in the following manner. First, a molecular dynamics simulation with the initial structure taken from bulk lithium peroxide20 was performed. Next, the resulting structure was optimized as a singlet state at the PBE/PW level and then done allowing spin polarization. This led to the quintet state (4 unpaired electrons)

3. RESULTS AND DISCUSSION 3.1. Energy and Structure of (Li2O2)n, n = 1−4. The B3LYP/6-31G(2df)-optimized structures of the most stable singlet and triplet state clusters located for n = 1−4 are shown in Figure 1. The singlet−triplet energy differences of the n = 1− 4 clusters for the lowest energy structures located are given in Table 1 and plotted in Figure 2. Numerous possible structures were investigated for the clusters. The structures were chosen based on likely interaction scenarios between the monomers. Although the lowest energy structures located in Figure 1 are not necessarily the global minima, the results shown in Figure 2 and Table 1 should give a good account of the singlet−triplet energy differences. In Figure 3, the relative energies of the 42 (Li2O2)4 structures that were investigated are given with respect to the lowest energy (Li2O2)4 triplet configuration. We also investigated the effect of a larger basis set with diffuse functions, B3LYP/6-311+G (2df), and found little change (Figure S1 in Supporting Information). The B3LYP density functional results in Table 1 and Figure 2 indicate that, for a cluster size of n = 2, the triplet is more stable than the singlet based on electronic energies (Ee), although the difference is small ( 1, can be characterized (see Figures 1 and 5) by the presence of one or more O−O superoxide-like pairs based on their bond distances (1.3−1.4 Å) and a localized unpaired spin as discussed above. Therefore, we refer to these particular O−O species on the surfaces of the lithium oxide clusters as superoxide-like surface structures since their electronic properties are similar to what is found for O−O pairs in bulk lithium superoxide.5 We note that these high spin clusters with the distinct superoxide-like structures still have Li2O2 stoichiometry. These superoxidelike surface structures likely act to relieve the strain present in small clusters, which prevent the Li2O2 units from having their preferred planar geometries. The Li2O2 superoxide-like units are characterized by a net positive charge and a bent structure, which are balanced by Li2O2 units with a net negative charge and a more planar structure. One would also expect that these types of superoxide-like surface structures might also be present in some high energy crystal facets. We have found this to be true in spin polarized studies of Li2O2 surfaces.9 If these superoxide-like structures are present on surfaces of stoichiometric lithium peroxide nanoparticles formed in lithium−air batteries, they could have significant implications for charge and discharge chemistries. For example, these surface defect sites may play a role in surface conductivity mechanisms such as has been suggested by Siegal et al. in a study23 of crystalline faces of Li2O2 and in lowering the charge overpotential. They may also affect electrolyte surface reactions at the interfaces of the lithium peroxide surface and result in electrolyte decomposition, which can cause cell failure. The

possible existence of such surface species should be considered in modeling of charge and discharge chemistries of lithium peroxide.

4. CONCLUSIONS The following conclusions can be drawn from this theoretical study of the structures and electronic states of Li2O2 clusters (n = 1−4, 16). (1) Density functional calculations based on B3LYP and PBE functionals predict that (Li2O2)n clusters, n = 2−4, will have triplet spin states in the gas phase. High level G4 theory calculations confirm that the triplet state is significantly stabilized relative to the singlet in these clusters compared to the monomer. The G4 results indicate that singlet and triplet states of the dimer are nearly equal in energy and that the triplet state is more stable than the singlet for clusters larger than the dimer. The density functional calculations also show that an n = 16 cluster has a high spin state. (2) The high spin states of the clusters can be characterized by O−O pairs protruding from the surface but still chemically bonded to the Li of the clusters. These O−O pairs have short distances of 1.3−1.4 Å compared to 1.5−1.6 Å for a peroxide pair, which is also present in the clusters. (3) The distinct O−O pairs found on the high spin stoichiometric Li2O2 clusters can be characterized as superoxide-like surface structures because they have properties similar to bulk lithium superoxide including short O−O distances and a localized unpaired spin compared to no spin for a peroxide pair as found in a Li2O2 bulk crystal. These superoxide-like surface structures may have important implications for the electrochemistry of formation and 23895

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(15) Frisch, M. J.; et al. Gaussian 09, revision B.01; Gaussian, Inc.: Wallingford CT, 2009; see the Supporting Information for complete citation. (16) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (17) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758. (18) Kresse, G.; Furthmüller, J. Efficiency of ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15. (19) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953. (20) Föppl, H. Z. Anorg. Allg. Chem. 1957, 291, 12−50. (21) Bader, A. F. M. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, U.K., 1990. (22) Read, A. E.; Curtiss, L. A.; Weinhold, F. Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint. Chem. Rev. 1998, 88, 899−926. (23) Radin, M. D.; Rodriguez, J. F.; Tian, F.; Siegel, D. J. Lithium Peroxide Surfaces Are Metallic, While Lithium Oxide Surfaces Are Not. J. Am. Chem. Soc. 2012, 134, 1093−1103.

decomposition of lithium peroxide in Li−air batteries, including surface electronic conductivity and electrolyte surface reactions.

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ASSOCIATED CONTENT

S Supporting Information *

Energies of all 42 tetramer (Li2O2)4 structures relative to the lowest energy (Li2O2)4 triplet configuration; total energy based on ab initio molecular dynamics; Bader charge analysis; NBO analysis; complete ref 15. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy Office of Basic Energy Science-Division of Materials Science and Engineering and Division of Scientific User Facilities under contract DE-AC02-06CH11357. J.G. acknowledges a DOE Early Career award from the Office of Science, Office of Basic Energy Sciences, under contract DE-AC02-06CH11357.

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REFERENCES

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