Pathways to triplet or singlet oxygen during the dissociation of alkali superoxides - Insights by multireference calculations of molecular model systems.

Abstract Recent experimental investigations demonstrated the generation of singlet oxygen during charging at high potentials in lithium/oxygen batteries. To contribute to the understanding of the underlying chemical reactions a key step in the mechanism of the charging process, namely, the dissociation of the intermediate lithium superoxide to oxygen and lithium, was investigated. Therefore, the corresponding dissociation paths of the molecular model system lithium superoxide (LiO2) were studied by CASSCF/CASPT2 calculations. The obtained results indicate the presence of different dissociation paths over crossing points of different electronic states, which lead either to the energetically preferred generation of triplet oxygen or the energetically higher lying formation of singlet oxygen. The dissociation to the corresponding superoxide anion is energetically less preferred. The understanding of the detailed reaction mechanism allows the design of strategies to avoid the formation of singlet oxygen and thus to potentially minimize the degradation of materials in alkali metal/oxygen batteries. The calculations demonstrate a qualitatively similar but energetically shifted behavior for the homologous alkali metals sodium and potassium and their superoxide species. Fundamental differences were found for the covalently bound hydroperoxyl radical.


Introduction
The electrochemical oxidation of alkali metals and subsequent reduction of the oxidation products attracts great interest due to the recent development of alkali metal/oxygen batteries. [1,2] Lithium-, sodium-, and potassium-based metal/oxygen batteries are investigated as potential post-lithium-ion battery systems. [2,3] The Li/O 2 system is especially appealing owing to its very high theoretical energy density, which is about ten times higher than that of the lithium-ion battery. [1] A nonaqueous alkali metal/oxygen battery comprises a solid metal anode, a porous separator filled with organic, liquid electrolyte, and a porous cathode that is flooded with the electrolyte. Oxygen is not carried inside the battery; it is provided by the surrounding gas atmosphere at the cathode. Two main processes occur at the cathode of an alkali metal/oxygen battery: 1) discharging, which proceeds with an oxygen reduction reac-tion (ORR), in which electrons, metal ions, and dissolved oxygen are converted to a solid metal oxide; and 2) charging, which is associated with the oxygen evolution reaction (OER), in which decomposition of the solid metal oxide releases oxygen species, metal ions, and electrons. The different alkali metals form different oxygen reduction compounds. [2] Whereas in the case of the Li/O 2 system lithium peroxide (Li 2 O 2 ) is observed as product of the ORR, the superoxide phases NaO 2 and KO 2 are reported for the Na/O 2 and K/O 2 systems, respectively. [3] Depending on the cell configuration and the electrolytes used, also the formation of Na 2 O 2 (mostly as peroxide hydrate Na 2 O 2 ·x H 2 O) has been reported. [4][5][6] Traces of water and protons in the electrolyte can alter the nature of the sodium oxide species formed. [7,8] Although the final product of the ORR in the Li/O 2 battery is lithium peroxide, the importance of lithium superoxide as an intermediate has been demonstrated in experimental studies on ORR and OER. [9,10] On the basis of these studies, the first step of the OER process is described as the reaction from the lithium peroxide to the superoxide [Eq. (1)]: Secondly, disproportionation of the superoxide can take place [Eq. (2)]: The third reaction corresponds to the dissociation of the superoxide intermediate to oxygen, a lithium ion, and an electron [Eq. (3)]: For the ORR process the same elementary reactions-except for the disproportionation-have been proposed to take place in the reverse direction.
Recently, experimental investigations have demonstrated that the generation of singlet oxygen at potentials higher than 3.5 V might play a role in the charging processes of Li/O 2 systems. [12] The highly reactive singlet oxygen has been detected as small fraction of 0.5 % of the produced oxygen species, whereas some part of the singlet oxygen might already have been quenched in side reactions with the cathode materials. Further, Mahne et al. found that singlet oxygen forms at the cathode from the onset of charging in a Li/O 2 system, [13] and it is presumed that the singlet oxygen can destroy the electrode and electrolytes in the battery cell. Mahne et al. even accounted for the main part of the side reactions to singlet oxygen generation. [13] Thus, besides the generation of triplet oxygen, the generation of singlet oxygen needs to be understood in detail in order to develop strategies to avoid its formation and thus to diminish the degradation of the cathode materials. The formation of singlet oxygen has also been detected as the main driver for degradation in Na/O 2 cells. [14] The ORR and the OER in alkali metal/oxygen systems have already been investigated by several theoretical studies. Calculations of the bulk phase of reduced or oxidized compounds and surface as well as molecular or cluster structures have been reported. DFT calculations of the OER mechanism on different low-index surfaces of lithium peroxide provide understanding of the formation superoxide intermediate as well as the dependence on the surface orientation. [15] The energetically preferred OER path takes place via superoxide intermediates. Also, DFT calculations of the mixture of Li 2 O 2 /LiO 2 as bulk phase were used to explain magnetic properties of the system. [16] An insight into the LiO 2 disproportionation reaction and its dependence on the cluster size and surface composition has been given by DFT calculations on small clusters. [17] Also, the stability of LiO 2 dimers in the gas phase was evaluated by coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] calculations, which indicated low barriers for the disproportionation to Li 2 O 2 and the triplet oxygen molecule. [18] On the basis of these studies Mahne et al. identified disproportionation as a possible source of singlet oxygen. [13] Furthermore, the stability of different lithium peroxide and sodium peroxide clusters as well as superoxide clusters has been determined by means of the surface energy of the corresponding oxides. [19] Also, molecular lithium and sodium superoxides containing just one alkali metal atom have been investigated. These model systems have the advantage that a higher level of theory could be used for their description, namely Møller-Plesset perturbation theory of the fourth order (MP4), CCSD(T), and complete active space self-consistent (CASSCF) calculations with an active space smaller than (7,8). These calculations have been used to estimate the bond dissociation energies, which have been compared to experimental results of kinetic gas-phase studies at high temperatures. [20][21][22] So far, a computational study that includes the role of singlet oxygen in the reaction mechanism at a molecular level has not been performed.
Thus, the focus of this work was to investigate the reaction mechanism of the OER (related to the charging process) by employing a model system for which singlet oxygen generation can be considered in detail. Our starting point is the intermediately present lithium superoxide and the dissociation reaction towards the triplet/singlet oxygen molecule and lithium. In order to employ highly accurate multireference post-Hartree-Fock methods such as CASSCF, complete active space perturbation theory of the second order (CASPT2), and multireference configuration interaction (MRCI), we chose molecular lithium superoxide as model system, since it contains just three atoms. The chosen methods are especially relevant for the description of excited states and accurate calculations of their dissociation processes.
Our goal was to identify whether the formation of singlet oxygen can take place from lithium superoxide on the molecular level. This goal was achieved by calculating the potentialenergy surfaces of different electronic states during the dissociation of lithium superoxide. Furthermore, we investigated whether the obtained dissociation behavior is similar for other alkali metal superoxides, namely, sodium superoxide and potassium superoxide. With the same question in mind, we considered similarities and differences between the alkali metal systems and the covalently bound system of the hydroperoxyl radical. Furthermore, we performed first test calculations for the LiO 2 system including solvent effects of the electrolyte in order to qualitatively study their influence on the dissociation path. We believe that our tailored model system allows the fundamental underlying chemistry of the alkali metal/oxygen systems to be understood and that it can be used to make suggestions on how to avoid the formation of singlet oxygen molecules.

Computational Details
All quantum chemical calculations were performed by using the software package MOLPRO v.2015.1. [23,24] The structure optimizations of the molecular superoxides HO 2 , LiO 2 , NaO 2 , and KO 2 utilized the Hartree-Fock (HF) method, the multireference configuration interaction (MRCI) approach, the complete active space selfconsistent field (CASSCF) method, [25,26] and the second-order complete active space perturbation theory (CASPT2) [24] over the lowest doublet state. For the elements H, O, Li, and Na the Dunning-type basis sets (aug)-cc-pVXZ (X = D,T,Q,5) were employed. [23,[27][28][29][30][31] Basisset convergence was reached for (aug)-cc-pV5Z; thus, this basis set was applied for most of the calculations. The augmented functions have nearly no influence on the structure and energetics, so diffuse functions were just used in test calculations. These basis sets were not available for the element K; hence, we used the def2-QZVPD basis set. [32] In addition, we tested the def2-QZVPD basis set for the element Na to test the comparability to the Dunning-type basis set. The point group of the hydroperoxyl radical (HO 2 ) was determined to be C s , and the point group of the superoxides MO 2 to be C 2v (M = Li, Na, K). The minimum structures were confirmed by frequency calculations at the CASSCF/CASPT2 level of theory. On the basis of the optimized structures, potential-energy surfaces (PES) were calculated by using the MRCI, CASSCF, and CASPT2 methods and remaining symmetry. Thereby, we considered doublet and quartet spin states.
The CASSCF calculations employed the state average procedure (SA-CASSCF), and all states were chosen to have equal weights. Different number of states were used and tested for the SA-CASSCF calculations. The active space of LiO 2 and NaO 2 consisted of 13 electrons in 12 active orbitals [CASSCF (13,12)]; the orbitals are shown in Figure S1 of the Supporting Information for LiO 2 as an example. The orbitals of the active space were chosen by considering different relevant points at the PES of the dissociation. The most important orbitals for the bonding nature and the description of the dissociation process of the alkali metal superoxides are the highest occupied p Ã OO orbitals of oxygen and the lowest unoccupied atomic orbital of the alkali metal atom 2s Li . Three virtual orbitals in the active space were Rydberg orbitals for a better description of correlations between metallic states and energetically high orbitals. These Rydberg orbitals contain higher molecular orbitals of oxygen and their linear combination with higher atomic orbitals of the metal atoms. A stable active space of KO 2 was obtained by considering 13 electrons in 9 active orbitals [CASSCF (13,9)], whereby the three Rydberg orbitals 3p OO , 4p OO , 3p Ã OO are removed compared to LiO 2 /NaO 2 because of a lower stability of the active space, probably due to the use of the non-correlation-consistent basis set. The active space of HO 2 consisted of 13 electrons in 9 active orbitals [CASSCF (13,9)]. The orbitals of the active space are shown in Figure S2 of the Supporting Information. The orbitals of HO 2 contain bonding contributions between oxygen orbitals and the 1s hydrogen orbitals. The same active spaces were selected for the MRCI calculations. Furthermore, the oxygen molecule in its triplet and singlet state as well as the superoxide anion O 2 À were calculated at the CASSCF(12,8)/CASPT2 level of theory with a cc-pV5Z basis set. The calculated bond lengths were determined to be 1.210 ( 3 O 2 , 3 AE g À ), 1.220 ( 1 O 2 , 1 D g ), and 1.357 (O 2 À , 2 Q g ).
A natural bond orbital (NBO) analysis with the NBO6.0 program was performed at the CASSCF level of theory to characterize the electronic states regarding their chemical bonding nature. [33] The NBO method is based on the transformation of atomic basis functions to an orthonormal set of natural atomic orbitals (NAOs) with known occupation. The NAOs are used to form a set of polarized and hybrid coefficients, which are used to create the NBOs. In contrast to natural orbitals, NBOs are localized at one or two atoms. In the context of the NBO method the Wiberg bond index (WBI) was calculated. WBIs are the sum of the square nondiagonal matrix elements between atoms in the NAO representation. The analysis was employed for single states of different symmetry at the optimized ground-state structures. For the KO 2 system the bonding analysis was performed by using the restricted active space self-consistent field method RASSCF (13,9) with the restriction of only considering the main configuration interaction (CI) state. The reason for this is a strong mixing of states by using the non-correlation-consistent basis set.
In order to study superoxide dissociation we constructed potentialenergy surfaces (PESs) of the molecular systems. The PES in two dimensions were calculated by considering four electronic states for the HO 2 radical and eight electronic states for the MO 2 radicals; for the PES in three dimensions we considered four electronic states. Two fundamental different two-dimensional PES were generated: a PES created by linearly interpolated internal coordinates (LIIC), which we denote PES LIIC , and a PES with a fixed OÀO bond length, which we call PES fOO .
For the PES LIIC the starting point was chosen to be the superoxide energy minimum R GS . The final point was chosen to be a structure for which the energy states as well as the CI vectors no longer change along the reaction coordinates considering a OÀO bond fixed with the O 2 distance of triplet oxygen (1.210 ). Thereby, a distance of about 4.000 for LiO 2 and 4.500 for NaO 2 between the alkali metal atom and the center of the oxygen dimer was reached, which is denoted R Diss . Thus, the interpolation formula [Eq. (4)]: with n as step number and N as total number of calculated points was employed. For PES LIIC 52 points ranging from equilibrium distance R GS to R Diss were calculated for the different superoxides.
For the PES fOO calculations the OÀO bond lengths of the optimized superoxide structures were employed. Fixing the OÀO bond had two reasons. First, the OÀO distance variation during the dissociation ( % 0.15 ) does not change the qualitative picture of the dissociation pathway. Whereas the qualitative order of electronic states is unchanged, the energetics significantly changes. Thus, these PES fOO were used to qualitatively interpret the dissociation paths. Second, accounting for a change in the OÀO distance decreases the stability of the active spaces in many cases. This decrease in stability arises because higher-order orbitals of the oxygen atoms participate in the active space during dissociation. Including all orbitals would lead to too large an active space, which cannot be treated. For the calculation of the HO 2 radical only the PES fOO was calculated. The PES fOO for the HO 2 radical dissociation was constructed by the variation of the HÀO distance from 0.82 to 4.23 in 51 steps with a fixed bond angle q O-O-H . Due to the higher symmetry of the MO 2 superoxide systems, here the reaction coordinate was selected as distance between the metal atom and the center of the OÀO bond. This distance was varied from 1.06 to 4.23 in 52 steps.
Furthermore, we constructed PESs to prove the obtained structures to be minima and to identify crossing points. The PESs of the alkali metal superoxides were constructed in a reduced symmetry, namely the C s point group. The bond lengths R OOÀLi and bond angles q O-O-M were varied, whereas the OÀO bond distance was fixed. In addition, the PES along the bond lengths R OOÀM and R OÀO were calculated near determined crossing points. Here it was possible to include the change of the OÀO coordinate due to the small crossing point area.
To include solvent effects in the dissociation process, test calculations with the conductor-like screening model (COSMO) model were performed. [34] These test calculations only have to be performed at the restricted open-shell Hartree-Fock (ROHF) level of theory to consider the qualitative influence of solvent effects. The COSMO model is based on an electrostatic energy calculation of a system by applying screened charges. The charges are calculated from the electronic density and screened with a dielectric constant f(e). Diglyme [bis(2-methoxyethyl) ether] -a solvent commonly used for Na/O 2 batteries -was accounted for in the COSMO model by using e r = 7.23. [35] All molecular structures and orbitals were visualized with the program Chemcraft 1.8. [36] Diagrams have been plotted with the programs Gnuplot 5.0, OriginPro 2016G, and Matlab R2018b. [37,38,39] Results and Discussion

Determination of the molecular structures
Structure optimizations of the superoxide systems were performed at the HF, CASSCF, CASSCF/CASPT2, and MRCI levels of theory. The CASSCF/CASPT2 results are summarized in Table 1, and the results of all other methods in Table S1 of the Supporting Information. Visualization of the two different fundamental structures is shown in Figure 1.
The structure optimization of the molecular superoxides at the MRCI/aug-cc-pV5Z level of theory served as benchmark. The structures, which were optimized by the CASSCF(13,9/ 13,12)/CASPT2/aug-cc-pV5Z (K: def2-QZVPD) methodology, agree very well with the MRCI benchmark. In particular, R OÀM and R OÀO bond lengths vary by less than 0.011 , and the q O-M-O and q O-O-H bond angles by less than 0.318. The differences in structural parameters due to using the cc-pV5Z basis set without diffuse basis functions compared to the aug-cc-pV5Z basis set are very small. Structures obtained by the CASSCF(13,9/ 13,12)/cc-pV5Z approach also agree very well with the benchmark structures, whereas significant differences were obtained by just using the HF method.
The agreement of structural details of molecular LiO 2 with the corresponding experimental results of refs. [22,40] is reasonable, whereas there is a larger deviation from experimental data for the NaÀO bond length of molecular NaO 2 . Also, our calculated KÀO distance is much longer than the related experimental one. Considering the increasing ionic radii from lithium to potassium, we believe our calculated increase in MÀO bond length to be reliable. The small experimental KÀO distance may be due to a packing effect of the condensed KO 2 /Ar phase structure. This conclusion is supported by the comparison of the different MO 2 molecules with solid-state structures. Here, the increase of the MÀO distance from LiO 2 to NaO 2 is similar to the increase from NaO 2 to KO 2 . The comparison of the molecular alkali metal superoxide radicals with the solidstate structures of the alkali metal superoxides is discussed in the Supporting Information (Table S2 and Figure S3).
The HO 2 molecule with C s point group exhibits a doublet ground (D 0 ) state 2 A', and the alkali metal superoxides with C 2v point group have a doublet ground state 2 A 2 . Calculations of the PESs while varying the MÀO bond length and the q O-M-O and q O-O-H bond angles at CASSCF level of theory were carried out to confirm the minimum-energy structures in addition to the frequency calculations. The corresponding Born-Oppenheimer surfaces of the ground state (D 0 ) and the first excited state (D 1 ) are plotted in Figure S4 of the Supporting Information. The superoxides HO 2 , NaO 2 and KO 2 exhibit only one stable structure in the ground state. For LiO 2 a second possible structure with linear configuration but higher relative energy (about 0.75 eV) was identified. Corresponding potential-energy curves of the angle dependence at a higher level of theory including dynamic correlation are plotted in Figure S5 of the Supporting Information. The molecular LiO 2 structure previously calculated at the CASSCF(7,8)/TZP level of theory agrees well with our structure (see Table S1 of the Supporting Information). [22] The linear configuration of LiO 2 was also found by ROHF and CISD calculations in ref. [22].

Analysis of the molecular structures and bonding nature
The structure, bonding nature, and the charge distribution of the hydroperoxyl radical (HO 2 ) are different from those of the alkali metal superoxides. The HO 2 molecule shows a slightly shorter OÀO distance than the alkali metal superoxides and the calculated free superoxide anion (CASSCF(13,8)/CASPT2/cc-pV5Z: 1.357 ), which is in agreement with the experimental data. [39] The WBI, which can be interpreted as the quantum chemical analogue to the bond order, together with the charge distribution indicates polar covalent binding for the angled HO 2 molecule (see Table 2). This bonding nature is also supported by the molecular orbital diagram (see Figure 2 a and Figure S3 of the Supporting Information). There are s OH binding contributions in energetically  [22] 1.809 -1.388 exptl [40] 1.77 AE 0.  [43] 2.10 AE 0.14 37 AE 2 1.33  low lying s OO and s Ã OO molecular orbitals as well as in energetically higher lying p OO and p Ã OO molecular orbitals. All triangle-shaped alkali superoxides MO 2 (M = Li, Na, K) exhibit an OÀO distance that agrees very well with the OÀO distance of the free optimized superoxide anion. The R OÀM distances are strongly increased compared with HO 2 (see Table 1). Interestingly, the R OÀM distance increases more from Li to Na (by about 0.39 ) than from Na to K (by about 0.31 ), whereas the ionic radii would indicate the opposite (increase of 0.26 from Li to Na and 0.36 from Na to K). [44] In accordance with the increasing R OÀM distance, the bond angle q O-M-O decreases. For the metal superoxide radicals the WBI and charge distribution indicates an ionic bonding nature (see Table 2). This ionic character increases slightly from Li (0.92 e) to K (0.96 e), and is responsible for the higher-symmetry molecular structure of the alkali metal superoxides without the presence of a localized bond as in HO 2 . However, the WBI indicates a small covalent binding contribution for LiO 2 . The molecular orbital diagram also indicates the ionic character (see Figure 2 b and Figure S4 of the Supporting Information). The ns M orbital exhibits hardly any overlap with the oxygen orbitals (just slightly for LiO 2 ). Thus, the molecular orbital diagram shows nearly an overlay of the orbital diagrams of the molecular superoxide anion and the atomic metal cation.

Qualitative analysis of the dissociation processes
To evaluate and interpret the dissociation mechanism of superoxide, the calculated PESs of the molecular systems are used in the following. The PESs were constructed as two-dimensional and three-dimensional graphs of the energy for different electronic states over the main reaction coordinates for the dissociation.

Hydroperoxyl radical
The dissociation of the HO 2 radical was calculated along the main reaction coordinate, the HÀO distance, by PES fOO . Therefore, four states (two A' states, two A'' states) were considered. The corresponding atomic charges and WBIs of the two lowest states in the Franck-Condon region are given in Table S3 of the Supporting Information. The dissociation curves and the corresponding character of the states are shown in Figure 3. The ground-state D 0 curve exhibits no crossing with other states during the dissociation and represents the breaking of the localized covalent HÀO bond to give a hydrogen atom and an oxygen molecule in its triplet state ( 3 AE g À ): HO 2 ! 3 O 2 + H.
During this dissociation the molecular orbitals change to molecular orbitals with the shape of atomic orbitals (corresponding CI coefficients are given in Tables S5 and S6 of the Supporting Information). Our calculated ground-state dissociation curve agrees well with the study on the reverse reaction of an H atom with O 2 , which shows no barrier. [45] In addition, Walsh  to OH and O, which we did not consider in the present work. [45] The charge distribution and the WBI for the first excited state (1p * OO !2p Ã OO ) are very similar to those of the ground state and lie only about 1 eV higher in energy. The dissociation path along the first excited state (D 1 ) leads to the generation of singlet oxygen ( 1 D g ). The second, D 2 , state exhibits an excitation from a 2p OO orbital to a 2p Ã OO orbital, which also leads to generation of the singlet oxygen molecule ( 1 D g ).

Alkali metal superoxides
Lithium superoxide: The dissociation curves of the lithium superoxide model system were calculated by a PES LIIC along the main reaction coordinate, which has been determined to be the distance between the lithium atom and the center of mass of the oxygen fragment. The eight lowest states corresponding to different symmetry in the Franck-Condon region (two A 1 states, two A 2 states, two B 1 states, and two B 2 states) were followed during the dissociation, although the focus was on the lowest four states. Next to the excitation to the 2p * OO orbital -as for HO 2 -especially the excitation to the 2s Li orbital is present in the Franck-Condon region (see Figure 4 and Table S8 and the CI coefficients in Table S7 of the Supporting Information). The four energetically lowest states provide the ionic nature for A 2 and B 2 symmetry, and the uncharged van der Waals nature for A 1 and B 1 (see Table S4 of the Supporting Information).
The PES LIIC of the dissociation and the most relevant characters of the states are plotted in Figure 4. The ground-state curve D 0 of the ionic bound lithium superoxide indicates a qualitatively different dissociation path compared with the covalent bound hydroperoxyl radical. The ground-state curve crosses several other curves with different electronic character. This behavior indicates that electronically different dissociation products can be obtained by changing the pathway. Following the ground-state D 0 (1A 2 ) curve, the dissociation path leads to the formation of Li + and O 2 À , which in the gas phase is energetically less preferred than other paths. The thermodynamically most stable dissociation product is reached following the first crossing point (CP 1 ) with the Franck-Condon D 2 state [p * OO (b 2 ) ! 2s Li (a 1 )], which leads to a triplet oxygen molecule ( 3 AE g À ) and a lithium atom for which the spin of the electron is in the opposite direction to those of triplet oxygen. A quartet state with all spins in the same direction and the same energy can be calculated as well (see Figure S7 of the Supporting Information). The results imply that the most preferable reaction path is the formation of the triplet oxygen molecule and lithium. The lithium atom might also be considered as the Li + /e À pair but is not separated in our model. The reaction Li ! Li + + e À would increase the potential energy in the dissociation limit. The crossing point indicates an electron-transfer process at an LiÀ(OO) distance of about 2.75 . To reach the crossing point, an energy of about 2.5 eV corresponding to the PES LIIC is necessary. Considering the reverse reaction of a lithium atom with triplet oxygen, this reaction can take place without or with just a small kinetic barrier.
The PES at the CASSCF/cc-pV5Z level of theory near this first crossing point was calculated to determine the geometric structure including the variation of the OÀO bond length (see Figure 5 and Figure S8 of the Supporting Information). It can be concluded that the OÀO bond-length change has a large influence on the energies but not on the other structural parameters and on the order of the different states. The PES (see Figure 5) shows a crossing seam mainly along the reaction coordinate R OÀO with the lowest energy difference between the states at values of R OOÀM = 2.62 and R OÀO = 1.26 . Thus, the PES LIIC are able to qualitatively describe the dissociation paths in the relevant region. At crossing point CP 1 , the PES LIIC (see Figure 4) and PES (see Figure S8) give evidence that nearly three states, that is, the two ionic states D 0 and D 1 as well as the nonionic state D 2 , are degenerate. The reason for the D 0 /D 1 degeneration lies in the vanishing energy difference between the two p Ã OO (b 2 ) energy levels along the dissociation path. Following the D 0 (1A 2 ) curve even further leads to a second crossing point (CP 2 ), which lies energetically about 0.9 eV higher than CP 1 . The second crossing point, which is characterized by the D 3 and D 4 states [1A 1 ,1B 1 , p Ã OO (b 2 )!2s Li (a 1 )], enables formation of a singlet oxygen molecule ( 1 D g ) and a lithium atom. The second crossing point indicates an alternative electron-transfer step at an LiÀ(OO) distance of about 3.5 (PES-determined structural parameters according to Figure 5 at the CASSCF level of theory: R OOÀLi = 2.91 , R OÀO = 1.23 ). Also at this point, three states are nearly degenerate (see Figure S8 of the Supporting Information). For larger distances the degeneration of the two ionic states vanishes. There is nearly no additional kinetic barrier to overcome. The higher-lying dissociation products were not considered in our study. Calculating the dissociation path of the linear LiO 2 configuration results in the same qualitative picture, which implies that the general dissociation mechanism and the order of states do not change with the configuration of LiO 2 .
Sodium and potassium superoxide: We also calculated the PES LIIC describing the dissociation of sodium superoxide (see Figure 4). For the KO 2 system only the calculation of the PES fOO with a long OÀO distance was possible owing to instabilities of the active space (see Figure S9 of the Supporting Information). The order of the states and the character of the excitations in the Franck-Condon region and during the dissociation are the same as for the LiO 2 system (the CI coefficients of the Franck-Condon region are listed in Tables S8 and S9 of the Supporting  Information, and the WBIs and charge distributions in  Table S4). Thus, curves qualitatively similar to those of LiO 2 were obtained for the molecular systems NaO 2 and KO 2 . For NaO 2 only a slightly longer NaÀ(OO) distance for the first crossing point was found with a value of 2.95 . The energetically lowest path that leads to the formation of triplet oxygen lies about 1 eV lower for NaO 2 and KO 2 compared with LiO 2 . The energetic difference for the generation of triplet or singlet oxygen is between 0.81 and 0.89 eV higher depending on the alkali metal atom. The splitting of the states D 3 and D 4 for the PEC LIIC of NaO 2 occurs due to strong mixing of CI vectors of higher states. The D 3 and D 4 curves are degenerate on the PES fOO , which is physically more likely (see Figure S6 of the Supporting Information). In summary, the calculations demonstrate a similar dissociation mechanism for the ionically bound alkali metal superoxides, and thus, similar to the Li/O 2 system, formation of singlet oxygen should be also possible for the Na/O 2 and K/O 2 systems.

Dissociation energies of the superoxide systems
The dissociation energies were calculated by considering the dissociation limit of the PES fOO curves and correcting the energy dependent on OÀO bond length to the equilibrium energy of triplet oxygen or singlet oxygen to get consistent values for all considered superoxides. In this way we obtained the 3 E theo and 1 E theo values (see Table 3). These values agree well with the values obtained from the PES LIIC for LiO 2 and NaO 2 . The 3 E theo value decreases in the order H > Li > Na > K, whereas the dissociation energies for the set of HO 2 and LiO 2 and for the set of NaO 2 and KO 2 , respectively, are almost equal. Including the thermodynamic correction and considering elevated temperatures of around 1000 K (as used in experimental studies; often flame/combustion studies) increases our calculated dissociation energies marginally by up to 0.1 eV. The large difference between the dissociation energies of LiO 2 and the other alkali metal superoxides may be explained by the smaller ionic radius of lithium, associated with a stronger electrostatic interaction and a small covalent contribution of the LiÀO bonds, which results in higher lying nonionic excited states. We also state 1 E theo for the alkali metal superoxides, for which crossing points to singlet oxygen were observed on the PES. Here, the dissociation energies are about 0.8-0.9 eV higher than for the formation of the triplet oxygen molecule.
Experimental data for dissociation energies of the molecular LiO 2 and NaO 2 systems have been obtained from gas-phase measurements by Plane et al. and Dougherty et al. [20,46] Dissociation energies of molecular KO 2 have been reported in a number of studies, whereby gas-phase measurements of Sorvajäri et al. represent the most recent work. [21] Whereas the data for the experimentally determined dissociation energies of molecular LiO 2 and NaO 2 differ by 0.9 and 0.7 eV, respectively, the experimental values for KO 2 agree well within 0.2 eV (see Table 3). For LiO 2 and NaO 2 the experimental dissociation energies are close to our calculated dissociation energies for the generation of triplet oxygen as well as for the generation of singlet oxygen. The experimental dissociation energies for KO 2 are all close to our calculated case of singlet oxygen formation. However, the dissociation energies are usually determined by flame experiments, which are known to show large measurement errors. [21] Thus, it could be possible that the experimental values are either overestimated or underestimated. Considering a possible overestimation, also the high dissociation energies for LiO 2 and NaO 2 as well as the experimental results of KO 2 would agree with our calculated 3 E theo value. In accordance with the experiments, the dissociation energies of In summary, the comparison with experimental data indicates that the dissociation leads to the thermodynamically favored species, the triplet oxygen molecule. Since the experimental values reported vary and the formation of triplet oxygen is preferred on the calculated PES, it is likely that triplet oxygen was formed in the experiments we consider in our comparisons.
A comparison of our calculated multireference calculations to previous theoretical work is given in Table 3. The dissociation energy of HO 2 calculated at the CASSCF level of theory by Walch et al. is slightly smaller than our value. [45] Earlier theoretical investigations at the QCISD, UMP4, and CCSD(T) levels of theory for LiO 2 , NaO 2 and KO 2 yielded dissociation energies higher in energy than the values we obtained. The calculated dissociation energies by Allen et al., which are the most accurate ones related to the applied level of theory in the literature, as well as highly correlated single-reference calculations using CCSD(T) for LiO 2 and NaO 2 are closer (difference of about 0.3 eV) to our calculated values than UMP4 results determined by Plane et al. [20,22,47] The calculated CCSD(T) dissociation energies for KO 2 are about 0.8 eV higher than our calculated 3 E theo value and in agreement with the experimentally determined value. Our additional calculation of the KO 2 system at the CCSD(T)/def2-QZVPD level of theory resulted also in a formation energy for triplet oxygen of 1.95 eV. Thus, the difference of the 3 E theo value calculated at the CASSCF(13,12)/CASPT2/ def2-QZVPD level of theory compared with the CCSD(T)/def2-QZVPD value appears to be related to a larger multireference character of the system, not, for example, the basis set. A further investigation of the multireference character of the system might be necessary in order to understand the origin of this difference. In summary, the application of a more accurate level of theory, large active spaces for CASSCF, and large basis set allowed us to predict revised theoretical dissociation energies for LiO 2 , NaO 2 , and KO 2 molecular systems.

Influence of the solvent on the molecular model systems
To estimate the impact of a solvent on the dissociation paths, we performed test calculations (only at the ROHF level of theory, Figure 6) on molecular LiO 2 in diglyme, a solvent commonly used in the electrolyte of aprotic Na/O 2 batteries. [51] The obtained PES including solvent effects show a clear impact on the order of the electronic states of the curves. The application of a van der Waals radius for our applied solvent model results in a shift of the ionic curve between the curves for formation of triplet and singlet oxygen molecules. This would indicate a dissociation mechanism that leads either to triplet-oxygen formation or to the superoxide anion and might be an advanta- Table 3. Computed dissociation energies for the formation of triplet oxygen ( 3 E theo ) and singlet oxygen ( 1 E theo ) at the CASSCF(13,12)/CASPT2/cc-pV5Z (K: CASSCF (13,9)/CASPT2/def2-QZVPD) level of theory. The 3 E theo values in parentheses include the thermodynamic correction at 298 K (the temperature of the kinetic experiments at 1100 K would lead to an additional energy change of 0.07 eV). All energies are given in electron volts. 3.14 gas-phase study [20] 3.17 UMP4/6-311G [20] 3.07 flame study [46] 2.30 QZ2P + R + fUMP4(SDTQ) [22] : 2.56 CCSD(T)/CBS-DTQ [47] 2.59 NaO 2 1.26 (1.30) 2.16 gas-phase study [20] 2.09 UMP4/6-311G [20] 1.92 flame study [46] : 2.43 CCSD(T)/CBS-DTQ [47] 1.58 flame study [48] : 1.69 flame study [49] : 1.80 KO 2 1.04 1.83 CPFAAS [a] [21] 1.88 CCSD(T)/aug-cc-pwCV5Z [21] 1.85 flame study [48] 1.80 CCSD(T)/CBS-DTQ [47] 1.79 flame study [49] 1.76 molecular-beam study [50] 1.95 [a] Collinear photofragmentation and atomic absorption spectroscopy. geous way to avoid singlet-oxygen formation, because this dissociation path is not reached. This shows that the dissociation mechanism of the molecular system can be significantly changed in solution by shifting of the electronic-state curves. Also, a shift of the ground-state curve below the curve that leads to generation of the oxygen molecule is possible. In this case a weakly interacting LiO 2 ion pair would be formed, which has been already described in a combined study by DFT-based molecular dynamics simulations and DFT on LiO 2 in the explicit modeled solvents dimethyl sulfoxide, dimethoxyethane, and propylene carbonate. [52] However, a more detailed study will be necessary to investigate the influence of the solvent effects at a higher level of theory as well as in combination with the structure of the metal oxide surface.

Conclusion
To contribute to the fundamental understanding of the chemical processes during the charging of aprotic metal/oxygen batteries (focusing on lithium) and the corresponding decomposition of alkali metal superoxides, we considered the reaction leading from the intermediate lithium superoxide to the oxygen molecule and lithium. We studied the smallest possible model system, namely, molecular LiO 2 , in order to employ a high level of theory that allowed us to investigate different electronic states during the dissociation. Thus, we have performed high-level CASSCF/CASPT2 calculations of the dissociation paths of the molecular structure of LiO 2 to a triplet or singlet oxygen molecule and lithium. The dissociation of lithium superoxide leads via two different crossing points to the thermodynamically preferred triplet oxygen and a lithium atom or to the formation of singlet oxygen and a lithium atom via a path lying about 0.9 eV higher. Thus, the calculations clearly demonstrate two possible dissociation paths leading to a triplet or singlet oxygen molecule. This indicates the possibility of singlet-oxygen formation for the molecular LiO 2 system, but a higher driving force (e.g., higher voltage in the Li/O 2 battery) than for the triplet-oxygen formation is necessary. Depending on the probability of the electron jump from the initial superoxide ground state to the final curve of oxygen-molecule formation, not only the energetically preferred path of the triplet oxygen molecule can be observed but also that of the singlet oxygen molecule. Our calculations give evidence that the peroxide molecule is not necessary as starting point for the generation of singlet oxygen. We note that the potential-energy curves demonstrate fundamental differences between the ionically bound alkali metal superoxides and the covalently bound HO 2 .
Concerning the relevance of the results for metal/oxygen batteries, on the one hand the solvent effects of the environment need to be considered, and on the other hand the surface structure of the solid superoxides plays an integral role. Also, other battery components can influence the reaction. Furthermore, the application of an electric field must be implemented for future work. Regarding the electric field, we interpret our results by assuming a potential shift of stationary states. As for bulk or surface superoxides (experimental and theoretical studies), the gas-phase reaction yields molecular oxygen. Anyhow, we clearly showed that the fundamental chemistry of alkali metal superoxide dissociation to different electronic states can be observed. The gained results indicate similar mechanisms of singlet-oxygen formation for LiO 2 and NaO 2 . Furthermore, formation may be also possible for KO 2 systems by applying higher potentials and, at least for NaO 2 , there is already experimental evidence. [14] The gained knowledge on the underlying dissociation mechanism of the alkali metal superoxides can give access to strategies to avoid the formation of the highly reactive singlet oxygen. First, it could be investigated whether a beneficial choice of solvent/surface structure combination shifts the electronic dissociation curve with the path to the lithium cation and the superoxide anion between the formation curves for triplet and singlet oxygen, so that either triplet-oxygen formation or dissociation to the ionic components takes place (see Figure 7). It is likely that this is also transferable to the disproportionation reaction, but this needs to be investigated in future research. Second, the manipulation of the crossing points by, for example, taking advantage of spin-orbit coupling effects by introducing heavy elements may be an option to avoid singlet-oxygen formation by creating avoided crossings (see Figure 7). These suggestions go beyond the recently addressed use of quenching agents in the electrolyte of metal/ oxygen batteries, [53] which are aimed at deactivating the highly reactive singlet-oxygen species during battery cycling. Our study can help to shape further research studies shedding light on how to prevent the formation of singlet oxygen in the first place, and ultimately help to minimize the deleterious influence of unwanted side reactions in aprotic metal/oxygen batteries.