Electrochemical Oxidation Stability of Anions for Modern Battery Electrolytes: a Cbs and Dft Study Electronic Supplementary Information Molecule an Cc Red Cc Ox Cc an Mp2 Red Mp2 Ox Mp2 an Hf Red Hf Ox Hf Br

This table shows the level that was possible to calculate each step of the CBS calculations. Abbreviations used in the header are, The values show the basis sets that were used for each calculation, thus TQ is aug-cc-pVTZ and aug-cc-pVQZ, and TQ5 is aug-cc-pVTZ, aug-cc-pVQZ and aug-cc-pV5Z.


Introduction
Electrolytes are a key component of batteries and their electrochemical stability windows (ESWs); the potential range wherein none of its components breaks down due to oxidation or reduction, currently limit the capabilities of Li-ion batteries (LIBs). 1 This is due to the high voltages possible for LIBs, often above 4 V.As there is a strong desire to produce even higher voltage cathodes, 2 to allow for even higher energy density LIBs -a very high oxidation stability (preferably 45 V vs. Li + /Li) is aimed at for future electrolytes.For the complementary/competing sodiumion battery technology, 3 currently seeing a rapid increase in attention, the overall development is foreseen to take the same direction.In order to reduce trial-and-error efforts, tools to predict electrochemical stability from chemical structure alone are of large interest.Generally, one way is by in silico screening, which allows for rapid evaluation of candidates for future synthesis.
5][6] This is in part due to the large importance of the solid electrolyte interphase (SEI) passivation layer on the LIB anode, formed by (controlled) electrolyte degradation. 7][10][11] While the reduction limit of the anions has been studied in special solvents such as ionic liquids, [12][13][14] the anions are not in general reduced in LIB (or SIB) electrolytes.The creation of a SEI, partially by anion reduction, is a vast subject outside the scope of this paper.
In contrast, it is the (lithium) salt anion that often sets the oxidation limit, e.g. for ClO 4 À it is 6.1 V vs. Li + /Li, while it is 6.8 V for PF 6 À in the same solvent. 15In contrast, the solvents used are known to have a fair stability vs. oxidation, e.g. the standard blend of ethylene and dimethyl carbonate (EC/DMC) was found to have a limit of 6.7 V vs. Li + /Li. 4 The stability of the anions versus oxidation are therefore often reported whenever novel salts for LIBs or SIBs are reported, either as experimental 16 or computed 17 values.
The experimentally measured ESWs have some variance due to the large number of factors affecting the final value, such as the sweep rate, solvent(s), and electrode(s) used. 4,15,18,19Thus reference values for the ESWs, e.g. the intrinsic anion redox potentials, properties solely of the anions and independent of the electrode/ solvent chemistry and physics, are highly warranted.
For the anion oxidation stability, a common approach is to calculate the HOMO energy, 20 E HOMO , due to the correlation between E HOMO and the oxidation stability (based on the Koopmans theorem 21 ).This approach can for example utilize Hartree-Fock (HF) methods with a small to medium sized basis set (e.g.6-31G* or 6-311+G*) and is applicable to a vast number of compounds as it is computationally inexpensive.
To increase the accuracy, electron correlation must be taken in to account, such as with density functional theory (DFT).4][25] Thus an alternative approach, using the energy difference from a vertical excitation, is often used, either within the Frank-Condon approximation 26,27 (DE v ) or allowing also for geometry relaxation of the excited state 28 to obtain the ionization potential (IP).Both approaches are illustrated in Fig. 1.
As hybrid (or better) functionals are recommended for anions, 22 the computational cost for such calculations is higher than for a pure HF calculation, as this approach at least involves an extra singlepoint calculation and significantly higher if geometry optimization of the excited state is performed.Allowing for geometry relaxation, however, also allows for a thermodynamic approach. 28,29If doublehybrid functionals are used, the computational cost increases even more.
Yet another approach is to study the chemical hardness, Z -a concept that arises naturally from conceptual DFT: 30 which is the resistance of the electronic chemical potential, m, to the changing of the number of electrons.To our knowledge, this is only the second attempt to utilize this concept for the anion ESW. 31 Here the first systematic study involving CCSD(T), MP2, and DFT calculations with a series of basis sets is presented -employed to obtain reference values for the intrinsic anion oxidation potentials at the complete basis set (CBS) limit.[28] 2 Computational methodology A number of anions that all at some point have been considered for LIB electrolytes were selected to be studied in detail (a subset of those previously studied by us 32 ); BF 4 Im(BF 3 ) 2 À and N 5 C 10 À .A number of small anions were also added, as a control set.Additionally, some anions were found to be too large for the CBS method, and only partial results are therefore listed in the ESI.† Single point energies were calculated with each of the following DFT functionals (with the 6-311+G* basis set): B3LYP, [33][34][35] BMK, 36 PBE0, 37 TPSS, 38 TPSSh, 39 the M06 suite (M06, M06-2X, M06-L), 40 VSXC, 41,42 B2PLYP, 43 and mPW2PLYP. 44he B3LYP/6-311+G* equilibrium geometry was used for the anions and for the oxidized and reduced species.
The CCSD(T) calculations with the aug-cc-pVXZ (X = T, Q, 5) basis sets used an extrapolation to the CBS limit: 45 where n is the cardinality of the basis set used, i.e. n = 3 for augcc-pVTZ.This formula, chosen for its simplicity and performance, 46 was used to extrapolate the HF, MP2 and CCSD(T) energies.A separate extrapolation for the correlated part of the energy and the HF energy proved to have no significant effect on the results.Due to the O(N 7 ) scaling of CCSD(T), the rise in computational cost and time is staggering ‡ -making the full CCSD(T)/CBS treatment not feasible at present for all of the anions.Therefore, a mixed CBS method was employed, wherein a correction term is added to a MP2/CBS value (also extrapolated using eqn (2)).The correction term, DCCSD(T), was calculated with MP2/6-31G* and CCSD(T)/ 6-31G* (a small but reasonable basis set for our purpose 47 ): The CCSD(T)/CBS values are then: Values obtained with this method are forthcoming designated as DCBS.
A finite difference scheme was used for the calculation of the chemical hardness: where E N is the energy of the anion, and E N+1 and E NÀ1 are the energies of the reduced and oxidized anion species, respectively.The reduced anion species, E N+1 , could be considered an unphysical approximation, however, this is countered by the experimental observation of such species. 12 HOMO values were extracted from the HF/6-311+G* calculations.The vertical anion oxidation potentials, DE v , were calculated using single point energies (DE v = E NÀ1 À E N ).As the experimental results in general are given vs. Li + /Li, the computed DE v are all shifted by 1.46 V. 8 The Gaussian 09 48 program was used for all calculations and the Int = ExactBasisTransform keyword was used for the CBS calculations in order to ensure that no basis functions that contribute to the energy were pruned away during basis transformations.

Results & discussion
The analysis of the results starts with a comparison between the CBS and the DCBS methods for small anions, followed by a further analysis of DCBS values of larger anions.Thereafter, we compare the performance of different functionals.Each section treats and discusses the HOMO, DE v , and Z approaches.

CBS vs. DCBS
Only a portion of the anions were small enough to allow CCSD(T) calculations with the aug-cc-pV5Z basis sets.Therefore, most anions had to resort to the DCBS measure rather than CBS.As MP2 energies are included in the results of the CCSD(T) calculations, the anions in Table 1 can also function as an internal benchmark for the DCBS method.In general, the values obtained from the DCBS method are close to the values from the CCSD(T)/ CBS method.This holds for both the DE v and Z approaches, showing the general validity of the DCBS method.For BF 4 À , however, the DCBS values are 10% and 6% lower than the CBS values, giving a possible upper bound for possible errors.The BF 4 À values are close to revised experimental value of 6.2 V vs. Li + /Li.Surprisingly, neither the CBS nor the DCBS DE v values for the halides are in the expected order of F À 4 Cl À 4 Br À , instead Cl À 4 Br À 4 F À is observed.Comparing the E ox values with the DE v values for the halides, shows that the DE v value is drastically lower.Similarly, the experimental E ox value of ClO 4 À of 6.0 V vs. Li + /Li is far higher than expected from the CBS calculations, with a DE v value of 4.34 V vs. Li + /Li.It seems as if the atomic anions have a problem with a proper radical description affecting this measure.
The hardness, Z, has the expected ordering for the halides, furthermore, the hardness values are on average closer to the E ox than the DE v values.For example, BF Overall, the hardness has qualitatively similar predictive power, as the DE v values.In general, the Z values are close to the E ox values.Starting with the anions with single E ox values, the Z values are slightly higher, however, the difference is not as large as for the DE v values.BOB and MOB have the largest differences, both 0.8 V, between E ox and Z.The Z values of TFSI, Tf, PF 6 À and AsF 6 À are all within the range of reported E ox values.Looking at the relative stability of BOB and MOB, we note that the difference between the DE v values (0.6 V) is far higher than the Z values (0.1 eV), the latter being closer to the E ox difference.
The E HOMO values show an unexpected ordering of oxidative stability; the third most stable anion, is the BOB anion (À8.81 eV), more stable than TFSI (À8.60 eV) and TDI (À5.54 eV), despite both having higher E ox values than BOB.It is also notable that This journal is © the Owner Societies 2015 E HOMO is the only measure that indicates AsF 6 À to be more stable than PF 6 À , as obtained by the maximum E ox values.

Functional dependency
The analysis of the DFT functional performance is discussed first for DE v and subsequently for Z and grouped by functional type.
The DE v values from DFT and HF in Table 3 in general underestimate DE v -using DCBS as reference -with an average deviation negative for HF and all functionals (except M06-2X, +0.01 V), as seen in Fig. 2.
Starting with HF, one notable issue is the values for F À and HS À , both negative (vs.Li + /Li).In practice this means that HF predicts that these anions would reduce Li + .HF also has the highest average and standard deviations.Notably, the Hu ¨ckel anions (N 5 C 2n À , excluding N 5

À
) have far lower values than the DCBS reference, with the difference ranging from 1.47 V to 2.09 V.The highly symmetric and quite special anion N 5 À is, however, slightly higher in energy than the reference, by 0.18 V. Other notable anions are AsF 6 À and PF 6 À , higher by 0.78 V and 0.38 V, respectively.
Each of the functionals used have different issues, a few observations, grouped by functional complexity, are here highlighted.
Starting with the non-hybrid functionals, VSXC has the largest average deviation (À0.73 V) of the DFT functionals.It underestimates the DE v of a few anions by more than 2 V: PF 6 À is underestimated by 2.65 V, AsF 6 À by 2.19 V, and BOB by 2.07 V.A few other anions are underestimated by more than 1 V: Tf, TFSI, MOB and BF 4 À .Two anions have their DE v overestimated compared to the reference; Cl À (by 0.22 V) and CH 3 COO À (by 0.33 V).M06-L has the second highest average deviation (À0.70 V) of the DFT functionals.The problematic anions are the same as for VSXC with only slightly different values.
The hybrid functionals have better performance characteristics, however, B3LYP has the same problematic cases as VSXC and M06-L.Though, as the average deviation implies, the errors are smaller in magnitude; PF 6 À is underestimated by 1.91 V and AsF 6 À by 1.38 V and most others anions are below 1 V in difference.However, the overestimates of CH 3 COO À and Cl À are somewhat large, 0.72 V and 0.28 V, respectively.PBE0 has similar performance characteristics as B3LYP -including the same problems with PF 6 À , underestimated by 1.79 V, BOB by 1.28 V, and AsF 6 À by 1.27 V.
TPSSh performs somewhat worse than B3LYP.It is also the only hybrid functional that has any value that is underestimated by more than 2 V: PF 6 À by 2.41 V.The deviations for AsF6 and BOB are also large: 1.91 V and 1.81 V, respectively.M06-2X has the distinction of having the lowest deviation of all of the functionals.However, it has a number of overestimates such as CH 3 COO À by 0.80 V, BF4 by 0.50 V, and NO 3 À by 0.48 V.
Furthermore, the underestimates are low; PF 6 À 0.72 V, F À 0.53 V, and BOB 0.46 V.It is also notable that AsF 6 À is underestimated by only 0.14 V. Interestingly, the BF 4 À value of 6.85 V is closer to the CBS value (7.03 V), than the DCBS value (6.35 V).The two double hybrid functionals have very small deviations, as mPW2PLYP has the second lowest average deviation (À0.29 V) and only has two values that differ by more than 1 V: PF 6 À and BOB are underestimated by 1.41 V and 1.14 V, respectively.B2PLYP is similar to mPW2PLYP, however, it has a slightly higher deviation; À0.35 V.It also has three anions that differ by more than 1 V from the reference: PF 6 À is underestimated by 1.62 V, AsF 6 À by 1.16 V, and BOB by 1.33 V.
When the results from all the DFT functionals are taken together, a few points become apparent.First, a larger number of electronegative groups present in the anion structure, tends to cause worse results.Thus heavily fluorinated molecules in general have DE v values underestimated by 1-2 V.This is readily apparent for the PF 6 À and AsF 6 À anions.This is also an issue for BOB, but to a less extent for the MOB variant, which has the less electronegative malonato moiety.This could be an issue for future ab initio work on novel electrolyte anions, as they tend to be themed around strongly electronegative groups.Second, while DFT on the whole results in too low DE v values, the DE v value for CH 3 COO À is in general overestimated from 0.5 V to 0.8 V.The DE v for Cl À is also often overestimated.
Third, in general the performance of the DFT functionals follows the Jacob's ladder of DFT. 57The hybrid functionals perform better than the local functionals, VSXC and M06-L, while the double-hybrid functionals, mPW2PLYP and B2PLYP, perform even better.There is one functional that performs far better, M06-2X, though that may be a fortunate cancellation of errors, as this functional is heavily parameterized.
Moving on to the chemical hardness measure, on average the DFT functionals overestimate the hardness (Table 4 and Fig. 3), as all average deviations are positive.Furthermore, with the large standard deviations, there will be outliers for each functional.Each functional must be inspected, following the same analysis layout as above.Starting with VSXC and M06-L, these have the same outliers, albeit differing slightly in magnitude.Both overestimate the F À and HF 2 À by over 2 eV, and also have issues with CH 3 COO À and Cl À .
The functionals in general underestimate the hardness of the Hu ¨ckel anions (N 5 C 2n , n = 2. ..), and BOB, by 0.5 eV or more.Furthermore, both functionals underestimate PF 6 À and AsF 6 À , M06-L by 0.89 eV and 0.75 eV and VSXC by 1.11 eV and 1.20 eV, respectively.Interestingly, the average deviations for the two functionals are small, 0.13 eV for VSXC and 0.39 eV for M06-L.
Looking at the hybrid functionals; B3LYP, M06-2X, PBE0, and TPSSh, all reveal the same pattern as for the VSXC and M06-L functionals, e.g. an overestimated hardness for F À and HF 2 À , in each case by Z2 eV.However, the underestimates of the PF 6 À and AsF 6 À anions are much reduced for all the hybrid functionals (except TPSSh).M06-2X has even a slight overestimate of the PF 6 À and AsF 6 À , by 0.16 eV and 0.14 eV, respectively.The double hybrid functionals, B2PLYP and mPW2PLYP, have some of the largest average deviations of all the functional of Table 4, however, they have some of the smallest standard deviations, implying that they tend to overestimate the hardness.
They also have many of the same outliers as the other functionals, in particular F À and HF 2 À , which are overestimated by Z2.4 eV.Furthermore, Cl À and CH 3 COO À continue to have some overestimation (E0.8 eV and 1.3 eV, respectively).The Hu ¨ckel anions (N 5 C 2n , n = 2. ..), continue to have some underestimation.However, the magnitude of the underestimate for PF 6 À and AsF 6 À is smaller than for most of the hybrid functionals, with 0.30 eV and 0.38 eV for B2PLYP and 0.21 eV and 0.38 eV for mPW2PLYP, respectively.Comparing the deviations from the reference values for both approaches, DE v (Fig. 2) and Z (Fig. 3), it must be noted that the magnitude of the deviations of Z are far larger (note the figure scales).Furthermore, looking at Fig. 1 and 2 of the ESI, † show that while DFT can tackle DE v calculations, the same is not clear for Z, due to the low correlation with the DCBS values.

Conclusions
For the calculation of the stability vs. oxidation for the present set of anions, using the methodology of DE v , a hybrid (or better yet, double hybrid) functional is recommended.Their resulting DE v values are closer to the benchmark, surpassing the previously recommended VSXC functional of older works. 26,27Out of the DFT functionals tested, M06-2X performs the best.
Using the E HOMO measure to predict the stability vs. oxidation is debatable, due to the unexpected ordering of the anions' oxidative stability.Furthermore, neither the E HOMO nor the DE v approaches were able to predict the expected ordering of F À 4 Cl À 4 Br À .
Hardness is another interesting property to study in connection with oxidation potentials, though the origin of its strong correlation with E ox is not clear.Out of the many DFT functionals tested, no strong general recommendation can be made, however, the double hybrids and M06-2X are candidates for the calculation of hardnesses.

Fig. 1
Fig. 1 Illustration of the different approaches used to calculate the anion oxidation potential using DFT; the vertical excitation energy (DE v ) and the ionization potential (IP).

Fig. 2
Fig.2The deviation, dDE v of the DE v value from the DCBS reference value for each of the methods.Average and standard deviations are also shown.
HOMO values have the same issues for the halides as the DE v values, i.e. wrong ordering.Unfortunately, it is not the same ordering, i.e.Cl À 4 F À 4 Br À .Looking at the E ox values, the E HOMO value for BF 4À is very large, À10.45 eV, far larger than expected.It is not clear what causes BF 4 À to stand out for all measures.3.2DCBSInTable2weshow the DCBS values only for the larger anions for which CBS was not viable.A comparison vs. experimental data show that the DE v approach tends to overestimate the oxidation potentials.This includes the BOB (by 1.63 V) and MOB (by 1.09 V) anions -with BOB correctly described to be more stable.Furthermore, some values are very close to the measured E ox with Im(BF 3 ) 2 À as the stellar example (only 0.07 V difference).For some other anions, a definite comparison is not possible, due to the large variations in E ox values.These include TFSI, where the DE v value is close to some of the E ox values.Both AsF 6 À and PF 6 À have DE v values close to the E ox maximum values.
4À has a hardness that is well within the range of the E ox values, despite having the highest difference between Z values calculated by CBS and DCBS.BF 4 À is also the only anion with a higher DE v than Z. ClO 4 À is the only anion for which all E ox values are larger than the hardness.The E

Table 1
Anions with full CCSD(T)/CBS results.All values are given in V vs. Li + /Li, except Z and E HOMO (eV).E ox is experimental values

Table 2
Anions with DCBS results for DE v and Z.All values are given in V vs. Li + /Li, except Z and E HOMO which are in eV

Table 3
Vertical oxidation potential (DE v ) of anions from selected DFT functionals and HF.DCBS values given for comparison.All values in V vs. Li + /Li.The average and standard deviations are comparative to the DCBS values

Table 4
Hardness (Z) of anions from selected DFT functionals and HF.DCBS values given for comparison.All values in eV.The average and standard deviations are comparative to DCBS values This journal is © the Owner Societies 2015