First Principles Study of Decomposition Reactions in the Electrolyte System Ethylene Carbonate and Lithium Hexafluorophosphate

The decomposition mechanisms of electrolyte mixtures in lithium-ion batteries are still not completely understood, although the degradation of the electrolyte has a direct effect on the efficiency and lifetime of these devices. The main aim of this study is to investigate the decomposition reaction of ethylene carbonate and LiPF6, two common components of electrolyte mixtures for lithium-ion batteries. The main focus is the analysis of the reaction kinetics on the basis of the corresponding activation barriers using density functional theory. We show that this method provides reasonable molecular structures and qualitative trends, whereas coupled cluster calculations are required to provide more accurate energies. We furthermore investigate the influence of different conducting salts on the decomposition barrier of ethylene carbonate, finding that appropriate salts can raise the barrier and thus mitigate the decomposition reaction. In particular, the results suggest that substitution of LiPF6 by lithium bis(oxalato)borate could drastically inhibit the reaction. Furthermore, we study the potential decomposition of LiPF6 to PO2F2−, proposing an alternative route to the common hydrolysis reaction.

The suppression of the electrolyte degradation in lithium-ion batteries is of great importance due to their wide area of usage, especially in the electronic and automotive industry. 1,2Overall, a better understanding of the decomposition reactions is crucial for the improvement of lifetime and working stability of the cells.Therefore, detailed information about the decomposition reactions in the so-called solid electrolyte interface (SEI) 3,4 and the corresponding activation barriers are strongly desired in order to improve the electrolyte composition and ensure the best working conditions for the involved cathode and anode systems. 5,6First insights about decomposition reactions have already been provided from theory and experiment, [7][8][9][10][11][12][13][14][15][16][17][18] but a more in-depth and systematic approach is missing.Ab initio calculations can provide insights on an atomistic level and can help to distinguish various possible decomposition pathways.
A commonly utilized electrolyte mixture is the ethylene carbonate/LiPF 6 system.This specific study aims to predict the activation barriers of common decomposition reactions for both ethylene carbonate (EC) and LiPF .6 For EC, we focus on the reductive decomposition into ethylene and carbonate.While the electron transfer between anode and electrolyte has already been studied by ab initio molecular dynamics simulations based on Möller-Plesset perturbation (MP2) calculations, 19 we treat the subsequent molecular mechanisms in this study.
Two suggested mechanisms are shown in Fig. 1.Reaction 1 consists of two steps: Step 1 corresponds to a ring opening and step 2 represents the cleavage into ethylene and carbonate.An alternative path has recently been proposed by Leißing et al. 20 that involves the additional participation of a hydrogen radical (reaction 2 in Fig. 1).The exact mechanism of the generation of the hydrogen radical is not conclusively known, but could be postulated based on initial proposals of decomposition reactions. 20However, this is outside the scope of this study.We therefore aim to identify the most probable reaction mechanism of the reductive decomposition of EC, as shown below.
2][23] Therefore, we investigate a selection of commonly used conducting salts with regards to their effect on the electrolyte degradation.
Regarding the decomposition of LiPF , 6 we focus on the reaction path leading to the formation of PO F .− This compound was reported as a possible intermediate decomposition product, which can potentially reduce the surface impedance due to the SEI formation and also improve the cyclability performance of lithiumion batteries, making it potentially interesting from a practical point of view. 24,25e consider two reactions both starting from the initial hydrolysis of LiPF 6 to POF 3 as shown in Fig. 2. The hydrolysis pathway (reaction 3 and 4) is commonly assumed in the literature, 26,27 while the path involving the POF 4 − anion (reaction 7 and 8) has been suggested as another route. 28he initial hydrolysis process consists of two steps.First, the salt decomposes into lithium fluoride and PF .
5 An activation barrier of about 104 kJ mol −1 is reported for the reaction of solid LiPF 6 to gaseous PF 5 and solid lithium fluoride. 29Starting from POF , 3 one route is the further hydrolysis to form PO F 2 2 − (reaction 5 and 6). 30n the alternative path an initial POF 4 − molecule is formed through the reaction of POF 3 and a fluoride anion (reaction 7) which subsequently reacts with another POF 3 (reaction 8) to form PO F 2 2 − by releasing PF 5 (reaction 9). 28A variation of reaction 9 has also been proposed 28 including the reaction between POF OPF and F − to form PF 6 − as a side product.However, the reaction between two anions seems unfavorable and the subsequent addition of F − to PF 5 from reaction 9 is more likely.
Most available studies only utilized DFT calculations 11,31,32 or a reactive force field approach 33 to investigate the reactions in electrolyte systems.In order to evaluate this procedure, we test a more accurate method in a qualitative manner, namely coupled cluster with single and double excitations (CCSD).In a previous study, single and double excitations with perturbative triple excitations (CCSD(T)) calculations were found to result in higher barriers compared to DFT. 34 Thus, the computationally more demanding method can potentially improve the quality of the predicted activation barriers, which is important if highly accurate results are needed for kinetic analysis and not just the qualitatively correct trends provided by DFT.Here, the reliability of this approach is z E-mail: mroz@pc.rwth-aachen.deECS Advances, 2023 2 030506 evaluated by a T1 diagnostic 35 to ensure reasonable results by estimating the multireference effect on the wave function.Solvation effects are considered by an implicit solvation model, 36 adopting the polarizable continuum model (PCM). 37,38In this study the EC/DEC system was chosen as a suitable test system.

Computational Method
All calculations were performed with Gaussian 09 39,40 and visualized with GaussView. 41The geometry optimizations for the molecular structures were conducted at the DFT level with the 6-311 ++G(d,p) basis set and initially with various functionals, namely the hybrid functionals B3PW91 [42][43][44][45] and B3LYP, 42,46,47 the GGA functional PBE 48,49 and the meta-GGA functional TPSS. 50The B3PW91 functional was chosen as the most suitable one throughout this study.The contributions of the Gibbs free energies at room temperature and zero-point corrections were obtained from frequency calculations on the coupled cluster (CCSD) level with the 6-311++G(d,p) and the aug-cc.-pVDZbasis sets together with a frozen core approximation.The CCSD calculations were based on the optimized structures from DFT calculations with the aug-cc-pVDZ basis set and the energetical differences for optimizations with DFT and CCSD methods are predicted to be negligible, which was tested for the 6-311++G(d,p) basis set.Calculations for the combination of a conducting salt and an electrolyte molecule as well as the investigation of the decomposition of LiPF 6 were limited to DFT to maintain a feasible computational demand for the screening of various configurations and the larger system size.Therefore, a reduced 6-31++G(d,p) basis set was utilized for the former calculations, while the latter calculations were performed with a 6-311++G(d,p) basis set.A polarizable continuum model [36][37][38] was applied to include the effect of solvation in all calculations.The reported value of 18.5 for the relative dielectric constant 51 of a 3/7 solvent mixture of EC/ethyl methyl carbonate was used as an estimate for the EC/DEC solvent mixture, which is an experimentally relevant electrolyte system.The individual dielectric constants are 95.3 and 2.82 for EC and DEC, respectively. 52A value of 1.94 was used for the dynamic dielectric constant calculated from the sum of the squares of the refractive indices of EC and DEC, 53,54 weighted with the given ratio.The evaluation of explicit solvent molecules was performed for three test configurations with the 6-31++G(d,p) basis set due to the larger system size.

Results and Discussion
Activation barriers of the EC decomposition.-Theactivation barriers of EC decomposition were calculated for reactions 1 and 2 as given in Fig. 1 without and with a hydrogen radical, respectively.The results based on DFT with different functionals and CCSD with the aug-cc-pVDZ basis set are given in Table I.The structural data of the structures predicted by DFT with the B3PW91 functional is given in the Supporting Information.Furthermore, the activation   Table I.Activation energies E A of the decomposition reaction of EC calculated with various DFT functionals and CCSD in kJ mol −1 for TS1 and TS2 of reaction 1 and 2. In some cases, the functionals failed to predict a corresponding structure as indicated by -. barriers calculated with CCSD and a smaller 6-311++G(d,p) basis set are also given in Supporting information.The transition states for step 1 (TS1) and step 2 (TS2) are visualized in Fig. 3 for both reactions.

Functional
All CCSD calculations in this study have been performed in conjunction with a T1-diagnostic. 35All values for closed-shell systems were below the threshold of 0.02, which is considered to represent a limit for reliable results. 35For open-shell systems, some values larger than 0.02 were found, reaching up to 0.036.However, this is to be expected for open-shell systems and it has been suggested 55 that values of up to 0.044 are acceptable for these cases.Therefore, we expect reliable results for all species involved.
Overall, the CCSD results with two different basis sets give similar results.In general, CCSD calculations with the larger basis set predict slightly lower activation barriers.
The activation energies themselves clearly indicate that the proposed reaction involving an additional hydrogen radical (reaction 2) is energetically unfavorable.For the second step, the predicted energy difference at the CCSD level with the aug-cc-pVDZ basis set is about 86 kJ mol −1 .Furthermore, a difference of about 35 kJ mol −1 is calculated with regard to the rate determining steps.Thus, the calculations suggest a higher probability for reaction 1, with the first step, i.e., the ring opening, being the rate determining one due to the much higher activation barrier for this reaction.
The activation energies of the two pathways vary to a significant degree, although the structures of the transition states in Fig. 3 are similar and therefore an accurate theoretical description is important.
The comparison of the different DFT functionals with respect to the CCSD calculation for reaction 1 shows that B3PW91 [42][43][44][45] performs the best with all other functionals significantly deviating from the CCSD results.In addition, none of the other functionals was able to predict geometries for either or both of substrate and transition state of the second step of reaction 1.
Therefore, B3PW91 [42][43][44][45] was chosen as the functional to be used for all further DFT calculations in this study.
A more detailed comparison between the DFT and CCSD level shows, that all barriers predicted by CCSD are significantly higher while the overall trend is maintained with DFT.This behavior of CCSD is consistent with the literature, which gives a range of different CCSD(T) barriers for the first reaction step of reaction 1 with an additional lithium ion. 34Various basis sets were screened and the reported electronic reaction energies are between 61.4 kJ mol −1 and 69.8 kJ mol −1 , which fits well with our value of 67.7 kJ mol −1 .In this case only reaction energies were reported and therefore a comparison with Gibbs free energies was not possible.It should be noted that in our study CCSD was used as a qualitative comparison rather than quantitative benchmark, which would require even larger basis sets and the inclusion of CCSD(T) calculations, resulting in a significant increase in computation time that is not feasible.However, the agreement between our results and the CCSD (T) data shows the satisfying quality of our CCSD calculation.Therefore, this computationally less demanding method was used as a sufficient estimate.The most pronounced discrepancy occurs for the second reaction step in reaction 2 with an energetic difference of about 21 kJ mol −1 with regard to our CCSD calculations.Although DFT predicts the same qualitative trend, the inclusion of the computationally much more demanding but also more accurate coupled cluster method leads to different quantitative results and could turn out to be crucial for a realistic evaluation of the corresponding activation barriers.
The energy profiles for the DFT calculations of substrates, transition states and products are shown in Fig. 4.
The activation barrier of 41.5 kJ mol −1 as predicted by DFT corresponds nicely to the value of 46.9 kJ mol −1 for an EC molecule with an additional lithium ion in the literature. 11urthermore, the final step of reaction 2 involves an endergonic process in contrast to all other cases, which exhibit an exergonic behavior.This finding also shows that the reaction with an additional hydrogen radical is energetically unfavorable.
Impact of a varying electrolyte composition.-Buildingon our initial insight into the degradation mechanism, the impact of the EC/ DEC electrolyte mixture on the reaction kinetics was investigated by varying the corresponding dielectric constant.The rate determining first step of the favorable direct decomposition (reaction 1) was chosen as a test case.The results of the DFT calculations are summarized in Table II and the CCSD results as well as the structural data based on the DFT results are given in the Supporting Information.
The effect of different mixture ratios is below 1 kJ mol −1 for both the DFT and CCSD calculations.While the CCSD calculations give significantly higher activation barriers in general as indicated in the Supporting Information, the trend of the DFT calculations is the same.Therefore, at the current level of accuracy with an implicit solvation model, the calculations predict no effect of varying mixture ratios on the activation barriers.
In contrast, an earlier study 56 postulated the significant effect of explicit inclusion of interacting solvent molecules.Therefore, we tested the impact of explicitly considering the solvent molecules with three different configurations between EC and DEC.The molecules were placed in close proximity and rotated around the central EC molecule in order to find different local minima.This initial screening showed that extending the implicit model with explicit solvent molecules has a negligible effect, resulting in activation barriers very close to 41.5 kJ mol −1 as predicted by the implicit model alone.Further information about the structures and transition states is given in the Supporting Information.Nevertheless, we only screened three distinct configurations.To get a more accurate picture, a larger number of configurations would be needed, which could be a target of future studies.
2][23] In our subsequent analysis, we therefore investigated the influence of different commonly used conducting salts 57 on the activation barriers for the rate determining step of reaction 1.The considered salts are LiPF 6 as well as LiClO 4 and lithium bis(oxalato)borate (LiBOB).Calculations were limited to the DFT level due to the system size where coupled cluster calculations would turn out to be significantly more demanding.Nevertheless, qualitative trends are expected to be correct as shown in the previous section (Table I).Several starting ECS Advances, 2023 2 030506 configurations that differ in the orientation between the salt and the EC molecule were sampled by rotating the salt molecule close to the lithium ion.Representative structures of energetically favorable transition states are given in Fig. 5.
As the configurational space is too large to be completely sampled, the presented results do not ensure the global minimum.Especially in the case of LiBOB, the search for a minimum proved to be very challenging.However, the sampled configurations exhibit comparable energies and correct qualitative trends are expected.For reasons of comparability, a configuration that involves an oxygen lithium bond as seen for LiClO 4 and LiPF 6 is also investigated in the case of LiBOB.
The results of the DFT calculations are given In Table III.The structural data of the energetically most favorable configurations at the DFT level are given in the Supporting Information.The corresponding energy profile for the reaction with a conducting salt is given in Fig. 6.
The calculated activation barriers increase in the order LiClO 4 < no salt < LiPF 6 < LiBOB.In comparison to an activation barrier of 41.5 kJ mol −1 without a conducting salt, LiBOB (106.6 kJ mol −1 ) shows a strong increase of the activation barrier, while LiClO 4 leads to a slight lowering.This indicates that LiBOB could potentially suppress the formation of decomposition products and might be useful in new electrolyte mixtures, especially in contrast to the commonly used LiPF .
6 One possible explanation could be the degrees of freedom due to steric effects.LiBOB molecule itself can adopt various configurations in contrast to the other geometrically much more limited conducting salts.Therefore, a reorientation between the EC molecule and LiBOB is possible due to different electronical stabilizations for ground state and transition state because of the ring opening.This might explain the rather high barriers when LiBOB is present.Furthermore, the product is also significantly destabilized by LiBOB compared to the substrate.The other conducting salts exhibit clear exergonic behavior, whereas the addition of LiBOB leads to a neutral energy balance.However, it should be noted that this result should be interpreted as a qualitative hint due to the very large configurational space, which can of course create artifacts of calculations.Still, the general trend of a higher activation barrier is preserved for all sampled orientations.
According to the Eyring equation, 58,59 the reaction with LiBOB at room temperature would be about 1.17•10 10 times slower than with LiPF 6 and about 3.98•10 11 times slower than without a conducting salt.
The calculations clearly show that the effect of the conducting salt on the activation barrier is significant.This in turn allows to control the reaction rate of the decomposition reaction.For future ECS Advances, 2023 2 030506 studies we suggest the application of more elaborate solvation models and comprehensive sampling the configurational space whereby our results give a general trend and ideas for further experimental approaches.
Decomposition of LiPF 6 .-Although the conducting salt can mitigate the degradation of the EC electrolyte, it is subject to decomposition itself.Here we present the results for LiPF 6 decomposition as shown in Fig. 2.
The main reactions of interest are reactions 5 and 7-9.Our DFT calculations reveal that the hydrolysis of POF 3 (reaction 5) has a huge activation barrier of 153.9 kJ mol −1 .In contrast to this result the initial formation of POF 4 -(reaction 7) has a very low activation barrier of 34.9 kJ mol −1 .Therefore, the reaction between POF 3 and a fluoride anion is readily possible.The subsequent reactions also show rather low barriers.The reaction between POF 3 and POF 4 -(reaction 8) has a barrier of 56.5 kJ mol −1 and the barrier  6 The Gibbs free energies are given relative to the substrate EC from the first step of reaction 1 with the respective conducting salt.for the formation of PF 5 and PO 2 F 2 -(reaction 9) amounts about 87.0 kJ mol −1 , which is consistent with initial predictions that postulate low energy barriers, based on general chemical considerations. 28The corresponding transition states involved in reaction 5, 7, 8 and 9 are shown in Fig. 7.The structural data according to our DFT calculations is given in the Supporting Information.The corresponding energy profiles are shown in Fig. 8.
Overall, we predict that a reaction involving POF 3 will favor a reaction with POF 4 -rather than further hydrolysis with water based on the activation barriers.This finding is interesting, because it sheds light on a potential pathway that differs from the commonly assumed hydrolysis route. 30This in turn could help to investigate the decomposition mechanisms of LiPF 6 based on this prediction with a more refined experimental setup.However, it should be noted that reactions 5, 7 and 8 show exergonic behavior in contrast to reaction 9, which is endergonic.The resulting value of 79.1 kJ mol −1 is comparable to a value of about 56 kJ mol −1 , as reported by Spotte-Smith et al. 60 Although the energy balance is unfavorable, a subsequent reaction of the formed PF 5 could result in PF 6 again, which is predicted to be an overall exothermic process, as shown by Okamoto, 61 who predicts an endothermic process and gives an overall reaction energy of about 55 kJ mol −1 for reaction 3, assuming solvation effects and the formation of solid LiF.The reverse reaction would therefore be exothermic in nature.This in turn would withdraw PF 5 from the reaction equilibrium and thus enhance reaction 9. Furthermore, LiPO F 2 2 was shown to form stable SEI films, 62 which would further withdraw the reaction product from reaction 9 and thus shift the equilibrium to the product side.Alternative mechanisms have been proposed in the literature as well, such as a reaction of POF 3 with carbonates, which also involves rather low barriers as reported by Spotte-Smith et al. 60 They investigated the decomposition mechanism of LiPF 6 with a special focus on the reactions with carbonates.They also provide an activation barrier for reaction 9 that amounts to 84.9 kJ mol −1 with an additional lithium ion, which corresponds very well with our result.In comparison to reaction 8, they proposed another path with several substeps.One of these steps is comparable albeit not identical to reaction 8.The corresponding activation barrier amounts to 79.1 kJ mol −1 , which is not too far from the activation barrier of reaction 8.
While Spotte-Smith et al. 60 reported barriers for reaction 4 that amount to roughly 100 kJ mol −1 for the involved substeps, the proposed alternative involves the reaction with carbonates.The initial reactions with lithium carbonate are energetically more favorable with barriers smaller than 100 kJ mol −1 .Subsequent decomposition of POF 3 can also include lithium hydrogen carbonate, but the energy balance is not very favorable in this case.However, lithium carbonate will form a salt under the reaction conditions that cannot participate in liquid phase reaction.It is questionable, if the residual concentration of lithium carbonate in the solution is sufficient to react with the desired stoichiometry.Whether PF 5 reacts with water to form POF 3 or the alternative reaction with a carbonate is more probable, needs to be evaluated in more depth, especially in conjunction with the experiment.Furthermore, the formation of  PO 2 F 2 -would also proceed through a reaction with a carbonate.The barrier is low in this case, reaching roughly 22 kJ mol −1 for the highest barrier.In contrast, the alternative that involves the addition of a fluoride anion to POF 3 in reaction 7 involves species that can fully participate in the liquid phase.The higher activation barriers are balanced by the higher availability in the liquid phase.Overall, a conclusive evaluation would remain for further experimental and computational studies.

Conclusions
Two different reductive decomposition reactions of EC were characterized regarding the activation energies using DFT and CCSD.Among various commonly used functionals, B3PW91 was found to yield the best results on the basis of qualitative CCSD calculations with a more expansive basis set that result in more accurate activation barriers.The direct decomposition was found to be energetically favorable, with the first ring opening step being rate determining.DFT calculations predict correct structures and energetic trends and can therefore be used for a reasonable estimate, whereas coupled cluster calculations were found to give significantly higher energy barriers, which is important if highly accurate and quantitative kinetic data are desired.Changing the ratio of the electrolyte mixture as represented by the dielectric constant has only a negligible effect on the activation energy.Nevertheless, more detailed simulations considering explicit solvent molecules might be important to verify this finding.
Furthermore, different conducting salts were investigated with regard to their effect on the activation barriers.The barrier increased in the order LiClO 4 < no salt < LiPF 6 < LiBOB suggesting reduced amount of decomposition products in the presence of LiBOB.A more thorough sampling of the possible configurations could be the focus of a future study.Finally, our investigation of the possible decomposition of LiPF 6 revealed that a reaction of the involved POF 3 species with POF 4 -is favored with regard to the activation barriers in contrast to a commonly assumed hydrolysis reaction.However, alternative reactions with other reaction partners are also possible and would need to be studied in a more systematic and inclusive approach.
Overall, the results presented in this study can serve as a first semi-quantitative approach to characterize the decomposition reaction of EC and provide the experimentalists with new ideas for future battery design.

Figure 1 .
Figure 1.Decomposition reaction of EC to lithium carbonate and ethylene.Reaction 1 gives the direct decomposition path, while reaction 2 includes an additional hydrogen radical.

Figure 2 . 2
Figure 2. Possible decomposition pathways for LiPF .6 Reactions 3 and 4 represent the required initial reactions to yield POF 3 that can react in two different reaction routes.Reactions 5 and 6 represent the further hydrolysis and subsequent deprotonation of HPO F . 2 2 The anionic route contains three distinct reaction steps.Reaction 7 is the reaction of POF 3 with a fluoride anion to form POF .

4 − 5 − 2 −
This molecule can subsequently react with another POF 3 to form POF OPF 2 in reaction 8, which is split into PO F 2 and PF 5 in reaction 9.

Figure 3 .
Figure 3. Transition states TS1 and TS2 for reaction 1 and 2 according to Fig. 1 calculated with DFT.Carbon in grey, hydrogen in white and oxygen in red.

Figure 4 .
Figure 4. Energy profile for reactions 1 (top) and 2 (bottom) calculated with DFT.The Gibbs free energies are given relative to the substrate EC from the first steps of reactions 1 and 2.

Figure 5 .
Figure 5. Representative transition states of energetically favorable configurations for the first step of the direct decomposition reaction 1. 1 EC and LiClO , 4 2EC and LiPF 6 and 3 EC and LiBOB.Carbon in grey, oxygen in red, hydrogen in white, lithium in purple, chlorine in green, phosphorous in brown, fluorine in blue and boron in pink.

Figure 6 .
Figure 6.Energy profile for the first step of reaction 1 with an additional conducting salt.Top left: Profile for LiClO .4 Top right: Profile for LiBOB.Bottom: Profile for LiPF .6The Gibbs free energies are given relative to the substrate EC from the first step of reaction 1 with the respective conducting salt.

Figure 7 .
Figure 7. Transition states corresponding to the reactions in Fig. 2. Oxygen in red, phosphorous in brown, fluorine in blue and hydrogen in white.

Figure 8 .
Figure 8. Energy profile for the reactions 5, 7, 8 and 9. Top left: Profile for reaction 5. Top right: Profile for reaction 7. Bottom left: Profile for reaction 8. Bottom right: Profile for reaction 9.The Gibbs free energies are given relative to the respective substrate.

Table III .
Activation energies for the rate determining step of the direct decomposition reaction for three different conducting salts in kJ mol −1 .