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Solvent and salt effect on Lithium ion solvation and contact ion pair formation in organic carbonates: a quantum chemical perspective

Quantum chemical calculations have been employed to investigate the solvation of lithium cations in ethylene carbonate/propylene carbonate and propylene carbonate/dimethyl carbonate mixed electrolytes. The impact of the presence of the counteranion on the solvation of Li+ in pure propylene carbonate and dimethyl carbonate was also studied. The calculations revealed small free-energy changes for the transitions between different preferred structures in mixed solvents. This implies that transitions between distinct local arrangements can take place in the mixtures. The addition of dimethyl carbonate causes a significant increase of the dipole moment of solvation clusters, indicating important molecular-scale modifications when dimethyl carbonate is used as a co-solvent. The presence of an anion in the solvation shell of Li+ modifies the intermolecular structure comprising four carbonate molecules in dilute solutions, allowing only two carbonate molecules to coordinate to Li+. The bidentate complexation of Li+ with the anion electron donor atoms, however, maintains the local tetrahedral structure on interatomic length scales. The neutralization of the solvation shell of Li+ due to contact ion pair formation and the consequent implications on the underlying mechanisms provide a rational explanation for the ionic conductivity drop of electrolyte solutions at high salt concentrations.


Introduction
Rechargeable Lithium Ion Batteries (LIBs) are efficient and robust devices employed in various electronic applications, such as cellular phones and notebook computers, due to their high energy density and good reversibility [1][2][3][4] . Since the raise of LIBs in 1991, a tremendous amount of experimental and theoretical work has focused on investigating the chemistry involved in the utilized materials, in order to provide an efficient and environment-friendly system. A typical LIB consists of an anode (usually graphite) and a cathode (normally a transition metal oxide as, for example, LiFeO2, LiNiO2, LiMn2O4, or LiCoO2) [5][6][7][8][9][10] , separated by an electrolyte which acts as the ionic conducting medium and is typically composed by Lithium salts dissolved in non-aqueous organic carbonate solvents 1,11 . LIB performances are determined by the combination of the electrode materials, salts, and electrolyte solvents.
The choice of the electrolyte is capital, since it is involved in the Lithium ion transport, ultimately determines the conductivity, and controls the features (and quality) of the solid electrolyte interphase (SEI), [12][13][14][15][16][17] which forms on the electrode surface following the reductive decomposition of the electrolyte. This interphase strongly affects battery cyclability, lifetime, power and rate capabilities, and safety (flammability, for instance). Electrolytes employed in electrochemical devices must also be compatible with the electrodes, to ensure chemical stability, and exhibit a large electrochemical window between the lowest unoccupied and the highest occupied molecular orbitals (HOMO-LUMO), to provide thermochemical stability.
Issues such as the temperature range for stability and the solvent efficiency in dissolving Lithium salts must also be optimized.
Phase behaviour modifications upon mixing are an additional important aspect. For instance, ethylene carbonate (EC) is solid at room temperature; however, mixed with other solvents such as linear carbonates or propylene carbonate (PC), it becomes liquid in a wide temperature range, with significant impact on energy storage features. Indeed, present most widely used electrolytes are mixtures of cyclic carbonates, such as EC and PC, with linear carbonates, as dimethyl carbonate (DMC). A wide range of LIB electrolyte solvents has been scrutinized following this route, searching for innovative mixtures exhibiting optimal values of key features, including high chemical stability, low melting point, high ionic conductivity, wide temperature range performance, and low viscosity. [18][19][20][21][22][23] . A substantial amount of evidences interestingly points to a crucial observation: The mechanisms underlying Li + ion transport are determined by a complex interplay among details of nanostructure and dynamics of the solvation sphere around the ion, collective solvent properties like the viscosity and dielectric permittivity, and ion pairs formation.
Although several experimental and theoretical works have focused on systems formed by pure EC, PC and DMC with the Li + ion [24][25][26][27][28][29][30][31] , solvation structure and dynamics of the cation in these solvents is still a subject of debate. More in details, Density Functional Theory (DFT) studies have shown that a (four-coordinated) tetrahedral geometry Li + (EC)4, is the dominant species [32][33][34] . Ding et al. 35 performed DFT and Polarizable Continuum Model (PCM) studies to account for the coordination number around Li + ion, and suggested a transition between the most stable four-coordinated Li + (EC)4 and the three-coordinated trigonal Li + (EC)3 structures, due to a very low energy barrier separating the two geometries. On the other hand, Balbuena et al. 36 43 , in addition, reported that Li + is preferentially solvated by the cyclic and more polar components in the mixtures, as the electrostatic interactions overcome possible steric hindrances. We observe, however, that in that work the estimated Li + coordination number was found to range from 5 to 6, depending on the salt concentration, a conclusion in contrast with the vast majority of existing theoretical and experimental studies.
In the case of LiPF6 salt in mixed carbonate solvents, Morita et al. 44 49 concluded that EC solvates Li + more effectively than PC.
The above rapid (and partial) review clearly demonstrates both the complexity and the scope of the issues involved in a general description of the structure and preferential solvation properties of the Li + cations. It also points to two fundamental needs: first to verify systematically and on the same systems the compatibility of results coming from different numerical procedures employed at different length scales. Second, to clarify the relevance of the numerical results compared to experimental observations. In previous works 50, 51 we moved on this line, with the goal of contributing general systematic information on these issues. We therefore focused on one side on a comparison of the outcomes of DFT calculations for small clusters and of classical MD simulations of larger ensembles of molecules 50 . On the other, we attempted at relating numerical data with novel experimental measurements able to provide a direct determination of the coordination structure of the Li + cations 51 . In the experimental-theoretical study of Ref. 51 , in particular, based on femtosecond vibrational spectroscopy and DFT calculations we found that the EC coordination number around Li + cations strongly depends on salt concentration. For salt concentrations higher than 0.5 M, the coordination number of ethylene carbonate decreased to two, implying that both cation-anion interactions and ion-pair formation play a very important role on the structure and properties of the first solvation shell of Li + . Interestingly, another recently published combined experimental and theoretical study 52 also pointed out that the coordination number of propylene carbonate and dimethyl carbonate in the first solvation shell of Li + can decrease from 5 to 2 when increasing the salt concentration. This further validates our previous studies and emphasizes the importance of ion-pair formation on the determination of the structure around Li + cations at high salt concentrations.
Here, we make a significant step forward in this direction, providing additional insight on the quantum mechanical features of the solvated clusters and the role played by the counterions. We first focus on the electronic structure, thermodynamic stability and vibrational properties of small clusters of the Li + ion in mixed EC/PC and PC/DMC solvents. Next, we extend our investigation with an analysis of the counter anion effects on the properties of the investigated clusters, with an emphasis on the (cation-anion) contact ion pair formation. We complete our work by relating our findings with previous theoretical and experimental studies.

Computational details
Following our previous works 50,51 , quantum-chemical DFT calculations for several clusters of pure and binary electrolytes and counter anions around a lithium cation have been performed using the Amsterdam Density Functional (ADF) package 53 . In particular, the Perdew-Burke-Ernzerhof (PBE) GGA exchange correlation functional 54,55 was employed in our calculations, also using a TZP slater-type orbital (STO) basis set. Recent works 52 on systems similar to those investigated here also pointed out the increased accuracy of the PBE functional in predicting binding energies of solvated Li + complexes compared to possible alternatives like B3LYP or M05-2X. Our DFT calculations showed that the basis set superposition error (BSSE) 56 corrections are negligibly small, confirming a conclusion also reached in previous studies 34,57 . Vibrational frequency analysis were carried out for the optimized clusters, ensuring the absence of unstable (imaginary) modes and, therefore, confirming each structure as a minimum on the potential energy surface. Zero-Point Energy (ZPE) corrections have also been included. Thermodynamic quantities such as the entropy, enthalpy and Gibbs free energy were estimated at T=298.15 K, for all clusters.

Li + solvation in mixed electrolytes
In our previous studies 50 we found that the most thermodynamically stable complexes of solvent molecules around the Li + ion are tetra-coordinated. We also systematically studied the stability of the Li + (EC)n(DMC)m, clusters, revealing that the thermodynamically most stable cluster is Li + (EC)3(DMC). On this basis, we conducted structural optimizations for the remaining clusters types containing two types of solvent molecules, Li + (EC)n(PC)m and Li + (PC)n(DMC)m with n+m=4. For the entire database of structures, we have also performed a vibrational frequency analysis and investigated charge transfer effects, comparing all data.
The Gibbs free energy changes have been estimated for the transitions of the form 2 (1) where k+l=n+m=4. All possible combinations of the indexes were considered, in order to identify the most favourable cluster among those involved in the Li + coordination. The  Table 2 are rescaled by subtracting the minimum free energy value between the investigated fragments, and correspond to the free energy differences for the transition towards the most stable structure. The absolute values of the enthalpy and entropy of each cluster, as calculated with the ADF software, are provided in the Supporting Information (Table S1).
A few observations are in order. In general, the EC/PC/Li + clusters exhibit higher BE than We also note that the Li + (EC)(PC)3 cluster is the most thermodynamically stable in the case of mixed EC/PC composition, but is less stable than Li + ( were also investigated. The optimized geometry bond parameters are reported in Table 3, together with the results obtained for the Li + (EC)n(DMC)m clusters, and the structures are shown in Figure 1(a)-(f). As we can see from In addition to the above structural properties, the atomic point charge distributions of the investigated clusters were obtained by performing a Multipole Derived Charge (MDC) analysis 60 . The MDC analysis uses the atomic multipoles (obtained from the fitted density) and reconstructs these multipoles exactly by distributing charges over all atoms. We report here our results, also including in the discussion the optimized Li + (EC)n(DMC)m clusters of Ref. 50  The effect of the mixed solvent composition on the vibrational properties was next addressed by calculating the vibrational spectra of the optimized clusters, shown in Figure   2
Also, the free energy changes associated to the transition from Li + (DMCcc)2(A -) to Li + (DMCcc)(DMCct)(A -) and, finally, to Li + (DMCct)2(A -) ones (Table S5) are negative, implying that the relative stabilities of isolated DMC conformers are not crucial for the stabilization of solvation clusters. As a consequence, it is possible that different fractions of solvation structures containing different DMC conformers coexist in the condensed (bulk) phase. As pointed out in our previous study 50 , however, only large scale Molecular Dynamics simulations of the liquid phase can provide more accurate information about these effects.
Also, from a visual inspection of the configurations shown in Figure 3 it is clear that a bidentate coordination is obtained in the cases of the most thermodynamically stable clusters, Li + (PC)2(A -) and Li + (DMC)2(A -). Similar conclusions were reached in our previous DFT study on Li + (EC)n(Anion -) clusters 51 , which were also found to be in very good agreement with femtosecond vibrational spectroscopic measurements. These findings agree with previous studies 62-64 that also showed that at high salt concentration bi-dentate complexation of Li + with anions takes place.
Our data therefore show that, although the total molecular coordination number of Li + in the anion-containing first solvation reduces to three (including two solvent molecules and the anion), the Lithium cation is still closely interacting with four electron donor atoms. These features have two implications. First, the local molecular-scale tetrahedral structure comprising four carbonate solvent molecules around Li + , widely accepted in dilute conditions, is strongly modified in concentrated salt solutions, leading to a first coordination shell of Li + comprising only two carbonate solvent molecules and one anion. Second, even in the presence of these strongly modified molecular environments, the Li + cation still keeps a tetrahedral coordination at the interatomic scale, interacting with the carbonyl oxygen atoms of the two carbonate solvents, and two electron donor atoms of the anions. Also, we note that, due to this specific structural arrangement inside the first solvation shell of Li + , the charge of solvated Li + is neutralized by the anion and, as a consequence, we expect that its mobilty under an applied potential can be significantly reduced. The formation of such a cation/anion/solvent contact ion pair can therefore provide a rational explanation for the ionic conductivity drop of lithium salt /carbonate electrolyte solutions at high concentrations, as we will additionally discuss below.
We To address these issues, combined information obtained from multiscale approaches are necessary. This goes well beyond the present work, whose target is to study solvation effects in contact ion pairs. In this framework, we provide insight on the mechanisms active at short intermolecular distances, and treat quantum chemically intra-and intermolecular interactions at these specific length scales.
The Gibbs free energy changes, ΔG, related to the solvation mechanism where two solvent molecules in the Li + first solvation shell are replaced by an anion have also been calculated, and are reported in  03 D), DMCtt , has a free energy which is 15.6 and 12.6 kcal/mol higher than that of DMCcc and DMCct, respectively. Due to these high free energy differences, this conformer was not considered in the present calculations. The finding that the ion pair formation is more pronounced in the low-polar DMCcc than in the highly-polar PC and EC solvents is also consistent with the trends in their dielectric constants 66,67 , since ion pair formation is less pronounced in highly polar solvents. In addition, referring to the observed trends for the investigated anions, the substitution process is facilitated in the case of all solvents for BF4 -, followed by ClO4and finally by PF6 -. This finding hence additionally indicates that the contact ion pair formation is thermodynamically more favourable in the case of LiBF4, followed by LiClO4 , with LiPF6 being the least favourable case.
We conclude this discussion with an important observation. Previous works on electrical conductivity measurements 68,69 of LiPF6, LiClO4 and LiBF4 solutions in organic carbonate electrolytes have reported general trends in the conductivity drop at high salt concentration similar to those described above in the contact ion pair formation. Indeed, according to the experimental measurements, the conductivity drop at high salt concentration is more pronounced for LiBF4, followed by LiClO4 and finally LiPF6. In addition, the salt concentration corresponding to the maximum conductivity value is shown to increase following the trend LiBF4 < LiClO4 < LiPF6 (Figure 4 in Ref. 68 ). This finding is also consistent with our calculations since, in the cases where the contact ion pair formation is thermodynamically more pronounced, these effects should start manifesting at lower salt concentrations, since the probability to observe these ion pairs is in general higher.
Previous review works 1,70 have highlighted the fact that the behaviour of the conductivity in electrolyte solutions is a synergistic effect, controlled by both the viscosity of the solvent and the ion pair formation. It was also pointed out that the latter is probably the most important mechanism in the high salt concentration range. In contrast, in the opposite limit of low salt concentration, and until the point where the maximum conductivity value is observed, solvent viscosity and dielectric constant mainly control the conductivity. Our theoretical predictions, and their agreement with the experimental data, can therefore be considered as a further validation of the previously proposed mechanisms. From this point of view, they provide additional relevant insight that could be used as a springboard towards rational design of liquid electrolytes with optimal properties for battery applications.

Conclusions
Quantum

Supporting Information
Tables S1, S3, S4, S5. Indicated thermodynamic properties of the indicated solvation clusters.           Table S5. Calculated free energy changes for the transitions between different solvation structures containing the cis-cis and cis-trans conformers of DMC.