Ion Association in Aprotic Solvents for Lithium Ion Batteries RequiresDiscrete−Continuum Approach: Lithium Bis(oxalato)borate inEthylene Carbonate Based MixturesOleksandr M. Korsun,† Oleg N. Kalugin,*,† Igor O. Fritsky,‡ and Oleg V. Prezhdo*,§

†Department of Inorganic Chemistry, V. N. Karazin Kharkiv National University, Kharkiv 61022, Ukraine‡Department of Physical Chemistry, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine§Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

ABSTRACT: Ion association in solutions of lithium salts inmixtures of alkyl carbonates carries significant impact on theperformance of lithium ion batteries. Focusing on lithiumbis(oxalato)borate, LiBOB, in binary solvents based on ethylenecarbonate, EC, we show that neither continuum nor discretesolvation approaches are capable of predicting physicallymeaningful results. So-called mixed or the discrete−continuumsolvation approach, based on explicit consideration of an ionsolvatocomplex combined with estimation of the mediumpolarization effect, is required in order to characterize the ionassociation at the quantitative level. The calculated changes ofthe Gibbs free energy are overestimated by nearly an order ofmagnitude by the purely continuum and purely discreteapproaches, with the values having the opposite signs. The physically balanced discrete−continuum description predicts weakion association. The numerical data obtained with density functional theory are validated using coupled-cluster calculations andexperimental X-ray data. The study contributes to resolution of the challenge in solvation modeling in general, and develops areliable, practical method that can be used to screen ion association in a broad range of ion−molecular mixtures for lithium ionbatteries, especially for the solutions of LiBOB in EC based mixtures.

1. INTRODUCTION

Lithium ion batteries (LIBs) constitute a key component ofmost modern portable electronic devices and vehicles.Electrolyte solutions used in the batteries consist of a particularlithium salt dissolved in a mixture of aprotic organic solvents,such as cyclic and linear carbonates or esters.1 One of the mostimportant physicochemical properties of the salts is highsolubility with minimal ion association (assoc) in a givensolvent mixture. These operating conditions are necessary forensuring maximal electrical conductivity and, as a consequence,high specific power of LIBs.2

From the thermodynamic point of view, minimal ionassociation corresponds to maximal change in the standardGibbs free energy of ion association, ΔassocGT

o = −RT ln Kassoc.An experimental determination of the ion association constant,Kassoc, is quite a labor- and time-consuming procedure.Therefore, a reliable prediction of the sign and magnitude ofΔassocGT

o by molecular modeling constitutes an important task.A theoretical method capable of this task will have a significantimpact on selection and development of novel lithium salts andpolar aprotic cosolvents for design of advanced LIBs.Several quantum-chemical approaches have been considered,

most of which focus on aqueous media.3,4 Application of thediscrete−continuum approach to nonaqueous solutions of

lithium salts is quite rare. Recently the mixed approach hasbeen used to investigate the solvation free energies of the Li+

ion in acetonitrile,5 to characterize ion clustering for theLi[PF6] electrolyte in acetonitrile,6 and to demonstrate that thestructure of the Li+ first solvation shell can be predicted well inan organic carbonate mixture.7

In this work, we show that neither continuum nor discretesolvation models can provide a satisfactory description of ionsolvation and association in a typical LIB system. A mixeddiscrete−continuum description is required in order to obtain aphysically reasonable representation. We demonstrate with apopular lithium salt, dissolved in the EC based mixture of polaraprotic solvents, that the pure models err by nearly an order ofmagnitude and that the mentioned errors have opposite signs.The errors are corrected in the mixed approach, whichconsiders explicitly the first solvation shell of the solute particleand treats the rest of the solvent as a polarizable medium. Themethod predicts a small degree of ion association. Thedescribed approach can be used to screen a large number ofsystems suitable for LIB applications, assisting in design of

Received: June 13, 2016Revised: June 24, 2016Published: June 28, 2016

Article

pubs.acs.org/JPCC

© 2016 American Chemical Society 16545 DOI: 10.1021/acs.jpcc.6b05963J. Phys. Chem. C 2016, 120, 16545−16552

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novel and more efficient electrolyte solutions. The computa-tionally efficient level is validated using both higher levelcomputations and experimental data.Lithium bis(oxalato)borate (Li[B(C2O4)2], LiBOB) has been

extensively studied as a highly promising electrolyte for use inLIBs. For example, LiBOB solutions in alkyl carbonates havebeen found much more thermally stable than the widely usedLi[PF6] solutions. Also, the performance of lithiated graphiteelectrodes appears to be much better with LiBOB solutionsthan with any other known lithium salt solutions.8

It is known that there exists no suitable single solvent,exhibiting both high dielectric constant and low viscosity. Thesesolvent properties are needed to ensure good lithium saltsolubility and high ion mobility, correspondingly. Currently,ethylene carbonate (EC) is a commonly used component inmany LIB electrolyte solutions.1 The dimethyl carbonate(DMC), diethyl carbonate (DEC), or ethylmethyl carbonate(EMC) are usually added to EC as nonviscous cosolvents.The current study elucidates the utility of continuum,

discrete, and mixed discrete−continuum solvation approachesin application to association of the Li+ cation with the[B(C2O4)2]

− anion (BOB−). The previously unstudiedEC:DMC binary mixture with the 7:3 weight or ≈70%:30%mole ratio is chosen as the solvent. The EC:DMC binarymixtures with the component molar ratio ranging from50%:50% to 75%:25% exhibit sufficiently high dielectricconstants and relatively low viscosities, making themappropriate for applications in the LIB technology.9 Themain goal of the present study is to develop and validate anapproach that allows one to describe the ion association at thequantitative level without a need to refer to any experimentaldata. This task is important for advancing LIBs using the novelelectrolytes and solvent mixtures.

2. THEORETICAL METHODOLODYFor the target ion association process, Li+(solv) + BOB−

(solv) =[Li+BOB−](solv), the change in the corresponding standardthermodynamic potential (ΔassocΦT

o) at the arbitrary temper-ature (T) can be calculated using

Δ Φ = Δ Φ − Δ Φ − Δ Φ

+ Δ Φ

+ −

+ −

(Li ) (BOB )

([Li BOB ])

T T T T

T

assoco

assoc(g)o

solvo

solvo

solvo

(1)

Here, Δassoc(g)ΦTo is the change in the standard thermodynamic

potential for the gas phase (g) association process, Li+(g) +BOB−

(g) = [Li+BOB−](g), and ΔsolvΦTo are the standard

thermodynamic potential changes for solvation (solv) of theLi+ and BOB− ions and the [Li+BOB−] ion pair (IP). Note that,in addition to eq 1, the ΔsolvΦT

o value for a particle P in anarbitrary solvent can be computed rigorously according to

Δ Φ = Φ − Φ − ΦP P( ) (solution) (solvent) ( )T T T Tsolvo o o o

(g)

(2)

Taking into account that a statistical mechanical treatment ofthe condensed phases is expensive, instead, eq 3 is widely usedin the framework of quantum-chemical calculations of theΔsolvΦT

o potentials.

Δ Φ ≡ Φ − ΦP P P( ) ( ) ( )T T Tsolvo o

(solv)o

(g) (3)

The changes in the standard Gibbs free energy during ionassociation (ΔassocGT

o) and solvation (ΔsolvGTo) can be obtained

using the corresponding enthalpy and entropy data at T =

298.15 K. The enthalpy and entropy changes show weakvariation over a broad temperature range. The changes in ionassociation enthalpy (ΔassocH298

o ) and entropy (ΔassocS298o ) as

well as solvation Gibbs free energy (ΔsolvGTo) depend on the

accuracy of the enthalpy (ΔsolvH298o ) and entropy (ΔsolvS298

o ) ofsolvation of the ions and IP. The thermodynamic potentials canbe predicted using quantum-chemical calculations for the gasand condensed phases. The latter data can be obtained with theself-consistent reaction field (SCRF) methods.10,11

2.1. Approaches. In order to calculate the Gibbs freeenergy and equilibrium constant of ion association, we considerthree solvation approaches (A). According to the first one,continuum model (AI), the bare ions and IP are placed in astructureless polarized continuum (c) with the dielectricconstant of the solvent. The second, discrete solvationapproach (AII), involves an explicit consideration of thesolvatocomplexes of the ions and IP in the gas phase, includingsolvent molecules most strongly interacting with the solutes. Acombination of the approaches mentioned above constitutesthe mixed or discrete−continuum framework (AIII).Application of AI is straightforward. It involves computation

of the properties of the ions and IP in the gas phase and in thestructureless polarized continuum of the solvent mixture. AIIrequires gas phase calculations on a series of ion−molecularand IP−molecular solvatocomplexes. According to AIII, themost exergonic cation, anion, and IP solvatocomplexes fromAII should be considered in the solvent continuum, as in AI.In principle, a fully atomistic description of the solvent is

preferable to a continuum or discrete−continuum model. Atthe same time, an explicit solvent model has its own limitations,for instance, due to approximations of a particular densityfunctional, a basis set, or the size of the solvent shell that can beincluded in an explicit calculation given available computationalresources. Working within the limits of the current theoreticalapproximations for the explicit and continuum descriptions ofthe solvent, we demonstrate that the mixed discrete−continuum provides the best results, while, at the same time,remaining computationally efficient.The separation between the explicit and continuum

components of the mixed model is defined by solid physicalarguments. The explicit part includes the first solvation shell ofthe ions and IP surrounded by the most strongly interactingand abundant solvent molecules. Including the first solvationshell of the solvent without account for polarization of theremainder of the solvent leads to significant errors in solvationthermodynamics. Similarly, representing the entire complex bya continuum model ignores specific interactions between thesolute and the first solvation shell, providing another source oferror. The combination of the two descriptions gives a soundapproach, in which the two errors cancel.Chart 1 represents the set of solvation processes involving

Li+ and BOB− ions and the [Li+BOB−] IP and that are neededfor the thermodynamic calculations of ΔsolvΦ298

o within thethree approaches. The chart also shows the ion associationprocesses, for which the ΔassocΦ298

o values (Φ = H, S, G) werecomputed in the EC:DMC (7:3) binary solvent mixture. Dueto high dipole moment and favorable geometry, the ECmolecule has a higher affinity to the bare ions and IP than theDMC molecule, as observed experimentally for the Li+ ion.12,13

In combination with a considerably larger EC mole fraction in amixture with DMC, one expects preferential solvation of theion species by EC molecules. This expectation is enhanced

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further by the higher, ≈70% molar content of EC relative to≈30% DMC.2.2. Computations. The quantum-chemical calculations

were carried out with Gaussian 03.14 The 6-31+G(2d) basis setand the B3LYP exchange-correlational functional were used.15

The geometry optimization was done in two steps. First, thelocal minimum on the potential energy surface was foundedusing numerical second derivatives with respect to the nuclearcoordinates. Then, the optimization was continued with themore robust analytical second derivatives. The latter also gaveharmonic vibrational frequencies needed for thermodynamicanalysis. The analytic second derivatives were particularlyimportant for the construction of the solvent-saturatedsolvation shells for the AII approach, since these derivativeswere used to confirm that the found structures corresponded tolocal minima. The pressure p° = 101325 Pa (1 atm), and themost abundant isotopes were used for the thermodynamic datacalculation within the ideal gas approximation (gas standardstate). The basis set superposition error was taken into accountusing the counterpoise correction.The isodensity polarizable continuum model (IPCM)16 with

the dielectric constant of 51.0 for the EC:DMC (7:3) binarysolvent17 was applied to represent the structureless solventcontinuum in methods AI and AIII. Note that the SCRFcomputations employing the IPCM technique do not require apredefined or manually scaled atomic radii, in contrast to the

more traditional PCM model. It is known in the case of the Li+

ion that the van der Waals radius has to be scaled upsignificantly to obtain good results.5 The solute energies werecomputed in a solvent cavity with the isodensity surfacecontour equal to 0.0002 e·bohr−3. The solution standard statewas customarily defined to have the 1 mol·L−1 concentrationfor all solute particles, while at the same time, neglectingsolute−solute interactions.

2.3. Validation. The calculation results were validated bycomparison of the B3LYP/6-31+G(2d) level of theory with thereference coupled-cluster calculations and X-ray experimentaldata. The aug-cc-pVDZ and 6-31+G(2d) basis sets were used inthe CCSD(full) method. Geometric properties and dipolemoment of the EC molecule, geometric properties of the BOB−

ion, and the potential energy profile of the ion−molecularinteraction for the [Li(EC)]+ solvatocomplex were selected forvalidation. The experimental data for the EC molecule in thecrystal and liquid states, as well as for the BOB− ion in theMeBOBs (Me = Li, Na, K) and [Li(EC)4]BOB crystals, wereused for the comparison. Some geometrical parameters anddipole moment of the EC molecule and BOB− ion obtainedfrom the quantum-chemical calculations and experiments arepresented in Tables 1 and 2, respectively.The data of Tables 1 and 2 show excellent agreement

between the reference and basic levels of theory, and betweenthe theories and the X-ray experiments. This fact indicates thatthe B3LYP/6-31+G(2d) method is able to reproduce thestructure and charge distribution of the molecular and ionicspecies. Figure 1 shows the basic and reference profiles of thepotential energy surface for the gas phase [Li(EC)]+

solvatocomplex as a function of the ion−molecule distance.Figure 1 shows that the overall shape and location of the

minimum on the potential energy curve relevant to thesolvation process agree between the basic, B3LYP/6-31+G(2d),and highly rigorous, CCSD(full)/aug-cc-pVDZ, theory levels. Itis known that in some cases B3LYP can overestimate thesolvent binding energy;7 however, it is not the case here, asevidenced by the data of Figure 1. Thus, the B3LYP/6-31+G(2d) description provides a good representation ofthe ion−molecule interaction involved in the solvation process.

3. RESULTS AND DISCUSSION

3.1.1. Solvatocomplexes Formation. The gas phasestructures of the BOB− ion, [Li+BOB−] IP, EC molecule, and

Chart 1. Investigated Processes for the Solution of theLiBOB Salt in the EC:DMC (7:3) Binary Solvent Mixture,Obtained within the Continuum (AI), Discrete (AII), andMixed (AIII) Solvation Approachesa

ag, gas phase; c, continuum; n = 1−5, coordination numbers of the Li+

ion in the [Li(EC)n]+ solvatocomplexes, # = A−D, coordination types

of the EC molecule in the [BOB(EC)#]− solvatocomplexes defined inFigure 2i−l; m = 1, 2, coordination numbers of the Li+ ion by EC inthe [Li+(EC)mBOB

−] solvatocomplexes.

Table 1. Selected Bond Distances (d), Valence Angles (a), and Dipole Moment (μ) of the EC (C2) Molecule Obtained Usingthe Basic, B3LYP/6-31+G(2d), and Reference, CCSD(full)/aug-cc-pVDZ and 6-31+G(2d), Levels of Quantum-ChemicalTheory in Gas Phase and Those Deduced from the X-ray Experiments for the Condensed Phasesa

param CCSD(full)/aug-cc-pVDZ B3LYP/6-31+G(2d) CCSD(full)/6-31+G(2d) X-ray for crystal18/liquid19

d(C(c)O(c)), Å 1.196 1.191 1.187 1.15/1.20 ± 0.09d(OC(c)), Å 1.365 1.359 1.354 1.33/1.34 ± 0.12d(CO), Å 1.442 1.434 1.432 1.40/1.46 ± 0.13d(CC), Å 1.533 1.534 1.525 1.52/1.52 ± 0.11d(CH), Å 1.097/1.101 1.092/1.096 1.094/1.099a(OC(c)O(c)), deg 124.76 124.84 124.80 124.5/−a(OC(c)O), deg 110.48 110.32 110.40 111.0/−a(COC(c)), deg 108.93 109.83 109.00 109.0/−a(CCO), deg 102.51 103.03 102.31 102.0/−a(HCO), deg 108.53/108.72 108.53/108.51 108.68/108.69μ, D 5.47 5.54 5.61

aThe subscript “(c)” designates the carbonyl group.

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the [Li(EC)n]+ (n = 1−5), [BOB(EC)#]− (# = A−D), and

[Li+(EC)mBOB−] (m = 1, 2) solvatocomplexes are shown in

Figure 2.Table 3 contains selected geometric data for the EC

molecule, BOB− ion, [Li+BOB−] ion pair, and the [Li(EC)n]+

and [Li+(EC)mBOB−] solvatocomplexes. The data werecomputed in the gas phase at the B3LYP/6-31+G(2d) levelof theory. The Li+ ion strongly polarizes the carbonyl groups ofthe coordinated EC molecules and BOB− ion in the[Li(EC)n]

+, [Li+BOB−], and [Li+(EC)mBOB−] structures.This action results in the substantial lengthening of the doublebonds of the coordinated species. As the first coordinationsphere around the Li+ ion gets saturated, the distances from Li+

to the carbonyl oxygen atoms are increasing, and thecorresponding valence angles are decreasing, as a result ofligand repulsion and incrementing.The standard changes in the calculated thermodynamic

potentials of the [Li+BOB−] IP, and the [Li(EC)n]+ (n = 1−5),

[BOB(EC)#]− (# = A−D), and [Li+(EC)mBOB−] (m = 1, 2)

solvatocomplexes formation in the gas phase are collected inTable 4. This table contain Δassoc(g)Φ298

o potentials (ΔΦ298o

values for the [Li+BOB−](g)) that are significant for eq 1application. The data of Table 4 show that the contact IP

should be extremely stable, since ΔG298o = −486.7 kJ·mol−1, i.e.,

considerably less than zero. The IP stability arises due to bothCoulomb interaction and chelate bonding of Li+ by the BOB−

ion (see Figure 2b).Changes in the Gibbs free energy for the Li+(g) + nEC(g) =

[Li(EC)n]+(g) processes are negative and decrease to

−369.3 kJ·mol−1 for the four-coordinated solvatocomplex(see Figure 2d−g). Taking into account the higher affinity ofthe EC molecules to the bare Li+ ion compared to DMC andthe larger EC mole fraction, ≈70% vs ≈30% for DMC, it isreasonable to expect that the most exergonic solvatocomplex,[Li(EC)4]

+, as determined in the gas phase cluster calculation,

Table 2. Selected Bond Distances (d) and Valence Angles (a) of the BOB− (D2d) Ion Obtained Using the Basic, B3LYP/6-31+G(2d), and Reference, CCSD(full)/aug-cc-pVDZ and 6-31+G(2d), Levels of Quantum-Chemical Theory in Gas Phaseand Those Deduced from the X-ray Experiments for the Crystalsa

parameter CCSD(full)/aug-cc-pVDZ B3LYP/6-31+G(2d) X-ray after MeIBOBs20 X-ray for [Li(EC)4]BOB21

d(OB), Å 1.483 1.473 1.474 1.4707d(CO), Å 1.334 1.328 1.326 1.3320d(O(c)C), Å 1.209 1.203 1.198 1.1908d(CC), Å 1.553 1.554 1.538 1.536a(O(c)CO), deg 126.49 126.46 127.4a(O(c)CC), deg 125.93 126.37 124.5a(OCC), deg 107.58 107.17 108.0a(OBO), deg 105.43/111.53 105.06/111.72 109.5

aThe subscript “(c)” designates the carbonyl group.

Figure 1. Potential energy profiles, E, of the gas phase [Li(EC)]+ (C2)solvatocomplex along the lithium−oxygen coordinate, d(LiO(c)),obtained using the basic, B3LYP/6-31+G(2d) (blue circles), andreference, CCSD(full)/aug-cc-pVDZ (dark red diamonds), levels ofquantum-chemical theory. The subscript “(c)” designates the carbonylgroup. The basic curve is shifted up by 0.86 Ha.

Figure 2. Gas phase optimized structures of the BOB− ion (a), the[Li+BOB−] ion pair (b), the EC molecule (c), and the [Li(EC)1−5]

+

(d−h), [BOB(EC)A−D]− (i−l), and [Li+(EC)1,2BOB−] (m,n)solvatocomplexes. Symbols A−D refer to coordination types of theEC molecule with respect to the BOB− ion in the [BOB(EC)A−D]−

structures shown in the figure.

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should dominate in solution, and fractions of othersolvatocomplexes should be small.12,22,23 The difference inthe Gibbs free energy of formation of the [Li(EC)3]

+ and[Li(EC)4]

+ solvatocomplexes is less than 10 kJ·mol−1, whereasthe corresponding potential energy difference is much greater,approaching 50 kJ·mol−1. The example described abovedemonstrates that it is very important to consider the Gibbsfree energy rather than the potential energy changes. The latteris used often for the thermodynamic characterization of variousprocesses, since potential energy can be easily obtained fromquantum-chemical calculations.24,25 An even stronger case isformation of the [Li(EC)5]

+ (see Figure 2h) from [Li(EC)4]+.

This process has a negative potential energy change and apositive Gibbs free energy change. Thus, this unfavorableprocess can be predicted erroneously as favorable based on thepotential energy difference alone. The [Li(EC)5]

+ solvatocom-plex (ΔG298

o = −329.1 kJ·mol−1) has not been discussed

previously as a possible form of the [Li(EC)n]+ in

solution.7,24,26,27 Due to translational dynamics and strongdipole−dipole repulsions of EC molecules in [Li(EC)5]

+, thelatter is expected to be unstable in the bulk solution.Ion−dipole interactions between the BOB− ion and EC

molecules are extremely weak. The ΔG298o values for the

[BOB(EC)#]− formation, where # = A−D is the ECcoordination type (see Figure 2i−l), vary only from−5.4 kJ·mol−1 (type D) to −14.1 kJ·mol−1 (type C). Suchlow values can be explained by the large size of the BOB− ion,resulting in low specific density of the negative charge.Consequently, the BOB− anion cannot be strongly solvatedin solution even by highly polar molecules such as EC.The lithium site of the [Li+BOB−] contact IP is not sterically

saturated and can additionally attach one or two EC molecules(see Figure 2m,n). These processes are not as exergonic asformation of the [Li(EC)n]

+ solvatocomplexes discussed above.

Table 3. Selected Bond Distances (d) and Valence Angles (a) of the EC Molecule, BOB− ion, [Li+BOB−] Ion Pair, and the[Li(EC)n]

+ (n = 1−5) and [Li+(EC)mBOB−] (m = 1, 2) Solvatocomplexes Obtained Using the Basic, B3LYP/6-31+G(2d), Levelof Theory in Gas Phase (See Figure 2a−h,m,n)a

particle d(O(c)C(c)), Å d(LiO(c)), Å a(LiO(c)C(c)), deg

EC (C2) 1.191[Li(EC)]+ (C2) 1.224 1.734 180.0[Li(EC)2]

+ 1.216 1.783 180.0[Li(EC)3]

+ 1.208 1.849, 1.851, 1.850 171.8, 166.4, 174.0[Li(EC)4]

+ 1.204, 1.203, 1.204, 1.204 1.943, 1.927, 1.940, 1.932 144.6, 153.8, 142.3, 146.8[Li(EC)5]

+ 1.202, 1.200, 1.202, 1.199, 1.198 1.998, 2.148, 1.993, 2.266, 1.955 134.9, 139.3, 136.5, 138.7, 174.5BOB− (D2d) 1.203[Li+BOB−] (C2v) 1.230/1.192 1.893 101.9[Li+(EC)BOB−] 1.225/1.194,1.193//1.208 1.957, 1.956//1.848 103.1//151.7[Li+(EC)2BOB

−] 1.217/1.195, 1.196//1.205, 1.207 2.053, 2.049//1.909, 1.957 102.2, 102.3//134.9, 129.2aThe subscript “(c)” designates the carbonyl group.

Table 4. Changes in Potential Energy (ΔE), Standard Internal Energy (ΔU298o ), Enthalpy (ΔH298

o ), Entropy (ΔS298o ), and GibbsFree Energy (ΔG298

o ) of Gas Phase (g) Formation of the [Li+BOB−] Ion Pair, and the [Li(EC)n]+ (n = 1−5), [BOB(EC)#]− (# =

A−D), and [Li+(EC)mBOB−] (m = 1, 2) Solvatocomplexesa

complex formation process ΔE, kJ·mol−1 ΔU298o , kJ·mol−1 ΔH298

o , kJ·mol−1 ΔS298o , J·mol−1·K−1 ΔG298o , kJ·mol−1

+ =+ − + −Li BOB [Li BOB ](g) (g) (g) −523.9 −517.3 −519.7 −110.9 −486.7

+ =+ +Li EC [Li(EC)](g) (g) (g) −212.4 −205.3 −207.8 −86.3 −182.0

+ =+ +Li 2EC [Li(EC) ](g) (g) 2 (g) −374.1 −357.2 −362.2 −188.1 −306.1

+ =+ +Li 3EC [Li(EC) ](g) (g) 3 (g) −469.0 −446.1 −453.5 −310.3 −361.0

+ =+ +Li 4EC [Li(EC) ](g) (g) 4 (g) −523.9 −493.4 −503.3 −449.6 −369.3

+ =+ +Li 5EC [Li(EC) ](g) (g) 5 (g) −531.4 −496.8 −509.2 −604.0 −329.1

+ =− −BOB EC [BOB(EC) ]A(g) (g) (g) −46.1 −37.8 −40.3 −94.0 −12.3

+ =− −BOB EC [BOB(EC) ]B(g) (g) (g) −37.1 −28.9 −31.4 −85.4 −5.9

+ =− −BOB EC [BOB(EC) ]C(g) (g) (g) −40.1 −31.9 −34.4 −68.0 −14.1

+ =− −BOB EC [BOB(EC) ]D(g) (g) (g) −40.0 −34.3 −36.8 −105.3 −5.4

+ =+ − + −[Li BOB ] EC [Li (EC)BOB ](g) (g) (g) −101.5 −92.2 −94.7 −94.9 −66.4

+ =+ − + −[Li BOB ] 2EC [Li (EC) BOB ](g) (g) 2 (g) −166.8 −149.1 −154.1 −245.7 −80.8aThe symbols A, B, C, and D refer to coordination types of the EC molecule with respect to the BOB− ion in the [BOB(EC)A−D]− structures (seeFigure 2i−l).

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The corresponding ΔG298o values for the [Li+(EC)BOB−] and

[Li+(EC)2BOB−] are −66.4 and −80.8 kJ·mol−1. In other

words, the first EC molecule binds to [Li+BOB−] quitestrongly, while the affinity of the second EC molecule to the IPmonosolvate is small and comparable to the free Gibbs energyof the [BOB(EC)#]− formation. The two explicit EC moleculesare sufficient for the complete saturation of the lithiumsolvation shell in the [Li+BOB−] IP. Therefore, thecoordination number of Li+ in the solvated cation as well asin the solvated IP is defined by the carbonyl oxygen atoms andis equal to four.According to the gas phase calculations (Table 4), the

[Li(EC)4]+ cation, the [BOB(EC)C]− anion, and the

[Li+(EC)2BOB−] IP solvatocomplexes are the most stable

species. Therefore, these species were chosen in the frameworkof the discrete (AII) approach to characterize ion association ofLiBOB in the EC:DMC (7:3) binary mixture.3.1.2. SCRF Application. The SCRF quantum-chemical

calculations of the bare Li+ and BOB− ions, the [Li+BOB−] IP,the EC molecule, and the [Li(EC)4]

+ and [Li+(EC)2BOB−]

solvatocomplexes were carried out using the experimental valueof dielectric constant (51.0) of the EC:DMC (7:3) binarymixture.17 The changes in the standard enthalpy of solvationwithin the simplest AI model, Δsolv(I)H298

o , were estimatedaccording to

Δ = Δ + −

≡ Δ − · −

H E p V R

E

298.15

2.38 kJ mol

solv(I) 298o

solv(I)o o

solv(I)1

(4)

Here, Δsolv(I)E is the potential energy change during thesolvation within AI, and Vo = 0.001 m3·mol−1 is the standardmolar volume that is accessible for the solute particle in thesolution standard state.The isothermal compression stage of solvation decreases the

translational entropy of transferring particles within the AImodel. Those changes in the standard entropy of solvation,Δsolv(I)S298

o , were taken into account with

Δ = −

= − · ·− −

⎛⎝⎜⎜

⎛⎝⎜

⎞⎠⎟⎞⎠⎟⎟S R V

Rp

ln ln298.15

26.58 J mol K

solv(I) 298o o

o

1 1(5)

Since different standard states for the solvent and solute areusually used,28 the Vo value for EC in eqs 4 and 5, the molarvolume that is accessible for the particular cosolvent moleculesin target EC:DMC (7:3) binary solvent mixture, waspreliminarily calculated from experimental data29 and sub-stituted on VEC

o = 1.024 × 10−4 m3·mol−1.The changes in the standard thermodynamic potentials of

solvation within AIII, Δsolv(III)Φ298o , can be found as linear

combinations of the corresponding data obtained within AI andAII (see Chart 1).

3.2. Solvation Data. The changes in the standard enthalpy,entropy, and Gibbs free energy of the solvation processes aresummarized in Table 5 for the different solvation approaches(Δsolv(A)Φ298

o ). In spite of a significant dipole moment valueeven in the gas phase, the EC molecules gives a very smallmagnitude of Δsolv(I)G298

o = −12.6 kJ·mol−1. The bare Li+ ionhas a small radius and, consequently, a high polarizing action.Hence, its transfer into the structureless continuum ischaracterized by an extremely negative change in the standardGibbs free energy, which is equal to −579.2 kJ·mol−1. The samevalue for the saturated [Li(EC)4]

+ solvatocomplex is almostfour times smaller by module, because of the size increase uponbinding of the four EC molecules. The Δsolv(III)G298

o value forthe Li+ ion is intermediate between those for the AI and AIImodels and is equal to −463.9 kJ·mol−1.Taking into account that Δsolv(I)G298

o = −164.2 kJ·mol−1 forthe bare BOB− ion, its symmetric polarization by thestructureless continuum is almost 10 times more exergonic,as compared with the formation of [BOB(EC)C]− anion in thegas phase. Therefore, consideration of any EC unsaturatedsolvatocomplexes involving the BOB− ion is not reasonableand, as consequence, we have taken Δsolv(III)Φ298

o ≡ Δsolv(I)Φ298o

(see Table 5).

Table 5. Changes in Standard Enthalpy (Δsolv(A)H298o ), Entropy (Δsolv(A)S298

o ), and Gibbs Free Energy (Δsolv(A)G298o ) of Solvation

of the EC Molecule, the Li+ and BOB− ions, and the [Li+BOB−] Ion Pair in the EC:DMC (7:3) Binary Solvent, Obtained Usingthe Continuum (I), Discrete (II), and Mixed (III) Solvation Approaches (A) (g, Gas; c, Continuum)

particle A solvation process Δsolv(A)H298o , kJ·mol−1 Δsolv(A)S298

o , J·mol−1·K−1 Δsolv(A)G298o , kJ·mol−1

EC I =EC EC(g) (c) −26.1 −45.5 −12.6

Li+ I =+ +Li Li(g) (c) −587.1 −26.6 −579.2

II + =+ +Li 4EC [Li(EC) ](g) (g) 4 (g) −503.3 −449.6 −369.3

I =+ +[Li(EC) ] [Li(EC) ]4 (g) 4 (c) −152.8 −26.6 −144.9

III + =+ +Li 4EC [Li(EC) ](g) (c) 4 (c) −551.5 −294.0 −463.9

BOB− I =− −BOB BOB(g) (c) −172.1 −26.6 −164.2

II + =− −BOB EC [BOB(EC) ]C(g) (g) (g) −34.4 −68.0 −14.1

III + =− −BOB 0EC BOB(g) (c) (c) −172.1 −26.6 −164.2

[Li+BOB−] I =+ − + −[Li BOB ] [Li BOB ](g) (c) −51.9 −26.6 −44.0

II + =+ − + −[Li BOB ] 2EC [Li (EC) BOB ](g) (g) 2 (g) −154.1 −245.7 −80.8

I =+ − + −[Li (EC) BOB ] [Li (EC) BOB ]2 (g) 2 (c) −65.0 −26.6 −57.1

III + =+ − + −[Li BOB ] 2EC [Li (EC) BOB ](g) (c) 2 (c) −166.8 −181.2 −112.8

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As for the neutral [Li+BOB−] IP as well as for the morespatial extended [Li+(EC)2BOB

−] neutral solvatocomplex, thecorresponding Δsolv(I)G298

o values are around −50 kJ·mol−1, thatis almost a factor of 3 smaller than for the bare BOB− ion.Simultaneously, the Δsolv(II)G298

o value for the [Li+BOB−] IP isonly equal to −80.8 kJ·mol−1. Consequently, both discrete andcontinuum contributions to solvation of the [Li+BOB−] IP aresignificant and are accounted for within the AIII model. Thecorresponding change in the standard Gibbs free energy isequal to −112.8 kJ·mol−1.3.3. Ion Association. Table 6 presents the changes in the

standard enthalpy, entropy, and Gibbs free energy for the Li+

and BOB− ion association, obtained within the three differentsolvation approaches (Δassoc(A)Φ298

o ). The potentials werecalculated according to eq 1 using the correspondingΔassoc(g)Φ298

o values from Table 4 for the IP formation in thegas phase and the Δsolv(A)Φ298

o data for the solvation processesfrom Table 5. Solvation model AI predicts positive values of theΔassoc(I)H298

o and Δassoc(I)G298o . The values are similar and are

around 200 kJ·mol−1, since the entropic factor is unessential.Thus, the continuum solvation approach predicts an unphysicalbehavior: ion association is impossible for the LiBOB solutionin the EC:DMC (7:3) binary solvent at any temperature,because the entropic contribution is not properly taken intoaccount. Libration of the three EC molecules upon ionassociation according to solvation model AII leads to a largepositive change in Δassoc(II)S298

o = 161.0 J·mol−1·K−1. Thecorresponding Δassoc(II)H298

o value is strongly exothermic. As aconsequence, the discrete approach predicts a large negativevalue of Δassoc(II)G298

o = −184.1 kJ·mol−1: ion dissociation isimpossible at any temperature. The corresponding Kassoc isaround 1032. That is, the discrete model sharply overestimatesthe hypothetical ion association. Such a value of Kassoc wouldmake the lithium salt with a large anion, such as BOB−, totallyinsoluble even in the highly polar aprotic solvents.1,9 Solvationmodel AIII produces moderately positive values of allΔassoc(III)Φ298

o potentials. Their absolute values are significantlysmaller than the corresponding magnitudes obtained within AIand AII. Substitution of the two EC molecules in the[Li(EC)4]

+ solvatocomplex by the in abstracto nonsolvatedand continuum polarized BOB− anion explains qualitatively thepositive Δassoc(III)S298

o value. The entropic contribution does notexceed the Δassoc(III)H298

o contribution. As a result, the mixed ordiscrete−continuum approach gives Δassoc(III)G298

o = 28.6kJ·mol−1, corresponding to Kassoc on the order of 10−5. Thisresult allows one to conclude that LiBOB in the EC:DMC(7:3) binary mixture is associated weakly, which is favorable forthe LIBs applications. The predictions made in the presentwork could be verified experimentally by conductometrymethod or IR/Raman and NMR spectroscopies, as has beenachieved previously for Li+ ion solvation in other solvents.30

4. CONCLUSIONSIn conclusion, we showed that neither continuum nor discretesolvation models are capable of describing ion association oflithium salt in highly polar solvent mixtures and that acombined discrete−continuum (mixed) treatment is required.Using these approaches, we performed quantum-chemicalcalculations of the changes in the standard enthalpy, entropy,and Gibbs free energy of the ion association process forsolution of the LiBOB salt in the EC:DMC (7:3) binarysolvent. This is the first theoretical prediction for the solvated[Li+BOB−] IP formation from the solvated Li+ and BOB− ionsin an EC based solvent mixture. The results show that accuratedescription of the Li+ ion solvation requires both continuumpolarization of the solvent medium and binding of the fourexplicit EC molecules. On the contrary, in solvation of theBOB− anion is dominated polarization by the highly polarstructureless solvent continuum. Explicit interaction of polarEC molecules with the BOB− ion is extremely weak. Thediscrete and continuum contributions to the Gibbs free energyof solvation of the [Li+BOB−] IP are relatively small and aresimilar. Therefore, both components should be taken intoaccount in order to describe the [Li+BOB−] IP solvation, andthis can be achieved only with the mixed discrete−continuummodel.Most importantly, the discrete and continuum components

to the Gibbs free energies of the ion association process arelarge and have opposite signs. The continuum approachpredicts no association, while the discrete description producescomplete association. Both results are unphysical and contradictbetween themselves. The mixed discrete−continuum modelcombines both contributions. The resulting Gibbs free energyof ion association is an order of magnitude smaller, predictingreasonably weak association. The conclusions drawn in thecurrent work are particularly important for the selection ofnovel aprotic electrolyte salt solutions. The mixed discrete−continuum approach resolves the problems in determining theextent of ion association and can be used to screen theproperties of a broad range of ion−molecular mixtures for LIBs.

■ AUTHOR INFORMATIONCorresponding Authors*(O.N.K.) E-mail: onkalugin@gmail.com. Tel.: +380 503032813.*(O.V.P.) E-mail: prezhdo@usc.edu. Tel.: +1 213 8213116.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was performed using computational facilities of thejoint computational cluster of SSI “Institute for Single Crystals”and Institute for Scintillation Materials of the National

Table 6. Changes in Standard Enthalpy (Δassoc(A)H298o ), Entropy (Δassoc(A)S298

o ), and Gibbs Free Energy (Δassoc(A)G298o ) during Ion

Association for the LiBOB Salt in the EC:DMC (7:3) Binary Solvent, Obtained Using the Continuum (I), Discrete (II), andMixed (III) Solvation Approaches (A) (g, Gas; c, Continuum)

A association process Δassoc(A)H298o , kJ·mol−1 Δassoc(A)S298

o , J·mol−1·K−1 Δassoc(A)G298o , kJ·mol−1

I + =+ − + −Li BOB [Li BOB ](c) (c) (c) +187.6 −84.3 +212.7

II + = ++ + + −[Li(EC) ] [BOB(EC) ] [Li (EC) BOB ] 3ECC4 (g) (g) 2 (g) (g) −136.1 +161.0 −184.1

III + = ++ − + −[Li(EC) ] BOB [Li (EC) BOB ] 2EC4 (c) (c) 2 (c) (c) +37.1 +28.6 +28.6

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Academy of Science of Ukraine incorporated into the UkrainianNational Grid. O.M.K. and O.N.K. acknowledge the Fund ofthe Ministry of Education and Science of Ukraine for thefinancial support (Grant Nos. 0113U002426, 0116U000834).O.V.P. acknowledges support of the U.S. Department of Energy(Grant No. DE-SC0014429) and is grateful to the RussianScience Foundation for financial support of the calculations,Project No. 14-43-00052, base organization PhotochemistryCenter RAS.

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