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DFT Descriptors for Ionic Liquids and the Charge Transfer Interpretation of the Haven Ratio Frederik Philippi, Daniel Rauber, Michael Springborg, and Rolf Hempelmann J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b10827 • Publication Date (Web): 04 Jan 2019 Downloaded from http://pubs.acs.org on January 6, 2019

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The Journal of Physical Chemistry

DFT Descriptors for Ionic Liquids and the Charge Transfer Interpretation of the Haven Ratio Frederik Philippi,† Daniel Rauber,†,§ Michael Springborg,‡,∇ Rolf Hempelmann*,†,§ †Physical

Chemistry, Saarland University, Campus B 2 2, 66123 Saarbrücken, Germany. E-mail: [email protected], Phone 0049 681 302 4750

§Transfercenter

Sustainable Electrochemistry, Saarland University and KIST Europe, Am Markt, Zeile 3, 66125 Saarbrücken, Germany

‡Physical

and Theoretical Chemistry, Saarland University, Campus B 2 2, 66123 Saarbrücken, Germany

∇School

of Materials Science and Engineering, Tianjin University, Tianjin 300072, PR China

Abstract One of the few properties common to all ionic liquids is their inherent electrical conductivity, which makes them promising candidates for advanced electrochemical applications. A central finding in this respect is that the measured conductivity is almost always lower than the one obtained from the Nernst-Einstein relation. There has been much dispute about whether correlated motion, charge transfer, or some sort of aggregation is the reason for this difference. In this work, we apply density-functional-theory based descriptors to estimate the charge transfer 1 ACS Paragon Plus Environment

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in ionic liquids, which allow predictions for a large number of systems with minimal effort. The theoretical charge transfer was obtained from vertical ionization potentials and electron affinities at the RB3LYP/6-311+G(2d,p)//RB3LYP/6-31+G(d,p) level of theory. To be able to compare and classify the values obtained with this approach, another measure for charge transfer, available directly from the Nernst-Einstein relation, is introduced. The two quantities show significant correlation for some subsets of ionic liquids for which a sufficient amount of information is available. Additionally, the purely theoretical charge transfer values allow for identifying interesting systems that should be the subject of further investigation.

Introduction During the last few decades, ionic liquids have become important due to their unique and adjustable property combinations. The areas of interest cover very diverse fields and the first industrial applications have emerged.1,2 To find a suitable ionic liquid for a certain task is made difficult by the immense amount of possible combinations of cations and anions, and identifying the optimal systems for a given purpose from a purely empirical investigation is virtually impossible. It is therefore desirable to develop simple but still accurate models for the prediction of properties of ionic liquids and then check these models for their performance. Complex and diverse structuring on many scales is found for ionic liquids, which is simultaneously a challenging problem and a chance for flexible optimization.3,4 The continuous growth of computer performance makes it possible to apply theoretical methods to analyze dynamics and bulk structuring in the low-temperature molten salts.5,6 Accurate theoretical studies require multiscale methods with many different contributions that could supplement the modular design of ionic liquids.7 Molecular dynamics simulations to obtain quantities like diffusion coefficients are frequently used and can be considered reliable when properly parameterized.8,9 2 ACS Paragon Plus Environment

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As the low-temperature analogs of conventional fused salts, many publications focus on the use of ionic liquids as electrolytes with a broad range of potential applications in energy storage and in electrochemistry in general.10–12 One of the most central physicochemical properties in this respect is the inherent molar conductivity 𝛬𝑀 of neat ionic liquids. This macroscopic property can be related to the microscopic self-diffusion coefficients using the Nernst-Einstein relation (1):13 𝐹2 𝛬𝑁𝐸 = 𝑅𝑇

𝑄

∑𝑧 𝐷

2 𝑠 𝑖 𝑖

(1)

𝑖=1

The sum goes over all 𝑄 constituents with charges 𝑧𝑖 and self-diffusion coefficients 𝐷𝑠𝑖. 𝐹 is Faraday’s constant, 𝑅 is the ideal gas constant, and 𝑇 is the thermodynamic temperature. The self-diffusion coefficients are usually obtained from NMR diffusometry. Strictly speaking, the Nernst-Einstein relation is only valid for diluted spherical, non-interacting ions. Hence, it is not surprising that in most cases different values for 𝛬𝑁𝐸 and 𝛬𝑀 are found. These differences can be quantified through a correction factor, the Haven ratio 𝐻𝑅 or the Nernst-Einstein parameter 𝛥𝑁𝐸 as defined below.13,14 Note that the Haven ratio is in some literature defined reciprocal to the one shown here. 𝛬𝑀 = 𝐻𝑅𝛬𝑁𝐸

and

𝐻𝑅 = (1 ― 𝛥𝑁𝐸).

(2)

The deviations of 𝐻𝑅 from 1 or 𝛥𝑁𝐸 from 0 are often interpreted in terms of ion pairing.15–17 Ion pairing in dilute solution is well understood.18 For the case of ionic liquids, this interpretation is questionable and the subject of an ongoing dispute.1,19–21 It has been criticized numerous times for being too simple since the use of the Nernst-Einstein relation is questionable in the first 3 ACS Paragon Plus Environment


place. Additionally, the concept of ion pairs cannot be defined properly because of the absence of a neutral solvent. Hence, it may be more appropriate to consider the concepts of ionicity as a result of aggregation and cluster formation. According to another interpretation velocity crosscorrelation coefficients can be applied to explain the differences between 𝛬𝑀 and 𝛬𝑁𝐸.14,22,23 This theory – i.e. the assumption of (anti)correlated motions in the presence of an electric field as the driving force – is consistent in itself and provides a sound explanation for 𝐻𝑅 being different from 1. However, it suffers from its dependence on the reference frame chosen, and is more of a transformation of the experimental quantities into distinct quantities then an interpretation.24,25 It furthermore doesn’t take more complicated types of motion into account, like different states of aggregation or freedom that have been identified for ionic liquids using theoretical methods.26 So far, all models are based on the assumption of integer charges of the ions. However, the deviations of the Haven coefficient from 1 might also be rationalized through the assumption of non-integer charges.27 Since the ions are in close contact, wave function overlap between cations and anions can occur. This may eventually lead to a charge transfer of a non-integral number of electrons, reducing the overall charges of cations and anions. Consequently, such a charge transfer can provide an alternative explanation for HR ≠ 1. It can be anticipated that, in reality, all these effects come to play, so it is currently not possible to disentangle their contributions to this single parameter. For the sake of simplicity, we focus solely on charge transfer in this work, bearing in mind the presence of other contributions that are neglected. Indeed, several studies have suggested that the ionicity interpretation is negligible when compared to charge transfer.19,27 When attempting to theoretically study the non-integral charge 4 ACS Paragon Plus Environment

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transfers, one faces the problem that such a charge transfer is a quantum phenomenon that cannot be described by simple force fields. Yet rigorous ab initio calculations are not feasible for the large ensembles which in the ideal case would be required to properly describe the liquid phase, implying that force fields remain indispensable in many situations. The accuracy can be significantly increased by using polarizable force fields, although at the cost of higher computational demand.28 As a compromise, charges can be scaled with a factor of about 0.6 to 0.8 to produce more accurate results.29–31 The latter supports the charge-transfer interpretation and can, in addition, provide an estimate of the size of the charge transfer. Reliable MD (molecular dynamics) simulations are still a cumbersome and time-consuming task, especially when the goal is to include charge-transfer effects. Thus, they are not suitable for a study of many systems. Therefore, in the present work, we propose a simpler approach based on using density-functional theory (DFT) descriptors. Accordingly, we shall attempt to determine the charge-transfer from properties of the individual, non-interacting ions. This also provides a significant advantage: through calculations on only 10 cations and 10 anions, information on 100 ionic liquids becomes available. Although the results are expected to give only an approximate description of the reality, they should be sufficient to determine trends and to allow for identifying systems that might be promising for further investigation. These can then, in turn, be investigated by means of MD simulations or actual experiments. This includes for example pairs with extremely low or high values for the predicted charge transfer, where it would be of high interest whether the predicted charge transfer is mirrored in the experimental Haven ratios. It would also be attractive to prepare the systems with the least charge transfer to see whether their fluidity and molar conductivity is larger than usual. However, this is a suggestion beyond the

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scope of the present work that aims at discussing the utility of DFT descriptors and the chargetransfer interpretation of the Haven ratio for ionic liquids.

Charge transfer from NMR diffusometry The Nernst-Einstein relation (1) can be used to obtain Haven ratios, which are usually interpreted as ionicities. Since the true microscopical (including dynamical) behavior of the system is unknown, it is equally valid to assume that the differences between 𝛬𝑁𝐸 and 𝛬𝑀 arise from apparent, fractional charges 𝑧𝑎𝑝𝑝 instead of the integral charges that are assumed in Eq. (1). Thus, we write 𝐹2 ― )2 ― 𝐷 ) = 𝛬𝑀 ((𝑧 + )2𝐷 + + (𝑧𝑎𝑝𝑝 𝑅𝑇 𝑎𝑝𝑝

(3)

The reason for the difference between the integral charges of Eq. (1) and the fractional ones of Eq. (3) will be ascribed to a charge transfer 𝛥𝑞𝑁𝐸 from the anion to the cation. This charge transfer can then be extracted directly from the Haven ratio. For the case of an A+B− salt, one obtains: + 𝑧𝑎𝑝𝑝 = 1 ― 𝛥𝑞𝑁𝐸

𝑎𝑛𝑑

― 𝑧𝑎𝑝𝑝 = ―1 + 𝛥𝑞𝑁𝐸

(4)

which leads to: 𝑅𝑇 2

𝐹

2

𝛬 = (1 ― 𝛥𝑞𝑁𝐸) 𝐷 + + ( ―1 + 𝛥𝑞𝑁𝐸)2𝐷 ― 𝑀

= (𝐷

+

+ 𝐷 )(1 ― 2𝛥𝑞𝑁𝐸 + ―

)=

𝛥𝑞𝑁𝐸2

𝑅𝑇 𝐹2

(5) 𝐻 𝛬𝑁𝐸 = 𝐻𝑅(𝐷 𝑅


+

―

+𝐷 )

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where we in the last identity have used that the integral charges for 𝛬𝑁𝐸 equal ±1. From this we obtain: 𝛥𝑞𝑁𝐸2 ― 2𝛥𝑞𝑁𝐸 + 1 ― 𝐻𝑅 = 0

(6)

𝛥𝑞𝑁𝐸 = 1 ― 𝐻𝑅

(7)

or

This equation provides an experimental estimate for the charge transfer.

DFT descriptors and charge transfer The quantity of central interest at this point is the amount to which charge transfer occurs. To obtain this, the energy 𝐸 of a given molecule can be expanded around the number of electrons, 𝑁 , in a Taylor series. Terminating after the second-order term yields: 𝐸(𝑁) = 𝐸(𝑁0) ― µ𝛥𝑁 + 𝜂(𝛥𝑁)2

(8)

Here, 𝑁0 is the number of electrons in the reference system, i.e. of the cation or anion. Moreover, the hardness 𝜂 and the chemical potential for the electrons µ are given by32

µ=―

( ) ∂𝐸 ∂𝑁

𝑣

𝑎𝑛𝑑

𝜂=

( )

1 ∂2𝐸 2 ∂𝑁2

(9)

𝑣

µ can be introduced through the variational principle in DFT as a Lagrange parameter and has been shown to equal the first derivative of the energy with respect to the electron number, hence the term ‘DFT descriptors’.33–35 In passing, we notice that care has to be taken since µ is sometimes defined as the negative of the definition presented here.36,37 From Eq. (8) it is straightforward to derive finite-difference approximations for 𝜂 and µ: 7 ACS Paragon Plus Environment


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𝐸(𝑁0 + 1) ― 𝐸(𝑁0) ≃ 𝜂 ― µ

(10)

𝐸(𝑁0 ― 1) ― 𝐸(𝑁0) ≃ 𝜂 + µ

(11)

Subsequently, a pair of oppositely charged ions brought into contact is considered. The amount of charge transfer 𝛥𝑞𝐷𝐹𝑇 can be estimated as the minimum of the energy function with respect to the number of electrons transferred from the anion to the cation:38 𝑑𝐸𝑡𝑜𝑡𝑎𝑙 𝑑(𝛥𝑞)

=

𝑑 (𝐸 (𝑁 ) ― µ𝑐𝑎𝑡𝑖𝑜𝑛𝛥𝑞 + 𝜂𝑐𝑎𝑡𝑖𝑜𝑛𝛥𝑞2 + µ𝑎𝑛𝑖𝑜𝑛𝛥𝑞 + 𝜂𝑎𝑛𝑖𝑜𝑛𝛥𝑞2) = 0 (12) 𝑑(𝛥𝑞) 𝑡𝑜𝑡𝑎𝑙 0

⇔ 𝛥𝑞𝐷𝐹𝑇 =

µ𝑐𝑎𝑡𝑖𝑜𝑛 ― µ𝑎𝑛𝑖𝑜𝑛 2(𝜂𝑐𝑎𝑡𝑖𝑜𝑛 + 𝜂𝑎𝑛𝑖𝑜𝑛)

(13)

The subscript ‘DFT’ is used here for the sake of convenience. The quantity 𝛥𝑞𝐷𝐹𝑇 only includes charge transfer, whereas the experimentally available 𝛥𝑞𝑁𝐸 is a cumulative parameter, i.e., any effect that makes HR non-unity is included in this parameter. We add that 𝛥𝑞𝐷𝐹𝑇 has here been introduced as the charge transfer between a pair of otherwise non-interacting ions. However, it is equally applicable when assuming that each ion is surrounded by the same number of counterions. Eq. (12) has to be multiplied with this number, which does not alter 𝛥𝑞𝐷𝐹𝑇. Then, 𝛥𝑞𝐷𝐹𝑇 corresponds to the total charge that an ion is receiving from all the counterions. Since the charge transfer is a very local effect, this interpretation demonstrates that our theory is realistic even beyond that of a single pair of ions, as long as it is assumed that the number of counterions around a given ion is essentially constant. The Haven ratio quantifies the deviations from ideality, and several physical theories to explain these deviations have been mentioned. Apart from that, proton transfer is expected to occur in 8 ACS Paragon Plus Environment

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many cases to a greater or lesser extent. This chemical charge transfer is completely neglected at this point for the sake of brevity. The extent of proton transfer can be included into Eq. (12) as the energies for the underlying acids and bases can be obtained separately by theoretical methods, which will be the issue of a subsequent publication. Another concept closely connected to DFT descriptors is the Fukui functions. The Fukui function 𝑓(𝑟) is a three-dimensional function that quantifies the changes in the electron density 𝜌(𝑟) when 𝑁 is changed,39

𝑓(𝑟) =

∂𝜌(𝑟) ∂𝑁

( )

(14)

𝑣

It is relevant to emphasize that the energy is not continuously differentiable at integer values of 𝑁, which is also the case for 𝜌(𝑟).40,41 This has the consequence that one may introduce two relevant Fukui functions, which in a finite-difference approximation become: 𝑓 + (𝑟) ≃ 𝜌(𝑟)𝑁0 + 1 ― 𝜌(𝑟)𝑁0

(15)

𝑓 ― (𝑟) ≃ 𝜌(𝑟)𝑁0 ― 𝜌(𝑟)𝑁0 ― 1

(16)

The function 𝑓 + (𝑟) (𝑓 ― (𝑟)) takes larger values in those parts of the molecule that is susceptible for a nucleophilic (electrophilic) attack and is hence used for the characterization of cations (anions).32 In the present work, we shall use both the 𝛥𝑞𝐷𝐹𝑇 as determined above as well as the Fukui functions, all obtained through parameter-free density-functional calculations.

Computational Details



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The B3LYP hybrid functional has been chosen since it is known to produce reasonably accurate values for ionization potentials and electron affinities at acceptable computational cost.42 Similar calculations with B3LYP on ionic liquids are known in the literature, though with different foci such as radiation stability.43,44 The systems of interest were subjected to a Monte Carlo conformational search using the Merck molecular force field (MMFF), and the resulting structures were optimized at the PM6 level of theory. Conformation search and semiempirical optimization were performed using the SPARTAN 18 software package.45 The conformers of lowest energy were imported to the Gaussian 09 program and optimized at the RB3LYP/6-31+G(d,p) level of theory with an ultrafine integration grid.46 After frequencies were checked to be non-imaginary, the structures thus

obtained

were

subjected

to

single-point

internal

energy

calculations

at

the

R(O)B3LYP/6-311+G(2d,p) level of theory. These calculations were performed for the singly charged anion or cation as reference systems as well as for the same systems with one more or less electron, whereby in the latter calculations the structures were kept fixed. For all single-point calculations, a reduced SCF convergence criterion was used as suggested in the literature.47 The converged wave function of the reference system was used as initial guess for the systems with one electron added or removed if the default guess was unsuccessful. For cases where the SCF calculation did not converge after 500 cycles, the options ‘novaracc’, ‘damp’, and ‘vshift’ were requested subsequently in this order for the ‘scf’ keyword. Vertical ionization potentials and electron affinities were used rather than adiabatic ones since some of the systems were not stable with respect to dissociation/fragmentation, especially the doubly positively charged ones.


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The Fukui functions and the electrostatic potential were displayed on the 0.001 iso-electrondensity-surface of the reference system. For this purpose, cubefiles with 1503 points were generated from the output of the three calculations. Restricted (open-shell) calculations were chosen in order to avoid disproportionate stabilization of the open-shell systems, although spin contamination was found to be negligible in unrestricted calculations.

Results and Discussion The values for 𝛥𝑞𝑁𝐸 obtained from Haven ratios from the literature are listed in Table 1. The xyz files from the optimized structures as well as the structures corresponding to the abbreviations are given in the supporting information. Table 1: Calculated charge transfers 𝛥𝑞𝑁𝐸 as obtained from experimental NMR data.

System

𝜟𝒒𝑵𝑬

System

𝜟𝒒𝑵𝑬

[P4442O2][OTf]48 [P4442O2][TFA]48 [P4442O2][NTf2]48 [P4442O2][OMs]48 [P4442][NTf2]48 [P4446][NTf2]48 [P4448][NTf2]48 [P2228][NTf2]48 [P2225][NTf2]48 [P2222O2][NTf2]48 [P44410][NTf2]48 [C1C1IM][NTf2]16 [C2C1IM][NTf2]16 [C6C1IM][NTf2]16 [C8C1IM][NTf2]16

0.25 0.32 0.19 0.28 0.16 0.20 0.23 0.22 0.18 0.19 0.26 0.13 0.13 0.25 0.27

[C4C1TMG][BETI]49 [C4C1TMG][NTf2]49 [C1C0TMG][BETI]49 [C1C0TMG][NTf2]49 [C1C0TMG][OTf]49 [C1C0TMG][TFA]49 [C4C4TMG][BETI]49 [C4C4TMG][NTf2]49 [C4C4TMG][OTf]49 [C0C0TMG][BETI]49 [C4C1IM][ALHFIP4]17 [C6C1IM][ALHFIP4]17 [C8C1IM][ALHFIP4]17 [C4C1IM][NTf2]50 [C4C1IM][BETI]50

0.19 0.13 0.17 0.14 0.17 0.30 0.17 0.14 0.16 0.19 −0.01 0.15 0.09 0.22 0.21



[C4C1PYR][NTf2]16 [C4Py][NTf2]16 [N1114][NTf2]16 [C2C1IM][OMs]14 [C2C1IM][OTf]14 [C2C1IM][FAP]14

0.16 0.21 0.19 0.17 0.17 0.00

[C4C1IM][OTf]50 [C4C1IM][PF6]50 [C4C1IM][TFA]50 [C4C1IM][BF4]50 [C2C1IM][TCB]14

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0.24 0.18 0.29 0.19 0.20

Excluding the exceptional values for aluminum tetrakis(hexafluoroisopropanoate) [AlHFIP4]based systems, the charge transfer ranges from 0.13 to 0.32, corresponding to nominal charges of 0.68 – 0.87 of the ions. This coincides with a charge-scaling factor of 0.6 to 0.8 that often is used in molecular dynamics simulations.29–31 With increasing basicity of the anions, the increase of both ion pairing and charge transfer can be understood intuitively. Anions of only moderately strong corresponding acids like trifluoroacetate [TFA] exhibit large charge transfer, whereas weakly coordinating anions like hexafluorophosphate [PF6] or [AlHFIP4] are found to produce little to no charge transfer. One could expect the charge transfer to decrease with increasing cation size, as the positive charge then becomes better shielded. However, the values for imidazolium and phosphonium cations show the opposite behavior. Then again for guanidinium cations, nearly no variation of charge transfer is found within each set of ILs with the same anion. It has to be kept in mind that the various interpretations of the Haven ratio being different from 1 (e.g., as being related to ionicity, anticorrelations, or charge transfer) make it difficult to separate the various effects. DFT descriptors can in principle be used to distinguish between these different contributions, which will be the task of the following section.


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In the theoretical calculations we studied 50 cations and 26 anions separately, thus from the 3x(50+26)=228 single point calculations, the charge transfer 𝛥𝑞𝐷𝐹𝑇 can be estimated for 50x26=1300 cation-anion combinations. Cations and anions frequently used for ILs including some of their derivates were considered. The resulting values are shown in Figure 1, with columns and rows sorted according to their arithmetic mean.



23 24 25 25 25 26 26 27 27 27 27 28 27 27 27 28 28 28 28 29 29 29 29 29 29 30 30 30 31 29 31 31 31 31 33 33 32 32 32 34 33 34 35 36 38 39 37 38 42 42

25 26 27 27 27 27 28 28 28 28 29 29 29 29 29 30 30 30 30 30 30 31 30 31 30 31 31 31 32 31 32 32 32 33 34 34 33 33 33 34 34 35 36 37 38 40 38 39 42 42

24 26 27 27 27 28 28 28 29 29 29 29 29 29 29 30 30 30 30 30 31 31 31 31 31 32 32 32 32 31 33 32 33 33 34 35 34 34 34 35 35 36 37 38 39 41 39 40 43 43

25 26 27 27 27 28 28 29 29 29 29 30 29 29 30 30 30 30 31 31 31 31 31 31 31 32 32 32 33 32 33 33 33 34 35 35 34 35 34 36 35 36 38 39 40 41 40 41 43 44

26 27 28 28 29 29 29 30 30 30 30 31 30 30 31 31 31 31 31 32 32 32 32 32 32 33 33 33 33 33 34 34 34 35 36 36 35 35 35 36 36 37 38 39 40 42 41 42 44 44

26 28 29 29 29 29 30 30 30 30 31 31 31 31 31 32 32 32 32 32 32 33 32 33 32 33 33 33 34 33 34 34 34 35 36 36 35 36 35 36 36 37 38 39 40 42 41 42 43 44

26 28 29 29 29 30 30 30 31 31 31 31 31 31 31 32 32 32 32 32 33 33 33 33 33 34 34 33 34 34 34 34 35 35 36 36 36 36 36 37 37 38 39 40 41 42 41 42 44 45

27 29 30 30 30 31 31 31 32 32 32 32 32 32 33 33 33 33 33 34 34 34 34 34 34 35 35 35 35 35 36 36 36 37 37 38 37 38 38 38 38 39 41 42 42 44 44 45 46 47

28 30 31 31 31 31 32 32 32 33 33 33 33 33 33 34 34 34 34 34 34 35 35 35 35 35 35 35 36 36 36 36 37 37 38 38 37 38 38 38 38 39 41 41 42 44 43 44 45 46

29 31 32 32 32 32 33 33 33 33 34 34 34 34 34 35 35 35 35 35 35 35 35 36 36 36 36 36 36 37 37 37 37 38 39 39 38 39 39 39 39 40 42 42 43 44 45 46 46 47

31 33 34 34 34 34 34 35 35 35 35 36 36 36 36 36 36 36 37 37 37 37 37 37 37 38 38 38 38 38 38 39 39 40 40 40 40 40 41 41 41 42 43 44 44 46 46 47 47 48

32 35 36 36 36 36 36 37 37 37 37 37 37 38 38 38 38 38 39 39 39 39 39 39 39 39 40 40 40 40 40 41 41 42 42 41 42 42 43 42 43 43 45 45 45 47 48 49 48 50

32 35 36 36 36 36 36 37 37 37 37 37 38 38 38 38 38 38 39 39 39 39 39 39 39 40 40 40 40 41 40 41 41 42 42 42 42 42 43 43 43 44 46 46 46 47 49 49 48 50

33 35 36 36 36 36 36 37 37 37 37 38 38 38 38 38 38 38 39 39 39 39 39 39 39 40 40 40 40 41 40 41 41 42 42 42 42 42 43 42 43 44 45 45 45 47 48 49 48 50

32 35 36 36 36 36 37 37 37 38 38 38 38 38 39 38 38 39 39 39 39 39 40 39 40 40 40 40 40 41 40 42 42 42 42 42 43 43 43 43 43 44 46 46 46 48 49 50 49 51

32 35 36 36 36 37 37 37 37 38 38 38 38 38 39 39 39 39 39 40 40 40 40 40 40 40 40 40 41 41 41 42 42 43 43 42 43 43 44 43 44 45 47 46 46 48 50 51 49 51

33 35 36 36 37 37 37 37 38 38 38 38 38 38 39 39 39 39 40 40 40 40 40 40 40 40 41 41 41 42 41 42 43 43 43 43 43 43 44 44 44 45 47 47 47 49 50 51 50 52

34 37 38 38 38 38 38 39 39 39 39 39 40 40 41 40 40 40 41 41 41 41 42 41 42 42 42 42 42 43 42 43 44 44 44 43 44 44 45 44 45 46 48 48 47 49 51 52 50 52

35 38 39 39 39 39 39 40 40 41 40 40 41 41 42 41 41 41 42 42 42 42 43 42 43 43 43 43 43 44 43 45 45 45 45 44 46 45 47 45 46 47 49 49 48 50 53 53 51 53

35 38 39 39 39 40 40 40 40 41 41 41 41 41 42 42 41 42 42 43 43 42 43 42 43 43 43 43 43 44 43 45 45 45 45 45 46 46 47 45 46 47 49 49 48 50 52 53 51 53

Figure 1. Values for 100×𝛥𝑞𝐷𝐹𝑇 at the RB3LYP/6-311+G(2d,p)//RB3LYP/6-31+G(d,p) level of theory.


35 38 39 39 39 40 40 40 40 41 41 41 41 41 42 42 41 41 42 43 43 42 43 42 43 43 43 43 43 44 43 45 45 45 45 45 46 46 47 46 46 47 49 49 48 50 53 53 51 53

38 41 42 42 42 42 42 43 43 44 43 43 44 44 45 44 44 44 45 45 45 45 46 45 46 45 45 46 45 47 45 47 48 48 47 47 48 48 50 48 48 49 52 51 50 52 55 56 53 55

Pr2NCO2

23 24 25 25 25 26 26 27 27 27 27 27 27 27 27 28 28 28 28 28 28 29 28 29 29 30 30 29 30 29 31 30 30 31 32 33 31 32 31 33 33 34 34 36 37 38 36 37 41 41

OAc TCM DCA MMP OMs OTos CMs3 Me2PO4 HSO4 MeOSO3

22 23 24 24 25 25 25 26 26 26 26 27 26 26 26 27 27 27 27 27 28 28 28 28 28 29 29 29 29 28 30 29 29 30 31 32 30 31 30 32 32 33 33 35 36 38 35 36 40 40

TFA OTf PFBS P(CF3)2O2 Cp(CN)5 NTf2

21 23 24 24 24 24 25 25 26 25 26 26 26 26 26 27 27 27 27 27 27 28 27 28 27 29 28 28 29 28 30 29 29 30 31 32 30 31 30 32 32 33 33 35 37 38 35 36 40 40

FSI BETI NNf2

C4C1TMG P(2O2)3 10 P(2O2)3 2 P44410 P(2O2)3 1 P4448 P4442O2 P4445 P4446 P2228 P4442 N4441 P5551 P2222O2 C4C4TMG P444H N2225 P2225 N1112O2 C1C0TMG C0C0TMG C1C4Pyr P1112O2 N1115 C1C1TMG N1114 Chol P1115 P222H C8C1IM C1C1Pyr C6C1IM C4C1IM C2C1IM PMe4 N1111 C1C1IM Pr2NH2 P8HHH P111H H6Gua C0C0Pyr MEA EA C0C0IM PH4 C4Py C1Py NH4 C0Py

FAP BF4 Al(HFIP)4 B(CN)4 PF6 B(CF3)4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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The charge transfer found for [N111][BF4] and [C1C1Im][BF4] by this method is approximately twice the value obtained with the CHelpG scheme by Rigby et al.51 For [C1C1Im][NTf2], Ishizuka et al. obtained an effective charge of about 0.7, whereas the charge transfer predicted by using the DFT descriptors as discussed in the introduction is larger by approximately 20%.52 Although the DFT descriptors seem to overestimate the actual amount of charge transfer, they reasonably reproduce the above-mentioned correction factor of 0.6 to 0.8.29,30 In general, for large cations and fluorinated anions lower charge transfers are found. This can be attributed to the more delocalized distribution of the (positive) charge over a large molecule together with the high electronegativity of fluorine. However, there are several exemptions to this finding. Surprisingly, systems involving [C4C1TMG] show the smallest charge transfer, even less than the values for the bigger [C4C4TMG]. For the cations [E2225], [E1112O2], and [E1115], the charge transfer is larger when E=P than when E=N. This difference between phosphorus and nitrogen is inverted for very small ions like [E1111] and [EH4]. Carvalho et al. have shown that the charge of the cation is also more localized on the quarternary center for phosphonium ILs than for the equivalent ones based on ammonium.53 They argue that the charge delocalization in ammonium-based ionic liquids promotes cation-anion interactions and has consequently a negative impact on transport properties. On the other hand, it has also been suggested that a fractional charge transfer should improve transport phenomena since the IL then resembles more a molecular liquid.27 One might also argue that a very strong charge transfer might effectively lead to a coupling between the ions due to the energetic stabilization of the constructive interaction. Pronounced charge transfer in the cation is therefore not a guarantee for having ionic liquids with increased transport 15 ACS Paragon Plus Environment


properties, particularly since within this simple approach geometric aspects are not taken fully into account. Especially for protic ionic liquids like those based on [P111H], hydrogen bonding and cooperative effects can be relevant. These have been shown to be important for several systems and are not accounted for by the simple model used in the present work.3,54 For the set of anions investigated here, those located to the left of Figure 1 that show a lower charge transfer are weakly-coordinating anions. These are in general a good choice for ionic liquids with good transport properties and stand out as they have a high fluorine content. Exceptions are tetracyanoborate [B(CN)4] and pentacyanocyclopentadienide [Cp(CN)5]. These two weakly coordinating anions constitute fluorine-free alternatives and are as such interesting systems.55–57 Thus, [C2C1Im][B(CN)4] has shown superior electrochemical stability when compared to the corresponding dicyanamide [DCA] and tricyanomethanide [TCM] ionic liquids.58 With a viscosity of only 21 mPa s, it is even more fluid than [C2C1Im][NTf2].59 The salient features of the [B(CN)4] ion have already been observed in pKa measurements, with a unusually high acidity of the corresponding acid.60 [Cp(CN)5], on the other hand, is known to produce highly ordered structures which might be useful in adjusting the nanostructure of ionic liquids.61,62 However, precursors for both [B(CN)4] and [Cp(CN)5] ILs are expensive and not easily accessible. Similar limitations exist for the [B(CF3)4] anion, the synthesis of which requires specialized equipment and knowledge on the fluorination procedure.63,64 In contrast, several precursors for the widely used hexafluorophosphate [PF6] and tetrafluoroborate [BF4] anions are commercially available. A drawback of these two ions is that they might suffer from hydrolysis.65,66 The aluminate ion [Al(HFIP)4] is one of the few anions where experimental data for the Haven ratio are available showing exceptionally high values of up to 1 for [C4C1Im][Al(HFIP)4].17 Using the charge-transfer interpretation presented in Eq. (7), this agrees 16 ACS Paragon Plus Environment

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nicely with the low values of down to 0.23 in Figure 1. The less exotic fluorinated anions like bis(trifluoromethanesulfonyl)imide

[NTf2],67,68

tris(pentafluoroethyl)trifluorophosphate

[FAP],69,70 or bis(fluorosulfonyl)imide [FSI]71,72 with medium charge-transfer values are wellknown for various beneficial properties like a high fluidity and high electrochemical stability. Bis(trifluoromethyl)phosphinate [P(CF3)2O2] in combination with various cations shows a comparable charge transfer to [NTf2] and has already been identified as a potential alternative to [NTf2], especially for electrochemical applications.73 Hence, ionic liquids based on fluorinated anions like [NTf2] offer an excellent compromise between price and performance.74 A major drawback is that environmental and toxicological issues can be problematic.75 Then, the fluorine-free anions, which make up the right half of Figure 1 with increased charge transfer are preferable. In addition, some of the corresponding alkylating agents are commercially available in large quantities, including dimethyl sulfate, dimethyl methylphosphonate, and trimethyl phosphate. Then again, this is at the expense of chemical stability since these anions have higher basicity and might be susceptible to hydrolyzation.76–78 Biodegradable ionic liquids like cholinium alkanoates have been considered, but they suffer from a lower stability.79,80 The results presented above underline the ambivalence of ionic liquids, which is one of their main problems. Both with the choice of the cation and of the anion one has to make a compromise between factors like price, performance, stability, and biodegradability. We now turn to a more detailed discussion of our results and the charge transfers from the DFT descriptors. Since the performance of this theoretical approach is unknown, we consider first ILs for which experimental data are available. The 𝛥𝑞𝐷𝐹𝑇 values for these systems are displayed in Table 2 below for comparison with Table 1. 17 ACS Paragon Plus Environment


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Table 2: Selected values for the DFT charge transfer 𝛥𝑞𝐷𝐹𝑇 for the same systems as in Table 1.

System

𝜟𝒒𝑫𝑭𝑻

System

𝜟𝒒𝑫𝑭𝑻

[P4442O2][OTf] [P4442O2][TFA] [P4442O2][NTf2] [P4442O2][OMs] [P4442][NTf2] [P4446][NTf2] [P4448][NTf2] [P2228][NTf2] [P2225][NTf2] [P2222O2][NTf2] [P44410][NTf2] [C1C1IM][NTf2] [C2C1IM][NTf2] [C6C1IM][NTf2] [C8C1IM][NTf2] [C4C1PYR][NTf2] [C4Py][NTf2] [N1114][NTf2] [C2C1IM][OMs] [C2C1IM][OTf] [C2C1IM][FAP]

0.34 0.36 0.30 0.38 0.31 0.31 0.30 0.31 0.32 0.31 0.29 0.36 0.35 0.34 0.34 0.33 0.41 0.34 0.44 0.40 0.33

[C4C1TMG][BETI] [C4C1TMG][NTf2] [C1C0TMG][BETI] [C1C0TMG][NTf2] [C1C0TMG][OTf] [C1C0TMG][TFA] [C4C4TMG][BETI] [C4C4TMG][NTf2] [C4C4TMG][OTf] [C0C0TMG][BETI] [C4C1IM][ALHFIP4] [C6C1IM][ALHFIP4] [C8C1IM][ALHFIP4] [C4C1IM][NTf2] [C4C1IM][BETI] [C4C1IM][OTf] [C4C1IM][PF6] [C4C1IM][TFA] [C4C1IM][BF4] [C2C1IM][TCB]

0.25 0.26 0.32 0.32 0.37 0.39 0.31 0.31 0.36 0.32 0.31 0.31 0.29 0.35 0.34 0.39 0.29 0.41 0.32 0.31

The calculated charge transfer in this subset does not exceed 0.44 elemental charges. Most of the combinations, like [NH4][OAc], are ordinary inorganic salts with melting points above 100°C or are chemically unstable, which also includes many combinations with [PH4]. By comparing with available thermal and chemical data, we found that this holds true for systems with a theoretical charge transfer above around 0.40, separating the combinations that are unlikely to yield useful and realistic electrolytes. However, some applications might tolerate or even favor these systems


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due to chemical reasons. An example is the highly viscous [Pr2NH2][Pr2NCO2], which can be used for CO2 sensing.81 For easier comparison, Figure 2 displays the values for 𝛥𝑞𝑁𝐸 together with those for 𝛥𝑞𝐷𝐹𝑇. The whole range of sensible charge transfer is shown here to illustrate the relative position of the values obtained from NMR and DFT. Additionally, it can be seen that the latter values are skewed towards larger charge transfer.

Figure 2: Overview of charge transfer values from experiment and theory for several ionic liquids. The black line represents perfect agreement between 𝛥𝑞𝑁𝐸 and 𝛥𝑞𝐷𝐹𝑇.

Although the values appear to scatter strongly, the absolute range is rather small. Moreover, the experimentally derived values are based on different measurements with different methods and hence suffer from subtleties like the difference between PFGSTE and PGSE sequences.82,83 To mention an example, the values for [C4C1Im][BF4] by Harris et al.84 yield a 𝛥𝑞𝑁𝐸 of 0.25, which is 32% larger than the value obtained by Tokuda et al.50 for the same system. Another issue is that the purity of the samples might not be comparable throughout different publications. This 19 ACS Paragon Plus Environment


holds true especially for the water content, which is known to have a severe impact on the transport properties of ionic liquids.85,86 As was found for 𝛥𝑞𝑁𝐸, the purely theoretical 𝛥𝑞𝐷𝐹𝑇 values correspond to charge transfers that cover a range of about 0.2 elemental charges. Since it has been obtained from the experimental Haven ratio, 𝛥𝑞𝑁𝐸 contains other contributions like aggregation or domain formation for systems with extended alkyl side chains. Even if no charge transfer was present, the Haven ratio would still be below one because of, for example, correlated movements of ions. Due to Eq. (7), 𝛥𝑞𝑁𝐸 should hence be larger than 𝛥𝑞𝐷𝐹𝑇. This is, however, not what we find. A possible explanation for this deviation is the so-called charge-delocalization error.87 In reality, the total energy is a piecewise linear function of the number of electrons, N, with exceptions only at integral values where the slope changes. The presently used approximate density-functionals show, however, a continuous and differentiable behavior also at integral values of N and, moreover, too low values for non-integral N. Accordingly, these approximations tend to overestimate a fractional charge transfer between two (or more) interacting systems. On the other hand, it is a reasonable approximation to assume that this will lead to a systematic overestimate of the estimated charge transfers. We shall therefore assume that the DFT-derived charge transfers provide a correct description of the trends. Accordingly, at first, we will study the subset of the well-known and most thoroughly investigated imidazolium-based systems for which the charge transfers are shown in Figure 3.


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Figure 3: Comparison between 𝛥𝑞𝑁𝐸 with 𝛥𝑞𝐷𝐹𝑇 for the subset of imidazolium-based ionic liquids. Red diamonds show the correlation of 𝛥𝑞𝑁𝐸 (HR values from Tokuda et al.50) and 𝛥𝑞𝐷𝐹𝑇 for the [C4C1Im] cation with different anions, the red line indicates a linear regression with an R value of 0.95. Blue triangles show the correlation between 𝛥𝑞𝑁𝐸 (HR values from Ueno et al.16 and the data point for [C4C1Im][NTf2]) and 𝛥𝑞𝐷𝐹𝑇 for [CnC1Im][NTf2] ionic liquids with different n, the blue line indicates the linear regression with an R value of −0.92.

Although the data points appear to scatter strongly at first sight, a closer inspection reveals linear relationships for those data for which either the cation or the anion is kept fixed. To avoid inconsistencies in the interpretation, it is desirable to choose the data points from one source. The red diamonds in Figure 3 show the results for ILs with the [C4C1IM] cation, but different anions. Taking the simplicity of our theory into account, an R value of 0.95 represents a remarkable correlation. Additionally, the theory seems to be capable to reproduce the ordering of the 𝑝𝐾𝑎 values. Usually, a low 𝑝𝐾𝑎 is ascribed to a weakly coordinating anion, and increased 𝑝𝐾𝑎 values of the corresponding acids in the series [TFA] > [OTf] > [NTf2] corresponds to the order found in Figure 3Error! Reference source not found..60,88 Extremely weakly coordinating anions like [Al(HFIP)4] are consequently found to have the lowest values both for 𝛥𝑞𝑁𝐸 and 𝛥𝑞𝐷𝐹𝑇. Keeping 21 ACS Paragon Plus Environment


the anion unchanged, a linear relation between 𝛥𝑞𝑁𝐸 and 𝛥𝑞𝐷𝐹𝑇 is also visible for the [CnC1IM][NTf2] series as shown by the blue triangles in Figure 3. In this case, we find a negative correlation between 𝛥𝑞𝑁𝐸 and 𝛥𝑞𝐷𝐹𝑇. Therefore, the pure charge transfer decreases, whereas 𝛥𝑞𝑁𝐸 as a cumulative parameter incorporating many different effects increases. With this interpretation, the charge transfer is overcompensated by the other effects of non-ideality, including anticorrelation and ion aggregation. The latter is intuitively explained by the longer alkyl chains, which are known to induce pronounced structuring.3,6 Particularly for chain lengths exceeding n=4, the formation of polar ionic and apolar hydrocarbon domains has been reported for the bulk liquid in [CnC1Im] ILs, becoming more pronounced with increasing n.6 Next, in Figure 4 we show the results for the subset of phosphonium-based ionic liquids.


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Figure 4: Comparison of 𝛥𝑞𝑁𝐸 and 𝛥𝑞𝐷𝐹𝑇 for the subset of phosphonium-based ionic liquids. Red diamonds show the correlation of 𝛥𝑞𝑁𝐸 (HR values from earlier work48) and 𝛥𝑞𝐷𝐹𝑇 for [P444n][NTf2] ionic liquids with different n, the red line indicates a linear regression with an R value of -0.95.

In this case, we observe a behavior similar to what was found for the imidazolium-based systems with a positive correlation for different anions and a negative correlation for the subset with different side chain lengths. The latter is emphasized in Figure 4 by the red diamonds. An Rvalue of −0.95 is obtained in this case, and we assume that the same interpretation as for imidazolium systems applies here. Both findings can be rationalized through the coupling between the ions that slowly changes from being dominated by electrostatic and covalent interactions into coupling through van-der-Waals forces. Thereby, we point out that the qualitative order for the [P444n], [CnC1Im][NTf2], and [C4C1Im][Anion] series is identical for 𝛥𝑞𝑁𝐸 and 𝛥𝑞𝐷𝐹𝑇. Finally, Figure 5 shows the excerpt of Figure 2 for the guanidinium-based systems. 23 ACS Paragon Plus Environment


Figure 5: Comparison of 𝛥𝑞𝑁𝐸 and 𝛥𝑞𝐷𝐹𝑇 for the subset of guanidinium-based ionic liquids.

Interestingly, the results for the guanidinium-based ionic liquids are more scattered. This can be attributed to the fact that the choice of investigated systems is more inhomogeneous than in other sources, with only very few members in each subset. Additionally, many of the ionic liquids were solid under ambient conditions and could only be studied at elevated temperatures.49 In order to remove this additional source of inaccuracy, these data points were excluded from our discussion. The ionic liquid [C1C0TMG][TFA] stands out with a very high value for 𝛥𝑞𝑁𝐸. A similar behavior is found for other trifluoroacetate ILs like [P4442O2][TFA] as is shown in Figure 4. This indicates that not only a fractional charge transfer but also other effects like aggregation contribute significantly to the deviations of the Haven ratio from the value of 1 for [TFA]-based ionic liquids. For qualitative support of the identified trends, we calculated Fukui functions in the finitedifference approximation as defined by Eqs. (15) and (16) for a representative set of six cations and five anions. Additionally, the electrostatic potential (ESP) around the molecules is shown for


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comparison. At first, Figure 6 shows the mapped ESP and 𝑓 + functions for the [C4C1Im], [N1115], [P1115], [P1112O2], [P2225] and [P111H] cations.



Figure 6: ESP and 𝑓 + functions mapped on the van der Waals surface for a subset of the studied cations. Values in atomic units.


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In terms of the electrostatic potential on the van der Waals surface, the upper three ions [C4C1Im], [N1115], and [P1115] are comparable. As expected, the ether group in [P1112O2] slightly decreases the positive charge at the cation surface. Additionally, the charge is much more shielded for [P2225] when directly compared with [P1115] or even with [P111H]. Although smaller cations usually show preferable properties, the actual optimum should be [P2225] in this simple picture. Preferable in this respect means that the ESP values are small (i.e., there is less accessible positive charge) at the surface and that the same applies for the Fukui functions (i.e., the molecule is less susceptible to nucleophilic attack). There is virtually no difference in the Fukui functions for [N1115], [P1115], and [P1112O2], whereas [P111H] shows much larger values for 𝑓 + . This corresponds to the low ranking of [P111H] in Figure 1, since the Fukui functions are a measure for the ease with which electrons can be removed or added. Interestingly, the 𝑓 + values at the surface of [C4C1Im] are small except for the region near C2. This region is the chemical ‘weak point’ of the [C4C1Im], where deprotonation and consecutive decomposition reactions take place.76,89 The surfaces for the [AlHFIP4], [NTf2], [B(CN)4], [OTf], and [OMs] anions are shown in Figure 7.



Figure 7: ESP and 𝑓 ― functions mapped on the van der Waals surface for the anions. Values in atomic units.

The visible differences are much more pronounced than for the cations. For both the ESP and 𝑓 ― values on the surface, [AlHFIP4] is the most and [OMs] the least favorable system, which 28 ACS Paragon Plus Environment

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agrees with the experimental findings mentioned above and in the literature. For the anion, preferable means that the ESP values are large (i.e., there is less accessible negative charge) at the surface, whereas the Fukui function is small (i.e., the molecule is less nucleophilic). The positive effect of the fluorination is also visible in a direct comparison of [OMs] and [OTf] since the latter shows an increased electrostatic potential and a decreased value of the 𝑓 ― function on its van der Waals surface. Although being non-fluorinated, [B(CN)4] is comparable to [NTf2] in terms of the electrostatic potential on the van der Waals surface. The 𝑓 ― function is even more uniform for the [B(CN)4] anion. Although [NTf2] is much less nucleophilic than [OMs] and [OTf] within this approximation, it appears that the delocalization is more effective in the case of the tetracyanoborate. Further experimental information on diffusion properties for more ILs containing the [B(CN)4] anion would therefore be very desirable.

Summary and Conclusions At present, there is a lively discussion about the relative importance of aggregation, anticorrelation, and charge transfer in ionic liquids. However, a reasonable assumption is that charge-transfer effects are substantial although the determination of their quantitative importance is far from trivial. Thereby, the approaches suffer also from the fact that partition schemes for the electron density are somewhat arbitrary and not unique. This includes some of the commonly used approaches like the RESP or CHelpG schemes. The present work aims at providing a simple approach for deriving a quantitative estimate for the importance of the fractional charge transfer. Thereby, the description of the macroscopic properties of the ionic liquids is reduced to that of the microscopic properties of the individual, non-interacting ions that, moreover, were calculated only approximately. 29 ACS Paragon Plus Environment


Despite these crude approximations, our study shows that descriptors can be used to estimate the charge transfer that occurs for simple cation-anion combinations. An interesting aspect is that our approach is based on the energetics of the involved ions and that all properties can be calculated fairly easily. Nevertheless, our approach does suffer from a number of approximations. We used internal energies rather than zero-point corrected energies, vertical rather than adiabatic transitions, and restricted (open shell) calculations for a variety of reasons discussed above. Despite those approximations, a particularly appealing advantage is that the ions are studied separately, whereby effects due to relative orientations of the ions become irrelevant. Additionally, a very large matrix of combinations is accessible with only few straightforward calculations. A strong advantage of using DFT descriptors is that this approach is based on the energy of the ions. Other methods for the determination of charge transfer depend on methodological subtleties like the choice of a sampling grid for ESP charge fitting or the way a force field is parameterized in charge-scaled MD simulations. In contrast, the internal energy of a quantum mechanical system has a clearly defined value within the accuracy of the employed method and is hence less susceptible to the choice of the latter. We also used the Nernst-Einstein relation to derivate estimates for the charge transfer solely from experiment. The range of these charge-transfer values agrees very well with several theoretical values from other groups. The two quantities show a satisfactory correlation, although the descriptor-based method overestimates charge transfer. This latter is, we believe, to be attributed to the so-called charge-delocalization error of DFT. Taking the level of simplification, the computational results produce remarkably clear trends in terms of the anions. This may help in ion structure optimization and the search for interesting 30 ACS Paragon Plus Environment

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new ion combinations. One of the key results of our study is that ionic liquids based on pentacyanocyclopentadienide and, in particular, on tetracyanoborate are promising despite their high symmetry. Experimental data for the Haven ratios of [C4C1TMG][B(CN)4] and [P(2O2)3 10][B(CN)4] is not yet available, hence these systems will be subject of future investigations.

Supporting Information The following files are available free of charge: scheme with structural formulae and abbreviations for the ionic liquids used herein, optimized structures as xyz files, calculated single point energies, electron affinities, ionization potentials and values for the hardness and the chemical potential of the electrons.

Acknowledgment We gratefully acknowledge financial support by the German Research Foundation, DFG, grant number HE 2403/21-1. The authors would like to thank Nicolas Louis for his patient technical assistance. We are also thankful to Anna Quinten for her aid with data editing.

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