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Density Functional Theory Descriptors for Ionic Liquids and the Introduction of a Coulomb Correction Frederik Philippi, Anna Quinten, Daniel Rauber, Michael Springborg, and Rolf Hempelmann J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b01831 • Publication Date (Web): 16 Apr 2019 Downloaded from http://pubs.acs.org on April 17, 2019

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The Journal of Physical Chemistry

Density Functional Theory Descriptors for Ionic Liquids and the Introduction of a Coulomb Correction Frederik Philippi,† Anna Quinten,† Daniel Rauber,†,§ Michael Springborg,‡,∇ Rolf Hempelmann*,†,§ †Physical

Chemistry, Saarland University, Campus B 2 2, 66123 Saarbrücken, Germany. E-mail: [email protected]

§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

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Abstract As a result of continuing ionic liquid research, it becomes clearer that charge transfer in ionic liquids has a physical reality. In a recent publication, we demonstrated the utility of simple DFT descriptors to estimate charge transfer for a large number of ion combinations, which is possible because the ions are treated separately. A major disadvantage found was that the charge transfer was systematically overestimated. In this work, we introduce a correction to account for the losses in Coulomb attraction when charge is transferred from the anion to the cation. We find that accounting for these losses is important to describe charge transfer in ionic liquids appropriately. The advantage that the calculations can be performed separately on the individual, isolated ions is maintained. The corrected as well as the uncorrected charge transfer have been calculated

for

over

4000

cation-anion

combinations

at

the

R(O)B3LYP/6-

311+G(2d,p)//RB3LYP/6-31+G(d,p) level of theory. With the correction, the absolute values for the charge transfer are no longer unrealistically high and agree well with other charge transfer estimates from the literature. In general, the cumulative nature of the Haven ratio is now correctly mirrored in the relationship between the corrected theoretical charge transfer and the experimental estimate from the Nernst-Einstein relation. Earlier findings on the similarities between ether-functionalized and non-functionalized ionic liquids are confirmed. However, we also observe inconsistencies when using the experimental charge transfer estimates together with the ionicity interpretation of the Haven ratio. These can be interpreted as a hint towards the latter premise being wrong.


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Introduction The growing demand for alternative energy storage systems, for stationary and portable devices, and the challenges arising from climate change have enabled the field of ionic liquids to grow continuously over the last couple of decades.1 The general consensus is that an ionic liquid is a salt with a melting point below 100°C, although this definition is somewhat arbitrary. Furthermore, the majority of ionic liquids is based on singly charged cations and anions since doubly charged ions usually lead to the formation of classical salts with high melting points. Apart from electrochemical applications, such as in batteries2 or other devices relevant for energy storage,3 ionic liquids also are used in organic chemistry, as recyclable and tunable solvents or catalysts,4 just to mention a few of the countless examples. The systems studied in literature5–8 are usually composed of organic cations and inorganic or organic anions, with a typical representative being 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [C4C1Im][NTf2]. Many ionic liquids have unique properties like good conductivity, nonflammability, high thermal stability, and low vapor pressure.8–10 Ionic liquids were initially thought to inherently meet the requirements of green chemistry, especially due to their negligible vapor pressure.11 This postulate had to be put into perspective, especially when also considering factors like toxicity and biodegradability.9,12,13 The inherent charge of ionic liquids leads to a relatively high molar conductivity of these systems, which is very useful for their application as electrolytes. In this sense, an ‘ideal’ ionic liquid would consist only of free ions. However in practice, it has been shown that a significant part of the ions participate in the formation of larger clusters or aggregates, thus effectively reducing the number of free ions and hence the electrical conductivity.14–16 The amount of freely moving ions is often referred to as the ‘ionicity’ of an ionic liquid.17,18 By contrast, the term ‘ion 3 ACS Paragon Plus Environment


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pairing’ should be avoided. Although being well established for dilute ionic species in conventional solvents,19 ion pairing in ionic liquids is highly questionable and suffers from the arbitrary definition of a pair in a neat fused salt.20,21 Irrespective of their true nature, neutral subunits of every kind are expected to decrease the ionic conductivity by reducing the number of charge carriers. A key role in the quantification of this undesired decrease in conductivity plays the Haven ratio, which originates from solid state physics.22 We use the common definition within the field of ionic liquids as shown in eq (1).23–25

𝐻𝑅 =

Ʌ𝑁𝐸

𝐼𝐻𝑅 = 𝐻𝑅―1

𝑎𝑛𝑑

Ʌ𝑀

(1)

The Haven ratio is defined between the conductivity calculated from the Nernst-Einstein relation Ʌ𝑁𝐸 and the experimental molar conductivity Ʌ𝑀. Sometimes, the reciprocal of 𝐻𝑅 is used which can be interpreted as ionicity 𝐼𝐻𝑅. In contrast to our preceding publication, we use the form of (1) since it is more widely used throughout literature.26 While the concept of ionicity itself is confirmed by the nanostructure27 and dynamical diffusion states14 found for ionic liquids, the direct interpretation of the Haven ratio in terms of ionicity is problematic, as will be shown later. The quantity Ʌ𝑁𝐸 is the ideal molar conductivity of the ionic liquid in the case that the ions behave as dilute and spherical, and it is calculated from experimental self-diffusion coefficients via the Nernst-Einstein relation (2). 𝐹2 𝛬𝑁𝐸 = 𝑅𝑇

𝑄

∑𝑧 𝐷

2 𝑠 𝑖 𝑖

𝑖=1


(2)

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Here, 𝐹 is the Faraday constant, 𝑅 the ideal gas constant and 𝑇 the thermodynamic temperature. The summation covers all particles 𝑖 with the charges 𝑧𝑖. The self-diffusion coefficients 𝐷𝑠𝑖 are usually measured by NMR diffusometry. Combining (1) and (2), it is apparent that the only variable quantities that cannot be observed experimentally are the Haven ratio and the charges. The latter are usually set to the expected integer charges of the ions, and the Haven ratio is calculated and interpreted. However, this is not the only valid approach. The ions are in close contact with each other and the charges will be reduced by charge transfer from the anion to the cation. Such a charge transfer has been reported to be relevant for ionic liquids, although experimental work on this topic is limited.21,28–33 For instance, charge scaling can be estimated from the refractive index due to its relation to polarizability, which gives scaled charges of around 0.7 for several imidazolium and phosphonium ionic liquids.34 This would correspond to a charge transfer of 0.3 elementary charges, which has for instance been reported for 1,3-dimethylimidazolium chloride [C1C1Im][Cl] on a theoretical basis,31 together with similar scaling factors between 0.7 and 0.8.21 By arbitrarily setting the Haven ratio to 1, it is possible to calculate apparent charges from which an estimate of the charge transfer 𝛥𝑞𝑁𝐸 can be calculated as shown in (3).26

𝛥𝑞𝑁𝐸 = 1 ―

Ʌ𝑀 Ʌ𝑁𝐸

(3)

The aforementioned contributions like clustering or dynamical diffusion states are thus neglected entirely. More than that, cross-correlated movements between distinct species are also not taken into account.35,36 Although this might appear to be a rather incisive approximation, it is 5 ACS Paragon Plus Environment


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nevertheless inevitable since there is currently no tool to rigorously distribute the deviation from ideality between the Haven ratio and the charge transfer. A remaining issue is that the charge transfer cannot be measured directly, so that eq (3) must be assessed by comparison with theoretical values. For this purpose, we have chosen to use the charge transfer 𝛥𝑞𝐷𝐹𝑇 of eq (4) from descriptive DFT as a very simple, but powerful approach.37

𝛥𝑞𝐷𝐹𝑇 =

𝜇𝑐𝑎𝑡𝑖𝑜𝑛 ― 𝜇𝑎𝑛𝑖𝑜𝑛 2(𝜂𝑐𝑎𝑡𝑖𝑜𝑛 + 𝜂𝑎𝑛𝑖𝑜𝑛)

(4)

Here, 𝜇 is the chemical potential of the electrons, and 𝜂 is the hardness. For a given system, these quantities can be obtained from separate theoretical calculations on the cations and anions, so a large matrix of cation-anion combinations is easily accessible based on results from only a few calculations. In the present work, we have estimated the charge transfer for 4000 ion combinations based on calculations for 127 isolated cations and anions. The approach does not include any influence of the orientation of the ions relative to each other. Another crucial advantage of this approach is that it is based on the energy of the ions, which has a clearly defined value. This is unmatched by approaches like charge fitting, which often strongly depend on the used method and the conformation of the molecule.38 Nevertheless, we found that the charges predicted by eq (4) were unreasonably high.26 Thus, we have studied the reasons for this deviation and found that including Coulomb attractions between the cations and anions significantly improves the results. This Coulomb correction which is at the root of the present work will be described in the next Section.


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Implementing a Coulomb correction into DFT descriptors Since we are considering ionic liquids, the intermolecular interactions are dominated by electrostatic forces between the ions.39 The Coulomb attraction between anions and cations is partly reduced if charge transfer takes place. This is the physical reasoning behind introducing the Coulomb correction factor in this work. Even though there is still an ongoing discussion about the strength of ionic interactions and especially the screening length in ionic liquids,40 at this point it is a necessary step of adjusting the DFT descriptor theory so it can be applied to dense ionic fluids. The adjustment made to alter eq (4) in the desired way is easily comprehensible. The starting point is a second-order Taylor expansion (5) of the energy as a function of the number of electrons 𝐸(𝑁) around the reference system, i.e. the isolated anion or cation with the number of electrons 𝑁0. The Taylor series is terminated after the second-order term to simplify the calculations within a finite-difference approximation. Using a higher-order Taylor series would lead to an underdetermined system of equations, requiring calculations on triply charged ions. 𝐸(𝑁) = 𝐸(𝑁0) ― µ𝛥𝑁 + 𝜂(𝛥𝑁)2

(5)

Here, we used the definitions of µ and 𝜂 given in eq (6), with the external potential 𝑣 of the nuclei kept constant.41

µ=―

( ) ∂𝐸 ∂𝑁

𝑣

and

𝜂=

( )

1 ∂2𝐸 2 ∂𝑁2

𝑣


(6)


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Both quantities can be calculated using a finite-difference approximation from the energies of the reference system and the systems with one electron added and removed as shown in eqs (7) and (8).37

𝜂=

𝐸(𝑁0 ― 1) + 𝐸(𝑁0 + 1) 2

µ=

― 𝐸(𝑁0)

𝐸(𝑁0 ― 1) ― 𝐸(𝑁0 + 1)

(7)

(8)

2

with E(N) being the total energy for the system with N electrons. The total energy of both anion and cation can then be obtained from the sum of their two separate energies as given by eq (5), and solving this equation for a minimum yields eq (4) for the charge transfer. It has to be mentioned that eqs (7) and (8) are not the only means to obtain µ and 𝜂 from ab initio calculations. The electron affinity and ionization potential of a system can be directly converted to its hardness and the chemical potential of the electrons, and vice versa.37 Hence, Koopman’s theorem can be used in conjunction with energies of the Kohn-Sham orbitals to estimate the ionization potential directly from the energy of the highest occupied molecular orbital.42,43 Accordingly, the electron affinity can be estimated from the energy of the lowest unoccupied molecular orbital, thus all desired quantities are also accessible from calculations on the ions bearing their natural charge.44 Such calculations have already been performed for ionic liquids.45 An advantage of this approach is that notoriously difficult calculations on dianions are not necessary. This is, however, at the expense of employing frontier molecular orbital theory, which requires a careful choice of the functionals to be reliable.46,47 To avoid these problems, we use eqs (7) and (8) with explicit calculations of the systems with one electron removed and added. 8 ACS Paragon Plus Environment

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Furthermore, the very popular B3LYP functional used in this work performs suitably well with this method, although being inferior to other functionals regarding calculations of orbital energies.46,48 This can also be seen from the error estimation provided in the supporting information. To account for the losses in electrostatic attraction, the Coulomb correction itself is expressed as a function of the charge transfer, as shown in eq (9).

𝛥𝐸𝐶𝑜𝑢𝑙𝑜𝑚𝑏(𝛥𝑞) =

𝑞𝑐𝑎𝑡𝑖𝑜𝑛𝑞𝑎𝑛𝑖𝑜𝑛 𝑒2 =― (1 ― 𝛥𝑞)2 4𝜋𝜀0𝑑 4𝜋𝜀0𝑑

(9)

The charges 𝑞 of cation and anion are thus rewritten into ± 𝑒(1 ― 𝛥𝑞) with 𝑒 being the elementary charge and 𝜀0 the vacuum permittivity. The distance 𝑑 between the charges is an additional parameter, which we propose to estimate as the sum of the radii of the ions. This serves to maintain the key advantage of eq (4), which is that every required quantity can be determined for cations and anions separately. The Coulomb correction is then introduced by adding the electrostatic interaction energy 𝛥𝐸𝐶𝑜𝑢𝑙𝑜𝑚𝑏 between the ions to the total energy 𝐸total as shown in eq (10). 𝐸total = 𝐸total(𝑁0) ― µ𝑐𝑎𝑡𝑖𝑜𝑛𝛥𝑞 + 𝜂𝑐𝑎𝑡𝑖𝑜𝑛𝛥𝑞2 + µ𝑎𝑛𝑖𝑜𝑛𝛥𝑞 + 𝜂𝑎𝑛𝑖𝑜𝑛𝛥𝑞2 + 𝛥𝐸Coulomb(𝛥𝑞)

(10)

The total energy is given here as a function of the charge transfer 𝛥𝑞. Substituting (9) into (10); differentiating the total energy with respect to the charge transfer 𝛥𝑞 and setting the first derivative to zero lead to 𝛥𝑞 as given in eq (11). This is the desired expression for the corrected charge transfer 𝛥𝑞′𝐷𝐹𝑇. Note the ‘2’ in the denominator of the Coulomb terms, which is intentional. 9 ACS Paragon Plus Environment


𝜇 𝛥𝑞'𝐷𝐹𝑇

=

𝑐𝑎𝑡𝑖𝑜𝑛

―𝜇

𝑎𝑛𝑖𝑜𝑛

𝑒2 ― 2𝜋𝜀0𝑑

𝑒2 2(𝜂𝑐𝑎𝑡𝑖𝑜𝑛 + 𝜂𝑎𝑛𝑖𝑜𝑛) ― 2𝜋𝜀0𝑑

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(11)

Before turning to the results of the calculations, a few remarks on the approximations are necessary. Since only a single ion pair has been considered, the bulk is entirely neglected so far. This was not crucial when using eq (4) since both numerator and denominator would just be multiplied with the same value when assuming that every ion is surrounded by a shell of counterions. However, this is no longer the case with the Coulomb correction. To account for the bulk structure, eq (9) would have to be multiplied by a Madelung constant, so the simplicity of the approach would be lost. Madelung constants for ‘classical’ fused salts like KCl are usually around 1.1,49,50 and for ionic liquids around 1.3.51 The error introduced by neglecting this is hence relatively small, especially since the required constants would modify both the numerator and the denominator. Moreover, short-range corrections would take into account the nearest coordination shell of the ions. Since the average coordination number with which both numerator and denominator in eq (4) would have to be multiplied is most likely to be larger than 1.3, the charge transfers obtained by (11) will presumably be too small. Hence, both expressions together define a range for realistic charge transfer.


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Computational Details The Monte Carlo conformational search implemented in the SPARTAN 18 software package52 was used with the Merck molecular force field (MMFF) for every ion, followed by a refined structural optimization at the PM6 level of theory. The resulting geometry was further optimized at the RB3LYP/6-31+G(d,p) level of theory, using the Gaussian 09 software package.53 After verifying that no imaginary frequencies are present, single-point calculations were performed with the Gaussian 09 software package53 at the R(O)B3LYP/6-311+G(2d,p) level of theory for the reference system as well as the systems with one electron added or removed. The ultrafine integration grid was used for the calculations with Gaussian. For the single-point calculations, a reduced convergence criterion was necessary as suggested in the literature.54 For difficult cases where SCF convergence was not achieved after 500 cycles, the keywords ‘novaracc’, ‘DIIS’, ‘damp’, and ‘vshift’ were applied in this order. The converged wave functions of the singly charged ions were used as the initial guess. The sum of the ionic radii is taken as the distance between the charges to provide for a reasonable estimate of the Coulomb correction. Here, the radius of an ion is defined as the radius of a sphere with the same volume as the corresponding ion. The ion volumes were in turn obtained using the electron density from the converged wave function of the geometry optimization at the RB3LYP/6-31+G(d,p) level of theory. Electron density analysis was carried out using the Multiwfn software package.55,56 To this end, Multiwfn was invoked with the appropriately formatted checkpoint file and the command 12/2/11/3/0.15/0 as input.



Results and Discussion Together with the values from our previous work, single-point calculations on 63 cations and 64 anions are available, which means that the charge transfer for 63x64=4032 ion combinations can be estimated. Naturally, experimental Haven ratios are available only for a very small subset of this 63x64 matrix. Since it is impossible to comprehensively discuss all these results in detail, we will focus on the general influence of the correction factor and a comparison with 𝛥𝑞𝑁𝐸. The complete matrices for both corrected and uncorrected values for the theoretical charge transfer are given in the supporting information. Unless otherwise mentioned, the theoretical charge transfer values discussed here are always the corrected ones, and we restrict the discussion entirely to singly charged ions. The uncorrected, theoretical charge transfer for all ion combinations in this work ranges from 0.21 to 0.58 elementary charges. Upon introduction of the Coulomb correction, this changes clearly, with the corrected values ranging from 0.06 to 0.47 elementary charges. This rather strong change appears to be correct since eq (4) was found to overestimate the charge transfer.26 The influence of the anion structure on 𝛥𝑞′𝐷𝐹𝑇 is more pronounced than that of the cations and will be discussed first. As was found in the case of the uncorrected charge transfer, the fluorination has the strongest influence. The effect of fluorination is to roughly group all the anions into those with a low charge transfer in the resulting combinations (highly fluorinated systems) and those with a large charge transfer (non-fluorinated). This can be intuitively understood through the high electronegativity of the fluorine atom, leading to a very effective delocalization of the negative charge. The effect can be seen clearly by comparing isostructural pairs like acetate [OAc] and trifluoroacetate [TFA], where the charge transfer is decreased by 12 ACS Paragon Plus Environment

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19% in their combination with the [C4C1Im] cation. Consistent with this, the two anions tetrakis(trifluoromethyl)borate [B(CF3)4] and hexafluorophosphate [PF6] show the lowest values for the charge transfer when combined with various cations. However, their relative order changes due to the size dependence of the correction. The extremely weakly coordinating [B(CF3)4]57 shows higher values for 𝛥𝑞′𝐷𝐹𝑇 than [PF6], although the difference is very small. The same arguments hold true for the electron-withdrawing nitrile group, though to a lesser extent. The values for 𝛥𝑞′𝐷𝐹𝑇 increase in the series [B(CN)4]𝛥𝑞𝑁𝐸>𝛥𝑞′𝐷𝐹𝑇 is observed across the majority of cases, we have shown that it might be necessary to go beyond the ionicity interpretation in favour of other, more sophisticated models. This is similar to the concept of ion pairing, which more or less had to be abandoned. After all, ionic liquids are complex and non-ideal systems. Especially since many competing theories are available, the different contributions can hardly be separated. Cross terms could be important, ions can be in more than one diffusion state and anomalous diffusion behavior is sometimes found. One of these concepts of central importance is the charge transfer as discussed in the present work.


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Supporting Information Molecular structures and abbreviations for the cations and anions used in this work, calculated single point energies, values for hardness and chemical potential of the ions, error analysis for 𝛥𝑞𝐷𝐹𝑇 as well as self-diffusion coefficients for [C2C1Im][FAP]; Optimized structures as xyzfiles for the cations and anions; Comprehensive charge transfer table.

Acknowledgement We gratefully acknowledge financial support by the German Research Foundation, DFG, grant number HE 2403/21-1. We are sincerely thankful to Gemma Lawrence for proofreading.

References (1)

Welton, T. Ionic Liquids: A Brief History. Biophys. Rev. 2018, 10, 691–706.

(2)

Armand, M.; Tarascon, J.-M. Building Better Batteries. Nature 2008, 451, 652–657.

(3)

Gebresilassie Eshetu, G.; Armand, M.; Scrosati, B.; Passerini, S. Energy Storage Materials Synthesized from Ionic Liquids. Angew. Chemie Int. Ed. 2014, 53, 13342–13359.

(4)

Welton, T. Ionic Liquids in Catalysis. Coord. Chem. Rev. 2004, 248, 2459–2477.

(5)

Maton, C.; De Vos, N.; Stevens, C. V. Ionic Liquid Thermal Stabilities: Decomposition Mechanisms and Analysis Tools. Chem. Soc. Rev. 2013, 42, 5963.

(6)

Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. Physicochemical Properties and Structures of Room Temperature Ionic Liquids. 1. Variation of Anionic Species. J. Phys. Chem. B 2004, 108, 16593–16600.



(7)

Miran, M. S.; Kinoshita, H.; Yasuda, T.; Susan, M. A. B. H.; Watanabe, M. Physicochemical Properties Determined by ΔpKa for Protic Ionic Liquids Based on an Organic Super-Strong Base with Various Brønsted Acids. Phys. Chem. Chem. Phys. 2012, 14, 5178–5186.

(8)

Plechkova, N. V.; Seddon, K. R. Applications of Ionic Liquids in the Chemical Industry. Chem. Soc. Rev. 2008, 37, 123–150.

(9)

Ranke, J.; Stolte, S.; Störmann, R.; Arning, J.; Jastorff, B. Design of Sustainable Chemical Products - The Example of Ionic Liquids. Chem. Rev. 2007, 107, 2183–2206.

(10)

De Vos, N.; Maton, C.; Stevens, C. V. Electrochemical Stability of Ionic Liquids: General Influences and Degradation Mechanisms. ChemElectroChem 2014, 1, 1258–1270.

(11)

Anastas, P.; Eghbali, N. Green Chemistry: Principles and Practice. Chem. Soc. Rev. 2010, 39, 301–312.

(12)

Chatel, G.; Naffrechoux, E.; Draye, M. Avoid the PCB Mistakes: A More Sustainable Future for Ionic Liquids. J. Hazard. Mater. 2017, 324, 773–780.

(13)

Zhao, D.; Liao, Y.; Zhang, Z. Toxicity of Ionic Liquids. CLEAN – Soil, Air, Water 2007, 35, 42–48.

(14)

Feng, G.; Chen, M.; Bi, S.; Goodwin, Z. A. H.; Postnikov, E. B.; Urbakh, M.; Kornyshev, A. A. Kinetics of Ion Transport in Ionic Liquids: Two Dynamical Diffusion States. arXiv Prepr. arXiv1805.00697 2018.

(15)

Gouverneur, M.; Kopp, J.; van Wüllen, L.; Schönhoff, M. Direct Determination of Ionic


Page 38 of 50

Page 39 of 50 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


Transference Numbers in Ionic Liquids by Electrophoretic NMR. Phys. Chem. Chem. Phys. 2015, 17, 30680–30686. (16)

Canongia Lopes, J. N. a; Pádua, A. a H. Nanostructural Organization in Ionic Liquids. J. Phys. Chem. B 2006, 110, 3330–3335.

(17)

MacFarlane, D. R.; Forsyth, M.; Izgorodina, E. I.; Abbott, A. P.; Annat, G.; Fraser, K. On the Concept of Ionicity in Ionic Liquids. Phys. Chem. Chem. Phys. 2009, 11, 4962–4967.

(18)

Ueno, K.; Tokuda, H.; Watanabe, M. Ionicity in Ionic Liquids: Correlation with Ionic Structure and Physicochemical Properties. Phys. Chem. Chem. Phys. 2010, 12, 1649– 1658.

(19)

Marcus, Y.; Hefter, G. Ion Pairing. Chem. Rev. 2006, 106, 4585–4621.

(20)

Kirchner, B.; Malberg, F.; Firaha, D. S.; Hollóczki, O. Ion Pairing in Ionic Liquids. J. Phys. Condens. Matter 2015, 27, 463002.

(21)

Hollóczki, O.; Malberg, F.; Welton, T.; Kirchner, B. On the Origin of Ionicity in Ionic Liquids. Ion Pairing versus Charge Transfer. Phys. Chem. Chem. Phys. 2014, 16, 16880– 16890.

(22)

MURCH, G. The Haven Ratio in Fast Ionic Conductors. Solid State Ionics 1982, 7, 177– 198.

(23)

Susan, M. A. B. H.; Noda, A.; Watanabe, M. Diffusion in Ionic Liquids and Correlation with Ionic Transport Behavior. In Electrochemical Aspects of Ionic Liquids; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2005; pp 55–74.



(24)

Every, H. A.; Bishop, A. G.; MacFarlane, D. R.; Orädd, G.; Forsyth, M. Transport Properties in a Family of Dialkylimidazolium Ionic Liquids. Phys. Chem. Chem. Phys. 2004, 6, 1758–1765.

(25)

Frömling, T.; Kunze, M.; Schönhoff, M.; Sundermeyer, J.; Roling, B. Enhanced Lithium Transference Numbers in Ionic Liquid Electrolytes. J. Phys. Chem. B 2008, 112, 12985– 12990.

(26)

Philippi, F.; Rauber, D.; Springborg, M.; Hempelmann, R. Density Functional Theory Descriptors for Ionic Liquids and the Charge-Transfer Interpretation of the Haven Ratio. J. Phys. Chem. A 2019, 123, 851–861.

(27)

Hayes, R.; Warr, G. G.; Atkin, R. Structure and Nanostructure in Ionic Liquids. Chem. Rev. 2015, 115, 6357–6426.

(28)

Beichel, W.; Trapp, N.; Hauf, C.; Kohler, O.; Eickerling, G.; Scherer, W.; Krossing, I. Charge-Scaling Effect in Ionic Liquids from the Charge-Density Analysis of N,N′Dimethylimidazolium Methylsulfate. Angew. Chemie Int. Ed. 2014, 53, 3143–3146.

(29)

Hunt, P. A.; Kirchner, B.; Welton, T. Characterising the Electronic Structure of Ionic Liquids: An Examination of the 1-Butyl-3-Methylimidazolium Chloride Ion Pair. Chem. A Eur. J. 2006, 12, 6762–6775.

(30)

Bühl, M.; Chaumont, A.; Schurhammer, R.; Wipff, G. Ab Initio Molecular Dynamics of Liquid 1,3-Dimethylimidazolium Chloride. J. Phys. Chem. B 2005, 109, 18591–18599.

(31)

Youngs, T. G. A.; Hardacre, C. Application of Static Charge Transfer within an Ionic-


Page 40 of 50

Page 41 of 50 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


Liquid Force Field and Its Effect on Structure and Dynamics. ChemPhysChem 2008, 9, 1548–1558. (32)

Kirchner, B.; Hollóczki, O.; Canongia Lopes, J. N.; Pádua, A. A. H. Multiresolution Calculation of Ionic Liquids. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2015, 5, 202–214.

(33)

Cremer, T.; Kolbeck, C.; Lovelock, K. R. J.; Paape, N.; Wölfel, R.; Schulz, P. S.; Wasserscheid, P.; Weber, H.; Thar, J.; Kirchner, B.; et al. Towards a Molecular Understanding of Cation-Anion Interactions-Probing the Electronic Structure of Imidazolium Ionic Liquids by NMR Spectroscopy, X-Ray Photoelectron Spectroscopy and Theoretical Calculations. Chem. - A Eur. J. 2010, 16, 9018–9033.

(34)

Wendler, K.; Dommert, F.; Zhao, Y. Y.; Berger, R.; Holm, C.; Delle Site, L. Ionic Liquids Studied across Different Scales: A Computational Perspective. Faraday Discuss. 2012, 154, 111–132.

(35)

Kashyap, H. K.; Annapureddy, H. V. R.; Raineri, F. O.; Margulis, C. J. How Is Charge Transport Different in Ionic Liquids and Electrolyte Solutions? J. Phys. Chem. B 2011, 115, 13212–13221.

(36)

Harris, K. R. Can the Transport Properties of Molten Salts and Ionic Liquids Be Used To Determine Ion Association? J. Phys. Chem. B 2016, 120, 12135–12147.

(37)

Geerlings, P.; De Proft, F.; Langenaeker, W. Conceptual Density Functional Theory. Chem. Rev. 2003, 103, 1793–1874.

(38)

Francl, M. M.; Chirlian, L. E. The Pluses and Minuses of Mapping Atomic Charges to



Electrostatic Potentials. In Reviews in Computational Chemistry; 2007; Vol. 14, pp 1–31. (39)

Köddermann, T.; Paschek, D.; Ludwig, R. Ionic Liquids: Dissecting the Enthalpies of Vaporization. ChemPhysChem 2008, 9, 549–555.

(40)

Gebbie, M. A.; Smith, A. M.; Dobbs, H. A.; Lee, A. A.; Warr, G. G.; Banquy, X.; Valtiner, M.; Rutland, M. W.; Israelachvili, J. N.; Perkin, S.; et al. Long Range Electrostatic Forces in Ionic Liquids. Chem. Commun. 2017, 53, 1214–1224.

(41)

Jensen, F. Introduction to Computational Chemistry, 2nd ed.; John Wiley & Sons, Inc.: West Sussex, 2007.

(42)

Koopmans, T. Über Die Zuordnung von Wellenfunktionen Und Eigenwerten Zu Den Einzelnen Elektronen Eines Atoms. Physica 1934, 1, 104–113.

(43)

Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133–A1138.

(44)

Tozer, D. J.; De Proft, F. Computation of the Hardness and the Problem of Negative Electron Affinities in Density Functional Theory. J. Phys. Chem. A 2005, 109, 8923– 8929.

(45)

Thomas, E.; Vijayalakshmi, K. P.; George, B. K. Kinetic Stability of Imidazolium Cations and Ionic Liquids: A Frontier Molecular Orbital Approach. J. Mol. Liq. 2019, 276, 721– 727.

(46)

Ilawe, N. V.; Fu, J.; Ramanathan, S.; Wong, B. M.; Wu, J. Chemical and Radiation Stability of Ionic Liquids: A Computational Screening Study. J. Phys. Chem. C 2016, 120,


Page 42 of 50

Page 43 of 50 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


27757–27767. (47)

Mori-Sánchez, P.; Cohen, A. J.; Yang, W. Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction. Phys. Rev. Lett. 2008, 100, 146401.

(48)

Curtiss, L. A.; Redfern, P. C.; Raghavachari, K.; Pople, J. A. Assessment of Gaussian-2 and Density Functional Theories for the Computation of Ionization Potentials and Electron Affinities. J. Chem. Phys. 1998, 109, 42–55.

(49)

McQuarrie, D. A. THEORY OF FUSED SALTS 1. J. Phys. Chem. 1962, 66, 1508–1513.

(50)

Koslowski, T. Electronic Structure of Molten Salts: A Numerical Approach. Berichte der Bunsengesellschaft für Phys. Chemie 1996, 100, 95–100.

(51)

Izgorodina, E. I.; Bernard, U. L.; Dean, P. M.; Pringle, J. M.; MacFarlane, D. R. The Madelung Constant of Organic Salts. Cryst. Growth Des. 2009, 9, 4834–4839.

(52)

Spartan’18, Version 1.0.1; Wavefunction Inc., Irvine, CA, USA, 2018.

(53)

Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci,B.; Petersson, G. A. et al. Gaussian 09, Revision D.01; Gaussian, Inc.:Wallingford, CT, 2013.

(54)

Szarka, A. Z.; Curtiss, L. a; Miller, J. R. Calculation of Temporary Anion States Using Density Functional Theory. Chem. Phys. 1999, 246, 147–155.

(55)

Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem.



2012, 33, 580–592. (56)

Lu, T.; Chen, F. Quantitative Analysis of Molecular Surface Based on Improved Marching Tetrahedra Algorithm. J. Mol. Graph. Model. 2012, 38, 314–323.

(57)

Bernhardt, E.; Finze, M.; Willner, H. Mechanistic Study on the Fluorination of K[B(CN)4] with ClF Enabling the High Yield and Large Scale Synthesis of K[B(CF3)4] and K[(CF3)3BCN]. Inorg. Chem. 2011, 50, 10268–10273.

(58)

Shkrob, I. A.; Marin, T. W.; Wishart, J. F. Ionic Liquids Based on Polynitrile Anions: Hydrophobicity, Low Proton Affinity, and High Radiolytic Resistance Combined. J. Phys. Chem. B 2013, 117, 7084–7094.

(59)

Xu, W.; Cooper, E. I.; Angell, C. A. A. Ionic Liquids: Ion Mobilities, Glass Temperatures, and Fragilities. J. Phys. Chem. B 2003, 107, 6170–6178.

(60)

Xu, W.; Wang, L.-M.; Nieman, R. A.; Angell, C. A. Ionic Liquids of Chelated Orthoborates as Model Ionic Glassformers. J. Phys. Chem. B 2003, 107, 11749–11756.

(61)

Schröder, C. Comparing Reduced Partial Charge Models with Polarizable Simulations of Ionic Liquids. Phys. Chem. Chem. Phys. 2012, 14, 3089–3102.

(62)

Ishizuka, R.; Matubayasi, N. Effective Charges of Ionic Liquid Determined SelfConsistently through Combination of Molecular Dynamics Simulation and DensityFunctional Theory. J. Comput. Chem. 2017, 38, 2559–2569.

(63)

Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A Well-Behaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges: The


Page 44 of 50

Page 45 of 50 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


RESP Model. J. Phys. Chem. 1993, 97, 10269–10280. (64)

Blöchl, P. E. Electrostatic Decoupling of Periodic Images of Plane‐wave‐expanded Densities and Derived Atomic Point Charges. J. Chem. Phys. 1995, 103, 7422–7428.

(65)

Wendler, K.; Zahn, S.; Dommert, F.; Berger, R.; Holm, C.; Kirchner, B.; Delle Site, L. Locality and Fluctuations: Trends in Imidazolium-Based Ionic Liquids and Beyond. J. Chem. Theory Comput. 2011, 7, 3040–3044.

(66)

Rigby, J.; Izgorodina, E. I. Assessment of Atomic Partial Charge Schemes for Polarisation and Charge Transfer Effects in Ionic Liquids. Phys. Chem. Chem. Phys. 2013, 15, 1632– 1646.

(67)

Tokuda, H.; Tsuzuki, S.; Susan, M. A. B. H.; Hayamizu, K.; Watanabe, M. How Ionic Are Room-Temperature Ionic Liquids? An Indicator of the Physicochemical Properties. J. Phys. Chem. B 2006, 110, 19593–19600.

(68)

Landmann, J.; Sprenger, J. A. P.; Hennig, P. T.; Bertermann, R.; Grüne, M.; Würthner, F.; Ignat’ev,

N.

V.;

Finze,

M.

Perfluoroalkyltricyanoborate

and

Perfluoroalkylcyanofluoroborate Anions: Building Blocks for Low-Viscosity Ionic Liquids. Chem. - A Eur. J. 2018, 24, 608–623. (69)

Koller, T.; Rausch, M. H.; Schulz, P. S.; Berger, M.; Wasserscheid, P.; Economou, I. G.; Leipertz, A.; Fröba, A. P. Viscosity, Interfacial Tension, Self-Diffusion Coefficient, Density, and Refractive Index of the Ionic Liquid 1-Ethyl-3-Methylimidazolium Tetracyanoborate as a Function of Temperature at Atmospheric Pressure. J. Chem. Eng. Data 2012, 57, 828–835.



(70)

Sanchez-Ramirez, N.; Martins, V. L.; Ando, R. A.; Camilo, F. F.; Urahata, S. M.; Ribeiro, M. C. C.; Torresi, R. M. Physicochemical Properties of Three Ionic Liquids Containing a Tetracyanoborate Anion and Their Lithium Salt Mixtures. J. Phys. Chem. B 2014, 118, 8772–8781.

(71)

Ignat’ev, N. V.; Finze, M.; Sprenger, J. A. P.; Kerpen, C.; Bernhardt, E.; Willner, H. New Hydrophobic Ionic Liquids with Perfluoroalkyl Phosphate and Cyanofluoroborate Anions. J. Fluor. Chem. 2015, 177, 46–54.

(72)

Lo Celso, F.; Yoshida, Y.; Castiglione, F.; Ferro, M.; Mele, A.; Jafta, C. J.; Triolo, A.; Russina, O. Direct Experimental Observation of Mesoscopic Fluorous Domains in Fluorinated Room Temperature Ionic Liquids. Phys. Chem. Chem. Phys. 2017, 19, 13101– 13110.

(73)

Pereiro, A. B.; Pastoriza-Gallego, M. J.; Shimizu, K.; Marrucho, I. M.; Lopes, J. N. C.; Piñeiro, M. M.; Rebelo, L. P. N. On the Formation of a Third, Nanostructured Domain in Ionic Liquids. J. Phys. Chem. B 2013, 117, 10826–10833.

(74)

Fraser, K. J.; MacFarlane, D. R. Phosphonium-Based Ionic Liquids: An Overview. Aust. J. Chem. 2009, 62, 309–321.

(75)

Philippi, F.; Rauber, D.; Zapp, J.; Präsang, C.; Scheschkewitz, D.; Hempelmann, R. Multiple Ether-Functionalized Phosphonium Ionic Liquids as Highly Fluid Electrolytes. ChemPhysChem 2018.

(76)

Philippi, F.; Rauber, D.; Zapp, J.; Hempelmann, R. Transport Properties and Ionicity of Phosphonium Ionic Liquids. Phys. Chem. Chem. Phys. 2017, 19, 23015–23023.


Page 46 of 50

Page 47 of 50 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


(77)

Kashyap, H. K.; Santos, C. S.; Daly, R. P.; Hettige, J. J.; Murthy, N. S.; Shirota, H.; Castner, E. W.; Margulis, C. J. How Does the Ionic Liquid Organizational Landscape Change When Nonpolar Cationic Alkyl Groups Are Replaced by Polar Isoelectronic Diethers? J. Phys. Chem. B 2013, 117, 1130–1135.

(78)

Araque, J. C.; Hettige, J. J.; Margulis, C. J. Modern Room Temperature Ionic Liquids, a Simple Guide to Understanding Their Structure and How It May Relate to Dynamics. J. Phys. Chem. B 2015, 119, 12727–12740.

(79)

Rauber, D.; Philippi, F.; Zapp, J.; Kickelbick, G.; Natter, H.; Hempelmann, R. Transport Properties of Protic and Aprotic Guanidinium Ionic Liquids. RSC Adv. 2018, 8, 41639– 41650.

(80)

Rupp, A.; Roznyatovskaya, N.; Scherer, H.; Beichel, W.; Klose, P.; Sturm, C.; Hoffmann, A.; Tübke, J.; Koslowski, T.; Krossing, I. Size Matters! On the Way to Ionic Liquid Systems without Ion Pairing. Chem. - A Eur. J. 2014, 20, 9794–9804.

(81)

Seki, S.; Hayamizu, K.; Tsuzuki, S.; Fujii, K.; Umebayashi, Y.; Mitsugi, T.; Kobayashi, T.; Ohno, Y.; Kobayashi, Y.; Mita, Y.; et al. Relationships between Center Atom Species (N, P) and Ionic Conductivity, Viscosity, Density, Self-Diffusion Coefficient of Quaternary Cation Room-Temperature Ionic Liquids. Phys. Chem. Chem. Phys. 2009, 11, 3509–3514.

(82)

Rüther, T.; Kanakubo, M.; Best, A. S.; Harris, K. R. The Importance of Transport Property Studies for Battery Electrolytes: Revisiting the Transport Properties of Lithium– N-Methyl-N-Propylpyrrolidinium Bis(Fluorosulfonyl)Imide Mixtures. Phys. Chem. Chem.



Phys. 2017, 19, 10527–10542. (83)

Harris, K. R.; Kanakubo, M. Self-Diffusion Coefficients and Related Transport Properties for a Number of Fragile Ionic Liquids. J. Chem. Eng. Data 2016, 61, 2399–2411.

(84)

Seddon, K. R.; Stark, A.; Torres, M.-J. Influence of Chloride, Water, and Organic Solvents on the Physical Properties of Ionic Liquids. Pure Appl. Chem. 2000, 72, 2275– 2287.

(85)

Scammells, P. J.; Scott, J. L.; Singer, R. D. Ionic Liquids: The Neglected Issues. Aust. J. Chem. 2005, 58, 155.

(86)

Widegren, J. A.; Laesecke, A.; Magee, J. W. The Effect of Dissolved Water on the Viscosities of Hydrophobic Room-Temperature Ionic Liquids. Chem. Commun. 2005, No. 12, 1610–1612.

(87)

Ermantraut, A.; Radtke, V.; Gebel, N.; Himmel, D.; Koslowski, T.; Leito, I.; Krossing, I. The Ideal Ionic Liquid Salt Bridge for Direct Determination of Gibbs Energies of Transfer of Single Ions, Part II: Evaluation of the Role of Ion Solvation and Ion Mobilities. Angew. Chemie Int. Ed. 2018, 57, 2348–2352.

(88)

Raabe, I.; Wagner, K.; Guttsche, K.; Wang, M.; Grätzel, M.; Santiso-Quiñones, G.; Krossing, I. Tetraalkylammonium Salts of Weakly Coordinating Aluminates: Ionic Liquids, Materials for Electrochemical Applications and Useful Compounds for Anion Investigation. Chem. - A Eur. J. 2009, 15, 1966–1976.

(89)

Seki, S.; Serizawa, N.; Hayamizu, K.; Tsuzuki, S.; Umebayashi, Y.; Takei, K.; Miyashiro,


Page 48 of 50

Page 49 of 50 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


H. Physicochemical and Electrochemical Properties of 1-Ethyl-3-Methylimidazolium Tris(Pentafluoroethyl)Trifluorophosphate

and

1-Ethyl-3-Methylimidazolium

Tetracyanoborate. J. Electrochem. Soc. 2012, 159, A967–A971. (90)

Harris, K. R. Relations between the Fractional Stokes−Einstein and Nernst−Einstein Equations and Velocity Correlation Coefficients in Ionic Liquids and Molten Salts. J. Phys. Chem. B 2010, 114, 9572–9577.

(91)

Taylor, A. W.; Licence, P.; Abbott, A. P. Non-Classical Diffusion in Ionic Liquids. Phys. Chem. Chem. Phys. 2011, 13, 10147.

(92)

Abbott, A. P. Model for the Conductivity of Ionic Liquids Based on an Infinite Dilution of Holes. ChemPhysChem 2005, 6, 2502–2505.

(93)

Abbott, A. P. Application of Hole Theory to the Viscosity of Ionic and Molecular Liquids. ChemPhysChem 2004, 5, 1242–1246.

(94)

Guo, J.; Baker, G. A.; Hillesheim, P. C.; Dai, S.; Shaw, R. W.; Mahurin, S. M. Fluorescence Correlation Spectroscopy Evidence for Structural Heterogeneity in Ionic Liquids. Phys. Chem. Chem. Phys. 2011, 13, 12395–12398.



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