Collective rotational dynamics in ionic liquids: A computational and experimental study of 1-butyl-3-methyl-imidazolium tetrafluoroborate

Dielectric Response and Linear Absorption Spectroscopy of Ionic Systems

Time-dependent electric fields applied to ionic systems can induce both a dielectric and a conductive response, leading to the generation of macroscopic polarization and current, respectively. It has long been recognized that it is not possible to determine the two types of responses separately. However, this aspect is often not adequately accounted for in dielectric and absorption spectroscopies of ionic systems. To clarify this, we theoretically investigate the dielectric and conductive responses of ionic systems containing polyatomic ions based on linear response theory. We derive general expressions for the frequency-dependent dielectric functions, conductivity, and absorption coefficient, including those measured experimentally. Furthermore, we show that the dielectric and conductive responses cannot be uniquely distinguished even at the theoretical level and, therefore, cannot represent experimentally measured quantities. Instead, dielectric and absorption spectra of ionic systems should be expressed in terms of the generalized dielectric function that encompasses both dielectric and conductive responses. We propose a computational method to calculate this generalized dielectric function reliably. Model calculations on concentrated aqueous solutions of NaCl, a monatomic salt, and LiTFSI, a polyatomic salt, show that the dielectric and linear absorption spectra of the two systems based on the generalized dielectric function are significantly different from purely dielectric counterparts in the far-IR, terahertz, and lower-frequency regions. Moreover, the spectra are mainly determined by the autocorrelations of total dipole and total current, but dipole-current cross-correlation can also significantly contribute to the spectra of the LiTFSI solution. The present theoretical approach could be extended to nonlinear spectroscopy of ionic liquids and electrolyte solutions.

Spectroscopic and Chemical Properties of Ionic Liquids: Computational Study

A brief account is given of highlights of our computational efforts - often in collaboration with experimental groups - to understand spectroscopic and chemical properties of ionic liquids (ILs). Molecular dynamics, including their inhomogeneous character, responsible for key spectral features observed in dielectric absorption, infra-red (IR) and fluorescence correlation spectroscopy (FCS) measurements are elucidated. Mechanisms of chemical processes involving imidazolium-based ILs are illustrated for CO2 capture and related reactions, transesterification of cellulose, and Au nanocluster-catalyzed Suzuki cross-coupling reaction with attention paid to differing roles of IL ions. A comparison with experiments is also made.

Dielectric relaxation and dielectric decrement in ionic acetamide deep eutectic solvents: Spectral decomposition and comparison with experiments

Frequency-dependent dielectric relaxation in three deep eutectic solvents (DESs), (acetamide+LiClO4/NO3/Br), was investigated in the temperature range, 329 ≤ T/K ≤ 358, via molecular dynamics simulations. Subsequently, decomposition of the real and the imaginary components of the simulated dielectric spectra was carried out to separate the rotational (dipole-dipole), translational (ion-ion), and ro-translational (dipole-ion) contributions. The dipolar contribution, as expected, was found to dominate all the frequency-dependent dielectric spectra over the entire frequency regime, while the other two components together made tiny contributions only. The translational (ion-ion) and the cross ro-translational contributions appeared in the THz regime in contrast to the viscosity-dependent dipolar relaxations that dominated the MHz-GHz frequency window. Our simulations predicted, in agreement with experiments, anion-dependent decrement of the static dielectric constant (ɛs ∼ 20 to 30) for acetamide (ɛs ∼ 66) in these ionic DESs. Simulated dipole-correlations (Kirkwood g factor) indicated significant orientational frustrations. The frustrated orientational structure was found to be associated with the anion-dependent damage of the acetamide H-bond network. Single dipole reorientation time distributions suggested slowed down acetamide rotations but did not indicate presence of any "rotationally frozen" molecule. The dielectric decrement is, therefore, largely static in origin. This provides a new insight into the ion dependence of the dielectric behavior of these ionic DESs. A good agreement between the simulated and the experimental timescales was also noticed.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.

Langevin behavior of the dielectric decrement in ionic liquid water mixtures

Large scale polarizable simulations of ionic liquid water mixtures reveal an universal Langevin behavior of the dielectric decrement.

Effective charges of ionic liquid determined self-consistently through combination of molecular dynamics simulation and density-functional theory

A self-consistent scheme combining the molecular dynamics (MD) simulation and density functional theory (DFT) was recently proposed to incorporate the effects of the charge transfer and polarization of ions into non-poralizable force fields of ionic liquids for improved description of energetics and dynamics. The purpose of the present work is to analyze the detailed setups of the MD/DFT scheme by focusing on how the basis set, exchange-correlation (XC) functional, charge-fitting method or force field for the intramolecular and Lennard-Jones interactions affects the MD/DFT results of 1,3-dimethylimidazolium bis(trifluoromethylsulfonyl) imide ( [C1mim][NTf2]) and 1-ethyl-3-methylimidazolium glycinate ( [C2mim][Gly]). It was found that the double-zeta valence polarized or larger size of basis set is required for the convergence of the effective charge of the ion. The choice of the XC functional was further not influential as far as the generalized gradient approximation is used. The charge-fitting method and force field govern the accuracy of the MD/DFT scheme, on the other hand. We examined the charge-fitting methods of Blöchl, the iterative Hirshfeld (Hirshfeld-I), and REPEAT in combination with Lopes et al.'s force field and general AMBER force field. There is no single combination of charge fitting and force field that provides good agreements with the experiments, while the MD/DFT scheme reduces the effective charges of the ions and leads to better description of energetics and dynamics compared to the original force field with unit charges. © 2017 Wiley Periodicals, Inc.

Charged, dipolar soft matter systems from a combined microscopic-mesoscopic viewpoint

As an example of charged, dipolar soft matter, the ionic liquid 1-ethyl-3-methyl-imidazolium dicyanamide is studied by coarse-grained molecular dynamics simulations. We focus on the link between microscopic and mesoscopic properties for both structure and dynamics. Thereby, the generalized Kirkwood g K-factor plays a central role in establishing this link which is not possible on the basis of molecular hydrodynamics. The decoupling between translational and rotational motion is indicative of the dynamical heterogeneity in ionic liquids.

Dissecting ion-specific dielectric spectra of sodium-halide solutions into solvation water and ionic contributions

Using extensive equilibrium molecular dynamics simulations we determine the dielectric spectra of aqueous solutions of NaF, NaCl, NaBr, and NaI. The ion-specific and concentration-dependent shifts of the static dielectric constants and the dielectric relaxation times match experimental results very well, which serves as a validation of the classical and non-polarizable ionic force fields used. The purely ionic contribution to the dielectric response is negligible, but determines the conductivity of the salt solutions. The ion-water cross correlation contribution is negative and reduces the total dielectric response by about 5%-10% for 1 M solutions. The dominating water dielectric response is decomposed into different water solvation shells and ion-pair configurations, by this the spectral blue shift and the dielectric decrement of salt solutions with increasing salt concentration is demonstrated to be primarily caused by first-solvation shell water. With rising salt concentration the simulated spectra show more pronounced deviations from a single-Debye form and can be well described by a Cole-Cole fit, in quantitative agreement with experiments. Our spectral decomposition into ionic and different water solvation shell contributions does not render the individual contributions more Debye-like, this suggests the non-Debye-like character of the dielectric spectra of salt solutions not to be due to the superposition of different elementary relaxation processes with different relaxation times. Rather, the non-Debye-like character is likely to be an inherent spectral signature of solvation water around ions.

Dielectric spectra of ionic liquids and their conversion to solvation dynamics: a detailed computational analysis of polarizable systems

For the three molecular ionic liquids 1-ethyl-3-methylimidazolium tetrafluoroborate, 1-ethyl-3-methylimidazolium trifluoromethanesulfonate and 1-butyl-3-methylimidazolium tetrafluoroborate, dielectric spectra were calculated from molecular dynamics simulations based on polarizable force fields. Using the reaction field continuum model the dielectric spectra were converted to the solvation dynamics of coumarin 153. It is shown in detail that the inclusion of the static conductivity in this model is essential. When simplifying the dielectric spectrum to the static conductivity hyperbola, the solvation response function becomes mono-exponential. Taking into account the frequency dependence of the conductivity, the typical two time-regimes of the solvation response function in ionic liquids are already obtained. However, the mean relaxation time remains the same. When converting the complete dielectric spectrum, i.e. also including frequency-dependent dielectric permittivity, quantitative changes are observed, but the qualitative shape is conserved. In accordance with previous experimental studies, solvation dynamics in ionic liquids predicted by the reaction field continuum model is too fast for longer times. This correlates with the suppression of the fine structure of the dielectric spectrum at low frequencies by the static conductivity hyperbola. By scaling down the static conductivity this effect can be partially amended. In addition to the impact of the solvent dielectric spectrum on solvation dynamics, solute-specific effects, i.e. anisotropy in shape and charge distribution as well as polarizability, were also studied.

On the collective network of ionic liquid/water mixtures. IV. Kinetic and rotational depolarization

Dielectric spectroscopy is a measure of the collective Coulomb interaction in liquid systems. Adding ionic liquids to an aqueous solution results in a decrease of the static value of the generalized dielectric constant which cannot be attributed to kinetic depolarization models characterized by the static conductivity and rotational relaxation constant. However, a dipolar Poisson-Boltzmann model computing the water depolarization in the proximity of ions is not only successful for simple electrolytes but also in case of molecular ionic liquids. Moreover, our simple geometric hydration model is also capable to explain the dielectric depolarization. Both models compute the dielectric constant of water and obtain the overall dielectric constant by averaging the values of its components, water and the ionic liquid, weighted by their volume occupancies. In this sense, aqueous ionic liquid mixtures seem to behave like polar mixtures.

Comparing reduced partial charge models with polarizable simulations of ionic liquids

Molecular ionic liquids are typically characterized by strong electrostatic interactions resulting in a charge ordering and retardation of their translational and rotational behaviour. Unfortunately, this effect is often overestimated in classical molecular dynamics simulations. This can be circumvented in a twofold way: the easiest way is to reduce the partial charges of the ions to sub-integer values of ±0.7-0.9 e. The more realistic model is to include polarizable forces, e.g. Drude-oscillators, but it comes along with an increasing computational effort. On the other hand, charge-scaled models are claimed to take an average polarizability into account. But do both models have the same impact on structure and dynamics of molecular ionic liquids? In the present study several molecular dynamics simulations of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate are performed with different levels of polarization as well as with varying charge scaling factors of 0.74 to 0.90. The analysis of the structural and dynamical results are performed in different levels: from the atomic point of view over the molecular level to collective properties determined by the complete sample.

Collective translational motions and cage relaxations in molecular ionic liquids

In this computational study, the collective translational motions of 1-ethyl-3-methylimidazolium triflate, characterized by its current correlation function and its collective dipolar displacement, are interpreted in terms of an ion cage around a central ion. Thereby, a coincidence of the relevant time constants is observed. Furthermore, the ion cage is long living and its composition is rather heterogeneous. Besides high numbers of counter ions, several ions of like charge populate the first shell around a central ion. In contrast to the strong influence of the local environment on the collective translational motion, rotations are strictly collective. In other words, a local picture falls short of describing the overall antiparallel alignment of ionic dipoles. A further issue of this work is the interpretation of the initial region of the collective dipolar displacement. It can be related to all collective translational processes showing up in the computational dielectric spectrum. In particular, slow translational processes which are invisible in the current correlation function can be detected. The inclusion of these slow processes allow for an excellent computational reconstruction of the experimental spectrum of the generalized dielectric constant.

A new view of the bacterial cytosol environment

The cytosol is the major environment in all bacterial cells. The true physical and dynamical nature of the cytosol solution is not fully understood and here a modeling approach is applied. Using recent and detailed data on metabolite concentrations, we have created a molecular mechanical model of the prokaryotic cytosol environment of Escherichia coli, containing proteins, metabolites and monatomic ions. We use 200 ns molecular dynamics simulations to compute diffusion rates, the extent of contact between molecules and dielectric constants. Large metabolites spend ∼80% of their time in contact with other molecules while small metabolites vary with some only spending 20% of time in contact. Large non-covalently interacting metabolite structures mediated by hydrogen-bonds, ionic and π stacking interactions are common and often associate with proteins. Mg²⁺ ions were prominent in NIMS and almost absent free in solution. Κ⁺ is generally not involved in NIMSs and populates the solvent fairly uniformly, hence its important role as an osmolyte. In simulations containing ubiquitin, to represent a protein component, metabolite diffusion was reduced owing to long lasting protein-metabolite interactions. Hence, it is likely that with larger proteins metabolites would diffuse even more slowly. The dielectric constant of these simulations was found to differ from that of pure water only through a large contribution from ubiquitin as metabolite and monatomic ion effects cancel. These findings suggest regions of influence specific to particular proteins affecting metabolite diffusion and electrostatics. Also some proteins may have a higher propensity for associations with metabolites owing to their larger electrostatic fields. We hope that future studies may be able to accurately predict how binding interactions differ in the cytosol relative to dilute aqueous solution.

The cytosol is the major cellular environment housing the majority of cellular activity. Although the cytosol is an aqueous environment, it contains high concentrations of ions, metabolites, and proteins, making it very different from dilute aqueous solution, which is frequently used for in vitro biochemistry. Recent advances in metabolomics have provided detailed concentration data for metabolites in E.coli. We used this information to construct accurate atomistic models of the cytosol solution. We find that, unlike the situation in dilute solutions, most metabolites spend the majority of their time in contact with other metabolites, or in contact with proteins. Furthermore, we find large non-covalently interacting metabolite structures are common and often associated with proteins. The presence of proteins reduced metabolite diffusion owing to long lasting correlations of motion. The dielectric constant of these simulations was found to differ from that of pure water only through a large contribution from proteins as metabolite and monatomic ion effects largely cancel. These findings suggest specific protein spheres of influence affecting metabolite diffusion and the electrostatic environment.

Solvation studies of a zinc finger protein in hydrated ionic liquids

The solvation of the zinc finger protein with the PDB-ID “5ZNF” in hydrated ionic liquids was studied at varying water content. 1-Ethyl-3-methylimidazolium and trifluoromethanesulfonate were the cation and anion, respectively. The protein stability as well as the solvation structure, the shell dynamics and the shell resolved dielectric properties were investigated by means of molecular dynamics simulations. The lengths of the respective trajectories extended up to 200 nanoseconds in order to cover the complete solvent dynamics. Considering the above mentioned properties as a function of the water content they all exhibit a maximum or minimum at the very same mole fraction. While the exact value x(H(2)O) = 0.927 depends on the underlying force field, its origin may be traced back to the competition between the van der Waals and the electrostatic energy of the protein as well as to the transition from aqueous dielectric screening to ionic charge screening with decreasing water content. The parameter-free Voronoi decomposition of space served as a basis for the analysis of most results. In particular, solvation shells were naturally inferred from this concept. In addition to the molecular analysis a mesoscopic view is given in terms of dielectric properties. Thereby, the net dielectric constant is decomposed into contributions from the protein, the first and second solvation shells as well as the bulk. Cross-terms between these components are given, too.

Parametrization of linear dielectric response

The quantum linear response of a dielectric to an external electric field yields expressions for the dielectric susceptibility and the associated impulse response function. These are measured properties that, during analysis, are often "curve-fitted" to diverse forms of parametric functional forms that shall herein be referred to as fit-functions. The main purpose of this paper is to show, from a very general linear response formalism that encompasses virtually all microscopic models of dielectric response, that there are constraints on the forms that the susceptibilities must obey and to examine common parametrizations of the dielectric function in light of these constraints. Naturally these constraints should, whenever possible, be in-built into the fit-functions employed. The linear response approach due to Madden and Kivelson [Adv. Chem. Phys. 56, 467 (1984)], where the cause is considered to be a uniform external field, E(ext)(t), is utilized as it affords a much more straightforward interaction term, viz., -M·E(ext)(t), (M being the system's total electric dipole moment operator) than would be the case if the mean internal field (or "Maxwell field") were taken as the cause. It is shown that this implies definite relations between the quasipermittivity, ζ(ω), of the Madden-Kivelson approach and the normal permittivity, χ(ω)≡ε(ω)-ε(0). These relations indicate a condition for the divergence of the normal susceptibility, which, arguably, marks the onset of a ferroelectric transition in "sufficiently polar" dielectrics. Finally, some common parametric "fit-function" forms are investigated as to whether they comply with the constraints that the formalism imposes, and examples are given of their associated Cole-Cole plots in typical cases involving one or more relaxation times.

Simulating polarizable molecular ionic liquids with Drude oscillators

The Drude oscillator model is applied to the molecular ionic liquid 1-ethyl-3-methyl-imidazolium triflate. The range of manageable Drude charges is tested. The strength of the polarizability is systematically varied from 0% to 100%. The influence on the structure, single particle dynamics, and collective dielectric properties is investigated. The generalized dielectric constant can be decomposed into a dielectric permittivity, a dielectric conductivity, and an optical dielectric constant ɛ(∞). The major part of the static generalized dielectric constant comes from the collective rotation of the ions, i.e., the dielectric permittivity. The translational contribution from the dielectric conductivity is about 58% of the dielectric permittivity. For the evaluation of the optical dielectric contribution, the computational dielectric theory was adapted to the case of heterogeneous polarizabilities. In case of 100% polarizability, it reaches a value of approximately 2.

Mode-coupling theoretical analysis of transport and relaxation properties of liquid dimethylimidazolium chloride

The mode-coupling theory for molecular liquids based on the interaction-site model is applied to a representative molecular ionic liquid, dimethylimidazolium chloride, and dynamic properties such as shear viscosity, self-diffusion coefficients, reorientational relaxation time, electric conductivity, and dielectric relaxation spectrum are analyzed. Molecular dynamics (MD) simulation is also performed on the same system for comparison. The theory captures the characteristics of the dynamics of the ionic liquid qualitatively, although theoretical relaxation times are several times larger than those from the MD simulation. Large relaxations are found in the 100 MHz region in the dispersion of the shear viscosity and the dielectric relaxation, in harmony with various experiments. The relaxations of the self-diffusion coefficients are also found in the same frequency region. The dielectric relaxation spectrum is divided into the contributions of the translational and reorientational modes, and it is demonstrated that the relaxation in the 100 MHz region mainly stems from the translational modes. The zero-frequency electric conductivity is close to the value predicted by the Nernst-Einstein equation in both MD simulation and theoretical calculation. However, the frequency dependence of the electric conductivity is different from those of self-diffusion coefficients in that the former is smaller than the latter in the gigahertz-terahertz region, which is compensated by the smaller dispersion of the former in the 100 MHz region. The analysis of the theoretical calculation shows that the difference in their frequency dependence is due to the different contribution of the short- and long-range liquid structures.