Redox potentials in ionic liquids: Anomalous behavior?

Redox potentials depend on the nature of the solvent/electrolyte through the solvation energies of the ionic solute species. For concentrated electrolytes, ion solvation may deviate significantly from the Born model predictions due to ion pairing and correlation effects. Recently, Ghorai and Matyushov [J. Phys. Chem. B 124, 3754-3769 (2020)] predicted, on the basis of linear response theory, an anomalous trend in the solvation energies of room temperature ionic liquids, with deviations of hundreds of kJ/mol from the Born model for certain size solutes/ions. In this work, we computationally evaluate ionic solvation energies in the prototypical ionic liquid, 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM/BF4), to further explore this behavior and benchmark several of the approximations utilized in the solvation energy predictions. For comparison, we additionally compute solvation energies within acetonitrile and molten NaCl salt to illustrate the limiting behavior of purely dipolar and ionic solvents. We find that the overscreening effect, which results from the inherent charge oscillations of the ionic liquid, is substantially reduced in magnitude due to screening from the dipoles of the molecular ions. Therefore, for the molten NaCl salt, for which the ions do not have permanent dipoles, modulation of ionic solvation energies from the overscreening effect is most significant. The conclusion is that ionic liquids do indeed exhibit unique solvation behavior due to peak(s) in the electrical susceptibility caused by the ion shell structure; redox potential shifts for BMIM/BF4 are of more modest order ∼0.1 V, but may be larger for other ionic liquids that approach molten salt behavior.

Generalized Helmholtz model describes capacitance profiles of ionic liquids and concentrated aqueous electrolytes.

In this work, we propose and validate a generalization of the Helmholtz model that can account for both "bell-shaped" and "camel-shaped" differential capacitance profiles of concentrated electrolytes, the latter being characteristic of ionic liquids. The generalization is based on introducing voltage dependence of both the dielectric constant "ϵr(V)" and thickness "L(V)" of the inner Helmholtz layer, as validated by molecular dynamics (MD) simulations. We utilize MD simulations to study the capacitance profiles of three different electrochemical interfaces: (1) graphite/[BMIm+][BF4-] ionic liquid interface; (2) Au(100)/[BMIm+][BF4-] ionic liquid interface; (3) Au(100)/1M [Na+][Cl-] aqueous interface. We compute the voltage dependence of ϵr(V) and L(V) and demonstrate that the generalized Helmholtz model qualitatively describes both camel-shaped and bell-shaped differential capacitance profiles of ionic liquids and concentrated aqueous electrolytes (in lieu of specific ion adsorption). In particular, the camel-shaped capacitance profile that is characteristic of ionic liquid electrolytes arises simply from combination of the voltage-dependent trends of ϵr(V) and L(V). Furthermore, explicit analysis of the inner layer charge density for both concentrated aqueous and ionic liquid double layers reveal similarities, with these charge distributions typically exhibiting a dipolar region closest to the electrode followed by a monopolar peak at larger distances. It is appealing that a generalized Helmholtz model can provide a unified description of the inner layer structure and capacitance profile for seemingly disparate aqueous and ionic liquid electrolytes.

Equation of state predictions for ScF3 and CaZrF6 with neural network-driven molecular dynamics.

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

N-Heterocyclic Carbene Formation in the Ionic Liquid [EMIM+][OAc-]: Elucidating Solvation Effects with Reactive Molecular Dynamics Simulations.

Recent experimental and theoretical work has debated whether N-heterocyclic carbenes (NHCs) are natively present in imidazolium-based ionic liquids (ILs) such as 1-ethyl-3-methylimidazolium acetate ([EMIM+][OAc-]) at room temperature. Because NHCs are powerful catalysts, determining their presence within imidazolium-based ILs is important, but experimental characterization is difficult due to the transient nature of the carbene species. Because the carbene formation reaction involves acid-base neutralization of two ions, ion solvation will largely dominate the reaction free energy and thus must be considered in any quantum chemical investigation of the reaction. To computationally study the NHC formation reaction, we develop physics-based, neural network reactive force fields to enable free energy calculations for the reaction in bulk [EMIM+][OAc-]. Our force field explicitly captures the formation of NHC and acetic acid by deprotonation of a EMIM+ molecule by acetate and in addition describes the dimerization of acetic acid and acetate. Using umbrella sampling, we compute reaction free energy profiles within the bulk IL and at the liquid/vapor interface to understand the influence of the environment on ion solvation and reaction free energies. Compared to reaction of the EMIM+/OAc- dimer in the gas phase, the bulk environment destabilizes formation of the NHC as expected due to the large ion solvation energies. Our simulations reveal a preference for the product acetic acid to share its proton with an acetate in solution and at the interface. We predict NHC content in bulk [EMIM+][OAc-] to be on the order of parts-per-million (ppm) levels, with order-of-magnitude enhancement of NHC concentration at the liquid/vapor interface. The interfacial enhancement of NHC content is due to both poorer solvation of the ionic reactants and solvophobic stabilization of the neutral NHC molecule at the liquid/vapor interface.

Excitations follow (or lead?) density scaling in propylene carbonate.

Structural excitations that enable interbasin (IB) barrier crossings on a potential energy landscape are thought to play a facilitating role in the relaxation of liquids. Here, we show that the population of these excitations exhibits the same density scaling observed for α relaxation in propylene carbonate, even though they are heavily influenced by intramolecular modes. We also find that IB crossing modes exhibit a Grüneisen parameter (γG) that is approximately equivalent to the density scaling parameter γTS. These observations suggest that the well-documented relationship between γG and γTS may be a direct result of the pressure dependence of the frequency of unstable (relaxation) modes associated with IB motion.

Flexibility is the key to tuning the transport properties of fluorinated imide-based ionic liquids.

Ionic liquids are becoming increasingly popular for practical applications such as biomass processing and lithium-ion batteries. However, identifying ionic liquids with optimal properties for specific applications by trial and error is extremely inefficient since there are a vast number of potential candidate ions. Here we combine experimental and computational techniques to determine how the interplay of fluorination, flexibility and mass affects the transport properties of ionic liquids with the popular imide anion. We observe that fluorination and flexibility have a large impact on properties such as viscosity, whereas the influence of mass is negligible. Using targeted modifications, we show that conformational flexibility provides a significant contribution to the success of fluorination as a design element. Contrary to conventional wisdom, fluorination by itself is thus not a guarantor for beneficial properties such as low viscosity.

DFT-based QM/MM with particle-mesh Ewald for direct, long-range electrostatic embedding.

We present a density functional theory (DFT)-based, quantum mechanics/molecular mechanics (QM/MM) implementation with long-range electrostatic embedding achieved by direct real-space integration of the particle-mesh Ewald (PME) computed electrostatic potential. The key transformation is the interpolation of the electrostatic potential from the PME grid to the DFT quadrature grid from which integrals are easily evaluated utilizing standard DFT machinery. We provide benchmarks of the numerical accuracy with choice of grid size and real-space corrections and demonstrate that good convergence is achieved while introducing nominal computational overhead. Furthermore, the approach requires only small modification to existing software packages as is demonstrated with our implementation in the OpenMM and Psi4 software. After presenting convergence benchmarks, we evaluate the importance of long-range electrostatic embedding in three solute/solvent systems modeled with QM/MM. Water and 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM/BF4) ionic liquid were considered as "simple" and "complex" solvents, respectively, with water and p-phenylenediamine (PPD) solute molecules treated at the QM level of theory. While electrostatic embedding with standard real-space truncation may introduce negligible errors for simple systems such as water solute in water solvent, errors become more significant when QM/MM is applied to complex solvents such as ionic liquids. An extreme example is the electrostatic embedding energy for oxidized PPD in BMIM/BF4 for which real-space truncation produces severe errors even at 2-3 nm cutoff distances. This latter example illustrates that utilization of QM/MM to compute redox potentials within concentrated electrolytes/ionic media requires carefully chosen long-range electrostatic embedding algorithms with our presented algorithm providing a general and robust approach.

Physics-based, neural network force fields for reactive molecular dynamics: Investigation of carbene formation from [EMIM+][OAc-].

Reactive molecular dynamics simulations enable a detailed understanding of solvent effects on chemical reaction mechanisms and reaction rates. While classical molecular dynamics using reactive force fields allows significantly longer simulation time scales and larger system sizes compared with ab initio molecular dynamics, constructing reactive force fields is a difficult and complex task. In this work, we describe a general approach following the empirical valence bond framework for constructing ab initio reactive force fields for condensed phase simulations by combining physics-based methods with neural networks (PB/NNs). The physics-based terms ensure the correct asymptotic behavior of electrostatic, polarization, and dispersion interactions and are compatible with existing solvent force fields. NNs are utilized for a versatile description of short-range orbital interactions within the transition state region and accurate rendering of vibrational motion of the reacting complex. We demonstrate our methodology for a simple deprotonation reaction of the 1-ethyl-3-methylimidazolium cation with acetate to form 1-ethyl-3-methylimidazol-2-ylidene and acetic acid. Our PB/NN force field exhibits ∼1 kJ mol-1 mean absolute error accuracy within the transition state region for the gas-phase complex. To characterize the solvent modulation of the reaction profile, we compute potentials of mean force for the gas-phase reaction as well as the reaction within a four-ion cluster and benchmark against ab initio molecular dynamics simulations. We find that the surrounding ionic environment significantly destabilizes the formation of the carbene product, and we show that this effect is accurately captured by the reactive force field. By construction, the PB/NN potential may be directly employed for simulations of other solvents/chemical environments without additional parameterization.

Deep Eutectic Solvents: Molecular Simulations with a First-Principles Polarizable Force Field.

The unique properties of deep eutectic solvents make them useful in a variety of applications. In this work we develop a first-principles force field for reline, which is composed of choline chloride and urea in the molar ratio 1:2. We start with the symmetry adapted perturbation theory (SAPT) protocol and then make adjustments to better reproduce the structure and dynamics of the liquid when compared to first-principles molecular dynamics (FPMD) simulations. The resulting force field is in good agreement with experiments in addition to being consistent with the FPMD simulations. The simulations show that primitive molecular clusters are preferentially formed with choline-chloride ionic pairs bound with a hydrogen bond in the hydroxyl group and that urea molecules coordinate the chloride mainly via the trans-H chelating hydrogen bonds. Incorporating polarizability qualitatively influences the radial distributions and lifetimes of hydrogen bonds and affects long-range structural order and dynamics. The polarizable force field predicts a diffusion constant about an order of magnitude larger than the nonpolarizable force field and is therefore less computationally intensive. We hope this study paves the way for studying complex hydrogen-bonding liquids from a first-principles approach.

A Transferable Polarizable Force Field for Urea Crystals and Aqueous Solutions.

Urea is an important chemical with many biological and industrial applications. In this work, we develop a first-principles polarizable force field for urea crystals and aqueous solutions within the symmetry-adapted perturbation theory (SAPT) protocol with the SWM4-NDP model for water. We make three adjustments to the SAPT force field protocol: We augment the carbonyl oxygen atom of urea with additional interaction sites in order to address the "chelated" bent double hydrogen bonds in urea, we reduce the polarizability of urea by a factor of 0.70 to reproduce experimental in-crystal dipole moments, and we re-fit atomic pre-exponential parameters to correct the predicted liquid structure. We find that the resulting force field is in good agreement for the static and dynamic properties of aqueous urea solutions when compared to experiment or first-principles molecular dynamics simulations. The polarizable urea model accurately reproduces the crystal-solution phase diagram in the temperature range of 261 to 310 K; for which, it is superior to non-polarizable models. We expect that this force field will be useful in the modeling of complex biomolecular systems and enable studies of polarizability effects of solid-liquid phase behavior of complex fluids.

Proton Transport in [BMIM+][BF4-]/Water Mixtures Near the Percolation Threshold.

The incorporation of ionic liquids into existing proton exchange membrane (PEM) materials has been shown to enhance thermal stability and improve conductivity at reduced water content. Because proton transport is dictated by an interplay between vehicular diffusion and the Grotthuss mechanism, it is expected that the nanoscale structure of the resulting ionic liquid/water networks will sensitively influence transport properties. In this work, we study proton transport in [BMIM+][BF4-]/water mixtures of systematically varying water volume fraction, focusing on concentrations near the percolation threshold in which water networks are connected over macroscopic length scales. We utilize reactive molecular dynamics within the multistate empirical valence bond (MS-EVB) framework to explicitly model Grotthuss hopping processes. Excellent agreement with experimental conductivity data is obtained within the Nernst-Einstein approximation, indicating that proton transport proceeds in a largely uncorrelated manner even at pH <0. We additionally study the changing topology of the hydrogen-bonded water network in these mixtures using percolation and graph theory analysis. We find that the proton diffusion coefficient and forward hop rate increase linearly with water content at concentrations ranging from dilute through the percolation threshold; surprisingly, we find no deviation in this trend at the percolation transition. The high concentration of BF4- anions inherently alters the fraction of Eigen and Zundel proton states, producing a net detrimental effect on proton transport rates relative to bulk water. This mechanistic insight is useful for selecting ideal ionic liquid candidates and determining the optimal ionic liquid concentration to incorporate into PEM materials.

Interference of electrical double layers: Confinement effects on structure, dynamics, and screening of ionic liquids.

Ionic liquids are widely used as electrolytes in electronic devices in which they are subject to nanoconfinement within nanopores or nanofilms. Because the intrinsic width of an electrical double layer is on the order of several nanometers, nanoconfinement is expected to fundamentally alter the double layer properties. Furthermore, in confined systems, a large portion of the ions are interfacial, e.g., at the electrode interface, leading to significant deviations of electrostatic screening and ion dynamics as compared to bulk properties. In this work, we systematically investigate the interference between electrical double layers for nanoconfined ionic liquids and the resulting influence on the structure, dynamics, and screening behavior. We perform molecular dynamics simulations for the ionic liquids [BMIm+][BF4 -] and [BMIm+][PF6 -] confined between two flat electrodes at systematic separation distances between 1.5 nm and 4.5 nm for both conducting and insulating boundary conditions. We find that while ion dynamics is expectedly slower than in the bulk (by ∼2 orders of magnitude), there is an unexpected non-linear trend with the confinement length that leads to a local maximum in dynamic rates at ∼3.5-4.5 nm confinement. We show that this nonlinear trend is due to the ion correlation that arises from the interference between opposite double layers. We further evaluate confinement effects on the ion structure and capacitance and investigate the influence of electronic polarization of the ionic liquid on the resulting properties. This systematic evaluation of the connection between electrostatic screening and structure and dynamics of ionic liquids in confined systems is important for the fundamental understanding of electrochemical supercapacitors.

Proper Thermal Equilibration of Simulations with Drude Polarizable Models: Temperature-Grouped Dual-Nosé-Hoover Thermostat.

An explicit treatment of electronic polarization is critically important to accurate simulations of highly charged or interfacial systems. Compared to the iterative self-consistent field (SCF) scheme, extended Lagrangian approaches are computationally more efficient for simulations that employ a polarizable force field. However, an appropriate thermostat must be chosen to minimize heat flow and ensure an equipartition of kinetic energy among all unconstrained system degrees of freedom. Here we investigate the effects of different thermostats on the simulation of condensed phase systems with the Drude polarizable force field using several examples that include water, NaCl/water, acetone, and an ionic liquid (IL) BMIM+/BF4-. We show that conventional dual-temperature thermostat schemes often suffer from violations of equipartitioning and adiabatic electronic state, leading to considerable errors in both static and dynamic properties. Heat flow from the real degrees of freedom to the Drude degrees of freedom leads to a steady temperature gradient and puts the system at an incorrect effective temperature. Systems with high-frequency internal degrees of freedom such as planar improper dihedrals or C-H bond stretches are most vulnerable; this issue has been largely overlooked in the literature because of the primary focus on simulations of rigid water molecules. We present a new temperature-grouped dual-Nosé-Hoover thermostat, where the molecular center of mass translations are assigned to a temperature group separated from the rest degrees of freedom. We demonstrate that this scheme predicts correct static and dynamic properties for all the systems tested here, regardless of the thermostat coupling strength. This new thermostat has been implemented into the GPU-accelerated OpenMM simulation package and maintains a significant speedup relative to the SCF scheme.

On the Miscibility and Immiscibility of Ionic Liquids and Water.

Although the ?like-dissolves-like? rule is often invoked to explain why sodium chloride dissolves in water, hidden behind this explanation is the delicate balance between the very large cohesive energy of the ionic crystal and large solvation energies of the ions. Room-temperature ionic liquids (ILs) are liquid analogues of ionic crystals and, as dictated by a similar energetic balance, may either fully mix with water or be immiscible with water depending on ion type and cation/anion combination. In this work, we study three hydrophobic and three hydrophilic ILs to examine whether a priori prediction of water miscibility is possible based on analysis of bulk properties alone. We find that hydrophilic and hydrophobic ILs exhibit distinct signatures in their (reciprocal space) Coulomb interactions that indicate predisposition to water mixing. Hydrophilic ILs exhibit a prominent peak in their electrostatic interactions at ?5?8 ? length scale, largely due to repulsion between neighboring anion shells. When mixed with water, this peak is significantly reduced in magnitude, indicating that electrostatic screening by water molecules is an important driving force for mixing. In contrast, hydrophobic ILs show no such peak, indicating no predisposition to mixing. In addition to this analysis, we compute and compare solvation free energies of the six different anions in water, ion-pairing free energies at ?infinitely? dilute concentration, and water absorption free energies in the different ILs. Analyzed within the context of empirical data, our calculations suggest that hydrophobicity trends of different ILs are very sensitive to precise water content at dilute conditions. For example, we predict that bis(fluorosulfonyl)imide-based ILs exhibit anomalously large water absorption free energies at zero water content, with increasing hydrophobicity as preferential absorption sites within the IL become saturated.

Understanding the Properties of Ionic Liquids: Electrostatics, Structure Factors, and Their Sum Rules.

The properties of room-temperature ionic liquids (ILs) may be viewed as resulting from a balance of electrostatic interactions that can be tuned at short range but constrained to satisfy universal, asymptotic screening conditions. Short-range interactions and ion packing provide ample opportunity for chemical tunability, while asymptotic sum rules dictate that the long-range structure and charge oscillation be similar to those of molten alkali halide salts. In this work, we study the structure factors and long-range electrostatic interactions in six ILs. The cation in all cases is 1-butyl-3-methylimidazolium (BMIM+), and we study six anions, namely, tetrafluoroborate (BF4-), hexafluorophosphate (PF6-), nitrate (NO3-), triflate (CF3SO3-), bisfluorosulfonylimide [(FSO2)2N-], and bistriflimide [(CF3SO2)2N-]. To gain insight, we perform similar computer simulations of a primitive molten salt model with and without electronic polarization. We emphasize universal similarities among ionic liquids and molten salts in the long-range ion ordering and the influence of electronic polarization on the screening conditions while also characterizing important differences in the short-range electrostatic interactions. We show that polarization systematically reduces charge oscillations by as much as ∼0.5-1 ion per radial shell, which we argue is general to all room-temperature ILs as well as molten salts. We suggest that a fundamentally important distinction among BMIM-based ionic liquids (with different anions) is the nature of the midrange, ∼1 Å-1 peak in the charge-correlation structure factor; while this correlation is straightforward to analyze in computer simulations, it may often be hidden in X-ray and/or neutron scattering structure factors.

Influence of Electronic Polarization on the Structure of Ionic Liquids.

The liquid structure and electrical screening ability of ionic liquids are fundamentally intertwined. The molecular nature of the charge carriers means that screening distances of external fields depend sensitively on the ion packing and structure of the ionic liquid. In this work, we quantitatively illustrate how the liquid structure itself is directly modulated by electrostatic screening conditions. In particular, electronic polarization fundamentally relaxes long-range ion structuring in asymmetric ionic liquids such as [BMIM+][BF4-], with the influence propagating to short-range ion-ion correlation. A consequence of the exact Stillinger-Lovett second moment condition is that, at fixed density, any pairwise-additive, nonpolarizable force field will necessarily predict artificially enhanced long-range ion structuring. This is because the screening condition is set by the infinite-frequency dielectric response. There is no ad-hoc fix: One has to use polarizable force fields to correctly reproduce the optical dielectric constant. Our illustration of this fundamental effect significantly clarifies interpretation of previous work comparing property prediction using polarizable and nonpolarizable force fields.

Ion Correlation and Collective Dynamics in BMIM/BF4-Based Organic Electrolytes: From Dilute Solutions to the Ionic Liquid Limit.

Quantifying ion association and collective dynamical processes in organic electrolytes is essential for fundamental property interpretation and optimization for electrochemical applications. The extent of ion correlation depends on both the ion concentration and dielectric strength of the solvent; ions may be largely uncorrelated in sufficiently high-dielectric solvents at low concentration, but properties of concentrated electrolytes are dictated by correlated and collective ion processes. In this work, we utilize molecular dynamics simulations to characterize ion association and collective ion dynamics in organic electrolytes composed of binary mixtures of 1-butyl-3-methylimidazolium tetrafluoroborate [BMIM+][BF4-] and 1,2-dichloroethane, acetone, acetonitrile, and water solvents. We illustrate different physical regimes of characteristically distinct ion correlations for the systematic range of electrolyte concentrations and solvent dielectric strengths. Dilute electrolytes composed of low-dielectric solvents exhibit significant counterion correlation in the form of ion pairing and clustering driven by both weak screening and relatively low solvation energies. This regime is characterized by enhanced ion coordination numbers and near equality of cation and anion diffusion coefficients, despite the significantly different ion sizes. In contrast, ion correlation in highly concentrated electrolytes is dominated by the anti-correlated motion of both like-charge and opposite-charge ions, approaching neat ionic liquid behavior. We show that the cross-over of these correlation regimes is clearly illuminated by quantifying the fractional self and distinct contributions to the net ionic conductivity. For organic electrolytes composed of low-dielectric solvents, we conclude that significant ion correlation exists at all concentrations but the nature of the correlation changes markedly from the dilute electrolyte to the pure ionic liquid limit.

Ab Initio Force Fields for Organic Anions: Properties of [BMIM][TFSI], [BMIM][FSI], and [BMIM][OTf] Ionic Liquids.

Room-temperature ionic liquids (ILs) composed of organic anions bis(trifluoromethanesulfonyl)imide (TFSI), bis(fluorosulfonyl)imide (FSI), and trifluoromethanesulfonate (OTf) exhibit interesting physical properties and are important for many electrochemical applications. TFSI and FSI form "hydrophobic" ILs, immiscible with water but miscible with many organic solvents and polymers; for computer simulation studies, it is thus essential to develop force fields for these anions that are transferable among this wide variety of chemical environments. In this work, we develop entirely ab initio force fields for the TFSI, FSI, and OTf anions and predict the properties of corresponding 1-butyl-3-methylimidazolium ILs. We discuss important subtleties in the force field development related to accurately modeling conformational flexibility, that is, relaxed torsional profiles and intramolecular electrostatic interactions. The TFSI anions have notable conformational flexibility in the IL, and we predict approximately 70% cisoid and 20% transoid conformations, which is largely driven by cation/anion ion-pair interactions and is opposite to the trend expected from the anion ab initio potential energy surface. The favorable interactions between the cation and cisoid TFSI conformations result in a shoulder in the cation/anion radial distribution function at short distances, whereas interconversion between cisoid and transoid conformations occurs on a commensurate time scale as ion diffusion processes. In addition to this physical insight on anion effects, we expect that these force fields will have important applications for studying a variety of complex electrolyte systems.