Ambiguities in Decomposing Molecular Polarizability into Atomic Charge Flow and Induced Dipole Contributions

The molecular dipole polarizability can be decomposed into components corresponding to the charge flow between atoms and changes in atomic dipole moments. Such decompositions are recognized to depend on how atoms are defined within a molecule, as, for example, by Hirshfeld, iterative Stockholder, or quantum topology partitioning of the electron density. For some of these, however, there are significant differences between the numerical results obtained by analytical response methods and finite field calculations. We show that this difference is due to analytical response methods accounting for (only) the change in electron density by a perturbation, while finite field methods may also include a component corresponding to a perturbation-dependent change in the definition of an atom within a molecule. For some atom-in-molecule definitions, such as the iterative Hirshfeld, iterative Stockholder, and quantum topology methods, the latter effect significantly increases the charge flow component. The decomposition of molecular polarizability into atomic charge flow and induced dipole components thus depends on whether the atom-in-molecule definition is taken to be perturbation-dependent.

Orientational wetting and dynamical correlations toward glass transition on the surface of imidazolium-based ionic liquids

Surface induces many fascinating physical phenomena, such as dynamic acceleration, surface anchoring, and orientational wetting, and, thus, is of great interest to study. Here, we report classic molecular dynamics simulations on the free-standing surface of imidazolium-based ionic liquids (ILs) [C4mim][PF6] and [C10mim][PF6]. On [C10mim][PF6] surface, a significant orientational wetting is observed, with the wetting strength showing a diverging tendency. Depth of the wetting was captured from the density and orientational order profile by a static length, which remarkably increases below the temperature Tstat upon cooling down. The dynamical correlation length that measures the distance of surface-dynamics acceleration into the bulk was characterized via the spatial-dependent mobility. The translational correlation exhibits a similar drastic increment at Tstat, while the rotational correlation drastically increases at a lower temperature Trot. We connect these results to the dynamics in bulk liquids, by finding Tstat and Trot that correspond to the onset temperatures where the liquids become cooperative for translational and rotational relaxation, respectively. This signifies the importance of collective dynamics in the bulk on the orientational wetting and surface dynamics in the ILs.

Collectivity in ionic liquids: a temperature dependent, polarizable molecular dynamics study

We use polarizable molecular dynamics simulations to study the thermal dependence of both structural and dynamic properties of two ionic liquids sharing the same cation (1-ethyl-3-methylimidazolium). The linear temperature trend in the structure is accompanied by an exponential Arrhenius-like behavior of the dynamics. Our parameter-free Voronoi tessellation analysis directly casts doubt on common concepts such as the alternating shells of cations and anions and the ionicity. The latter tries to explain the physico-chemical properties of the ionic liquids based on the association and dissociation of an ion pair. However, cations are in the majority of both ion cages, around cations and around anions. There is no preference of a cation for a single anion. Collectivity is a key factor in the dynamic properties of ionic liquids. Consequently, collective rotation relaxes faster than single-particle rotations, and the activation energies for collective translation and rotation are lower than those of the single molecules.

Recent Developments in Polarizable Molecular Dynamics Simulations of Electrolyte Solutions

Polarizable molecular dynamics simulations are a fast progressing field in the scientific research of ionic liquids. The fundamentals of polarizable simulations, as well as their application to ionic liquids, were summarized in a review [Bedrov, D.; Piquemal, J.-P.; Borodin, O.; MacKerell, Jr., A. D.; Roux, B.; Schröder, C. Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields. Chem. Rev. 2019, 119, 7940–7995] in 2019. Since then, new methods to treat intermolecular interaction of induced dipoles in these highly charged systems were developed. This concerns the damping of these interactions and additional charge transfer as well as the prediction of ionic materials with ultrahigh refractive indices. In addition to the progress of the polarizable force fields, also thermostats and barostats for polarizable simulations evolved recently.

DLPGEN: Preparing Molecular Dynamics Simulations with Support for Polarizable Force Fields

Preparing input files for molecular dynamics (MD) simulations can be a tedious task, particularly if different MD programs need to be used. Most simulation packages are accompanied by applications that handle this task, and, in some cases, software to perform interconversion between MD programs can be found. However, the conversion between different types of files is not always foolproof or the force field may not be fully supported, as quite often observed with polarization models. This work describes the program DLPGEN, which produces input files for the MD programs GROMACS, CHARMM, DL_POLY, and LAMMPS. The program can prepare polarizable force fields using a self-consistent field approach or with a dual thermostat-extended Lagrangian model. For GROMACS, a new polarization scheme suitable for the simulation of molecules containing more than one virtual particle is described. Results obtained for ethanol in the liquid state revealed that the system configurational energy, liquid density, and self-diffusion coefficient obtained with GROMACS are in good agreement with the data found with LAMMPS and CHARMM. In the case of DL_POLY, a problem with the Shells temperature control was found, suggesting that this program may not be suitable for the simulation of molecules containing multiple Drude particles.

Charge transfer and polarisability in ionic liquids: a case study

The practical use of ionic liquids (ILs) is benefiting from a growing understanding of the underpinning structural and dynamic properties, facilitated through classical molecular dynamics (MD) simulations. The predictive and explanatory power of a classical MD simulation is inextricably linked to the underlying force field. A key aspect of the forcefield for ILs is the ability to recover charge based interactions. Our focus in this paper is on the description and recovery of charge transfer and polarisability effects, demonstrated through MD simulations of the widely used 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide [C₄C₁im][NTf₂] IL. We study the charge distributions generated by a range of ab initio methods, and present an interpolation method for determining atom-wise scaled partial charges. Two novel methods for determining the mean field (total) charge transfer from anion to cation are presented. The impact of using different charge models and different partial charge scaling (unscaled, uniformly scaled, atom-wise scaled) are compared to fully polarisable simulations. We study a range of Drude particle explicitly polarisable potentials and shed light on the performance of current approaches to counter known problems. It is demonstrated that small changes in the charge description and MD methodology can have a significant impact; biasing some properties, while leaving others unaffected within the structural and dynamic domains.

Using atomic charges to model molecular polarization

We review different models for introducing electric polarization in force fields, with special focus on methods where polarization is modelled at the atomic charge level. While electric polarization has been included in several force fields, the common approach has been to focus on atomic dipole polarizability. Several approaches allow modelling electric polarization by using charge-flow between charge sites instead, but this has been less exploited, despite that atomic charges and charge-flow is expected to be more important than atomic dipoles and dipole polarizability. A number of challenges are required to be solved for charge-flow models to be incorporated into polarizable force fields, for example how to parameterize the models and how to make them computational efficient.

A Differentiable Neural-Network Force Field for Ionic Liquids

We present NeuralIL, a model for the potential energy of an ionic liquid that accurately reproduces first-principles results with orders-of-magnitude savings in computational cost. Built on the basis of a multilayer perceptron and spherical Bessel descriptors of the atomic environments, NeuralIL is implemented in such a way as to be fully automatically differentiable. It can thus be trained on ab initio forces instead of just energies, to make the most out of the available data, and can efficiently predict arbitrary derivatives of the potential energy. Using ethylammonium nitrate as the test system, we obtain out-of-sample accuracies better than 2 meV atom-1 (<0.05 kcal mol-1) in the energies and 70 meV Å-1 in the forces. We show that encoding the element-specific density in the spherical Bessel descriptors is key to achieving this. Harnessing the information provided by the forces drastically reduces the amount of atomic configurations required to train a neural network force field based on atom-centered descriptors. We choose the Swish-1 activation function and discuss the role of this choice in keeping the neural network differentiable. Furthermore, the possibility of training on small data sets allows for an ensemble-learning approach to the detection of extrapolation. Finally, we find that a separate treatment of long-range interactions is not required to achieve a high-quality representation of the potential energy surface of these dense ionic systems.

Computer Simulations of Deep Eutectic Solvents: Challenges, Solutions, and Perspectives

Deep eutectic solvents (DESs) are one of the most rapidly evolving types of solvents, appearing in a broad range of applications, such as nanotechnology, electrochemistry, biomass transformation, pharmaceuticals, membrane technology, biocomposite development, modern 3D-printing, and many others. The range of their applicability continues to expand, which demands the development of new DESs with improved properties. To do so requires an understanding of the fundamental relationship between the structure and properties of DESs. Computer simulation and machine learning techniques provide a fruitful approach as they can predict and reveal physical mechanisms and readily be linked to experiments. This review is devoted to the computational research of DESs and describes technical features of DES simulations and the corresponding perspectives on various DES applications. The aim is to demonstrate the current frontiers of computational research of DESs and discuss future perspectives.

Modeling LiF and FLiBe Molten Salts with Robust Neural Network Interatomic Potential

Lithium-based molten salts have attracted significant attention due to their applications in energy storage, advanced fission reactors, and fusion devices. Lithium fluorides and particularly 66.6%LiF-33.3%BeF₂ (Flibe) are of considerable interest in nuclear systems, as they show an excellent combination of favorable heat transfer, neutron moderation, and transmutation characteristics. For nuclear salts, the range of possible local structures, compositions, and thermodynamic conditions presents significant challenges in atomistic modeling. In this work, we demonstrate that atom-centered neural network interatomic potentials (NNIPs) provide a fast method for performing molecular dynamics of molten salts that is as accurate as ab initio molecular dynamics. For LiF, these potentials are able to accurately reproduce ab initio interactions of dimers, crystalline solids under deformation, crystalline LiF near the melting point, and liquid LiF at high temperatures. For Flibe, NNIPs accurately predict the structures and dynamics at normal operating conditions, high-temperature-pressure conditions, and in the crystalline solid phase. Furthermore, we show that NNIP-based molecular dynamics of molten salts are scalable to reach long time scales (e.g., nanosecond) and large system sizes (e.g., 10⁵ atoms) while maintaining ab initio density functional theory accuracy and providing more than 3 orders of magnitude of computational speedup for calculating structure and transport properties.

Targeted modifications in ionic liquids - from understanding to design

Ionic liquids are extremely versatile and continue to find new applications in academia as well as industry. This versatility is rooted in the manifold of possible ion types, ion combinations, and ion variations. However, to fully exploit this versatility, it is imperative to understand how the properties of ionic liquids arise from their constituents. In this work, we discuss targeted modifications as a powerful tool to provide understanding and to enable design. A 'targeted modification' is a deliberate change in the structure of an ionic liquid. This includes chemical changes in an experiment as well as changes to the parameterisation in a computer simulation. In any case, such a change must be purposeful to isolate what is of interest, studying, as far as is possible, only one concept at a time. The concepts can then be used as design elements. However, it is often found that several design elements interact with each other - sometimes synergistically, and other times antagonistically. Targeted modifications are a systematic way of navigating these overlaps. We hope this paper shows that understanding ionic liquids requires experimentalists and theoreticians to join forces and provides a tool to tackle the difficult transition from understanding to design.

The Effect of Concentration of Lithium Salt on the Structural and Transport Properties of Ionic Liquid-Based Electrolytes

Ionic liquids (ILs) are used as electrolytes in high-performance lithium-ion batteries, which can effectively improve battery safety and energy storage capacity. All atom molecular dynamics simulation and experiment were combined to investigate the effect of the concentration of lithium salt on the performance of electrolytes of four IL solvents ([C_nmim][TFSI] and [C_nmim][FSI], n = 2, 4). The IL electrolytes exhibit higher density and viscosity; meanwhile, larger lithium ion transfer numbers as the concentration of LiTFSI increases. Furthermore, in order to explore the effect of the concentration of lithium salt on the ionic associations of Li⁺ and anion of IL, the microstructures of the lithium salt in various IL electrolytes at different concentrations were investigated. The structural analysis indicated that strong bidentate and monodentate coordination was found between Li⁺ and anion of all IL electrolytes. Both cis and trans isomerism of [FSI]⁻ were observed in [FSI]⁻-type IL electrolyte systems. Furthermore, the existence of the ion cluster [Li[anion]_x]^(x−1)− in IL electrolytes and the cluster became more closed and compact as the concentration of LiTFSI increases.

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.

Insights into the solvation and dynamic behaviors of a lithium salt in organic- and ionic liquid-based electrolytes

Fundamental molecular insights were provided to understand the advantages of IL solvent electrolytes with high conductivity over organic solvent electrolytes.

ForConX: A forcefield conversion tool based on XML

The force field conversion from one MD program to another one is exhausting and error-prone. Although single conversion tools from one MD program to another exist not every combination and both directions of conversion are available for the favorite MD programs Amber, Charmm, Dl-Poly, Gromacs, and Lammps. We present here a general tool for the force field conversion on the basis of an XML document. The force field is converted to and from this XML structure facilitating the implementation of new MD programs for the conversion. Furthermore, the XML structure is human readable and can be manipulated before continuing the conversion. We report, as testcases, the conversions of topologies for acetonitrile, dimethylformamide, and 1-ethyl-3-methylimidazolium trifluoromethanesulfonate comprising also Urey-Bradley and Ryckaert-Bellemans potentials. © 2017 Wiley Periodicals, Inc.

Mechanical heterogeneity in ionic liquids

Molecular dynamics (MD) simulations of five ionic liquids based on 1-alkyl-3-methylimidazolium cations, [C _n C₁im]⁺, have been performed in order to calculate high-frequency elastic moduli and to evaluate heterogeneity of local elastic moduli. The MD simulations of [C _n C₁im][NO₃], n = 2, 4, 6, and 8, assessed the effect of domain segregation when the alkyl chain length increases, and [C₈C₁im][PF₆] assessed the effect of strength of anion-cation interaction. Dispersion curves of excitation energies of longitudinal and transverse acoustic, LA and TA, modes were obtained from time correlation functions of mass currents at different wavevectors. High-frequency sound velocity of LA modes depends on the alkyl chain length, but sound velocity for TA modes does not. High-frequency bulk and shear moduli, K _∞ and G _∞ , depend on the alkyl chain length because of a density effect. Both K _∞ and G _∞ are strongly dependent on the anion. The calculation of local bulk and shear moduli was accomplished by performing bulk and shear deformations of the systems cooled to 0 K. The simulations showed a clear connection between structural and elastic modulus heterogeneities. The development of nano-heterogeneous structure with increasing length of the alkyl chain in [C _n C₁im][NO₃] implies lower values for local bulk and shear moduli in the non-polar domains. The mean value and the standard deviations of distributions of local elastic moduli decrease when [NO₃]^- is replaced by the less coordinating [PF₆]^- anion.

Mapping the Drude polarizable force field onto a multipole and induced dipole model

The induced dipole and the classical Drude oscillator represent two major approaches for the explicit inclusion of electronic polarizability into force field-based molecular modeling and simulations. In this work, we explore the equivalency of these two models by comparing condensed phase properties computed using the Drude force field and a multipole and induced dipole (MPID) model. Presented is an approach to map the electrostatic model optimized in the context of the Drude force field onto the MPID model. Condensed phase simulations on water and 15 small model compounds show that without any reparametrization, the MPID model yields properties similar to the Drude force field with both models yielding satisfactory reproduction of a range of experimental values and quantum mechanical data. Our results illustrate that the Drude oscillator model and the point induced dipole model are different representations of essentially the same physical model. However, results indicate the presence of small differences between the use of atomic multipoles and off-center charge sites. Additionally, results on the use of dispersion particle mesh Ewald further support its utility for treating long-range Lennard Jones dispersion contributions in the context of polarizable force fields. The main motivation in demonstrating the transferability of parameters between the Drude and MPID models is that the more than 15 years of development of the Drude polarizable force field can now be used with MPID formalism without the need for dual-thermostat integrators nor self-consistent iterations. This opens up a wide range of new methodological opportunities for polarizable models.

Quantum mechanical determination of atomic polarizabilities of ionic liquids

We present an accurate and simple quantum mechanical methodology to calculate atomic polarizabilities of charged species.

Quantum Chemical Methods for the Prediction of Energetic, Physical, and Spectroscopic Properties of Ionic Liquids

The accurate prediction of physicochemical properties of condensed systems is a longstanding goal of theoretical (quantum) chemistry. Ionic liquids comprising entirely of ions provide a unique challenge in this respect due to the diverse chemical nature of available ions and the complex interplay of intermolecular interactions among them, thus resulting in the wide variability of physicochemical properties, such as thermodynamic, transport, and spectroscopic properties. It is well understood that intermolecular forces are directly linked to physicochemical properties of condensed systems, and therefore, an understanding of this relationship would greatly aid in the design and synthesis of functionalized materials with tailored properties for an application at hand. This review aims to give an overview of how electronic structure properties obtained from quantum chemical methods such as interaction/binding energy and its fundamental components, dipole moment, polarizability, and orbital energies, can help shed light on the energetic, physical, and spectroscopic properties of semi-Coulomb systems such as ionic liquids. Particular emphasis is given to the prediction of their thermodynamic, transport, spectroscopic, and solubilizing properties.

Determining polarizable force fields with electrostatic potentials from quantum mechanical linear response theory

We developed a new method to calculate the atomic polarizabilities by fitting to the electrostatic potentials (ESPs) obtained from quantum mechanical (QM) calculations within the linear response theory. This parallels the conventional approach of fitting atomic charges based on electrostatic potentials from the electron density. Our ESP fitting is combined with the induced dipole model under the perturbation of uniform external electric fields of all orientations. QM calculations for the linear response to the external electric fields are used as input, fully consistent with the induced dipole model, which itself is a linear response model. The orientation of the uniform external electric fields is integrated in all directions. The integration of orientation and QM linear response calculations together makes the fitting results independent of the orientations and magnitudes of the uniform external electric fields applied. Another advantage of our method is that QM calculation is only needed once, in contrast to the conventional approach, where many QM calculations are needed for many different applied electric fields. The molecular polarizabilities obtained from our method show comparable accuracy with those from fitting directly to the experimental or theoretical molecular polarizabilities. Since ESP is directly fitted, atomic polarizabilities obtained from our method are expected to reproduce the electrostatic interactions better. Our method was used to calculate both transferable atomic polarizabilities for polarizable molecular mechanics' force fields and nontransferable molecule-specific atomic polarizabilities.

An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications

Molecular mechanics force fields that explicitly account for induced polarization represent the next generation of physical models for molecular dynamics simulations. Several methods exist for modeling induced polarization, and here we review the classical Drude oscillator model, in which electronic degrees of freedom are modeled by charged particles attached to the nuclei of their core atoms by harmonic springs. We describe the latest developments in Drude force field parametrization and application, primarily in the last 15 years. Emphasis is placed on the Drude-2013 polarizable force field for proteins, DNA, lipids, and carbohydrates. We discuss its parametrization protocol, development history, and recent simulations of biologically interesting systems, highlighting specific studies in which induced polarization plays a critical role in reproducing experimental observables and understanding physical behavior. As the Drude oscillator model is computationally tractable and available in a wide range of simulation packages, it is anticipated that use of these more complex physical models will lead to new and important discoveries of the physical forces driving a range of chemical and biological phenomena.

Additive polarizabilities in ionic liquids

An extended designed regression analysis of experimental data on density and refractive indices of several classes of ionic liquids yielded statistically averaged atomic volumes and polarizabilities of the constituting atoms. These values can be used to predict the molecular volume and polarizability of an unknown ionic liquid as well as its mass density and refractive index. Our approach does not need information on the molecular structure of the ionic liquid, but it turned out that the discrimination of the hybridization state of the carbons improved the overall result. Our results are not only compared to experimental data but also to quantum-chemical calculations. Furthermore, fractional charges of ionic liquid ions and their relation to polarizability are discussed.

Simulations of room temperature ionic liquids: from polarizable to coarse-grained force fields

This perspective article summarizes the recent advances in the classical molecular modelling of room temperature ionic liquids.