Development of Complex Classical Force Fields through Force Matching to ab Initio Data: Application to a Room-Temperature Ionic Liquid

Machine Learning Directed Optimization of Classical Molecular Modeling Force Fields

Accurate force fields are necessary for predictive molecular simulations. However, developing force fields that accurately reproduce experimental properties is challenging. Here, we present a machine learning directed, multiobjective optimization workflow for force field parametrization that evaluates millions of prospective force field parameter sets while requiring only a small fraction of them to be tested with molecular simulations. We demonstrate the generality of the approach and identify multiple low-error parameter sets for two distinct test cases: simulations of hydrofluorocarbon (HFC) vapor-liquid equilibrium (VLE) and an ammonium perchlorate (AP) crystal phase. We discuss the challenges and implications of our force field optimization workflow.

Computational Characterization of a Cholesterol-Based Molecular Rotor in Lipid Membranes

Biophysical properties of cellular membranes critically depend on their content of cholesterol and its interaction with various other lipid species. Cholesterol-dependent friction at the nanoscale can be studied with molecular rotors, whose quantum yield depends on rotational dynamics of functional groups during their excited state lifetime. Here, we present a detailed computational analysis of a phenyl-BODIPY-linked cholesterol based molecular rotor in direct comparison with the well-known TopFluor-cholesterol. We describe a new parametrization strategy of force field parameters for the BODIPY moiety and carry out extensive molecular dynamics simulations of the probe in membranes in the absence or presence of cholesterol. Our study quantifies the extent of membrane perturbation by these probes, analyzes their tilting resistance in the bilayer and derives dynamic properties directly related to the rotor propensity. We show that phenyl-BODIPY-cholesterol bears potential as a cholesterol-dependent molecular rotor to report about microviscosity of sterol-containing model and cell membranes.

Atomic charges of sulfur in ionic liquids: experiments and calculations

A wide variety of experimental and computational methods are used to probe sulfur atomic charges in ionic liquids.

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.

Developing accurate molecular mechanics force fields for conjugated molecular systems

A rapid method to parameterize the intramolecular component of classical force fields is proposed and applied to a molecular semiconductor, oligomers of conjugated polymers and a biological chromophore.

Computational approaches to understanding reaction outcomes of organic processes in ionic liquids

The utility of using a combined experimental and computational approach for understanding ionic liquid media, and their effect on reaction outcome, is highlighted through a number of case studies.

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.

Intra- and intermolecular effects on the Compton profile of the ionic liquid 1,3-dimethylimidazolium chloride

We present a comprehensive simulation study on the solid-liquid phase transition of the ionic liquid 1,3-dimethylimidazolium chloride in terms of the changes in the atomic structure and their effect on the Compton profile. The structures were obtained by using ab initio molecular dynamics simulations. Chosen radial distribution functions of the liquid structure are presented and found generally to be in good agreement with previous ab initio molecular dynamics and neutron scattering studies. The main contributions to the predicted difference Compton profile are found to arise from intermolecular changes in the phase transition. This prediction can be used for interpreting future experiments.

The electronegativity equalization method fused with molecular mechanics: a fluctuating charge and flexible body potential function for [Emim][Gly] ionic liquids

Recently, experimental and theoretical studies on amino acid ionic liquid (AAIL) systems have attracted much attention. A transferable intermolecular potential approach that includes fluctuating charges and a flexible body based on a combination of the electronegativity equalization method and molecular mechanics (EEM/MM), and its application to an AAIL system containing 1-ethyl-3-methylimidazolium ([Emim](+)) and glycine ([Gly](-)) are explored and tested in this study. A consistent integration of EEM with MM requires the input of the EEM charges of all atoms into the MM intermolecular electrostatic interaction term. Compared with ionic liquid (IL) force fields, the EEM/MM model has an outstanding feature: the EEM/MM model not only presents the electrostatic interaction of atoms and their changes in response to different ambient environments but also introduces "the H-bond interaction region" in which a new parameter kHB(RHB) is used to describe the electrostatic interaction of hydrogen atoms in [Emim](+) and oxygen atoms in [Gly](-), which can form hydrogen bonds. The EEM/MM model gives quite accurate predictions for gas-phase state properties of [Emim](+), [Gly](-), and ion pairs, such as optimized geometries, dipole moments, vibrational frequencies, and cluster interaction energies. Due to its explicit description of charges and hydrogen bonds, the EEM/MM model also performs well for the liquid-phase properties of [Emim][Gly] under ambient conditions. The calculated properties, such as density, heat of vaporization, the self-diffusion coefficient, and ionic conductivity, are fairly consistent with available experimental results.

Systematic Parametrization of Polarizable Force Fields from Quantum Chemistry Data

We introduce ForceBalance, a method and free software package for systematic force field optimization with the ability to parametrize a wide variety of functional forms using flexible combinations of reference data. We outline several important challenges in force field development and how they are addressed in ForceBalance, and present an example calculation where these methods are applied to develop a highly accurate polarizable water model. ForceBalance is available for free download at https://simtk.org/home/forcebalance.

A simple AIMD approach to derive atomic charges for condensed phase simulation of ionic liquids

The atomic charges for two ionic liquids (ILs), 1-n-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) and 1-ethyl-3-methylimidazolium hexafluorophosphate ([EMIM][PF6]), were derived from periodic crystal phase calculations with density functional theory (DFT) and plane wave basis sets (denoted as "AIMD-c charge"). For both ILs, the total charge was found to be ±0.8 e for the cation and anion, respectively, due to the charge transfer between ions and polarization caused by the environment. These atomic charges were used in a force field developed within the general Amber force field framework. Using this force field, static, dynamic, and thermodynamic properties were computed for the two ILs using molecular dynamics simulation. The results were compared against results obtained using the same Amber force field but four different sets of partial charges, denoted as full charge, scaled charge, AIMD-l charge, and AIMD-b charge, respectively. The full charge was derived from quantum chemistry calculation of isolated ions in a vacuum and resulted in a total charge of unity on each ion. The scaled charge was obtained by uniformly scaling the full charge by 0.8. AIMD-l and AIMD-b charges were derived from liquid phase ab initio molecular dynamics simulations. The scaled charges have the same total charge on the ions as the AIMD-c charge but different distributions. It was found that simulation results not only depend on the total charge of each ion, but they are also sensitive to the charge distribution within an ion, especially for dynamic and thermodynamic properties. Overall, for the two ILs under study, the AIMD-c charge was found to predict experimental results better than the other four sets of charges, indicating that fitting charges from crystal phase DFT calculations, instead of extensive sampling of the liquid phase configurations, is a simple and reliable way to derive atomic charges for condensed phase ionic liquid simulations.

Dispersion interactions in room-temperature ionic liquids: results from a non-empirical density functional

The role of dispersion or van de Waals (VDW) interactions in imidazolium-based room-temperature ionic liquids is studied within the framework of density functional theory, using a recently developed non-empirical functional [M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)], as efficiently implemented in the SIESTA code [G. Román-Pérez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009)]. We present results for the equilibrium structure and lattice parameters of several crystalline phases, finding a general improvement with respect to both the local density (LDA) and the generalized gradient approximations (GGA). Similar to other systems characterized by VDW bonding, such as rare gas and benzene dimers as well as solid argon, equilibrium distances and volumes are consistently overestimated by ≈7%, compared to -11% within LDA and 11% within GGA. The intramolecular geometries are retained, while the intermolecular distances and orientations are significantly improved relative to LDA and GGA. The quality is superior to that achieved with tailor-made empirical VDW corrections ad hoc [M. G. Del Pópolo, C. Pinilla, and P. Ballone, J. Chem. Phys. 126, 144705 (2007)]. We also analyse the performance of an optimized version of this non-empirical functional, where the screening properties of the exchange have been tuned to reproduce high-level quantum chemical calculations [J. Klimes, D. Bowler, and A. Michaelides, J. Phys.: Condens. Matter 22, 074203 (2010)]. The results for solids are even better with volumes and geometries reproduced within 2% of experimental data. We provide some insight into the issue of polymorphism of [bmim][Cl] crystals, and we present results for the geometry and energetics of [bmim][Tf] and [mmim][Cl] neutral and charged clusters, which validate the use of empirical force fields.

Communication: Hybrid ensembles for improved force matching

Force matching is a method for parameterizing empirical potentials in which the empirical parameters are fitted to a reference potential energy surface (PES). Typically, training data are sampled from a canonical ensemble generated with either the empirical potential or the reference PES. In this Communication, we show that sampling from either ensemble risks excluding critical regions of configuration space, leading to fitted potentials that deviate significantly from the reference PES. We present a hybrid ensemble which combines the Boltzmann probabilities of both potential surfaces into the fitting procedure, and we demonstrate that this technique improves the quality and stability of empirical potentials.

Towards large-scale, fully ab initio calculations of ionic liquids

Ionic liquids have attracted a substantial amount of interest as replacement of traditional electrolytes in high efficiency electrochemical devices for generation and storage of energy due to their superior physical and chemical properties, especially low volatility and high electrochemical stability. For enhanced performance of the electrochemical devices ionic liquids are required to be highly conductive and low viscous. Long-range Coulomb and short-range dispersion interactions between ions affect physical and chemical properties of ionic liquids in a very complex way, thus preventing direct correlations to the chemical structure. Considering a vast combination of available cations and anions that can be used to synthesize ionic liquids, development of predictive theoretical approaches that allow for accurate tailoring of their physical properties has become crucial to further enhance the performance of electrochemical devices such as lithium batteries, fuel and solar cells. This perspective article gives a thorough overview of current theoretical approaches applied for studying thermodynamic (melting point and enthalpy of vapourisation) and transport (conductivity and viscosity) properties of ionic liquids, emphasizing their reliability and limitations. Strategies for improving predictive power and versatility of existing theoretical approaches are also outlined.

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.

A wave-function based approach for polarizable charge model: Systematic comparison of polarization effects on protic, aprotic, and ionic liquids

We first describe a wave-function based formalism of polarizable charge model by starting from the Hartree product ansatz for the total wave function and making the second-order expansion of individual molecular energies with the use of partial charge operators. The resulting model is shown to be formally equivalent to the charge response kernel model that starts from the linear-response approximation to partial charges, and also closely related to a family of fluctuating charge models that are based on the electronegativity equalization principle. We then apply the above model to a systematic comparison of polarization effects on qualitatively different liquids, namely, protic solvents (water and methanol), an aprotic polar solvent (acetonitrile), and imidazolium-based ionic liquids. Electronic polarization is known to decelerate molecular motions in conventional solvents while it accelerates them in ionic liquids. To obtain more insights into these phenomena, we consider an effective decomposition of total polarization energy into molecular contributions, and show that their statistical distribution is well-correlated with the acceleration/deceleration of molecular motions. In addition, we perform effective nonpolarizable simulations based on mean polarized charges, and compare them with fully polarizable simulations. The result shows that the former can reproduce structural properties of conventional solvents rather accurately, while they fail qualitatively to reproduce acceleration of molecular motions in ionic liquids.

Simulations of imidazolium ionic liquids: when does the cation charge distribution matter?

We compare the properties of models of liquids and crystals constructed from a number of intermolecular potentials for dimethylimidazolium chloride [dmim][Cl]. The force fields differ in the charge distribution in the cation but all include short range interactions which determine the shape of the cation. In addition to 'realistic' models intended for simulation of [dmim][Cl] we take two extreme 'unrealistic' models in which the cation charge is localized on the ring atoms or at the ring centre in order to study the effects of the cation charge distribution. The effects of polarizability are investigated by using shell models for the chloride ion. We find that, while equilibrium properties such as energetics, crystal structure, liquid structure and charge screening depend on the charge distribution in the cation but are little affected by including polarizability, dynamical properties such as diffusion are strongly affected by polarizability.

Ionic liquids: just Molten salts after all?

While there has been much effort in recent years to characterise ionic liquids in terms of parameters that are well described for molecular solvents, using these to explain reaction outcomes remains problematic. Herein we propose that many reaction outcomes in ionic liquids may be explained by considering the electrostatic interactions present in the solution; that is, by recognising that ionic liquids are salts. This is supported by evidence in the literature, along with studies presented here.

Application of static charge transfer within an ionic-liquid force field and its effect on structure and dynamics

The effects of linear scaling of the atomic charges of a reference potential on the structure, dynamics, and energetics of the ionic liquid 1,3-dimethylimidazolium chloride are investigated. Diffusion coefficients that span over four orders of magnitude are observed between the original model and a scaled model in which the ionic charges are +/-0.5 e. While the three-dimensional structure of the liquid is less affected, the partial radial distribution functions change markedly--with the positive result that for ionic charges of +/-0.7 e, an excellent agreement is observed with ab initio molecular dynamics data. Cohesive energy densities calculated from these partial-charge models are also in better agreement with those calculated from the ab initio data. We postulate that ionic-liquid models in which the ionic charges are assumed to be +/-1 e overestimate the intermolecular attractions between ions, which results in overstructuring, slow dynamics, and increased cohesive energy densities. The use of scaled-charge sets may be of benefit in the simulation of these systems--especially when looking at properties beyond liquid structure--thus providing an alternative to computationally expensive polarisable force fields.

Refined potential model for atomistic simulations of ionic liquid [bmim][PF6]

Refined parameters of an atomistic interaction potential model for the room temperature ionic liquid 1-n-butyl,3-methylimidazolium hexafluorophosphate are presented. Classical molecular dynamics simulations have been carried out to validate this fully flexible all-atom model. It predicts the density of the liquid at different temperatures between 300 and 500 K within 1.4% of the experimental value. Intermolecular radial distribution functions and the spatial distribution functions obtained from the new model are in close agreement with ab initio simulations. The calculated diffusion coefficients of ions and the surface tension of the liquid agree well with experiment.

Understanding ionic liquids through atomistic and coarse-grained molecular dynamics simulations

Understanding the physical properties of ionic liquids (ILs) via computer simulation is important for their potential technological applications. The goal of our IL research is to obtain a unified understanding of the properties of ILs with respect to their underlying molecular structure. From atomistic molecular dynamics simulations, the many-body electronic polarization effect was found to be important for modeling ILs, especially their dynamics. The multiscale coarse-graining methodology has also been employed to increase the simulation speed by a factor of 100 or more, thereby making it possible to study the mesoscopic behavior of ILs by computer simulations. With these simulation techniques, ILs with an amphiphilic cation were found to exhibit a spatial heterogeneity due to the aggregation of their nonpolar alkyl tails. This spatial heterogeneity is a key feature in interpreting many physical phenomena of ILs, such as their heterogeneous self-diffusion and surface layering, as well as their surfactant-like micelles formed in IL/water mixtures.

Simulations of ionic liquids, solutions, and surfaces

We have been using atomistic simulation for the last 10 years to study properties of imidazolium-based ionic liquids. Studies of dissolved molecules show the importance of electrostatic interactions in both aromatic and hydrogen-bonding solutes. However, the local structure strongly depends upon ion-ion and solute-solvent interactions. We find interesting local alignments of cations at the gas-liquid and solid-liquid interfaces, which give a potential drop through the surface. If the solid interface is charged, this charge is strongly screened over distances of a few nanometres and this screening decays on a fast time scale. We have studied the sensitivity of the liquid structure to force-field parameters and show that results from ab initio simulations can be used in the development of force fields.

Clusters, liquids, and crystals of dialkyimidazolium salts. A combined perspective from ab initio and classical computer simulations

We summarize results obtained by a combination of ab initio and classical computer simulations of dialkylimidazolium ionic liquids in different states of aggregation, from crystals to liquids and clusters. Unusual features arising from the competition between electrostatic, dispersion, and hydrogen-bonding interactions are identified at the origin of observed structural patterns. We also discuss the way Brønsted acids interact with ionic liquids leading to the formation of hydrogen-bonded anions.

Effective potentials from complex simulations: a potential-matching algorithm and remarks on coarse-grained potentials

The projection of complex interactions onto simple distance-dependent or angle-dependent classical mechanical functions is a long-standing theoretical challenge in the field of computational sciences concerning biomolecules, colloids, aggregates and simple systems as well. The construction of an effective potential may be based on theoretical assumptions, on the application of fitting procedures on experimental data and on the simplification of complex molecular simulations. Recently, a force-matching method was elaborated to project the data of Car-Parrinello ab initio molecular dynamics simulations onto two-particle classical interactions (Izvekov et al 2004 J. Chem. Phys. 120 10896). We have developed a potential-matching algorithm as a practical analogue of this force-matching method. The algorithm requires a large number of configurations (particle positions) and a single value of the potential energy for each configuration. We show the details of the algorithm and the test calculations on simple systems. The test calculation on water showed an example in which a similar structure was obtained for qualitatively different pair interactions. The application of the algorithm on reverse Monte Carlo configurations was tried as well. We detected inconsistencies in a part of our calculations. We found that the coarse graining of potentials cannot be performed perfectly both for the structural and the thermodynamic data. For example, if one applies an inverse method with an input of the pair-correlation function, it provides energetics data for the configurations uniquely. These energetics data can be different from the desired ones obtained by all atom simulations, as occurred in the testing of our potential-matching method.