Finding the best density functional approximation to describe interaction energies and structures of ionic liquids in molecular dynamics studies

Machine learning-driven investigation of the structure and dynamics of the BMIM-BF4 room temperature ionic liquid

Room-temperature ionic liquids are an exciting group of materials with the potential to revolutionize energy storage. Due to their chemical structure and means of interaction, they are challenging to study computationally. Classical descriptions of their inter- and intra-molecular interactions require time intensive parametrization of force-fields which is prone to assumptions. While ab initio molecular dynamics approaches can capture all necessary interactions, they are too slow to achieve the time and length scales required. In this work, we take a step towards addressing these challenges by applying state-of-the-art machine-learned potentials to the simulation of 1-butyl-3-methylimidazolium tetrafluoroborate. We demonstrate a learning-on-the-fly procedure to train machine-learned potentials from single-point density functional theory calculations before performing production molecular dynamics simulations. Obtained structural and dynamical properties are in good agreement with computational and experimental references. Furthermore, our results show that hybrid machine-learned potentials can contribute to an improved prediction accuracy by mitigating the inherent shortsightedness of the models. Given that room-temperature ionic liquids necessitate long simulations to address their slow dynamics, achieving an optimal balance between accuracy and computational cost becomes imperative. To facilitate further investigation of these materials, we have made our IPSuite-based training and simulation workflow publicly accessible, enabling easy replication or adaptation to similar systems.

Uncovering the Properties of Dicationic Ionic Liquid Nanodroplets through Ab Initio Molecular Dynamics Simulations

The behavior of nanodroplets of an imidazolium-based dicationic ionic liquid, i.e., [C1(mim)2][PF6]2, was investigated in this study using ab initio molecular dynamics simulations. The vibrational features as well as the structural, interfacial, and dynamical properties of different sized droplets were analyzed and compared to the bulk phase system. Structural properties of the droplets, such as π-π stacking, radial distribution functions, structure factors, combined distribution functions, and angular distribution functions were analyzed to understand the interactions and orientations of their ions. The vibrational features and hydrogen bonding strength of droplets were studied by calculating their infrared (IR) and power spectra, determining the contribution of different types of hydrogen bonding to each vibrational mode. The calculated spectra showed good overall agreement with the experimental results. The interfacial properties of the droplets and the orientation of their ions were analyzed using density profiles and an exposed surface. The results showed that, in all systems studied, cations and anions were equally likely to exist in both inner and outer layers, and the cations tended to be oriented toward the center of droplets with obtuse angles. Additionally, the droplet densities were extrapolated to predict the bulk phase density with less than 2% deviation. The dynamical properties of hydrogen bonds, mean square displacement, and van Hove correlations of cations and anions were also analyzed. The results indicated that there was no regular trend in the dynamic properties of droplets with an increasing system size.

Assignment of the Crystal Structure to the Aza-Pinacol Coupling Product by X-ray Diffraction and Density Functional Theory Modeling

Aza-pinacol coupling of N-benzyl-1-phenylmethanimine using Zn dust affords a mixture of R,S- or R,R-diastereomers in a 1:1 ratio. The R,S-diastereomer is solid with an m.p. of 135 °C, while the R,R-diastereomer is liquid at room temperature. The configuration of stereocenters was determined by combining X-ray powder diffraction and density functional theory (DFT) modeling.

"Red Carbon": A Rediscovered Covalent Crystalline Semiconductor

Carbon suboxide (C₃ O₂ ) is a unique molecule able to polymerize spontaneously into highly conjugated light-absorbing structures at temperatures as low as 0 °C. Despite obvious advantages, little is known about the nature and the functional properties of this carbonaceous material. In this work, the aim is to bring "red carbon," a forgotten polymeric semiconductor, back to the community's attention. A solution polymerization process is adapted to simplify the synthesis and control the structure. This allows one to obtain this crystalline covalent material at low temperatures. Both spectroscopic and elemental analyses support the chemical structure represented as conjugated ladder polypyrone ribbons. Density functional theory calculations suggest a crystalline structure of AB stacks of polypyrone ribbons and identify the material as a direct bandgap semiconductor with a medium bandgap that is further confirmed by optical analysis. The material shows promising photocatalytic performance using blue light. Moreover, the simple condensation-aromatization route described here allows the straightforward fabrication of conjugated ladder polymers and can be inspiring for the synthesis of carbonaceous materials at low temperatures in general.

Comparison between Ab Initio Molecular Dynamics and OPLS-Based Force Fields for Ionic Liquid Solvent Organization

OPLS-based force fields (FFs) have been shown to provide accurate bulk-phase properties for a wide variety of imidazolium-based ionic liquids (ILs). However, the ability of OPLS to reproduce an IL solvent structure is not as well-validated given the relative lack of high-level theoretical or experimental data available for comparison. In this study, ab initio molecular dynamics (AIMD) simulations were performed for three widely used ILs: the 1-butyl-3-methylimidazolium cation with chloride, tetrafluoroborate, or hexafluorophosphate anions, that is, [BMIM][Cl], [BMIM][BF₄], and [BMIM][PF₆], respectively, as a basis for further assessment of two unique IL FFs: the ±0.8 charge-scaled OPLS-2009IL FF and the OPLS-VSIL FF. The OPLS-2009IL FF employs a traditional all-atom functional form, whereas the OPLS-VSIL FF was developed using a virtual site that offloads negative charge to inside the plane of the ring with careful attention given to reproducing hydrogen bonding. Detailed comparisons between AIMD and the OPLS FFs were made based on radial distribution functions (RDFs), combined distribution functions (CDFs), and spatial distribution functions (SDFs) to examine cation-anion interactions and π⁺-π⁺ stacking between the imidazolium rings. While both FFs were able to correctly capture the general solvent structure of these popular ILs, the OPLS-VSIL FF quantitatively reproduced interaction distances more accurately. In addition, this work provides further insights into the different short- and long-range structure patterns of these popular ILs.

A general justification for hybrid functionals in DFT by means of linear response theory

In the present work, resorting to linear response theory, we examine the plausibility of postulating Kohn-Sham (KS)-type equations which contain, by definition, an effective hybrid potential made up by some arbitrary mixture of local and non-local terms. In this way a general justification for the construction of hybrid functionals is provided without resorting to arguments based on the adiabatic connection, the generalized KS theory or the Levy's constrained search (or its variations). In particular, we examine the cases of single-hybrid functionals, derived from non-local exchange and of double-hybrid functionals, emerging from non-local second-order expressions obtained from the KS perturbation theory. A further generalization for higher-order hybrid functionals is also included.

Structures and properties of ionic crystals and condensed phase ionic liquids predicted with the generalized energy-based fragmentation method

The generalized energy-based fragmentation (GEBF) approach is extended to facilitate ab initio investigations of structures, lattice energies, vibrational spectra and ¹ H NMR chemical shifts of ionic crystals and condensed-phase ionic liquids (ILs) with the periodic boundary conditions (PBC). For selected periodic systems, our results demonstrate that the so-called PBC-GEBF approach can provide satisfactory descriptions on ground-state energies, structures, and vibrational spectra of ionic crystals and IL crystals. The PBC-GEBF approach is then applied to three realistic condensed phase systems. For three ionic crystals (LiCl, NaCl, and KCl), we apply the PBC-GEBF approach with MP2 theory as well as some popular DFT methods to investigate their crystal structures and lattice energies. Our calculations indicate that the crystal structures obtained with PBC-GEBF-MP2/6-311 + G** are very close to the corresponding X-ray structures, while PBC-GEBF-ωB97X-D/6-311 + G** provides satisfactory prediction for crystal structures and lattice energies. For two polymorphs of [n-C₄ mim][Cl] crystals, we find that the PBC-GEBF approach at the M06-2X/6-311 + G** level can give a satisfactory descriptions on structures and Raman spectra of these two crystals. Furthermore, for [C₂ mim][BF₄ ] ILs, we demonstrate that their ¹ H NMR chemical shifts can be estimated from averaging over 5 typical snapshots (extracted from MD simulations) with the PBC-GEBF approach at the B97-2/pcSseg-2 level. The calculated results account for the observed experimental data quite well. Therefore, we expect that the PBC-GEBF approach, combined with various quantum chemistry methods, will become an effective tool in predicting structures and properties of ionic crystals and condensed-phase ILs.

Chemistry Dissolved in Ionic Liquids. A Theoretical Perspective

The theoretical treatment of ionic liquids must focus now on more realistic models while at the same time keeping an accurate methodology when following recent ionic liquids research trends or allowing predictability to come to the foreground. In this Perspective, we summarize in three cases of advanced ionic liquid research what methodological progress has been made and point out difficulties that need to be overcome. As particular examples to discuss we choose reactions, chirality, and radicals in ionic liquids. All these topics have in common that an explicit or accurate treatment of the electronic structure and/or intermolecular interactions is required (accurate methodology), while at the same time system size and complexity as well as simulation time (realistic model) play an important role and must be covered as well.

Influence of Small Quantities of Water on the Physical Properties of Alkylammonium Nitrate Ionic Liquids

This paper presents a comprehensive study of two alkylammonium nitrate ionic liquids. As part of this family of materials, mainly ethylammonium nitrate (EAN) and also propylammonium nitrate (PAN) have attracted a great deal of attention during the last decades due to their potential applications in many fields. Although there have been numerous publications focused on the measurement of their physical properties, a great dispersion can be observed in the results obtained for the same magnitude. One of the critical points to be taken into account in their physical characterization is their water content. Thus, the main objective of this work was to determine the degree of influence of the presence of small quantities of water in EAN and PAN on the measurement of density, viscosity, electrical conductivity, refractive index and surface tension. For this purpose, the first three properties were determined in samples of EAN and PAN with water contents below 30,000 ppm in a wide range of temperatures, between 5 and 95 °C, while the last two were obtained at 25 °C. As a result of this study, it has been concluded that the presence of water is critical in those physical properties that involve mass or charge transport processes, resulting in the finding that the absolute value of the average percentage change in both viscosity and electrical conductivity is above 40%. Meanwhile, refractive index (≤0.3%), density (≤0.5%) and surface tension (≤2%) present much less significant changes.

Benchmarking London dispersion corrected density functional theory for noncovalent ion-π interactions

The strongly attractive noncovalent interactions of charged atoms or molecules with π-systems are important binding motifs in many chemical and biological systems. These so-called ion-π interactions play a major role in enzymes, molecular recognition, and for the structure of proteins. In this work, a molecular test set termed IONPI19 is compiled for inter- and intramolecular ion-π interactions, which is well balanced between anionic and cationic systems. The IONPI19 set includes interaction energies of significantly larger molecules (up to 133 atoms) than in other ion-π test sets and covers a broad range of binding motifs. Accurate (local) coupled cluster values are provided as reference. Overall, 19 density functional approximations, including seven (meta-)GGAs, eight hybrid functionals, and four double-hybrid functionals combined with three different London dispersion corrections, are benchmarked for interaction energies. DFT results are further compared to wave function based methods such as MP2 and dispersion corrected Hartree-Fock. Also, the performance of semiempirical QM methods such as the GFNn-xTB and PMx family of methods is tested. It is shown that dispersion-uncorrected DFT underestimates ion-π interactions significantly, even though electrostatic interactions dominate the overall binding. Accordingly, the new charge dependent D4 dispersion model is found to be consistently better than the standard D3 correction. Furthermore, the functional performance trend along Jacob's ladder is generally obeyed and the reduction of the self-interaction error leads to an improvement of (double) hybrid functionals over (meta-)GGAs, even though the effect of the SIE is smaller than expected. Overall, the double-hybrids PWPB95-D4/QZ and revDSD-PBEP86-D4/QZ turned out to be the most reliable among all assessed methods for the description of ion-π interactions, which opens up new perspectives for systems where coupled cluster calculations are no longer computationally feasible.

A Systematic Study of DFT Performance for Geometry Optimizations of Ionic Liquid Clusters

Clusters of two ion pairs of imidazolium-based ionic liquids were optimized with 43 different levels of theory, including DFT functionals and MP2-based methods combined with varying Dunning's basis sets, and added dispersion corrections. Better preforming DFT functionals were then applied to clusters consisting of four ion pairs. Excellent performance of some DFT functionals for the two ion pair clusters did not always match that of the four ion-paired clusters despite interionic distances remaining constant between the optimized two and four ion-paired clusters of the same ionic liquid. Combinations of DFT functional and basis set such as ωB97X-D/cc-pVDZ, M06-2X/aug-cc-pVDZ, B3LYP-D3/cc-pVTZ, and TPSS-D3/cc-pVTZ gave excellent results for geometry optimization of two ion-paired clusters of imidazolium ionic liquids but gave larger deviations when applied to the four ion-paired clusters of varying ionic liquids. Empirical dispersion corrections were seen to be crucial in correctly capturing correlation effects in the studied ionic liquid clusters, becoming more important in larger clusters. Dunning's double-ζ basis set, cc-pVDZ, is associated with the smallest root mean squared deviations for geometries; however, it also produces the largest deviations in total electronic energies. ωB97X-D and M06-2X produced the best performance with the augmented version of this basis set. The triple-ζ basis set, cc-pVTZ, leads to the best performance of most of the DFT functionals (especially the dispersion-corrected ones) used, whereas its augmented version, aug-cc-pVTZ, was not seen to improve results. The combinations of functional and basis set that gave the best geometry and energetics in both two and four ion-paired clusters were PBE-D3/cc-pVTZ, ωB97X-D/aug-cc-pVDZ, and BLYP-D3/cc-pVTZ. All three combinations are recommended for geometry optimizations of larger clusters of ionic liquids. PBE-D3/cc-pVTZ performed the best with an average deviation of 2.3 kJ mol^-1 and a standard deviation of 3.4 kJ mol^-1 for total electronic energy when applied to four ion-paired clusters. Geometries optimized with FMO2-SRS-MP2/cc-pVTZ produced total energy within 2.0 kJ mol^-1 off the benchmark in two ion-paired clusters, with the cc-pVDZ basis set performing unsurprisingly poorly with the same method. The error increased to 4.8 kJ mol^-1 on average in four ion-paired clusters, with the smallest RMSD deviations in geometries when compared to the benchmark ones. This study is the first report that investigated the performance of DFT functionals for two and four ion-paired clusters of a wide range of ionic liquids consisting of commonly used cations such as pyrrolidinium, imidazolium, pyridinium, and ammonium. It also identified the importance of assessing the performance of quantum chemical methods for ionic liquids on a variety of cation-anion combinations.

Effect of anion reorientation on proton mobility in the solid acids family CsHyXO4(X = S, P, Se,y= 1, 2) fromab initiomolecular dynamics simulations

The high temperature phases of the solid acids CsHSeO₄, CsHSO₄and CsH₂PO₄show extraordinary high proton conductivities, which are enabled by the interplay of high proton transfer rates and frequent anion reorientation.

Fast Quantum Chemical Simulations of Infrared Spectra of Organic Compounds with the B97-3c Composite Method

The ability of the quantum chemical computations to reproduce spectral positions and relative intensities of infrared (IR) bands for experimental vibrational spectra of organic molecules is assessed. The efficient B97-3c density functional approximation, routinely applicable to hundreds of atoms on a single processor, has been applied for the simulation of IR spectra for species containing up to 216 atoms. The results demonstrate that B97-3c, being much faster than the well-recognized hybrid functional B3LYP, offers similarly good quantitative performance in comparison to experimental data for relative IR intensities and fundamental frequencies (ν ≤ 2200 cm^-1) for isolated molecules comprising from 3 to 21 first- or second-row atoms.

Mechanisms of Iodide⁻Triiodide Exchange Reactions in Ionic Liquids: A Reactive Molecular-Dynamics Exploration

Efficient charge transport has been observed in iodine-doped, iodide-based room-temperature ionic liquids, yielding high ionic conductivity. To elucidate preferred mechanistic pathways for the iodide ( I - )-to-triiodide ( I 3 - ) exchange reactions, we have performed 10 ns reactive molecular-dynamics calculations in the liquid state for 1-butyl-3-methylimidazolium iodide ([BMIM][I]) at 450 to 750 K. Energy-barrier distributions for the iodine-swapping process were determined as a function of temperature, employing a charge-reassignment scheme drawn in part from electronic-structure calculations. Bond-exchange events were observed with rate-determining energy barriers ranging from ~0.19 to 0.23 ± 0.06 eV at 750 and 450 K, respectively, with an approximately Arrhenius temperature dependence for iodine self-diffusivity and reaction kinetics, although diffusion dominates/limits the bond-exchange events. This charge transfer is not dissimilar in energetics to those in solid-state superionic conductors.

Cation influence on heterocyclic ammonium ionic liquids: a molecular dynamics study

Four different ionic liquids (ILs) consisting of the bis(trifluoromethanesulfonyl)imide ([NTf₂]⁻) anion, with structurally similar systematically varying cations, are investigated herein through classical molecular dynamics.

Solvation Properties of Silver and Copper Ions in a Room Temperature Ionic Liquid: A First-Principles Study

Understanding the behavior of metal ions in room temperature ionic liquids (ILs) is essential for predicting and optimizing performance for technologies like metal electrodeposition; however, many mechanistic details remain enigmatic, including the solvation properties of the ions in ILs and how they are governed by the intrinsic interaction between the ions and the liquid species. Here, we utilize first-principles molecular dynamics simulations to unravel and compare the key structural properties of Ag⁺ and Cu⁺ ions in a common room temperature IL, 1-ethyl-3-methylimidazolium trifluoromethanesulfonate. We find that, when compared to Cu⁺, the larger Ag⁺ shows a more disordered and flexible solvation structure with a more frequent exchange of the IL species between its solvation shells. In addition, our simulations reveal an interesting analog in the solvation behavior of the ions in the IL and aqueous environments, particularly in the effect of the ion electronic structures on their solvation properties. This work provides fundamental understanding of the intrinsic properties of the metal ions in the IL, while offering mechanistic understanding and strategy for future selection of ILs for metal electrodeposition processes.