Static Dielectric Constant from Simulations Revisited: Fluctuations or External Field?

Accuracy limit of non-polarizable four-point water models: TIP4P/2005 vs OPC. Should water models reproduce the experimental dielectric constant?

The last generation of four center non-polarizable models of water can be divided into two groups: those reproducing the dielectric constant of water, as OPC, and those significantly underestimating its value, as TIP4P/2005. To evaluate the global performance of OPC and TIP4P/2005, we shall follow the test proposed by Vega and Abascal in 2011 evaluating about 40 properties to fairly address this comparison. The liquid-vapor and liquid-solid equilibria are computed, as well as the heat capacities, isothermal compressibilities, surface tensions, densities of different ice polymorphs, the density maximum, equations of state at high pressures, and transport properties. General aspects of the phase diagram are considered by comparing the ratios of different temperatures (namely, the temperature of maximum density, the melting temperature of hexagonal ice, and the critical temperature). The final scores are 7.2 for TIP4P/2005 and 6.3 for OPC. The results of this work strongly suggest that we have reached the limit of what can be achieved with non-polarizable models of water and that the attempt to reproduce the experimental dielectric constant deteriorates the global performance of the water force field. The reason is that the dielectric constant depends on two surfaces (potential energy and dipole moment surfaces), whereas in the absence of an electric field, all properties can be determined simply from just one surface (the potential energy surface). The consequences of the choice of the water model in the modeling of electrolytes in water are also discussed.

PMC-IZ: A Simple Algorithm for the Electrostatics Calculation in Slab Geometric Molecular Dynamics Simulations

Slab geometric systems are widely utilized in molecular simulations. However, an efficient, straightforward, and accurate method for calculating electrostatic interactions in these systems for molecular dynamics (MD) simulations is still needed. This review introduces a PME-like approach called PMC-IZ, specifically designed for slab geometric systems. Traditional approaches for long-range electrostatic interaction calculations in slab geometry typically involve Ewald summation, where the Gaussian charge density is summed within 3D unit cells and then integrated in the 2D periodic space. In the proposed approach here, the Poisson equation was solved for a single Gaussian charge density within 2Dl periodic space, followed by convolution within 3D unit cells using an effective potential as the convolution kernel for summation. The effective potential ensures that the solution within the region of interest adheres strictly to 2D periodic boundary conditions while inherently possessing 3D periodic boundary condition properties. The PMC-IZ method provides for such systems accurate treatment of electrostatic interactions, overcomes limitations associated with finite vacuum layers, and offers improved computational efficiency. We thus postulate that this method provides a valuable tool for studying electrostatic interactions in slab geometric system MD simulations. It has promising applications in various areas such as surface science, catalysis, and materials research, where accurate modeling of slab geometric electrostatic interactions is essential.

Osmotic Force Balance Evaluation of Aqueous Electrolyte Osmotic Pressures and Chemical Potentials

Concentrated aqueous salt solutions are ubiquitous in problems of biological and environmental relevance. The development of accurate force fields that capture the interactions between dissolved species in solution is crucial to simulating these systems to gain molecular insights into the underlying processes under saline conditions. The osmotic pressure is a relatively simple thermodynamic property connecting the experimental and simulation measurements of the associative properties of the ions in solution. Milner [C. Gillespie and S. T. Milner, Soft Matter, 16, 9816 (2020)] proposed a simulation approach to evaluate the osmotic pressures of salts in solution by applying a restraint potential to the ions alone in solution and determining the resulting pressure required to balance that potential, referred to here as the osmotic force balance. Here, we expand Milner's approach, demonstrating that the chemical potentials of the salts in solution as a function of concentration can be fitted to the concentration profiles determined from simulation, additionally providing an analytical expression for the osmotic pressure. This approach is used to determine the osmotic pressures of 15 alkali halide salts in water from simulations. The cross interactions between cations and anions in solution are subsequently optimized to capture their experimental osmotic pressures.

Probing the size-dependent polarizability of mesoscopic ionic clusters and their induced-dipole interactions

Mesoscopic clusters composed of oppositely charged particles are ubiquitous in synthetic and biological soft materials. The effective interaction between these clusters is influenced by their polarizability, that is, the ability of their constituent charges to re-arrange in response to an external electrical field. Here, using coarse-grained simulations, we show that the polarizability of electrically neutral ionic clusters decreases as the number of constituent charges increases and/or their Coulombic interaction strength increases for various ion valencies, ion densities, and degrees of cluster boundary hardness. For clusters of random ionomers and their counterions, their polarizability is shown to depend on the number of polymer chains. The variation of the cluster polarizability with the cluster size indicates that throughout the assembly, the induced-dipole interactions between the clusters may be reduced substantially as they acquire more charges while maintaining zero net charge. Under certain conditions, the induced-dipole interactions may become repulsive, as inferred from our simulations with a polarizable solvent. As a result, the dipole-induced related interactions can serve as a counterbalancing force that contributes to the self-limiting aggregation of charge-containing assemblies.

Activity coefficients of aqueous electrolytes from implicit-water molecular dynamics simulations

We obtain activity coefficients in NaCl and KCl solutions from implicit-water molecular dynamics simulations, at 298.15 K and 1 bar, using two distinct approaches. In the first approach, we consider ions in a continuum with constant relative permittivity (ɛ_r) equal to that of pure water; in the other approach, we take into account the concentration-dependence of ɛ_r, as obtained from explicit-water simulations. Individual ion activity coefficients (IIACs) are calculated using gradual insertion of single ions with uniform neutralizing backgrounds to ensure electroneutrality. Mean ionic activity coefficients (MIACs) obtained from the corresponding IIACs in simulations with constant ɛ_r show reasonable agreement with experimental data for both salts. Surprisingly, large systematic negative deviations are observed for both IIACs and MIACs in simulations with concentration-dependent ɛ_r. Our results suggest that the absence of hydration structure in implicit-water simulations cannot be compensated by correcting for the concentration-dependence of the relative permittivity ɛ_r. Moreover, even in simulations with constant ɛ_r for which the calculated MIACs are reasonable, the relative positioning of IIACs of anions and cations is incorrect for NaCl. We conclude that there are severe inherent limitations associated with implicit-water simulations in providing accurate activities of aqueous electrolytes, a finding with direct relevance to the development of electrolyte theories and to the use and interpretation of implicit-solvent simulations.

Dielectric Constant of Liquid Water Determined with Neural Network Quantum Molecular Dynamics

The static dielectric constant ϵ_{0} and its temperature dependence for liquid water is investigated using neural network quantum molecular dynamics (NNQMD). We compute the exact dielectric constant in canonical ensemble from NNQMD trajectories using fluctuations in macroscopic polarization computed from maximally localized Wannier functions (MLWF). Two deep neural networks are constructed. The first, NNQMD, is trained on QMD configurations for liquid water under a variety of temperature and density conditions to learn potential energy surface and forces and then perform molecular dynamics simulations. The second network, NNMLWF, is trained to predict locations of MLWF of individual molecules using the atomic configurations from NNQMD. Training data for both the neural networks is produced using a highly accurate quantum-mechanical method, DFT-SCAN that yields an excellent description of liquid water. We produce 280×10^{6} configurations of water at 7 temperatures using NNQMD and predict MLWF centers using NNMLWF to compute the polarization fluctuations. The length of trajectories needed for a converged value of the dielectric constant at 0°C is found to be 20 ns (40×10^{6} configurations with 0.5 fs time step). The computed dielectric constants for 0, 15, 30, 45, 60, 75, and 90°C are in good agreement with experiments. Our scalable scheme to compute dielectric constants with quantum accuracy is also applicable to other polar molecular liquids.

Multiscale modeling shows that dielectric differences make NaV channels faster than KV channels

The generation of action potentials in excitable cells requires different activation kinetics of voltage-gated Na (Na_V) and K (K_V) channels. Na_V channels activate much faster and allow the initial Na⁺ influx that generates the depolarizing phase and propagates the signal. Recent experimental results suggest that the molecular basis for this kinetic difference is an amino acid side chain located in the gating pore of the voltage sensor domain, which is a highly conserved isoleucine in K_V channels but an equally highly conserved threonine in Na_V channels. Mutagenesis suggests that the hydrophobicity of this side chain in Shaker K_V channels regulates the energetic barrier that gating charges cross as they move through the gating pore and control the rate of channel opening. We use a multiscale modeling approach to test this hypothesis. We use high-resolution molecular dynamics to study the effect of the mutation on polarization charge within the gating pore. We then incorporate these results in a lower-resolution model of voltage gating to predict the effect of the mutation on the movement of gating charges. The predictions of our hierarchical model are fully consistent with the tested hypothesis, thus suggesting that the faster activation kinetics of Na_V channels comes from a stronger dielectric polarization by threonine (Na_V channel) produced as the first gating charge enters the gating pore compared with isoleucine (K_V channel).

Molecular dynamics simulations of liquid-liquid interfaces in an electric field: The water-1,2-dichloroethane interface

The polarized interface between two immiscible liquids plays a central role in many technological processes. In particular, for electroanalytical and ion extraction applications, an external electric field is typically used to selectively induce the transfer of ionic species across the interfaces. Given that it is experimentally challenging to obtain an atomistic insight into the ion transfer process and the structure of liquid-liquid interfaces, atomistic simulations have often been used to fill this knowledge gap. However, due to the long-range nature of the electrostatic interactions and the use of 3D periodic boundary conditions, the use of external electric fields in molecular dynamics simulations requires special care. Here, we show how the simulation setup affects the dielectric response of the materials and demonstrate how by a careful design of the system it is possible to obtain the correct electric field on both sides of a liquid-liquid interface when using standard 3D Ewald summation methods. In order to prove the robustness of our approach, we ran extensive molecular dynamics simulations with a rigid-ion and polarizable force field of the water/1,2-dichloroethane interface in the presence of weak external electric fields.

Dissipative particle dynamics for systems with polar species: Interactions in dielectric media

In this work, we develop a method for simulating polar species in the dissipative particle dynamics (DPD) method. The main idea behind the method is to treat each bead as a dumb-bell, i.e., two sub-beads kept at a fixed distance, instead of a point-like particle. The relation between the bead dipole moment and the bulk dielectric permittivity was obtained. The interaction force of single charges in polar liquid showed that the effective dielectric permittivity is somewhat smaller than that obtained for the bulk case at large separation between the charges. In order to understand the reasons behind the observed drop in the dielectric permittivity, we calculate the electric field of an isolated charge in a polar liquid; no permittivity drop is observed for this case. We can assume that the behavior observed for the force is due to the fact that the probing point is always associated with the charged bead, which is a force center, which essentially leads to a non-homogeneous density distribution around it on average; this is not the case when the field is measured. The interaction of a single charge with an interface between two liquids with different permittivities was studied after that; the model is found to correctly reproduce the "mirror image" effects. Finally, we show why it is necessary to treat the polar species in DPD explicitly by investigating the behavior of a charged colloidal particle at a liquid-liquid interface.

How Ethylene Glycol Chains Enhance the Dielectric Constant of Organic Semiconductors: Molecular Origin and Frequency Dependence

Incorporating ethylene glycols (EGs) into organic semiconductors has become the prominent strategy to increase their dielectric constant. However, EG's contribution to the dielectric constant is due to nuclear relaxations, and therefore, its relevance for various organic electronic applications depends on the time scale of these relaxations, which remains unknown. In this work, by means of a new computational protocol based on polarizable molecular dynamics simulations, the time- and frequency-dependent dielectric constant of a representative fullerene derivative with EG side chains is predicted, the origin of its unusually high dielectric constant is explained, and design suggestions are made to further increase it. Finally, a dielectric relaxation time of ∼1 ns is extracted which suggests that EGs may be too slow to reduce the Coulombic screening in organic photovoltaics but are definitely fast enough for organic thermoelectrics with much lower charge carrier velocities.

Molecular dynamics simulation of microwave heating of liquid monoethanolamine (MEA): An evaluation of existing force fields

We present a complete classical molecular dynamics (MD) study of the dielectric heating of liquid monoethanolamine (MEA) at microwave (MW) frequencies ranging from 1.0 to 10.0 GHz. The detailed dielectric properties predicted by a series of existing empirical force fields of MEA were carefully compared to experimental results. We find that all the evaluated force fields were unable to accurately predict experimental static dielectric constant, frequency-dependent dielectric spectra, and MW heating profiles of liquid MEA, although GROMOS-aa (all-atom GROningen molecular simulation) is the most accurate of those tested. With an isotropic scaling of partial atomic charges, the modified GROMOS-aa and OPLS-aa (all-atom optimized potentials for liquid simulations) force fields could accurately reproduce the experimental static dielectric constant and frequency-dependent dielectric spectra, but they failed to predict MW heating rates directly from MD heating simulations. Thus, the recently presented approach [F. J. Salas et al., J. Chem. Theory Comput. 11, 683 (2015); A. P. de la Luz et al., ibid. 11, 2792 (2015)] to tune existing force fields is not an ideal approach to produce force fields suitable for accurate dielectric heating studies.

Ionic Solution: What Goes Right and Wrong with Continuum Solvation Modeling

Solvent-mediated electrostatic interactions were well recognized to be important in the structure and function of molecular systems. Ionic interaction is an important component in electrostatic interactions, especially in highly charged molecules, such as nucleic acids. Here, we focus on the quality of the widely used Poisson-Boltzmann surface area (PBSA) continuum models in modeling ionic interactions by comparing with both explicit solvent simulations and the experiment. In this work, the molality-dependent chemical potentials for sodium chloride (NaCl) electrolyte were first simulated in the SPC/E explicit solvent. Our high-quality simulation agrees well with both the previous study and the experiment. Given the free-energy simulations in SPC/E as the benchmark, we used the same sets of snapshots collected in the SPC/E solvent model for PBSA free-energy calculations in the hope to achieve the maximum consistency between the two solvent models. Our comparative analysis shows that the molality-dependent chemical potentials of NaCl were reproduced well with both linear PB and nonlinear PB methods, although nonlinear PB agrees better with SPC/E and the experiment. Our free-energy simulations also show that the presence of salt increases the hydrophobic effect in a nonlinear fashion, in qualitative agreement with previous theoretical studies of Onsager and Samaras. However, the lack of molality-dependency in the nonelectrostatics continuum models dramatically reduces the overall quality of PBSA methods in modeling salt-dependent energetics. These analyses point to further improvements needed for more robust modeling of solvent-mediated interactions by the continuum solvation frameworks.

Size and Origins of Long-Range Orientational Water Correlations in Dilute Aqueous Salt Solutions

Long-range ordering of water around solutes has been repeatedly invoked as the key to its biological function. Recently, it has been shown that in an 8 mM aqueous NaCl solution the orientational correlation between water molecules extends beyond 8 nm. This was interpreted as arising from ion-induced long-range effects on the water collective hydrogen-bond interactions. Each ion was suggested to affect >10 000 water molecules, leading to a picture involving nanoscopic "ordered domains". Using molecular dynamics simulations, we show that the very small long-range tail in the correlation function is caused primarily by pairs of water molecules belonging to different ions' hydration shells and can be made to practically disappear by rearranging the ionic positions. This means that the ion-induced water orientational ordering in millimolar salt solutions cannot be separated from ion-ion interaction effects, for which the Debye-Hückel screening length shrinks to less than 1 nm at physiological ionic strengths.

Dielectric constant and low-frequency infrared spectra for liquid water and ice Ih within the E3B model

Two intrinsic difficulties in modeling condensed-phase water with conventional rigid non-polarizable water models are: reproducing the static dielectric constants for liquid water and ice Ih, and generating the peak at about 200 cm(-1) in the low-frequency infrared spectrum for liquid water. The primary physical reason for these failures is believed to be the missing polarization effect in these models, and consequently various sophisticated polarizable water models have been developed. However, in this work we pursue a different strategy and propose a simple empirical scheme to include the polarization effect only on the dipole surface (without modifying a model's intermolecular interaction potential). We implement this strategy for our explicit three-body (E3B) model. Our calculated static dielectric constants and low-frequency infrared spectra are in good agreement with experiment for both liquid water and ice Ih over wide temperature ranges, albeit with one fitting parameter for each phase. The success of our modeling also suggests that thermal fluctuations about local minima and the energy differences between different proton-disordered configurations play minor roles in the static dielectric constant of ice Ih. Our analysis shows that the polarization effect is important in resolving the two difficulties mentioned above and sheds some light on the origin of several features in the low-frequency infrared spectra for liquid water and ice Ih.