Polarizable Potential Model Research Articles

Structures and stability of K+ cation solvated in Arn clusters

The solvation of K+ cation plays an important role in various phenomena such as biological procedures, geological time, and archaeological properties. Monte Carlo (MC) simulation and DFT method are employed to study the structural and energetic characteristics of the K + Arn (n = 1–14) clusters. The potential model (PM) and the Basin-Hopping (BH) method are the foundation of the MC simulation. The pairwise PM (PW-PM) is improved by introducing the N-body interactions via the polarizable potential model (PPM). On the other side, the DFT functional M05–2X, combined with the 6–311++G(3d2f,2p) basis set, and the Grimme dispersion correction GD3 was used to deeply investigate the geometrical properties and the relative stability of the K + Arn clusters. Starting from n = 12, a structural transition from square antiprism (SA) to icosahedron (ICOS) form is detected. Additionally, the PPM allows us to examine the largest sizes (n = 15–54). Herein, the first ICOS layers are found for n = 12 and 54 cluster sizes, respectively. The binding energy and the second energy difference as a function of cluster size are used to evaluate the relative stability of K + Arn clusters. The obtained data are in concordance with the available results in the literature.

Does the Sign of Charge Affect the Surface Affinity of Simple Ions?

The role the charge sign of simple ions plays in determining their surface affinity in aqueous solutions is investigated by computer simulation methods. For this purpose, the free surface of aqueous solutions of fictitious salts is simulated at finite concentration both with nonpolarizable point-charge and polarizable Gaussian-charge potential models. The salts consist of monovalent cations and anions that are, apart from the sign of their charge, identical to each other. In particular, we consider the small Na+ and the large I- ions together with their charge-inverted counterparts. In an attempt to avoid the interference even between the behavior of cations and anions, we also simulate systems containing only one of the above ions, and determine the free energy profile of these ions across the liquid-vapor interface of water at infinite dilution by potential of mean force (PMF) calculations. The obtained results reveal that, in the case of small ions, the anion is hydrated considerably stronger than the cation due to the close approach of water H atoms, bearing a positive fractional charge. As a consequence, the surface affinity of a small anion is even smaller than that of its cationic counterpart. However, considering that small ions are effectively repelled from the water surface, the importance of this difference is negligible. Further, a change in the hydration energy trends of the two oppositely charged ions is observed with their increasing size. This change is largely attributed to the fact that, with increasing ion size, the factor of 2 in the magnitude of the fractional charge of the closely approaching water atoms (i.e., O around cations and H around anions) outweighs the closer approach of the H than the O atom in the hydration energy. Thus, for large ions, being already surface active themselves, the surface affinity of the anion is larger than that of its positively charged counterpart. Further, such a difference is seen even in the case when the sign of the surface potential favors the adsorption of cations.

The Polarizable continuum potential model in the liquid state Calculations. Density functional computational analysis of the anharmonic vibrational spectrum of liquid water

A Density Functional calculation, using the Gaussian 03 W protocol with the B3LYP functional and the SCRF-Polarizable Continuum model (SCRF-PCM), has been performed on a pentameric unit, constituted by a central water molecule tetrahedrically coordinated to four other surrounding molecules by hydrogen bond (HB) interactions. The calculation has been aimed at reproducing vibrational distributions of the intra-molecular and intermolecular modes, which contribute at widening the stretching and bending OH bands in the liquid vibrational spectrum, and those at low frequencies, commonly considered intermolecular motions of O-H…O stretching and bending type, in the HB tetrahedral network of liquid water. The so called librational large distribution has been also nicely reproduced by this calculation. Energetic and geometrical considerations have been discussed for the equilibrium structure of this pentameric assembly, representing the basic unit presently used to simulate more space-extended structures of liquid water. These are constituted by different domains of ordered (open, or ice-like) and unordered (closed) patches of water clusters. Although the small cluster used in this calculation represents only an approximation to treat the real organization existing in the liquid water complex system, our results seems to reproduce quite well both the vibrational spectrum and the energetic and geometric situations for this very important liquid.

Hydrogen-Bonding Polarizable Intermolecular Potential Model for Water.

A polarizable intermolecular potential model with short-range directional hydrogen-bonding interactions was developed for water. The model has a rigid geometry, with bond lengths and angles set to experimental gas-phase values. Dispersion interactions are represented by the Buckingham potential assigned to the oxygen atom, whereas electrostatic interactions are modeled by Gaussian charges. Polarization is handled by a Drude oscillator site, using a negative Gaussian charge attached to the oxygen atom by a harmonic spring. An explicit hydrogen-bonding term is included in the model to account for the effects of charge transfer. The model parameters were optimized to density, configurational energy, pair correlation function, and the dielectric constant of water under ambient conditions, as well as the minimum gas-phase dimer energy. Molecular dynamics and Gibbs ensemble Monte Carlo simulations were performed to evaluate the new model with respect to the thermodynamic and transport properties over a wide range of temperature and pressure conditions. Good agreement between model predictions and experimental data was found for most of the properties studied. The new model yields better performance relative to the majority of existing models and outperforms the BK3 model, which is one of the best polarizable models, for vapor-liquid equilibrium properties, whereas the new model is not better than the BK3 model for representation of other properties. The model can be efficiently simulated with the thermalized Drude oscillator algorithm, resulting in computational costs only 3 times higher than those of the nonpolarizable TIP4P/2005 model, whereas having significantly improved properties. Because it involves only a single Drude oscillator site, the new model is significantly faster than polarizable models with multiple sites. With the explicit inclusion of hydrogen-bond interactions, the model may provide a better description of the phase behavior of aqueous mixtures.

Gaussian-Charge Polarizable and Nonpolarizable Models for CO2.

A polarizable intermolecular potential model using three classical Drude oscillators on the atomic sites has been developed for CO2. The model is rigid with bond lengths and molecular geometries set to their experimental values. Electrostatic interactions are represented by three Gaussian charges connected to the molecular frame by harmonic springs. Nonelectrostatic interactions are represented by the Buckingham exponential-6 potential, with potential parameters optimized to vapor-liquid equilibria (VLE) data. A nonpolarizable CO2 model that shares the other ingredients of the polarizable model was also developed and optimized to VLE data. Gibbs ensemble Monte Carlo and molecular dynamics simulations were used to evaluate the two models with respect to a variety of thermodynamic and transport properties, including the enthalpy of vaporization, second virial coefficient, density in the one-phase fluid region, isobaric and isochoric heat capacities, radial distribution functions, self-diffusion coefficient, and shear viscosity. Excellent agreement between model predictions and experimental data was found for all properties studied. The polarizable and nonpolarizable models provide a similar representation of CO2 properties, which indicates that the properties of pure CO2 fluid are not strongly affected by polarization. The polarizable model, which has an order of magnitude higher computational cost than the nonpolarizable model, will likely be useful for the study of a mixture of CO2 and polar components for which polarization is important.

Computer Simulation of Methanol Exchange Dynamics around Cations and Anions.

In this paper, we present the first computer simulation of methanol exchange dynamics between the first and second solvation shells around different cations and anions. After water, methanol is the most frequently used solvent for ions. Methanol has different structural and dynamical properties than water, so its ion solvation process is different. To this end, we performed molecular dynamics simulations using polarizable potential models to describe methanol-methanol and ion-methanol interactions. In particular, we computed methanol exchange rates by employing the transition state theory, the Impey-Madden-McDonald method, the reactive flux approach, and the Grote-Hynes theory. We observed that methanol exchange occurs at a nanosecond time scale for Na(+) and at a picosecond time scale for Cs(+), Cl(-), and I(-). We also observed a trend in which, for like charges, the exchange rate is slower for smaller ions because they are more strongly bound to methanol.

Computational Studies of [bmim][PF6]/n-Alcohol Interfaces with Many-Body Potentials

In this paper, we present the results from molecular dynamics simulations of the equilibrium properties of liquid/liquid interfaces of room temperature ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) and simple alcohols (i.e., methanol, 1-butanol, and 1-hexanol) at room temperature. Polarizable potential models are employed to describe the interactions among species. Results from our simulations show stable interfaces between the ionic liquid and n-alcohols, and we found that the interfacial widths decrease from methanol to 1-butanol systems and then increase for 1-hexanol interfaces. Angular distribution analysis reveals that the interface induces a strong orientational order of [bmim] and n-alcohol molecules near the interface, with [bmim] extending its butyl group into the alcohol phase, whereas the alcohol has the OH group pointing into the ionic liquid region, which is consistent with the recent sum-frequency-generation experiments. We found the interface to have a significant influence on the dynamics of ionic liquids and n-alcohols. The orientational autocorrelation functions illustrate that [bmim] rotates more freely near the interface than in the bulk, whereas the rotation of n-alcohol is hindered at the interface. Additionally, the time scale associated with the diffusion along the interfacial direction is found to be faster for [bmim] but slowed down for n-alcohols approaching the interface. We also calculate the dipole moment of n-alcohols as a function of the distance normal to the interface. We found that, even though methanol and 1-butanol have different dipole moments in bulk phase, they reach a similar value at the interface.

Computational studies of water exchange around aqueous Li+ with polarizable potential models

To enhance our understanding of the mechanism of water-exchange around aqueous Li(+), we carried out a systematic study on this system using molecular dynamics simulations with polarizable potential models. The mechanistic properties associated with the water-exchange process, such as potentials of mean force, time dependent transmission coefficients, and the corresponding rate constants, were examined using transition rate theory, the reactive flux method, and Grote-Hynes treatments of the dynamic response of the solvent. We compared the computed rate theory results with results from previous corresponding studies in which classical non-polarizable force fields were used. Our computed barrier heights for water exchange are significantly larger than those obtained using classical non-polarizable force fields. We also studied the effect of pressure on water-exchange rates and the corresponding activation volume. Our computed rate results for water exchange increase with pressure; therefore, a small negative activation volume is observed.

Cation−π Interactions: Accurate Intermolecular Potential from Symmetry-Adapted Perturbation Theory

Symmetry-adapted perturbation theory (SAPT) is used to decompose the total intermolecular interaction energy between the ammonium cation and a benzene molecule into four physically motivated individual contributions: electrostatics, exchange, dispersion, and induction. Based on this rigorous decomposition, it is shown unambiguously that both the electrostatic and the induction energy components contribute almost equally to the attractive forces stabilizing the dimer with a nonnegligible contribution coming from the dispersion term. A polarizable potential model for the interaction of ammonium cation with benzene is parametrized by fitting these four energy components separately using the functional forms of the AMOEBA force field augmented with the missing charge penetration energy term calculated as a sum over pairwise electrostatic energies between spherical atoms. It is shown that the proposed model is able to produce accurate intermolecular interaction energies as compared to ab initio results, thus avoiding error compensation to a large extent.

Comparison of select polarizable and non-polarizable water models in predicting solvation dynamics of water confined between MgO slabs

We present a molecular dynamics simulation study in which we compare and contrast the performance of a polarizable shell water potential model and non-polarizable water force field-extended simple point charge (SPC/EF) model in predicting the solvation dynamics of confined water molecules sandwiched between MgO(100) slabs. Structural features based on radial distribution functions, atomic density profiles, adsorption patterns, orientational ordering and dynamical correlations such as diffusional characteristics, hydrogen bonding lifetimes and residence probabilities are used as metrics for comparison. The simulations yield significant ordering of water molecules in the two layers adjacent to the oxide interface and the extent of ordering decreases with increasing distance from the oxide–water interface. These results elucidate that the dependence of local ordering and solvation dynamics on the molecular geometry and charge distribution, observed for typical three- and four-site water models, is generally lost for confined water if polarization is explicitly included. While the interfacial water structure predicted by the polarizable and non-polarizable models are similar, the confinement and interface proximity effects on the solvation dynamics are seen to be more pronounced for polarizable water models in comparison to non-polarizable ones. The study also shows that the polarizable water model over predicts the orientational order and under predicts the transport properties of confined water. In addition, analysis of the orientational preferences and hydrogen bonding characteristics of water near oxide interfaces suggests a higher degree of tetrahedral disorder in the polarizable shell compared to the non-polarizable SPC/E flexible model. The origin of the differences in solvation behavior of confined water between oxide slabs is analyzed based on the energetic contributions of the dispersive and electrostatic terms in the two force fields. Our findings suggest some new considerations regarding the role of polarization terms in predicting confinement and interface proximity effects that may guide future development of reliable polarizable water models for confined liquids.

Molecular Dynamics Investigation of Alkali Metal Ions in Liquid and Aqueous Ammonia

A polarizable potential model for M(+)-NH3 interactions (M(+) = Li(+), Na(+), K(+), Rb(+), Cs(+)) is optimized based on the ab initio properties of the ion-ammonia dimers calculated at the MP2 level of theory. The optimized model reproduces the ab initio binding energies of M(+)(NH3)n (n = 2-4) and M(+)(NH3)n(H2O)m (n, m = 1-3 and n + m ≤ 4) clusters and gives relative solvation free energies in liquid ammonia in good agreement with experimental data, without further adjustments. It also reproduces binding cooperativity in ion-ammonia and ion-ammonia-water clusters. The model is used in molecular dynamics simulations of isolated ions in liquid ammonia and in aqueous ammonia solutions with various ammonia molar fractions (0.0 ≤ xNH3 ≤ 1.0). Simulations in liquid ammonia show coordination numbers of 4.0 for Li(+), 5.3 for Na(+), 6.1 for K(+), 6.7 for Rb(+), and 7.7 for Cs(+), in very good agreement with available experimental results. Simulations of ions in aqueous ammonia show preferential solvation by water in their first solvation shells and preferential solvation by ammonia in their second shells. Potentials of mean force are calculated between each ion and NH3 in liquid water, and between each ion and H2O in liquid ammonia. The results suggest that, in liquid water, Li(+) and Na(+) bind NH3 in their second solvation shells only, while Cs(+) binds NH3 in its first solvation shell only (K(+) and Rb(+) ions show only weak affinity for NH3 in water). In liquid ammonia, the ions bind H2O in their first solvation shells with an affinity following the trend Li(+) > Na(+) > K(+) ≈ Rb(+) > Cs(+).

Molecular Mechanism of Specific Ion Interactions between Alkali Cations and Acetate Anion in Aqueous Solution: A Molecular Dynamics Study

Specific ion interactions between alkali cations (i.e., Li(+), Na(+), and K(+)) and an acetate anion in aqueous solution were studied using molecular dynamics simulation techniques and polarizable potential models. The ions-acetate systems were used as a model for understanding the interactions between ions and protein surfaces. We computed free energy profiles for different ion pairs using constrained mean force methods. Upon analyzing the computed free energy profiles for the Na(+)/K(+)-acetate ion-pairs, we observed a deeper contact ion minimum and also a larger association constant for the Na(+)-acetate pair as compared to the corresponding K(+)-acetate pair. These observations help to demonstrate the preferential binding of Na(+) over K(+) to protein surfaces. We also applied various rate theories to study the kinetics of ion pair interconversion.

Note: Interionic potentials of mean force for Ca2+-Cl− in polarizable water

We describe our molecular dynamics simulation studies of the inter-ionic potentials of mean force (PMF) for the Ca2+-Cl− ion pair in water. Ion-water and ion-ion polarizable potential models were constructed to reproduce experimental ion-hydration enthalpies as well as the electronic-structure calculations of the minimum energy for the Ca2+-Cl− interactions. Our study predicted a PMF with no contact ion pair state and a shallow solvent-separated ion-pair state. In addition, our computed radial distribution function, gCa-Cl, for a 1-M CaCl2 electrolyte solution indicated that there is no contact ion pair but, instead, showed a maximum near 5 Å. This observation is consistent with our PMF calculation. These new results are discussed and compared to the recent classical and ab initio PMF calculations on the same system reported by Timko et al. [J. Chem. Phys. 134, 204510 (2011)]10.1063/1.3595261.

A distributed point polarizable force field for carbon dioxide

A distributed point polarizable model potential for carbon dioxide, with explicit terms for charge penetration and induction, is introduced. This model potential accurately describes the structures and interaction energies of small (CO2) n clusters and also gives the second virial coefficients and radial distribution functions of supercritical CO2 in excellent agreement with experiment.

Cation-π and π-π Interactions in Aqueous Solution Studied Using Polarizable Potential Models.

Polarizable potential models for the interaction of Li(+), Na(+), K(+), and NH4(+) ions with benzene are parametrized based on ab initio quantum mechanical calculations. The models reproduce the ab initio complexation energies and potential energy surfaces of the cation-π dimers. They also reproduce the cooperative behavior of "stacked", cation-π-π trimers and the anticooperative behavior of "sandwiched", π-cation-π trimers. The NH4(+) model is calibrated to reproduce the energy of the NH4(+)-H2O dimer and yields correct free energy of hydration and hydration structure without further adjustments. The models are used to investigate cation-π interactions in aqueous solution by calculating the potential of mean force between each of the four cations and a benzene molecule and by analyzing the organization of the solvent as a function of the cation-benzene separation. The results show that Li(+) and Na(+) ions are preferentially solvated by water and do not associate with benzene, while K(+) and NH4(+) ions bind benzene with 1.2 and 1.4 kcal/mol affinities, respectively. Molecular dynamics simulations of NH4(+) and of K(+) in presence of two benzene molecules in water show that cation-π and π-π affinities are mutually enhanced compared to the pairwise affinities, confirming that the cooperativity of cation-π and π-π interactions persists in aqueous solution.

Computational Studies of Aqueous Interfaces of SrCl2 Salt Solutions

The electron density profiles and corresponding surface structures of an aqueous interface of SrCl(2) salt solution were computed by use of molecular dynamics simulations. We used both polarizable and nonpolarizable potential models to describe molecular interactions. The results demonstrate that the polarizable models captured the essential features of the corresponding X-ray reflectivity experimental data while the corresponding nonpolarizable models could not. In addition, we demonstrated that the shape of the X-ray reflectivity curve could be quantitatively reproduced if the simulations were carried out at lower SrCl(2) concentrations, making it likely that the polarizable models used in this study somewhat overestimate the surface concentration of ions. However, significant interfacial enhancement of both Sr(2+) and Cl(-) appears necessary to reproduce the experimental spectra. This is in contrast to systems with monovalent cations, which have generally been found to have a double layer, in which anions are enhanced at the surface but cations are repelled.

A fast path integral method for polarizable force fields

A quantum simulation of an imaginary time path integral typically requires around n times more computational effort than the corresponding classical simulation, where n is the number of ring polymer beads (or imaginary time slices) used in the calculation. It is however possible to improve on this estimate by decomposing the potential into a sum of slowly and rapidly varying contributions. If the slowly varying contribution changes only slightly over the length scale of the ring polymer, it can be evaluated on a contracted ring polymer with fewer than the full n beads (or equivalently on a lower order Fourier decomposition of the imaginary time path). Here we develop and test this idea for systems with polarizable force fields. The development consists of iterating the induction on the contracted ring polymer and applying an appropriate transformation to obtain the forces on the original n beads. In combination with a splitting of the Coulomb potential into its short- and long-range parts, this results in a method with little more than classical computational effort in the limit of large system size. The method is illustrated with simulations of liquid water at 300 K and hexagonal ice at 100 K using a recently developed flexible and polarizable Thole-type potential energy model.

Computational studies of aqueous interfaces of RbBr salt solutions

We computed the structure factor and the corresponding x-ray reflectivity of an aqueous interface of RbBr salt solution and used molecular dynamics techniques to compare polarizable and nonpolarizable potential models for molecular interaction. Our computed electron and number density profiles clearly demonstrate that the polarizable Br(-) anions are enhanced at the water/vapor surface while the nonpolarizable Br(-) anions are depleted from it. The observation of Br(-) ions at the interface contradicts a recent interpretation that was based on experimentally measured x-ray reflectivity data.

Computational Studies of Structures and Dynamics of 1,3-Dimethylimidazolim Salt Liquids and their Interfaces Using Polarizable Potential Models

The structures, thermodynamics, and dynamical properties of bulk and air/liquid interfaces of three ionic liquids, 1,3-dimethylimidazolium [dmim](+) with Cl(-), Br(-), and I(-) were studied using molecular dynamics techniques and polarizable potential models. In bulk melts, the radial distribution functions reveal a significant long-range structural correlation in these ionic liquids. The single-ion dynamics are studied via mean-square-displacements, velocity and orientational correlation functions. We observe that anion size plays an important role in the dynamics of ionic liquids, with larger anions inducing faster cation and anion motion. The computed density profiles of the ionic liquid/vapor interface exhibit oscillatory behavior, indicative of surface layering at the interface. The computed surface tensions indicate small differences between these ionic liquids and decrease with the increasing anion size. The magnitudes of the computed potential drops of these ionic liquids are found to be small and negative and increase with the decreasing anion size. These results could imply that the cation dipoles on average orient more in the interfacial plane than perpendicular to it. Our results showed that anion type plays a major role in determining IL interfacial behavior.

Structural and thermodynamic properties of different phases of supercooled liquid water

Computer simulation results are reported for a realistic polarizable potential model of water in the supercooled region. Three states, corresponding to the low density amorphous ice, high density amorphous ice, and very high density amorphous ice phases are chosen for the analyses. These states are located close to the liquid-liquid coexistence lines already shown to exist for the considered model. Thermodynamic and structural quantities are calculated, in order to characterize the properties of the three phases. The results point out the increasing relevance of the interstitial neighbors, which clearly appear in going from the low to the very high density amorphous phases. The interstitial neighbors are found to be, at the same time, also distant neighbors along the hydrogen bonded network of the molecules. The role of these interstitial neighbors has been discussed in connection with the interpretation of recent neutron scattering measurements. The structural properties of the systems are characterized by looking at the angular distribution of neighboring molecules, volume and face area distribution of the Voronoi polyhedra, and order parameters. The cumulative analysis of all the corresponding results confirms the assumption that a close similarity between the structural arrangement of molecules in the three explored amorphous phases and that of the ice polymorphs I(h), III, and VI exists.