Molecular dynamics study of polarization effects on AgI

Three different models of AgI are studied by molecular dynamics simulations. The first one is the rigid ion model (RIM) with the effective pair potential of the Vashishta and Rahman form and the parametrization proposed by Shimojo and Kobayashi. The other two are polarizable ion models in which the induced polarization effects have been added to the RIM effective pair potential. In one of them (PIM1), only the anions are assumed to be polarizable by the local electric field. In the other one (PIM2s), the silver polarization is also included, and a short-range overlap-induced polarization opposes the electrically induced dipole moments. This short-range polarization is proved to be necessary to avoid overpolarization when both species are assumed to be polarizable. The three models reproduce the superionic character of alpha-AgI at 573 K and the liquid behavior of molten AgI at 923 K. The averaged spatial distribution of the cations in the alpha-phase obtained for PIM1 appears to be in better agreement with experimental data analysis. The PIM1 also reproduces the structure factor prepeak at about 1 A(-1) observed from neutron diffraction data of molten AgI. The three models retain in the liquid phase the superionic character of alpha-AgI, as the mobility of the cations is significantly larger than that for the anions. The ionic conductivity for the polarizable ion models is in better agreement with experimental data for alpha-AgI and molten AgI.     

Molecular dynamics study of polarizable point dipole models for molten sodium iodide

The structure, the ionic transport properties, and the dynamics of long-wavelength charge-density fluctuations, for two polarizable point dipole models of molten NaI, have been studied by molecular dynamics simulations. These models are based on a rigid ion potential to which the induced dipole polarization of the anions is added. The polarization is added in such a way that point dipoles are induced on the anions by both local electric field and short-range damping interactions that oppose the electrically induced dipole moments. The two polarizable ion models differ only in the range of the damping polarization interactions. The influence of the induced anion polarization on the different properties of simulated molten NaI is discussed.     

Ab initio based polarizable force field parametrization

Experimental and simulation studies of anion-water systems have pointed out the importance of molecular polarization for many phenomena ranging from hydrogen-bond dynamics to water interfaces structure. The study of such systems at molecular level is usually made with classical molecular dynamics simulations. Structural and dynamical features are deeply influenced by molecular and ionic polarizability, which parametrization in classical force field has been an object of long-standing efforts. Although when classical models are compared to ab initio calculations at condensed phase, it is found that the water dipole moments are underestimated by approximately 30%, while the anion shows an overpolarization at short distances. A model for chloride-water polarizable interaction is parametrized here, making use of Car-Parrinello simulations at condensed phase. The results hint to an innovative approach in polarizable force fields development, based on ab initio simulations, which do not suffer for the mentioned drawbacks. The method is general and can be applied to the modeling of different systems ranging from biomolecular to solid state simulations.     

Conformational simulations of aqueous solvated alpha-conotoxin GI and its single disulfide analogues using a polarizable force field model

The solution conformation of alpha-conotoxin GI and its two single disulfide analogues are simulated using a polarizable force field in combination with the molecular fragmentation quantum chemical calculation. The polarizability is explicitly described by allowing the partial charges and fragment dipole moments to be variables, with values coming from the linear-scaling energy-based molecular fragmentation calculations at the B3LYP/6-31G(d) level. In comparison with the full quantum chemical calculations, the fragmentation approaches can yield precise ground-state energies, dipole moments, and static polarizabilities for peptides. The B3LYP/6-31G(d) charges and fragment-centered dipole moments are introduced in calculations of electrostatic terms in both AmberFF03 and OPLS force fields. Our test calculations on the gas-phase glucagon (PDB code: 1gcn) and solvated alpha-conotoxin GI (PDB code: 1not) demonstrate that the present polarization model is capable of describing the structural properties (such as the relative conformational energies, intramolecular hydrogen bonds, and disulfide bonds) with accuracy comparable to some other polarizable force fields (ABEEM/MM and OPLS-PFF) and the quantum mechanics/molecular mechanics (QM/MM) hybrid model. The employment of fragment-centered dipole moments in calculations of dipole-dipole interactions can save computational time in comparison with those polarization models using atom-centered dipole moments without much loss of accuracy. The molecular dynamics simulations using the polarizable force field demonstrate that two single disulfide GI analogues are more flexible and less structured than the native alpha-conotoxin GI, in agreement with NMR experiments. The polarization effect is important in simulations of the folding/unfolding process of solvated proteins.     

Electric dipole moments in polar solvents. II. Tetraisoamylammonium nitrate ion pairs in chlorobenzene. Effect of mutual polarization of the ions

The dielectric constant and conductivity of dilute solutions of tetraisoamylammonium nitrate in chlorobenzene are measured between –34.6° and 99.0°C to give association constants for the formation of ion pairs (K _A) and triple ions, and electric dipole moments. The quantityK _A as a function of temperature is reproduced by the Denison-Ramsey-Fuoss treatment for unolarized ion pairs [Eq. (2)] with a distance of closest approach of 4.90 Å. The dielectric data are reproduced by Onsager's equation with an inherent (gas-phase) dipole moment of the ion pairs of 14.2±0.3 D. Other methods of calculation lead to consistent dipole moments, confirming that the mutual polarization of the ions is important. The energetics of ionic association is considered on the basis that the ion pair may be treated as a polarizable dipole in a spherical cavity.     

The influence of polarizability on the dielectric spectrum of the ionic liquid 1-ethyl-3-methylimidazolium triflate

This work reports for the first time the computational, frequency-dependent dielectric spectrum of the polarizable molecular ionic liquid 1-ethyl-3-methylimidazolium triflate as well as its experimental analogue. In the frequency range from 500 MHz up to 20 GHz the agreement between the computational and the experimental spectrum is quantitative. For higher frequencies up to 10 THz the agreement is still remarkably good. The experimental asymptotic limit ε(∞) is 2.3. The difference in the computational value of 1.9 comes solely from the neglect of polarizability of the hydrogen atoms. For reasons of efficiency the simulations are based on the Lagrangian algorithm for the Drude oscillator model which cannot handle polarizable hydrogens. In the computational analysis the complete spectrum of the generalized dielectric constant ∑(0)*(ν) is splitted into its translational and non-translational components, called dielectric conductivity ?(0)(ν) and dielectric permittivity ε(ν). For 1-ethyl-3-methylimidazolium triflate both components contribute with equal weight and overlap in the complete frequency range. The inclusion of polarization forces, however, is quite different for the two components: the collective non-translational dynamics is accelerated and hence the dielectric permittivity is shifted to higher frequencies. The low frequency region of the dielectric conductivity is also affected while its high frequency part remains almost unchanged. Inductive effects are not only visible at high frequencies but also contribute in the sub-GHz region. The computational peak found in this region correlates with the experimental OKE-spectrum. It may be interpreted as the correlation between the induced dipole moment of the cations and the local electric field exerted by the anionic cage.     

Electrostatic properties of aqueous salt solution interfaces: a comparison of polarizable and nonpolarizable ion models

The effects of ion force field polarizability on the interfacial electrostatic properties of approximately 1 M aqueous solutions of NaCl, CsCl, and NaI are investigated using molecular dynamics simulations employing both nonpolarizable and Drude-polarizable ion sets. Differences in computed depth-dependent orientational distributions, "permanent" and induced dipole and quadrupole moment profiles, and interfacial potentials are obtained for both ion sets to further elucidate how ion polarizability affects interfacial electrostatic properties among the various salts relative to pure water. We observe that the orientations and induced dipoles of water molecules are more strongly perturbed in the presence of polarizable ions via a stronger ionic double layer effect arising from greater charge separation. Both anions and cations exhibit enhanced induced dipole moments and strong z alignment in the vicinity of the Gibbs dividing surface (GDS) with the magnitude of the anion induced dipoles being nearly an order of magnitude larger than those of the cations and directed into the vapor phase. Depth-dependent profiles for the trace and z z components of the water molecular quadrupole moment tensors reveal 40% larger quadrupole moments in the bulk phase relative to the vapor which mimics a similar observed 40% increase in the average water dipole moment. Across the GDS, the water molecular quadrupole moments increase nonmonotonically (in contrast to the water dipoles) and exhibit a locally reduced contribution just below the surface due to both orientational and polarization effects. Computed interfacial potentials for the nonpolarizable salts yield values 20-60 mV more positive than pure water and increase by an additional 30-100 mV when ion polarizability is included. A rigorous decomposition of the total interfacial potential into ion monopole, water and ion dipole, and water quadrupole components reveals that a very strong, positive ion monopole contribution is offset by negative contributions from all other potential sources. Water quadrupole components modulated by the water density contribute significantly to the observed interfacial potential increments and almost entirely explain observed differences in the interfacial potentials for the two chloride salts. By lumping all remaining nonquadrupole interfacial potential contributions into a single "effective" dipole potential, we observe that the ratio of quadrupole to "effective" dipole contributions range from 2:1 in CsCl to 1:1.5 in NaI, suggesting that both contributions are comparably important in determining the interfacial potential increments. We also find that oscillations in the quadrupole potential in the double layer region are opposite in sign and partially cancel those of the "effective" dipole potential.     

An efficient parallelization scheme for molecular dynamics simulations with many-body, flexible, polarizable empirical potentials: application to water

An efficient parallelization scheme for classical molecular dynamics simulations with flexible, polarizable empirical potentials is presented. It is based on the standard Ewald summation technique to handle the long-range electrostatic and induction interactions. The algorithm for this parallelization scheme is designed for systems containing several thousands of polarizable sites in the simulation box. Its performance is evaluated during molecular dynamics simulations under periodic boundary conditions with unit cell sizes ranging from 128 to 512 molecules employing two flexible polarizable water models [DC(F) and TTM2.1-F] containing 1 and 3 polarizable sites, respectively. The time-to-solution for these two polarizable models is compared with the one for a flexible, pairwise-additive water model (TIP4F). The benchmarks were performed on both shared and distributed memory platforms. As a result of the efficient calculation of the induced dipole moments, a superlinear scaling as a function of the number of the processors is observed. To the best of our knowledge, this is the first reported results of parallel scaling and performance for simulations of liquid water with a polarizable potential under periodic boundary conditions.     

Analytic energy gradient in combined second-order Møller-Plesset perturbation theory and polarizable force field calculation

Second-order M?ller-Plesset perturbation theory (MP2) is used to describe electronic correlation on the basis of Hartree-Fock (HF) variational calculations that incorporate induced dipole polarizable force fields (i.e., QM/MMpol style HF and MP2). The Z-vector equations for regular closed shell and open shell MP2 methods (RMP2, ZAPT2, and UMP2) are extended to include induced dipole contributions to determine the MP2 response density so that nuclear gradient and other properties can be efficiently evaluated. A better estimation of the induced dipole polarization energy can be obtained using the MP2 relaxed density. QM/MMpol style MP2 molecular dynamics simulations are performed for the ground state and first triplet state of acetone solvated by 1024 polarizable water molecules. A switching function is used to ensure energy conservation in QM/MM simulation under periodic boundary condition.     

CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.     

Evaluating polarizable potentials on distributed memory parallel computers: Program development and applications

The efficient evaluation of polarizable molecular mechanics potentials on distributed memory parallel computers is discussed. The program executes at 7–10 Mflops/node on a 32-node CM-5 partition and is 19 times faster than comparable code running on a single-processor HP 9000/735. On the parallel computer, matrix inversion becomes a practical alternative to the commonly used iterative method for the calculation of induced dipole moments. The former method is useful in cases such as free-energy perturbation (FEP) simulations, which require highly accurate induced dipole moments. Matrix inversion is performed 110 times faster on the CM-5 than on the HP. We show that the accuracy which is needed for FEP calculations with polarization can be obtained by either matrix inversion or by performing a large number of iteration cycles to satisfy convergence tolerances that are less than 10^?6 D. © 1995 by John Wiley & Sons, Inc.     

High-performance scalable molecular dynamics simulations of a polarizable force field based on classical Drude oscillators in NAMD

Incorporating the influence of induced polarization in large-scale atomistic molecular dynamics (MD) simulations is a critical challenge in the progress toward computations of increased accuracy. One computationally efficient treatment is based on the classical Drude oscillator in which an auxiliary charged particle is attached by a spring to each nucleus. Here, we report the first implementation of this model in the program NAMD. An extended Lagrangian dynamics with a dual-Langevin thermostat scheme applied to the Drude-nucleus pairs is employed to efficiently generate classical dynamic propagation near the self-consistent field limit. Large-scale MD simulations based on the Drude polarizable force field scale very well on massively distributed supercomputing platforms, the computational demand being only about 50-100% higher than for nonpolarizable models. As an illustration, a large-scale 150 mM NaCl aqueous salt solution is simulated, and the calculated ionic conductivity is shown to be in excellent agreement with experiment.     

Polarizable and nonpolarizable force fields for alkyl nitrates

Quantum-chemistry-based many-body polarizable and two-body nonpolarizable atomic force fields were developed for alkyl nitrate liquids and pentaerythritol tetranitrate (PETN) crystal. Bonding, bending, and torsional parameters, partial charges, and atomic polarizabilities for the polarizable force field were determined from gas-phase quantum chemistry calculations for alkyl nitrate oligomers and PETN performed at the MP2/aug-cc-pvDz level of theory. Partial charges for the nonpolarizable force field were determined by fitting the dipole moments and electrostatic potential to values for PETN molecules in the crystal phase obtained from molecular dynamics simulations using the polarizable force field. Molecular dynamics simulations of alkyl nitrate liquids and two polymorphs of PETN crystal demonstrate the ability of the quantum-chemistry-based force fields to accurately predict thermophysical and mechanical properties of these materials.     

Comparing reduced partial charge models with polarizable simulations of ionic liquids

Molecular ionic liquids are typically characterized by strong electrostatic interactions resulting in a charge ordering and retardation of their translational and rotational behaviour. Unfortunately, this effect is often overestimated in classical molecular dynamics simulations. This can be circumvented in a twofold way: the easiest way is to reduce the partial charges of the ions to sub-integer values of ±0.7-0.9 e. The more realistic model is to include polarizable forces, e.g. Drude-oscillators, but it comes along with an increasing computational effort. On the other hand, charge-scaled models are claimed to take an average polarizability into account. But do both models have the same impact on structure and dynamics of molecular ionic liquids? In the present study several molecular dynamics simulations of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate are performed with different levels of polarization as well as with varying charge scaling factors of 0.74 to 0.90. The analysis of the structural and dynamical results are performed in different levels: from the atomic point of view over the molecular level to collective properties determined by the complete sample.     

Structure of the liquid-vacuum interface of room-temperature ionic liquids: a molecular dynamics study

Molecular dynamics simulations for the liquid-vacuum interface of the ionic liquid 1-ethyl-3-methylimidazolium nitrate (EMIM+/NO3-) were performed for both electronically polarizable and nonpolarizable potential energy surfaces. The interfacial structural properties, such as the oscillation in the number density profile, the orientational ordering, and the local clustering in the interfacial region, were calculated. The simulations with both the polarizable and nonpolarizable model demonstrate the existence of an inhomogeneous interfacial structure normal to the surface layer. It was found for both models that the ethyl tail group on EMIM+ is likely to protrude outward from the surface. In the outmost surface layer, the cation is likely to lie on the surface with the imidazolium ring parallel to the interface, while there is a second region with enhanced density from that in the bulk where the cation preferably slants with the imidazolium ring tending to be perpendicular to the surface. The results also reveal that the electronic polarization effect is important for the ionic liquid interface. It is found that the cation is likely to be segregated at the ionic liquid surface for the polarizable model, while for the nonpolarizable model, the anion is found to be more likely to exhibit such behavior. The surface tension of the polarizable model (58.5 +/- 0.5 mN/m) is much smaller than that of the nonpolarizable model (82.7 +/- 0.6 mN/m), in better agreement with extrapolated experimental measurements on similar ionic liquid systems.     

Drude polarizable force field for aliphatic ketones and aldehydes,and their associated acyclic carbohydrates

The majority of computer simulations exploring biomolecular function employ Class I additive force fields (FF), which do not treat polarization explicitly. Accordingly, much effort has been made into developing models that go beyond the additive approximation. Development and optimization of the Drude polarizable FF has yielded parameters for selected lipids, proteins, DNA and a limited number of carbohydrates. The work presented here details parametrization of aliphatic aldehydes and ketones (viz. acetaldehyde, propionaldehyde, butaryaldehyde, isobutaryaldehyde, acetone, and butanone) as well as their associated acyclic sugars (d-allose and d-psicose). LJ parameters are optimized targeting experimental heats of vaporization and molecular volumes, while the electrostatic parameters are optimized targeting QM water interactions, dipole moments, and molecular polarizabilities. Bonded parameters are targeted to both QM and crystal survey values, with the models for ketones and aldehydes shown to be in good agreement with QM and experimental target data. The reported heats of vaporization and molecular volumes represent a compromise between the studied model compounds. Simulations of the model compounds show an increase in the magnitude and the fluctuations of the dipole moments in moving from gas phase to condensed phases, which is a phenomenon that the additive FF is intrinsically unable to reproduce. The result is a polarizable model for aliphatic ketones and aldehydes including the acyclic sugars d-allose and d-psicose, thereby extending the available biomolecules in the Drude polarizable FF.     

Brownian dynamics simulation of a model simple electrolyte in solvents of low dielectric constant

Brownian dynamics simulations are performed to investigate the ionic transport of model simple electrolytes, in which ions are interacting with each other through the repulsive core and Coulombic interactions. The equivalent conductivity and self-diffusion coefficient show minima as the function of the number density of ions when the dielectric constant of the solvent is low. Although the minimum of the former is in harmony with various experiments, no experiment has ever been reported on that of the latter. The analysis of time-dependent transport coefficients reveals that the presence of the minima is ascribed to the slow dynamics, rather than to static association models. The inclusion of a model function that resembles the short-range part of the potential of mean force induced by solvent affects the transport coefficients qualitatively, which suggests the importance of solvent-induced potential of mean force in the conduction mechanism of electrolytes in solvents of low dielectric constant.     

Polarizable molecular dynamics simulation of Zn(II) in water using the AMOEBA force field

The hydration free energy, structure, and dynamics of the zinc divalent cation are studied using a polarizable force field in molecular dynamics simulations. Parameters for the Zn(2+) are derived from gas-phase ab initio calculation of Zn(2+)-water dimer. The Thole-based dipole polarization is adjusted based on the Constrained Space Orbital Variations (CSOV) calculation while the Symmetry Adapted Perturbation Theory (SAPT) approach is also discussed. The vdW parameters of Zn(2+) have been obtained by comparing the AMOEBA Zn(2+)-water dimerization energy with results from several theory levels and basis sets over a range of distances. Molecular dynamics simulations of Zn(2+) solvation in bulk water are subsequently performed with the polarizable force field. The calculated first-shell water coordination number, water residence time and free energy of hydration are consistent with experimental and previous theoretical values. The study is supplemented with extensive Reduced Variational Space (RVS) and Electron Localization Function (ELF) computations in order to unravel the nature of the bonding in Zn(2+)(H(2)O)(n) (n=1,6) complexes and to analyze the charge transfer contribution to the complexes. Results show that the importance of charge transfer decreases as the size of Zn-water cluster grows due to anticooperativity and to changes in the nature of the metal-ligand bonds. Induction could be dominated by polarization when the system approaches condensed-phase and the covelant effects are eliminated from the Zn(II)-water interaction. To construct an "effective" classical polarizable potential for Zn(2+) in bulk water, one should therefore avoid over-fitting to the ab initio charge transfer energy of Zn(2+)-water dimer. Indeed, in order to avoid overestimation of condensed-phase many-body effects, which is crucial to the transferability of polarizable molecular dynamics, charge transfer should not be included within the classical polarization contribution and should preferably be either incorporated in to the pairwise van der Waals contribution or treated explicitly.     

Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: comparison between experiments, analytical calculations and numerical simulations

We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.