Solvation of ions in liquid solvents and proteins

Despite their well-known drawbacks, the approaches of continuum electrostatics are widely used at the analysis of the energies of solvation and reorganization. We propose a method to check the applicability of these approaches in the determination of the solvation energy, which is based on measuring the difference of redox potentials ΔE of two consecutive redox reactions, e.g. for the pairs Co(Cp) ₂ ⁺ /Co(Cp)₂/Co(Cp) ₂ ^? (here, Cp is cyclopentadienyl). In this difference, the solvophobic effects and the liquid junction potential between the working and reference electrodes, which is impossible to measure, cancel out. From the difference of ΔE in two different solvents, the sum of the electrostatic components of the cation-and anion-transfer energies is determined. It is shown that, for large low-charged ions in aprotic media, the continuum electrostatics proves to be true in a wide range of dielectric permittivities including those typical for proteins. The Stokes shift of fluorescence spectra for proflavine (PF) showed that the water reorganization energy and, hence, the energy of the static dielectric response are anomalously high. To study this effect on the solvation energy, we determined the redox potentials of the Co(Cp) ₂ ⁺ /Co(Cp)₂ pair in a number of water-organic media. The organic cosolvent breaks the water structure and reduces the reorganization energy. Accordingly, the redox potential turns more positive. This allowed us to determine the energy of transfer of Co(Cp) ₂ ⁺ ions (and, hence, of other ions) nonviolated by the water structure specifics. The experimental energies of the acetate transfer exceed those calculated by an order of magnitude. This demonstrates the incorrectness of the widely used semicontinuum calculations of the pK of ionogenic groups of proteins. A new algorithm, which permits overcoming this discrepancy, is proposed, namely, the short-range interactions are taken into account based on the experimental energies of the transfer to a model DMF solvent, while the transfer energy from this solvent to the protein is calculated electrostatically. The energy of the ion charging in a protein consists of two physically different components, namely, the charging energy in the pre-existing field of protein dipoles and charges and the energy of the dielectric response of the medium. The former energy is determined by the electronic polarization of the protein (its optical dielectric permittivity), while the latter is determined by all kinds of polarization (static permittivity). Taking into account all the aforementioned peculiarities leads to reasonable agreement with the experiment when estimating the pK of certain groups in α-chymotrypsin. These calculations as well as experimental data (both our and taken form the literature (molecular dynamics)) point to the enhanced dielectric permittivity of the outer layers of proteins.     

An improved pairwise decomposable finite-difference Poisson-Boltzmann method for computational protein design

Our goal is to develop accurate electrostatic models that can be implemented in current computational protein design protocols. To this end, we improve upon a previously reported pairwise decomposable, finite difference Poisson-Boltzmann (FDPB) model for protein design (Marshall et al., Protein Sci 2005, 14, 1293). The improvement involves placing generic sidechains at positions with unknown amino acid identity and explicitly capturing two-body perturbations to the dielectric environment. We compare the original and improved FDPB methods to standard FDPB calculations in which the dielectric environment is completely determined by protein atoms. The generic sidechain approach yields a two to threefold increase in accuracy per residue or residue pair over the original pairwise FDPB implementation, with no additional computational cost. Distance dependent dielectric and solvent-exclusion models were also compared with standard FDPB energies. The accuracy of the new pairwise FDPB method is shown to be superior to these models, even after reparameterization of the solvent-exclusion model.     

Stopping powers and inelastic mean free path from quantitative analysis of experimental REELS spectra for electrons in Ti,Fe, Ni,and Pd

Stopping power (SP) and inelastic mean free path (IMFP) of electrons in Ti, Fe, Ni, and Pd have been determined by using dielectric models. We have used energy loss function (ELF) determined from quantitative analysis of experimental reflection electron energy loss spectroscopy (REELS) spectra as the input parameter for this model. ELF in this study was determined from the previously published quantitative analysis of REELS spectra. The SP of Fe, Ni, Pd, and Ti was compared with several calculation methods for energies from 100 eV to 10 keV and shows SP in this study, which are in best agreement for medium to high energies (greater than or equal to 300 eV). The IMFP obtained in this study shows the best agreement with online database TPP2M and NIST and also calculation by Tanuma with a root mean square (rms ) less than 12%. The present approach shows ELF from quantitative analysis of REELS spectra has a high potential for the experimental determination of SP and IMFP of metals.     

FACTS: Fast analytical continuum treatment of solvation

An efficient method for calculating the free energy of solvation of a (macro)molecule embedded in a continuum solvent is presented. It is based on the fully analytical evaluation of the volume and spatial symmetry of the solvent that is displaced from around a solute atom by its neighboring atoms. The two measures of solvent displacement are combined in empirical equations to approximate the atomic (or self) electrostatic solvation energy and the solvent accessible surface area. The former directly yields the effective Born radius, which is used in the generalized Born (GB) formula to calculate the solvent-screened electrostatic interaction energy. A comparison with finite-difference Poisson data shows that atomic solvation energies, pair interaction energies, and their sums are evaluated with a precision comparable to the most accurate GB implementations. Furthermore, solvation energies of a large set of protein conformations have an error of only 1.5%. The solvent accessible surface area is used to approximate the nonpolar contribution to solvation. The empirical approach, called FACTS (Fast Analytical Continuum Treatment of Solvation), is only four times slower than using the vacuum energy in molecular dynamics simulations of proteins. Notably, the folded state of structured peptides and proteins is stable at room temperature in 100-ns molecular dynamics simulations using FACTS and the CHARMM force field.     

Molecular and collective relaxations of ferroelectric side chain liquid crystalline polysiloxanes

The influences of mesogenic group chemical structures on dielectric relaxation behavior were investigated for ferroelectric side chain liquid crystalline polymers (FLCPs). The relaxation time and activation energies of the Goldstone mode, α‐, and β‐relaxations decrease with increasing spacer length because of the plasticizer effect of the spacer. Moreover, the relaxation intensity increases with increasing spacer length for FLCPs. An FLCP with a longer spacer length exhibits a higher mesogenic group mobility, and subsequently leads to easier reorientation toward the alternating electrical field. An increase in mesogenic core rigidity results in an increase in the relaxation time and activation energies, and a decrease in the relaxation intensities for the Goldstone mode, α‐, and β‐relaxations. Moreover, the β‐relaxation is suppressed and cannot be observed in the glassy state for FLCPs containing naphthyl biphenylcarboxylate as the mesogenic group. Shorter relaxation time, smaller activation energies, and higher intensity of the α‐, and β‐relaxations were obtained for FLCPs containing chiral moiety with a flexible heptyl alkyl chain. However, the relaxation intensity of the Goldstone mode for FLCPs containing this chiral moiety was smaller than that for FLCPs containing the chiral moiety with a butyl alkyl chain. For FLCPs containing a chiral moiety with two asymmetrical centers, their Goldstone mode relaxation showed larger amplitude. The α‐ and β‐relaxations are suppressed for these FLCPs because of the dense packing and memory effect of the smectic phase. The relationship between the chemical structure of the mesogenic group and dielectric relaxations is discussed in great detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2035–2049, 2006     

Ionic Conductivity in Solutions of Poly(ethylene oxide) and Lithium Perchlorate

Summary: Solution casting technique served to prepare solid solutions of lithium perchlorate and poly(ethylene oxide) (PEO) having different molecular masses. Salt concentrations of solutions were varied between around 2 and 13 wt%. Crystallinity and melting point depression served to determine composition and content of amorphous phase as well as thermodynamic behavior of the solutions. Conductivity as a function of salt concentration in the amorphous phase follows a power law at constant temperature (30 °C). It results that both exponent and mobility of charge carriers increase with ascending molecular mass of PEO. The mobility follows an increase with molecular mass proportional to M^2.8 indicating dependence of mobility on interstitial volume between chain molecules. Deviation of solution from perfect behavior can be evaluated by melting point depression. Accordingly, increase in conductivity is preferably related to approach to perfect solution behavior. Determination of dielectric function allows some conclusion about ion pair formation in the systems under discussion. It turns out that probability of ion pair formation decreases with increasing molecular mass of PEO in agreement with thermodynamic behavior of the solutions.     

On the transferability of hydration-parametrized continuum electrostatics models to solvated binding calculations

Using molecular mechanics force field partial atomic charges, we show the nonuniqueness of the parametrization of continuum electrostatics models with respect to solute atomic radii and interior dielectric constant based on hydration (vacuum-to-water transfer) free energy data available for small molecules. Moreover, parameter sets that are optimal and equivalent for hydration free energy calculations lead to large variations of calculated absolute and relative electrostatic binding free energies. Hence, parametrization of solvation effects based on hydration data, although a necessary condition, is not sufficient to guarantee its transferability to the calculation of binding free energies in solution.     

Dielectric studies of As-Se glasses

Dielectric constants and loss tangents of As-Se glasses have been measured between 300 K and the respective glass transition temperatures and between 1 kHz and 20 kHz. The variation of dielectric constants has been interpreted in terms of both heteropolarity of bonds and average bond energies employing a chemically ordered network model. Various contributions to total molar polarizations have been estimated. Rapid rise of loss tangent in the vicinity of glass transitions has been interpreted in terms of rapid increase; of d.c. conductivity. Communication No. 108 from Solid State and Structural Chemistry Unit.     

The acquirement of desirable dielectric properties of carbon nanofiber composites based on the controlled crystallization

This study focused on uncovering the relationship among nanofiller, crystallization behavior, and dielectric property of polymer composites. The effects of carbon nanofibers (CNFs) and heat treatment on the crystalline structures and dielectric properties of the semi‐crystalline polymers were analyzed by using high density polyethylene (HDPE) as a matrix, which is a representative of non‐polar polymer and contains only one crystal structure. The experimental results showed that the degree of crystallinity, size distribution of crystallity, and relative amount of different crystal planes in the HDPE matrix were changing due to the addition of CNFs. With the increase of CNF loading, the dielectric constant, dielectric loss and AC conductivity of the HDPE composites were increased, presenting a typical percolation characteristic, and the dependence of the dielectric constant on frequency became more obvious. All kinds of electronic transmission, polarization effect, and relaxation behaviors in CNF/HDPE composite system were deeply analyzed. After heat treatment, the degree of crystallinity of HDPE composites was decreased with the enhanced cooling rate. For the CNF/HDPE composites with nanofiller content slightly higher than the percolation threshold, the significant increase of the dielectric constant and the dramatical reduction of the dielectric loss over a wide frequency range were realized simultaneously through rapid cooling treatment. The research indicated that a general commercial polymer material with excellent dielectric properties, which exhibited a high dielectric constant and a low dielectric loss, can be obtained by a simple technical approach different from traditional fabrication method of threshold composites.     

Dielectric relaxation studies in transition metal ions doped tellurite glasses

Vanadotellurite and vanado-cobalt tellurite glasses were investigated for dielectric properties in the frequency range 50 Hz to 5 MHz and temperature range 300–500 K. Hunt's model has been invoked to analyze the data and the results indicated that the relaxation process has a local character and can be described by hops between each pair of sites. Activation energies for dielectric loss process were determined and they were in close agreement with dc activation energies. Barton, Nakijama and Namikawa's (BNN) linear relation between ac and dc conductivities has been verified in both the glass systems.     

Dielectric relaxation in proteins: a continuum electrostatics model incorporating dielectric heterogeneity of the protein and time‐dependent charges

A boundary element formulation of continuum electrostatics is used to examine time‐independent dielectric relaxation and screening in two proteins, and time‐dependent relaxation in two simpler solutes. Cytochrome c oxidation is modeled by inserting partial charges on the heme, using one to three dielectric regions in the protein. It was suggested recently that for charge insertion on a protein‐bound ligand, all or part of the ligand should be treated as a cavity within the protein medium. Here, the effect of an internal cavity surrounding the central heme atoms is examined, considering separately the static and relaxation (or reorganization) free energies. The former is the free energy to remove the redox electron while maintaining the rest of the structure and charge distribution fixed; the latter is the free energy associated with the relaxation into the product state after the corresponding constraints are released. The effect of the cavity is found to be small for the static free energy, while for the relaxation free energy it is large, as polarization of groups immediately around the heme dominates the relaxation. If the protein surface groups are treated as a distinct medium with a dielectric of 25 (as suggested by recent molecular dynamics simulations), the relaxation free energy decreases significantly (from −37.0 to −43.9 kcal/mol), compared to a model where the whole protein has a dielectric constant of two. Therefore, with this model, although polarization of groups immediately around the heme still dominates the relaxation, polar groups near the protein surface also contribute significantly, and solvent negligibly. The screening of an applied field within myoglobin is calculated, with the protein surrounded by either a low‐dielectric or a high‐dielectric glass. In the vicinity of the CO ligand, the screening is approximately isotropic with a low‐dielectric glass. It is anisotropic with a high‐dielectric glass, but the applied and local fields are still approximately parallel. This has implications for experiments that probe dielectric screening in proteins with the newly developed technique of vibrational Stark spectroscopy: with a high‐dielectric glass, a single, rotationally averaged screening factor can be used, the local field being about 1.65 times the applied field. Finally, we calculate the time‐dependent relaxation in response to instantaneous charge insertion within a spherical cavity in a Debye solvent, and to photoexcitation of a tryptophan solute, illustrating the extension of the boundary element formulation to time‐dependent problems. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 290–305, 2001     

Implementation of the finite field perturbation method in the CRYSTAL program for calculating the dielectric constant of periodic systems

The finite field approach has been implemented in the periodic ab initio CRYSTAL program and been used for calculating the dielectric constants of crystalline LiF and MgO (FCC structure) and BeO (wurtzite structure). To maintain the periodicity along the applied field direction, a "sawtooth" potential is used in conjunction with a supercell scheme. Supercells four to five times longer than the primitive cell in the direction of the applied field provide well-converged results. The influence of the computational parameters is discussed. An alternative scheme has also been implemented, for inner check, that consists of applying a static electric field to a slab of increasing thickness in the direction orthogonal to the surface; the dielectric response at the center of the slab is shown to converge rapidly to the bulk value evaluated with the sawtooth field. The method is accurate and permits the determination of nonlinear corrections to the dielectric constant. When used in conjunction with the local density approximation (LDA) scheme, it provides for the dielectric constant of the three above-mentioned compounds values close to those recently obtained with a time-dependent density functional theory approach.     

浓差极化的介电模型——复合膜/溶液体系的数值模拟

提出了具有电导率和介电常数线性分布的介质的介电模型, 并导出了其内部电的和结构性质的参数与宏观测量的电容和电导之间定量关系的理论表达式, 以模拟复合膜中的多孔层部分的介电弛豫行为. 大量的模拟计算描述并解释了多孔层介电谱随介电常数分布、厚度等性质而变化的规律. 进一步对具有层状构造的复合膜以及复合膜和溶液相组成的多层体系的弛豫行为进行了数值模拟, 比较了三个体系(多孔层、复合膜、复合膜/液相层状体系)的介电谱, 结果揭示了介电谱对各层性质的依赖关系. 所提出的电导率和介电常数线性分布的多孔层的介电模型, 也可用于具有其他电导率、介电常数分布规律的体系.     

Effect of chemical nature of atoms on the electronic,dielectric, and dynamical properties of ABX3 halide perovskite

First-principles calculations within density functional theory were performed on a series of halide perovskite compounds ABX₃(A: Cs or Rb; B:Pb or Sn). Their electronic structure, lattice dynamics, and dielectric properties were studied in relationship with the change in atom species at each one of the three inequivalent crystallographic sites, to explain the origin of these properties. Thus, the variation of the bandgap with the overlap between the B cation lone pair and the electronic states of halide atoms, as well as with the distortion of the BX₆ octahedra network is discussed. It is shown that the vibrational modes, phonon frequencies, atomic displacements, and the possible ferroelectric instability in these compounds are dependent on masses of atoms, volume of AX₁₂ polyhedron, as well as on streoactivity of Pb lone pair. Also, the Born effective charges, dielectric constant, spontaneous polarization, and infrared spectra are calculated. The relation between these dielectric properties and the ions dynamics is discussed.     

Two and three-particles spatial correlation in weak coupling plasma and applications

In this work, we studied the pair and triplet correlation functions in plasma composed of particles interacting via the Debye screening potential in the conditions of weak coupling parameter (Γ ≤ 1). The pair correlation functions are analysed numerically and compared to the hypernetted chains data, to the Monte Carlo data and to the results of Abramo and Tosi ??The triplet correlation functions are also analysed numerically and compared to the Kirkwood superposition approximation. At the end of our work, we give some applications to static structure factor and the dielectric constant. The results are well satisfactory.     

Switchable Dielectric Phase Transition Induced by a Twisting Transformation in Diglycine Methanesulfonate

A new glycine‐based reversible phase transition compound diglycine methanesulfonate ( 1 ) has been successfully synthesized. Differential scanning calorimetry (DSC) measurements of 1 showed a pair of broad peaks around 134 K (T_c=phase transition temperature) with a slight thermal hysteresis during the heating/cooling cycle, thereby indicating that this compound undergoes a reversible second‐order phase transition. Dielectric measurements further confirmed the phase transition and revealed a switchable response to the ambient temperature change for the dielectric constants of 1 , namely, the dielectric constants have a distinctive step‐like anomaly switching between a high dielectric state in the room temperature phase (RTP) and a low state in the low temperature phase (LTP). Variable‐temperature single‐crystal X‐ray diffraction analyses show that 1 undergoes an atypical transition from the space group P2₁/m in the RTP to P2₁/c in the LTP. The origin of the switchable dielectric phase transition is ascribed to the movement of the moieties in 1 from the equilibrium position, and this stems from the twisting of the molecules in the compound. We believe that these findings will be useful in exploring switchable dielectric phase transition materials.     

Preparation of polyimide/BaTiO3‐nanocrystal hybrid thin films and their dielectric property

High dielectric constant is highly desirable in capacitors and memory devices. In this work, oleic acid (OA)‐capped BaTiO₃ nanocrystals were synthesized by a two‐phase approach. Polyimide (PI)/BaTiO₃‐nanocrystal composite thin films with high dielectric constant have been successfully fabricated. The morphologies and dielectric properties of the hybrid films were exploited. The results showed that BaTiO₃ nanocrystals can be uniformly dispersed in the PI thin films owing to the surface modification of OA‐capped BaTiO₃ nanocrystals. It was found that the dielectric constant of composite film varies with the volume fraction of BaTiO₃ nanocrystals and sintering temperatures and reaches a maximum value of 44.1, which is around 13 times higher than that of pristine PI thin film (3.2). These results demonstrated that PI/BaTiO₃‐nanocrystal composite films have considerable application potential in microelectronic fields.     

Implicit solvation based on generalized Born theory in different dielectric environments

In this paper we are investigating the effect of the dielectric environment on atomic Born radii used in generalized Born (GB) methods. Motivated by the Kirkwood expression for the reaction field of a single off-center charge in a spherical cavity, we are proposing extended formalisms for the calculation of Born radii as a function of external and internal dielectric constants. We demonstrate that reaction field energies calculated from environmentally dependent Born radii lead to much improved agreement with Poisson-Boltzmann solutions for low dielectric external environments, such as biological membranes or organic solvent, compared to previous methods where the calculation of Born radii does not depend on the environment. We also examine how this new approach can be applied for the calculation of transfer free energies from vacuum to a given external dielectric for a system with an internal dielectric larger than one. This has not been possible with standard GB theory but is relevant when scoring minimized or average structures with implicit solvent.     

Activation parameters associated with the β relaxation of poly(cyclohexyl acrylate)

The interpretation of the mechanical and dielectric β relaxations of poly(cyclohexyl acrylate) by the coupling scheme suggests that the dielectric relaxation process is more complex than the mechanical one, contrary to what occurs in the glass–rubber relaxation. The distribution of activation energies for the dielectric process, obtained from isochronal and isothermal loss curves, increases with temperature and frequencies. The determination of the distribution of the activation-free energy indicates a distribution of the activation entropy for both the mechanical and dielectric β process, suggesting that a distribution of preexponential factors in the Arrhenius equation also exists. © 1992 John Wiley & Sons, Inc.