Distribution Of Point Charges Research Articles

Point-charge models and averages for electromagnetic quantities considered in two relativistic inertial frames

Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space coordinates, averages of electrodynamic quantities at a single time will in general depend upon the inertial frame, and will differ between inertial frames. Here we illustrate how the use of continuous charge and current distributions rather than point-charge distributions can lead to physically mystifying and even inaccurate results for electromagnetic quantities and physical phenomena. The discrepancy noted between the average electric field values in different inertial frames is particularly striking because it is first order in the relatative velocity between the frames.

The Random Weierstrass Zeta Function II. Fluctuations of the Electric Flux Through Rectifiable Curves

Consider a random planar point process whose law is invariant under planar isometries. We think of the process as a random distribution of point charges and consider the electric field generated by the charge distribution. In Part I of this work, we found a condition on the spectral side which characterizes when the field itself is invariant with a well-defined second-order structure. Here, we fix a process with an invariant field, and study the fluctuations of the flux through large arcs and curves in the plane. Under suitable conditions on the process and on the curve, denoted Gamma , we show that the asymptotic variance of the flux through R,Gamma grows like R times the signed length of Gamma . As a corollary, we find that the charge fluctuations in a dilated Jordan domain is asymptotic with the perimeter, provided only that the boundary is rectifiable. The proof is based on the asymptotic analysis of a closely related quantity (the complex electric action of the field along a curve). A decisive role in the analysis is played by a signed version of the classical Ahlfors regularity condition.

Exact multicentered static point charge source distributions in the Born–Infeld theory of nonlinear electromagnetism and presence of electric and magnetic currents

Exact multicentered solutions to the governing equations of the Born–Infeld nonlinear theory of electrodynamics describing distributions of electric, magnetic, and dyonic point charge sources are constructed explicitly for the first time. The method of construction may effectively be adapted to obtain such solutions in generalized theories as well. As a consequence, the solutions unveil that, in order to achieve a balance between such multicentered electric or magnetic point charge distribution in equilibrium, a static magnetic or electric current must be present, resulting in non-conservativeness of the induced electric or magnetic intensity field, respectively and universally. Moreover, it is also shown that the methods of construction and conclusions drawn in the multicentered situation may be extended to obtain exact solutions and similar conclusions, explicitly, in the situation of continuously distributed charge source problems.

Plasma-Assisted Dinitrogen Activation via Dual Platinum Cluster Catalysis: A Strategy for Ammonia Synthesis under Mild Conditions

Plasma-Assisted Dinitrogen Activation via Dual Platinum Cluster Catalysis: A Strategy for Ammonia Synthesis under Mild Conditions

Zeta function regularization technique in the electrostatics context for discrete charge distributions

Spectral functions, such as the zeta functions, are widely used in quantum field theory to calculate physical quantities. In this work, we compute the electrostatic potential and field due to an infinite discrete distribution of point charges, using the zeta function regularization technique. This method allows us to remove the infinities that appear in the resulting expression. We found that the asymptotic behavior dependence of the potential and field is similar to the cases of continuous charge distribution. Finally, this exercise can be useful for graduate students to explore spectral and special functions.

Around a theorem of F. Dyson and A. Lenard: Energy equilibria for point charge distributions in classical electrostatics

We discuss several results in electrostatics: Onsager’s inequality, an extension of Earnshaw’s theorem, and a result stemming from the celebrated conjecture of Maxwell on the number of points of electrostatic equilibrium. Whenever possible, we try to provide a brief historical context and references.

Screened Coulomb interactions of general macroions with nonzero particle volume

The author shows that rigid colloidal particles of various shapes can be mapped to an effective point, line, or surface charge distributions. This allows closed-form integral expressions for the electrostatic potential and effective pair potential for particles of possibly arbitrary shape and particle configuration.

Extension of the fast multipole method for the rectangular cells with an anisotropic partition tree structure.

The fast multipole method (FMM) is an order N method for the numerically rigorous calculation of the electrostatic interactions among point charges in a system of interest. The FMM is utilized for massively parallelized software for molecular dynamics (MD) calculations. However, an inconvenient limitation is imposed on the implementation of the FMM: In three-dimensional case, a cubic MD unit cell is hierarchically divided by the octree partitioning under isotropic periodic boundary conditions along three axes. Here, we extended the FMM algorithm adaptive to a rectangular MD unit cell with different periodicity along the axes by applying an anisotropic hierarchical partitioning. The algorithm was implemented into the parallelized general-purpose MD calculation software designed for a system with uniform distribution of point charges in the unit cell. The partition tree can be a mixture of binary and ternary branches, the branches being chosen arbitrarily with respect to the coordinate axes at any levels. Errors in the calculated electrostatic interactions are discussed in detail for a selected partition tree structure. The extension enables us to execute MD calculations under more general conditions for the shape of the unit cell, partition tree, and boundary conditions, keeping the accuracy of the calculated electrostatic interactions as high as that with the conventional FMM. An extension of the present FMM algorithm to other prime number branches, such as 5 and 7, is straightforward.

Minimum-energy distribution of point charges confined to a square

The minimum-energy configurations of [Formula: see text] identical classical point charges confined within a square under the effect of a Coulombic [Formula: see text] potential have been determined by performing steepest-descent simulations. The energies of the final optimized configurations are given, along with their corresponding structural charge distributions. When all systems evolve in time to reach a minimum-energy configuration, local or global, they are all seen to be in quest of symmetry.

The Effect of Stabilizing Ligands on the Interaction between Colloidal Quantum Dots of Cadmium Selenide. Computer Simulation

Classical full-atomic molecular dynamics has been employed to study the effect of ligand environment on the dipole moments of colloidal quantum dots of cadmium selenide. Using trioctylphosphine oxide, hexadecylamine, and octadecylphosphonic acid as examples, it has been shown that the presence of uncompensated electrical charge at the polar group of a ligand molecule is the primary factor, while the distribution of point charges over the electrically neutral group is of secondary significance. Dipole–dipole interactions between CdSe nanoparticles make the greatest contribution upon the formation of dense layers, while, in solutions, this contribution is low as compared with the ordinary thermal motion.

The electric double layer at metal-water interfaces revisited based on a charge polarization scheme.

The description of electrode-electrolyte interfaces is based on the concept of the formation of an electric double layer. This concept was derived from continuum theories extended by introducing point charge distributions. Based on ab initio molecular dynamics simulations, we analyze the electric double layer in an approach beyond the point charge scheme by instead assessing charge polarizations at electrochemical metal-water interfaces from first principles. We show that the atomic structure of water layers at room temperature leads to an oscillatory behavior of the averaged electrostatic potential. We address the relation between the polarization distribution at the interface and the extent of the electric double layer and subsequently derive the electrode potential from the charge polarization.

The electrostatic embedding contribution to DFT calculations of ligand-amino acid residues interaction.

In this work, we demonstrate that the inclusion of long-range interactions has a significant impact on the estimation of ligand-protein binding energies. Within the scope of the electrostatically embedded adaptation of the molecular fragmentation with conjugated caps (EE-AMFCC) scheme, we unveil the role played by long-range contributions in distinct levels of quantum mechanical calculations. As a prototypical system, we consider ibuprofen coupled to the human serum albumin. In particular, we show that some relevant ligand-residue interaction energies can only be accurately captured in density functional theory (DFT) approaches when the electrostatic background is properly represented by an explicit point charge distribution. Graphical Abstract (left) The binding site FA3/FA4 of HSA containing the attached IBU. (right) Absolute value of difference between the biding energies calculated including the electrostatic embedding and the energies calculated without the electrostatic embedding using the HF, B3LYP, CAM-B3LYP, and MP2 methodologies.

A quantum mechanical computational method for modeling electrostatic and solvation effects of protein

An efficient computational approach for modeling protein electrostatic is developed according to static point-charge model distributions based on the linear-scaling EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) quantum mechanical (QM) method. In this approach, the Electrostatic-Potential atomic charges are obtained from ab initio calculation of protein, both polarization and charge transfer effect are taken into consideration. This approach shows a significant improvement in the description of electrostatic potential and solvation energy of proteins comparing with current popular molecular mechanics (MM) force fields. Therefore, it has gorgeous prospect in many applications, including accurate calculations of electric field or vibrational Stark spectroscopy in proteins and predicting protein-ligand binding affinity. It can also be applied in QM/MM calculations or electronic embedding method of ONIOM to provide a better electrostatic environment.

Real-space pairwise electrostatic summation in a uniform neutralizing background

Evaluating the total energy of an extended distribution of point charges, which interact through the Coulomb potential, is central to the study of condensed matter. With near ubiquity, the summation required is carried out using Ewald's method, which splits the problem into two separately convergent sums; one in real space and the other in reciprocal space. Density functional based electronic structure methods require the evaluation of the ion-ion repulsive energy, neutralised by a uniform background charge. Here a purely real-space approach is described. It is straightforward to implement, computationally efficient and offers linear scaling. When applied to the evaluation of the electrostatic energy of neutral ionic crystals, it is shown to be closely related to Wolf's method.

Modeling Halogen Bonds in Ionic Liquids: A Force Field for Imidazolium and Halo-Imidazolium Derivatives.

In this work, a force field for molecular dynamics and Monte Carlo simulations of ionic liquids containing imidazolium and halo-imidazolium derivatives is presented. This force field is an extension of the well-known CL&P and OPLS-AA models and was validated by comparing predicted crystalline structures for 22 ionic liquid compounds with the corresponding data deposited at the Cambridge Structural Database. The obtained results indicate that the proposed force field extension allows the reproduction of the crystal data with an absolute average deviation lower than 2.4%. Finally, it was also established that the halogen atoms covalently bound to the studied imidazolium cations are positively charged and do not exhibit a so-called σ-hole feature. For this reason, the formation of halogen bonds in the proposed force field appears naturally from the parametrized atomic point-charge distribution, without the necessity of any extra interaction sites.

Reduced Point Charge Models of Proteins: Effect of Protein–Water Interactions in Molecular Dynamics Simulations of Ubiquitin Systems

We investigate the influence of various solvent models on the structural stability and protein-water interface of three ubiquitin complexes (PDB access codes: 1Q0W , 2MBB , 2G3Q ) modeled using the Amber99sb force field (FF) and two different point charge distributions. A previously developed reduced point charge model (RPCM), wherein each amino acid residue is described by a limited number of point charges, is tested and compared to its all-atom (AA) version. The complexes are solvated in TIP4P-Ew or TIP3P type water molecules, involving either the scaling of the Lennard-Jones protein-Owater interaction parameters, or the coarse-grain (CG) SIRAH water description. The best agreements between the RPCM and AA models were obtained for structural, protein-water, and ligand-ubiquitin properties when using the TIP4P-Ew water FF with a scaling factor γ of 0.7. At the RPCM level, a decrease in γ, or the inclusion of SIRAH particles, allows weakening of the protein-water interactions. It results in a slight collapse of the protein structure and a less compact hydration shell and, thus, in a decrease in the number of protein-water and water-water H-bonds. The dynamics of the surface protein atoms and of the water shell molecules are also slightly refrained, which allow the generation of stable RPCM trajectories.

Quantum Molecular Dynamical Calculations of PEDOT 12-Oligomer and its Selenium and Tellurium Derivatives

We present simulation results, computed with the Car–Parrinello molecular dynamics method, at zero and ambient temperature (300 K) for poly(3,4-ethylenedioxythiophene) [PEDOT] and its selenium and tellurium derivatives PEDOS and PEDOTe, represented as 12-oligomer chains. In particular, we focus on structural parameters such as the dihedral rotation angle distribution, as well as how the charge distribution is affected by temperature. We find that for PEDOT, the dihedral angle distribution shows two distinct local maxima whereas for PEDOS and PEDOTe, the distributions only have one clear maximum. The twisting stiffness at ambient temperature appears to be larger the lighter the heteroatom (S, Se, Te) is, in contrast to the case at 0 K. As regards point charge distributions, they suggest that aromaticity increases with temperature, and also that aromaticity becomes more pronounced the lighter the heteroatom is, both at 0 K and ambient temperature. Our results agree well with previous results, where available. The bond lengths are consistent with substantial aromatic character both at 0 K and at ambient temperature. Our calculations also reproduce the expected trend of diminishing gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital with increasing atomic number of the heteroatom.

Electrostatic Embedding To Model the Impact of Environment on Photophysical Properties of Molecular Crystals: A Self-Consistent Charge Adjustment Procedure.

A case study of 1,8-dihydroxy-2-napthaldehyde (DHNA)-exhibiting an excited-state intramolecular double proton transfer resulting in photophysical properties sensitive to the surrounding environment-has been used to assess the performance of electrostatic embedding approaches designed to accurately recover the effects of a bulk crystalline environment on calculated photophysical properties. The first approach, based on time-dependent density functional theory (TD-DFT) applied in a QM/QM' scheme, makes use of a background point charge distribution which can accurately reproduce the exact ground-state Ewald potential of the bulk crystal. The second approach seeks to "optimize" these charges in a self-consistent manner in order to reproduce the electrostatic field produced by the environment at the excited state. Using these two approaches, both absorption and emission properties of molecular crystals, such as the position and the relative shift in the emission bands in the solid state with respect to solution, can be accurately reproduced. More generally, the results obtained show how these computationally affordable approaches can be used to predict the excited-state behavior of molecules in condensed phases, thus allowing their employment to predict or design new molecular materials with enhanced photophysical properties.

Method of uniform effective field in structure-dynamic approach of nanoionics

In the structure-dynamic approach of nanoionics, the method of a uniform effective field \( {F}_{\mathrm{eff}}^{j,k} \) of a crystallographic planeXjhas been substantiated for solid electrolyte nanostructures. The \( {F}_{\mathrm{eff}}^{j,k} \)is defined as an approximation of a non-uniform field \( {F}_{\mathrm{dis}}^j \)of Xj with a discrete- random distribution of excess point charges. The parameters of \( {F}_{\mathrm{eff}}^{j,k} \)are calculated by correction of the uniform Gauss field \( {F}_{\mathrm{G}}^j \) of Xj. The change in an average frequency of ionic jumps Xk → Xk + 1 between adjacent planes of nanostructure is determined by the sum of field additives to the barrier heights ηk,k + 1, and for \( {F}_{\mathrm{G}}^j \) and \( {F}_{\mathrm{dis}}^j \), these sums are the same decimal order of magnitude. For nanostructures with length ~4 nm, the application of \( {F}_{\mathrm{G}}^j \) (as \( {F}_{\mathrm{eff}}^{j,k} \)) gives the accuracy ~20 % in calculations of ion transport characteristics. The computer explorations of the “universal” dynamic response (Reσ∗ ∝ ωn) show an approximately the same power n < ≈1 for\( {F}_{\mathrm{G}}^j \) and \( {F}_{\mathrm{eff}}^{j,k} \).

Reduced point charge models of proteins: assessment based on molecular dynamics simulations

A reduced point charge distribution is used to model Ubiquitin and two complexes, Vps27 UIM-1–Ubiquitin and Barnase–Barstar. It is designed from local extrema in charge density distributions obtained from the Poisson equation applied to smoothed molecular electrostatic potentials. A variant distribution is built by locating point charges on atoms. Various charge fitting conditions are selected, i.e. from either electrostatic Amber99 (Assisted Model Building with Energy Refinement) Coulomb potential or forces, considering reference grid points located within various distances from the protein atoms, with or without separate treatment of main and side chain charges. The program GROMACS (Groningen Machine for Chemical Simulations) is used to generate Amber99SB molecular dynamics (MD) trajectories of the solvated proteins modelled using the various reduced point charge models (RPCMs) so obtained. Point charges that are not located on atoms are considered as virtual sites. Some RPCMs lead to stable MD trajectories. They, however, involve a partial loss in the protein secondary structure and lead to a less-structured solute solvation shell. The model built by fitting charges on Coulomb forces calculated at grid points ranging between 1.4 and 2.0 times the van der Waals radius of the atoms, with a separate treatment of main chain and side chain charges, appears to best approximate all-atom MD trajectories.