Uniform Background Charge Research Articles

Evidence of Sharp Transitions between Octahedral and Capped Trigonal Prism States of the Solvation Shell of the Aqueous Fe3+ Ion.

The structure of the solvation shell of the aqueous Fe3+ ion has been a subject of controversy due to discrepancies between experiments and different levels of theory. We address this issue by performing simulations for a wide range of ion concentrations, using various potential energy functions, supplemented by density functional theory calculations of selected configurations. The solvation shell undergoes abrupt transitions between two states: a hexacoordinated octahedral (OH) state and a capped trigonal prism (CTP) state with 7-fold coordination. The lifetime of these states is dependent on concentration. In dilute FeCl3 solutions, the lifetimes of both are similar (≈1 ns). However, the lifetime of the OH state increases with ion concentration, while that of the CTP state decreases slightly. When a uniform negative background charge is used instead of explicit counterions, the lifetime of the OH state is greatly overestimated. These findings underscore the need for further experimental measurements and higher-level simulations.

First-principles studies of charged defect states in intrinsic ferromagnetic semiconductors: the case of monolayer CrI3

Defects play significant roles in spin-current-related physical processes in intrinsic ferromagnetic semiconductors (FMSs), which are great promise for spintronics applications. However, current defect calculation methods cannot be used to investigate charged defects in FMSs due to the spin polarization of both the charged defect states and ionized carriers, which is not well treated in current defect calculation methods. In order to solve this problem, we propose a spin-distinguishable charge correction (SDCC) method that uses spin-polarized band edge charge density instead of spin-unpolarized uniform background charge density as the compensating charge for charged defects. We apply our method to study the defect properties of CrI3 monolayer and find it can be doped n-type under the Cr-rich growth condition but difficult to be doped p-type. The SDCC method proposed here is generally suitable for all FMSs, which will be useful for the studies of defect properties of magnetic semiconductors.

Effect of exchange-correlation functionals on the estimation of migration barriers in battery materials

Facile ionic mobility within host frameworks is crucial to the design of high-energy-density batteries with high-power-densities, where the migration barrier (Em) is the governing factor. Here, we assess the accuracy and computational performance of generalized gradient approximation (GGA), the strongly constrained and appropriately normed (SCAN), and their Hubbard U corrections, GGA+U and SCAN+U, within the density functional theory-nudged elastic band framework, in the prediction of Em as benchmarked against experimental data. Importantly, we observe SCAN to be more accurate than other frameworks, on average, albeit with higher computational costs and convergence difficulties, while GGA is a feasible choice for “quick” and “qualitative” Em predictions. Further, we quantify the sensitivity of Em with adding uniform background charge and/or the climbing image approximation in solid electrolytes, and the Hubbard U correction in electrodes. Our findings will improve the quality of Em predictions which will enable identifying better materials for energy storage applications.

Electronic structure calculations in electrolyte solutions: Methods for neutralization of extended charged interfaces.

Density functional theory (DFT) is often used for simulating extended materials such as infinite crystals or surfaces, under periodic boundary conditions (PBCs). In such calculations, when the simulation cell has non-zero charge, electrical neutrality has to be imposed, and this is often done via a uniform background charge of opposite sign ("jellium"). This artificial neutralization does not occur in reality, where a different mechanism is followed as in the example of a charged electrode in electrolyte solution, where the surrounding electrolyte screens the local charge at the interface. The neutralizing effect of the surrounding electrolyte can be incorporated within a hybrid quantum-continuum model based on a modified Poisson-Boltzmann equation, where the concentrations of electrolyte ions are modified to achieve electroneutrality. Among the infinite possible ways of modifying the electrolyte charge, we propose here a physically optimal solution, which minimizes the deviation of concentrations of electrolyte ions from those in open boundary conditions (OBCs). This principle of correspondence of PBCs with OBCs leads to the correct concentration profiles of electrolyte ions, and electroneutrality within the simulation cell and in the bulk electrolyte is maintained simultaneously, as observed in experiments. This approach, which we call the Neutralization by Electrolyte Concentration Shift (NECS), is implemented in our electrolyte model in the Order-N Electronic Total Energy Package (ONETEP) linear-scaling DFT code, which makes use of a bespoke highly parallel Poisson-Boltzmann solver, DL_MG. We further propose another neutralization scheme ("accessible jellium"), which is a simplification of NECS. We demonstrate and compare the different neutralization schemes on several examples.

High-density electron doping of SmNiO3 from first principles

Recent experimental work has realized a new insulating state of samarium nickelate (SmNiO$_3$), accessible in a reversible manner via high-density electron doping. To elucidate this behavior, we use the first-principles density functional theory (DFT) + U method to study the effect of added electrons on the crystal and electronic structure of SmNiO$_3$. First, we track the changes in the crystal and electronic structure with added electrons compensated by a uniform positive background charge at concentrations of $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$, and 1 electrons per Ni. The change in electron concentration does not rigidly shift the Fermi energy; rather, the added electrons localize on NiO$_6$ octahedra causing an on-site Mott transition and a change in the density of states resulting in a large gap between the occupied and unoccupied Ni $e_g$ orbitals at full doping. This evolution of the density of states is essentially unchanged when the added electrons are introduced by doping with interstitial H or Li ions.

Fourth Moment of the Charge Density Induced Around a Guest Charge in Two-Dimensional Jellium

The model under consideration is the classical two-dimensional one-component plasma (jellium) of pointlike particles with charge $e$, interacting pairwisely via the logarithmic Coulomb potential and immersed in a uniform neutralizing background charge density. The system is in thermal equilibrium at the inverse temperature $\beta$, its thermodynamics depends only on the coupling constant $\Gamma=\beta e^2$. We put into an infinite (homogeneous and translationally invariant) plasma a guest particle of charge $Ze$ with $Z>-2/\Gamma$ in order to prevent from the collapse of the jellium charges onto it. The guest particle induces a screening cloud (the excess charge density) in the plasma. The zeroth and second moments of this screening cloud were derived previously for any fluid value of $\Gamma$. In this paper, we propose a formula for the fourth moment of the screening cloud. The derivation is based on the assumption that the fourth moment is, similarly as the second moment, analytic in $Z$ around $Z=0$. An exact treatment of the limit $Z\to\infty$ shows that it is a finite (cube) polynomial in $Z$. The $\Gamma$-dependence of the polynomial coefficients is determined uniquely by considering the limits $Z\to 0$ and $Z\to\infty$, and the compressibility sum rule for $Z=1$. The formula for the fourth moment of screening cloud is checked in the leading and first correction orders of the Debye-H\"uckel limit $\Gamma\to 0$ and at the exactly solvable free-fermion point $\Gamma=2$. Sufficient conditions for sign oscillations of the induced charge density which follow from the second-moment and fourth-moment sum rules are discussed.

Computational description of key spectroscopic features of zeolite SSZ-13.

The catalytic properties of zeolites are intimately linked to the distribution and relative positions of Al atoms and defects in the pore network. However, characterizing this distribution is challenging, in particular when different local Al arrangements are considered. In this contribution we use a combination of first principles calculations and experimental measurements to develop a model for the Al-distribution in protonated SSZ-13. We furthermore apply this model to understand trends in OH-IR, 27Al-NMR and 29Si-NMR spectra. We use a Boltzmann distribution to predict the proton position for a given local Al configuration and show that for each configuration several H positions are occupied. Therefore a multi-peak spectrum in OH-IR vibrational spectroscopy is observed for all Al configurations, which is in line with experimentally measured spectra for zeolites at different Si/Al ratios. From NMR spectroscopy we find that the proton position leads to significant shifts in 27Al-NMR and 29Si-NMR spectra due to the modification of the local strain, which is lost when a uniform background charge is introduced. These findings are supported by experimental measurements. Finally we discuss the shortcomings of the presented model in terms of unit cell size and the impact of adjacent unit cells.

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.

Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge

Ewald summation, which has become the de facto standard for computing electrostatic interactions in biomolecular simulations, formally requires that the simulation box is neutral. For non-neutral systems, the Ewald algorithm implicitly introduces a uniform background charge distribution that effectively neutralizes the simulation box. Because a uniform distribution of counter charges typically deviates from the spatial distribution of counterions in real systems, artifacts may arise, in particular in systems with an inhomogeneous dielectric constant. Here, we derive an analytical expression for the effect of using an implicit background charge instead of explicit counterions, on the chemical potential of ions in heterogeneous systems, which (i) provides a quantitative criterium for deciding if the background charge offers an acceptable trade-off between artifacts arising from sampling problems and artifacts arising from the homogeneous background charge distribution, and (ii) can be used to correct this artifact in certain cases. Our model quantifies the artifact in terms of the difference in charge density between the non-neutral system with a uniform neutralizing background charge and the real neutral system with a physically correct distribution of explicit counterions. We show that for inhomogeneous systems, such as proteins and membranes in water, the artifact manifests itself by an overstabilization of ions inside the lower dielectric by tens to even hundreds kilojoules per mole. We have tested the accuracy of our model in molecular dynamics simulations and found that the error in the calculated free energy for moving a test charge from water into hexadecane, at different net charges of the system and different simulation box sizes, is correctly predicted by the model. The calculations further confirm that the incorrect distribution of counter charges in the simulation box is solely responsible for the errors in the PMFs.

Possibility of transforming the electronic structure of one species of graphene adatoms into that of another by application of gate voltage: First-principles calculations

Graphene provides many advantages for controlling the electronic structure of adatoms and other adsorbates via gating. Using the projected density of states and charge density obtained from first-principles density-functional periodic supercell calculations, we investigate the possibility of performing ``alchemy'' of adatoms on graphene, i.e., transforming the electronic structure of one species of adatom into that of another species by application of a gate voltage. Gating is modeled as a change in the number of electrons in the unit cell, with the inclusion of a compensating uniform background charge. Within this model and the generalized gradient approximation to the exchange-correlation functional, we find that such transformations are possible for K, Ca, and several transition-metal adatoms. Gate control of the occupation of the $p$ states of In on graphene is also investigated. The validity of the supercell approximation with uniform compensating charge and the model for exchange and correlation is also discussed.

Is the Schwinger model at finite density a crystal?

It has been believed since the paper by Fischler, Kogut, and Susskind that in ${\mathrm{QED}}_{2}$ at finite charge density the chiral condensate exhibits a spatially inhomogeneous, oscillating behavior. In this paper we demonstrate that this inhomogeneity is due to the explicit breaking of the translational invariance by a uniform background charge density. Moreover, we investigate in the context of a simple statistical model what happens if the neutralizing background is composed instead of heavy, but dynamical, particles. We find that in contrast to the standard picture of Fischler et al., the chiral condensate will not exhibit coherent oscillations on large distance scales, unless the heavy neutralizing particles themselves form a crystal and the density is high.

Comparison of two methods for circumventing the Coulomb divergence in supercell calculations for charged point defects

Density-functional-theory calculations were performed for the unrelaxed $+2$ Si vacancy and $+2$ self-interstitial utilizing periodic boundary conditions and two different methods---the uniform background charge method and the local moment counter charge method---for circumventing the divergence of the Coulomb potential. Formation energies in nominal 64-, 216-, 512-, 1000-, and 1728-atom supercells were converged with respect to Brillouin zone sampling and then extrapolated to an infinite sized supercell by fitting to a polynomial in odd powers of $1∕L$ where $L$ is the cubed root of the supercell volume. The extrapolated values from the two methods agreed very well ($2\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ difference for the vacancy and $13\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ difference for the interstitial) as expected from inspection of their respective energy expressions. The extrapolated values and fitting parameters were then employed to evaluate analytic correction formulas that have been proposed to remove spurious electrostatic contributions from defect formation energies. The results indicate that existing formulas are not capable of removing these contributions and that further development is needed in this area.

Ab initio calculations of charged point defects in GaN

The Generalized Gradient Approximation (GGA) of a Density Functional Theory (DFT) in LCAO basis is used to determine electronic structure of charged point defects in hexagonal GaN. Impurities of MgGa, ZnGa, SiN and CN (the most common dopants) were considered for charge states 0, ±1, –2. The vacancies of VGa and VN were considered for charge states 0 and 0, ±1, ±2 respectively. The defects in consideration are compared from the point of view of the one-electron states localization. All the calculations were performed for a supercell containing 96 atoms. The divergence due to periodically repeated charges has been eliminated by the use of a uniform background charge of an opposite sign. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Vortex in Maxwell-Chern-Simons models coupled to external backgrounds

We consider Maxwell-Chern-Simons models involving different non-minimal coupling terms to a non relativistic massive scalar and further coupled to an external uniform background charge. We study how these models can be constrained to support static radially symmetric vortex configurations saturating the lower bound for the energy. Models involving Zeeman-type coupling support such vortices provided the potential has a "symmetry breaking" form and a relation between parameters holds. In models where minimal coupling is supplemented by magnetic and electric field dependant coupling terms, non trivial vortex configurations minimizing the energy occur only when a non linear potential is introduced. The corresponding vortices are studied numerically

Dimensional changes as a function of charge injection in single-walled carbon nanotubes.

Motivated by the central importance of charge-induced dimensional changes for carbon nanotube electromechanical actuators, we here predict changes in nanotube length and diameter as a function of charge injection for armchair and zigzag nanotubes having different diameters. Density functional theory with periodic boundary conditions is used, which we show provides results consistent with experimental observations for intercalated graphites. Strain-versus-charge relationships are predicted from dimensional changes calculated with a uniform background charge ("jellium") for representing the counterions. These jellium calculations are consistent with presented calculations that include specific counterions for intercalated graphite, showing that hybridization between the ions and the graphite sheets is unimportant. The charge-strain relationships calculated with the jellium approximation for graphite and isolated single-walled nanotubes are asymmetric with respect to the sign of charge transfer. The dependence of nanotube strain on charge approaches that for a graphite sheet for intermediate-sized metallic nanotubes and for larger diameter semiconducting nanotubes. However, the strain-charge curves strongly depend on nanotube type when the nanotube diameter is small. This reflects both the dependence of the frontier orbitals for the semiconducting nanotubes on the nanotube type and the pi-sigma mixing when the nanotube diameter is small.

Dimensional changes as a function of charge injection for trans-polyacetylene: A density functional theory study

Charge-induced dimensional changes allow conducting polymers and single walled carbon nanotubes to function as electromechanical actuators. The unit cell of the prototypical conducting polymer, trans-polyacetylene, was calculated as a function of charge injection using density functional theory in combination with ultrasoft pseudopotentials using the solid-state Vienna ab initio simulation package. Test calculations on the charged pyridinium molecular ion give results in good agreement with the experimental geometry. Strain versus charge relationships are predicted from dimensional changes calculated using a uniform background charge (“jellium”) for representing the counterions, which we show provides results consistent with experiment for doped polyacetylenes. These jellium calculations are consistent with further presented calculations that include specific counterions, showing that hybridization between the guest dopant ions and the host polyacetylene chains is unimportant. The lack of guest–host orbital hybridization allows a qualitative rigid band interpretation of the amount of charge transfer for both acceptor and donor doping. For polyacetylene, asymmetry of strain along the chain with respect to the sign of the charge is predicted: negative charge elongates and positive charge shortens the polymer. For charge less than 0.05e per carbon, an approximately linear dependence is obtained for the dependence of chain-direction strain on the amount of injected charge.

Chern-Simons theories on the noncommutative plane.

We investigate U(N) Chern-Simons theories on the noncommutative plane. We show that for the theories to be consistent quantum mechanically, the coefficient of the Chern-Simons term should be quantized kappa = n/2pi with an integer n. This is a surprise for the U(1) gauge theory. When uniform background charge density rho(e) is present, the quantization rule changes to kappa+rho(e)straight theta = n/2pi with the noncommutative parameter straight theta. With the exact expression for the angular momentum, we argue in the U(1) theory that charged particles in the symmetric phase carry fractional spin 1/2n and vortices in the broken phase carry half-integer or integer spin -n/2.

Characteristic length scales and formation of vortices in the Ginzburg-Landau-Higgs model in the presence of a uniform background charge

In this brief report we consider a non-local Abelian Higgs model in the presence of a neutralizing uniform background charge. We show that such a system possesses vortices which key feature is a strong radial electric field. We estimate the basic properties of such an object and characteristic length scales in this model.

Charge Fluctuations in the Two-Dimensional One-Component Plasma

We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density −eρ in a region Λ inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in NΛ, the number of mobile particles of charge e. As expected, the distribution of NΛ has, for large Λ, a Gaussian form with a variance which grows only as ^κ|∂Λ|, where |∂Λ| is the length of the perimeter of Λ. The properties of this system depend only on the coupling parameter Γ=kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter Γ increases, ^κ(Γ) decreases to an asymptotic value ^κ(∞)∼^κ(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large Γ, the characteristic length ξL=2^κ/ρ associated with charge fluctuations behaves very differently from that of the Debye length, ξD∼1/\(\sqrt \Gamma \), which it approaches as Γ→0. The pair correlation function of the OCP is also studied.

Continuum Corrections to the Polarization and Thermodynamic Properties of Ewald Sum Simulations for Ions and Ion Pairs at Infinite Dilution

Ewald sum simulations of the solvation thermodynamics of charged solutes employ an unphysical uniform neutralizing background charge to ensure convergence of the periodic lattice sum. Continuum corrections to the solvation free energy, entropy, and volume of single ions and ion pairs for the effect of the neutralizing background and periodic boundary conditions at finite cell size are derived in order to allow efficient calculations of the ionic properties at infinite dilution. The derivation presented in this paper shows the physical origin of the effects and can be easily extended to multiple charge sites. Corrections are small for high dielectric constant solvents but become increasingly important as the ion size is increased, the dielectric constant is decreased, or the unit cell size is decreased. An alternative way of calculating the thermodynamic properties from Ewald sum simulations is proposed for which the corrections are small for low dielectric constant solvents. Tests for low and high dielectric constant water show that, after the appropriate continuum corrections are applied, the free energy of charging an ion using Ewald sum simulations agrees with the results for potential truncation simulations and spherical boundary simulations (when corrected for truncation effects). The corrected free energy of hydration is not sensitive to the system size even for low dielectric constants. The continuum model correctly predicts that Ewald sum simulations yield a solvent polarization at large distance from an ion that is smaller than the polarization of a truly infinite system.