Coulomb Terms Research Articles

Ohta–Kawasaki energy for amphiphiles: Asymptotics and phase-field simulations

We study the minimizers of a degenerate case of the Ohta–Kawasaki energy, defined as the sum of the perimeter and a Coulombic nonlocal term. We start by investigating radially symmetric candidates which give us insights into the asymptotic behaviors of energy minimizers in the large mass limit. In order to numerically study the problems that are analytically challenging, we propose a phase-field reformulation which is shown to Gamma-converge to the original sharp interface model. Our phase-field simulations and asymptotic results suggest that the energy minimizers exhibit behaviors similar to the self-assembly of amphiphiles, including the formation of lipid bilayer membranes.

Long-Range Effects in Topologically Defective Arm-Chair Graphene Nanoribbons.

The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ=2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model.

The role of the coupling matrix elements in time-dependent density functional theory on the simulation of core-level spectra of transition metal complexes

Time-dependent density functional theory (TD-DFT) stands out as an efficient tool for computing core-level spectra in large molecules, particularly transition metal complexes. However, despite their relatively moderate computational demands, TD-DFT methods can still pose challenges for typical computations involving transition metal complexes with over a thousand basis functions. In this study, we investigate the role of the Coulomb, Hartree–Fock exchange, and exchange-correlation kernel contributions to the TD-DFT coupling matrix elements when simulating core-level spectra in transition metal complexes. Our observations reveal that the exchange-correlation kernel contribution, responsible for more than 50% of the computational time in a hybrid TD-DFT calculation, surprisingly has no discernible impact on the qualitative aspects of the calculated spectra. While the Coulomb term plays a crucial role in describing L2,3 -edge spectra, its significance becomes negligible when considering K, L 1, and M4,5 edges. In contrast, the scaled Hartree–Fock exchange is demonstrated to be the most influential term, underscoring the necessity for hybrid density functional approximations in accurately simulating core-level spectra. These trends hold irrespective of the chosen basis set and exchange-correlation functional, providing valuable insights for the development of approximate methods for incorporating two-electron interactions within the realm of core-level spectroscopies.

Geometries, Electronic Structures, Bonding Properties, and Stability Strategy of Endohedral Metallofullerenes TM@C28 (TM = Sc−, Y−, La−, Ti, Zr, Hf, V+, Nb+, Ta+)

We performed quantum chemical calculations on the geometries, electronic structures, bonding properties, and stability strategy of endohedral metallofullerenes TM@C28 (TM = Sc−, Y−, La−, Ti, Zr, Hf, V+, Nb+, Ta+). Our calculations revealed that there are three different lowest-energy structures with C2v, C3v, and Td symmetries for TM@C28. The HOMO–LUMO gap of all these structures ranges from 1.35 eV to 2.31 eV, in which [V@C28]+ has the lowest HOMO–LUMO gap of 1.35 eV. The molecular orbitals are mainly composed of fullerene cage orbitals and slightly encapsulated metal orbitals. The bonding analysis on the metal–cage interactions reveals they are dominated by the Coulomb term ΔEelstat and the orbital interaction term ΔEorb, in which the orbital interaction term ΔEorb contributes more than the Coulomb term ΔEelstat. The addition of one or two CF3 groups to [V@C28]+ could increase the HOMO–LUMO gap and further increase the stability of [V@C28]+.

Dynamics of heavy quarks in the Fock space

This paper concerns a method of describing hadrons that starts with the canonical front form Hamiltonian of QCD. The method is developed in the relatively simple context of QCD with only heavy quarks. We regulate its canonical Hamiltonian by introducing a vanishingly small gluon mass mg. For positive mg, the small-x gluon divergences become ultraviolet and hence they are renormalized in the same way the ultraviolet transverse divergences are. This is done using the renormalization group procedure for effective particles. Up to the second order of expansion of the renormalized Hamiltonian in powers of the quark-gluon coupling constant g, only the quark mass-squared and gluon-exchange divergences require counterterms. In these circumstances, we calculate an effective potential between quarks in heavy quarkonia in an elementary way, replacing all the quarkonium-state components with gluons of mass mg by only one component with just one gluon that is assigned a mass mG, comparable to or exceeding the scale of typical relative momenta of bound quarks. In the limit of mg→0 and large mG two results are obtained. (1) While the color-singlet quarkonium mass eigenvalue stays finite and physically reasonable in that limit, the eigenvalues for single quarks and octet quarkonia are infinite. (2) Besides the coulomb terms, the effective quark-antiquark potential is quadratic as a function of the distance and spherically symmetric for typical separations between quarks but becomes logarithmic and no longer spherically symmetric for large separations. Our conclusion indicates how to systematically improve upon the approximations made in this paper. Published by the American Physical Society 2024

The [formula omitted]-deformation of the generalized DKP oscillator

We consider the Duffin–Kemmer–Petiau (DKP) oscillator for spin-zero bosons, coupled to a pseudoscalar Coulomb potential, in a (3+1)-dimensional noncommutative space–time characterized by κ-deformation. We use the method of Dirac derivatives to build the κ-deformed DKP equation. We work out the solutions of the generalized oscillator so obtained using a perturbation method: This allowed to examine first-order effects of the non-commutativity on its eigenenergies and eigenfunctions. Notably, we find that, due to the deformation, the energy levels of s-states become discontinuous at a certain critical value of the coupling constant of the Coulomb term. We also note an asymmetry between particle and antiparticle energies revealing the breaking of the charge-conjugation symmetry for deformed DKP equation. In addition, we discuss the κ-deformed DKP oscillator as a particular case of the considered model.

Confinement and nonlinear electrodynamics: Asymptotic Schwarzschild charged black hole

While most nonlinear electrodynamics (NED) models tend to Maxwell’s linear theory in the weak field regime, very recently a model of NED has been proposed in the context of heavy quark–antiquark confinement that gives the same limit in the strong field regime. This form of correction to Maxwell’s linear theory is shown to be applicable in such a confined system. In this model, the radial electric field of a point charge is described by E=qr2+ζqr which consists of a Coulomb term plus a term proportional to the NED parameter ζ. Here in this paper, we extend the previous study on the model and accordingly, first, present more on the properties of the model and then introduce the magnetic black hole solution obtained in the gravity coupled minimally to this NED. The solution due to the unique property of the NED is asymptotically Schwarzschild black hole. In addition to the thermodynamics of the black hole, we investigate the circular speed–radius curve of the hypothetical star orbiting the mentioned black hole. It is shown that again due to the correction of Maxwell’s theory in the weak field limit these curves are equivalent to the corresponding curves in the Schwarzschild black hole.

The application of differential constraint method for the solution of non-homogeneous generalized Riemann problem

This paper reports the solution to the Non-homogeneous Riemann problem by applying the approach of differential constraint for the one-dimensional (1 − D) generalized Chaplygin gas equations with non-constant initial data. Here we take source term as a Coulomb type constant frictional term. We reduced the governing non-homogeneous model into a homogeneous one by introducing a new velocity variable. By virtue of this advantage of frictional type source term, we would easily determine the solution of reformulated homogeneous governing model. We have computed the differential constraint and its consistency conditions for the specified model. Moreover, we have derived here the compatibility condition between the governing model and the differential constraints. The solutions to generalized Riemann problem for the 1 − D Euler’s equation of governing gas model are obtained as well as for the smooth and non-constant initial conditions the comprehensive overview of the solutions is studied.

Exact two-component theory becoming an efficient tool for NMR shieldings and shifts with spin–orbit coupling

We present a gauge-origin invariant exact two-component (X2C) approach within a modern density functional framework, supporting meta-generalized gradient approximations such as TPSS and range-separated hybrid functionals such as CAM-B3LYP. The complete exchange-correlation kernel is applied, including the direct contribution of the field-dependent basis functions and the reorthonormalization contribution from the perturbed overlap matrix. Additionally, the finite nucleus model is available for the electron-nucleus potential and the vector potential throughout. Efficiency is ensured by the diagonal local approximation to the unitary decoupling transformation in X2C as well as the (multipole-accelerated) resolution of the identity approximation for the Coulomb term (MARI-J, RI-J) and the seminumerical exchange approximation. Errors introduced by these approximations are assessed and found to be clearly negligible. The applicability of our implementation to large-scale calculations is demonstrated for a tin pincer-type system as well as low-valent tin and lead complexes. Here, the calculation of the Sn nuclear magnetic resonance shifts for the pincer-type ligand with about 2400 basis functions requires less than 1 h for hybrid density functionals. Further, the impact of spin–orbit coupling on the nucleus-independent chemical shifts and the corresponding ring currents of all-metal aromatic systems is studied.

New exact plasma equilibria with axial and helical symmetry

We derive new exact closed-form solutions of magnetohydrodynamics equations, with and without dynamics, which model astrophysical jets and other prolonged plasma configurations. The solutions are obtained in static and dynamic incompressible equilibrium settings, in axial and helical symmetry assumptions, and are given in terms of Whittaker, Coulomb, and Heun special functions. For each symmetry, two distinct families of physical solutions arise, corresponding to two distinct pressure profiles. One pressure profile models plasmas supported by an external pressure and is suitable for the description of plasma configurations in a medium, such as atmosphere. The second profile features higher pressure inside the plasma domain and can model plasmas residing in a vacuum. Examples of static and dynamic solutions in axially and helically symmetric settings, including solutions with boundary current sheets, are presented and discussed.

Study of α-decay half-life for axially symmetric deformed even–even isotopes of nuclei with atomic numbers 88≤Z≤104

In this paper, [Formula: see text]-decay half-life of axially symmetric deformed even–even isotopes with atomic numbers [Formula: see text] had been studied for the transition between the ground states of the parent and daughter nuclei. Quadrupole deformation of daughter nuclei (if any) is considered in calculations. The interaction between the [Formula: see text]-particle and daughter nucleus includes the nuclear double-folding, the Coulomb and rotational terms. Wang’s formula is used for coulomb interaction between spherical [Formula: see text]-particle and deformed daughter nucleus. The Q-value of [Formula: see text]-decay is calculated and used to obtain its half-life, based on the WKB approximation for the penetration probability of [Formula: see text]-particle through the potential barrier. A Q-value-related formula is used to estimate the [Formula: see text]-particle preformation factor. The calculated [Formula: see text]-decay half-lives are compared with the available experimental data. The standard deviation between computed results and experimental data is obtained equal to 0.288. Comparison of our obtained standard deviation indicates well the validity of our chosen theoretical model. Furthermore, the characteristic of [Formula: see text]-decay energy and half-lives confirms the shell effects at [Formula: see text] magic number. Also, the obtained results predict similar closed shells behavior at [Formula: see text] and [Formula: see text] neutron numbers.

The critical role of interfacial Coulomb force in the orientation alignment behavior of lubricant molecules

The non-bonding interactions of four interfaces with typical polar interfacial characteristics are simulated using molecular dynamics methods. The Coulomb and Van der Waals terms in the optimized potentials for liquid simulations all-atom (OPLS_AA) force field are distinguished and their effects on the arrangement behavior of the lubricant molecules are investigated. A mathematical model is proposed to quantitatively characterize the influence on the tilt degree of lubricant molecules (PAO4 and PEG200) near the nano-silica surfaces. The tilt degree of the lubricant molecules at the interface is determined by the molecular chain tilt factor γ, which is calculated by combining the "polar characteristics of the solid surface", the characteristics of the "polar units" within the liquid molecules, and the linking modes between them.

Investigating the Linear Response Function under Approximations Following the Coupled-Perturbed Approach for Atoms and Molecules.

The linear response kernel also referred to as linear response function (LRF) in the framework of conceptual density functional theory has gained tremendous success in time-dependent density functional theory. Comparatively less attention has been devoted to the LRF from a chemical reactivity perspective in its time- or frequency-independent context, although it has recently been used to qualitatively describe electron delocalization, (anti-)aromaticity, inductive and mesomeric effects, etc. Despite these successes, which were obtained by approximating the LRF using the independent particle approximation deriving from a coupled-perturbed Kohn-Sham computation, the robustness of this LRF approach needs to be assessed. In this work, we compute the LRF at four levels of approximation (independent particle approximation, random phase approximation, Hartree-Fock approximation, and the (exact) DFT (density functional theory) expression) using functionals from the first four rungs of Jacob's ladder of exchange-correlation energy functionals. To scrutinize the impact of these approximations, new visualization strategies are discussed and systematized. The overall conclusion is that the independent particle approximation yields qualitatively correct results (ergo previous conceptual applications of the LRF are trustworthy), but for quantitative results, LRF expressions including coulomb and exchange(-correlation) terms should be included. With respect to functionals, density-gradient contributions to the exchange-correlation kernel are less than 10% and may be omitted safely where that is preferable computationally.

Arbitrary $$\ell$$-state solutions of the Klein–Gordon equation with the Eckart plus a class of Yukawa potential and its non-relativistic thermal properties

We report bound-state solutions of the Klein–Gordon equation with a novel combined potential, the Eckart plus a class of Yukawa potential, by means of the parametric Nikiforov–Uvarov method. To deal the centrifugal and the coulombic behavior terms, we apply the Greene–Aldrich approximation scheme. We present any $$\ell$$ -state energy eigenvalues and the corresponding normalized wave functions of a mentioned system in a closed form. We discuss various special cases related to our considered potential which are utility for other physical systems and show that these are consistent with previous reports in literature. Moreover, we calculate the non-relativistic thermodynamic quantities (partition function, mean energy, free energy, specific heat and entropy) for the potential model in question, and investigate them for a few diatomic molecules. We find that the energy eigenvalues are sensitive with regard to the quantum numbers $$n_r$$ and $$\ell$$ as well as the parameter $$\delta$$ . Our results show that energy eigenvalues are more bounded at either smaller quantum number $$\ell$$ or smaller parameter $$\delta$$ .

Scalar Breit interaction for molecular calculations.

Variational treatment of the Dirac-Coulomb-Gaunt or Dirac-Coulomb-Breit two-electron interaction at the Dirac-Hartree-Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac-Coulomb-Gaunt and Dirac-Coulomb-Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac-Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin-spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Aun (n = 2-8) show that the scalar Dirac-Coulomb-Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac-Coulomb-Breit Hamiltonian. The scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

Coulomb Problem for Classical Spinning Particles

We consider the motion of a weakly relativistic charged particle with an arbitrary spin in central potential e/r in terms of classical mechanics. We show that the spin–orbital interaction causes the precession of the plane of orbit around the vector of total angular momentum. The angular velocity of precession depends on the distance of the particle from the centre. The effective potential for in-plane motion is central, with the corrections to Coulomb terms coming from spin–orbital interaction. The possible orbits of a quantum particle are determined by the Bohr–Sommerfeld quantization rule. We give examples of orbits corresponding to small quantum numbers, which were obtained by numerical integration of equations of motion. The energies of stationary states are determined by spin–orbital interaction.

Strong magnetic fields and pasta phases reexamined

In this work, we compute the structure and composition of the inner crust of a neutron star in the presence of a strong magnetic field, such as it can be found in magnetars. To determine the geometry and characteristics of the crust inhomogeneities, we consider the compressible liquid drop model, where surface and Coulomb terms are included in the variational equations, and we compare our results with previous calculations based on more approximate treatments. For the equation of state (EoS), we consider two non-linear relativistic mean-field models with different slopes of the symmetry energy, and we show that the extension of the inhomogeneous region inside the star core due to the magnetic field strongly depends on the behavior of the symmetry energy in the crustal EoS. Finally, we argue that the extended spinodal instability observed in previous calculations can be related to the presence of small amplitude density fluctuations in the magnetar outer core, rather than to a thicker solid crust. The compressible liquid drop model formalism, while in overall agreement with the previous calculations, leads to a systematic suppression of the metastable solutions, thus allowing a more precise estimation of the crust-core transition density and pressure, and therefore a better estimation of the crustal radius.

Atomic scale interfacial magnetism and origin of metal-insulator transition in (LaNiO_3)_n/(CaMnO_3)_m superlattices: a first principles study

Interfacial magnetism and metal-insulator transition at LaNiO_3-based oxide interfaces have triggered intense research efforts, because of the possible implications in future heterostructure device design and engineering. Experimental observation lack in some points a support from an atomistic view. In an effort to fill such gap, we hereby investigate the structural, electronic, and magnetic properties of (LaNiO_3)_n/(CaMnO_3)_m superlattices with varying LaNiO_3 thickness (n) using density functional theory including a Hubbard-type effective on-site Coulomb term. We successfully capture and explain the metal-insulator transition and interfacial magnetic properties, such as magnetic alignments and induced Ni magnetic moments which were recently observed experimentally in nickelate-based heterostructures. In the superlattices modeled in our study, an insulating state is found for n=1 and a metallic character for n=2, 4, with major contribution from Ni and Mn 3d states. The insulating character originates from the disorder effect induced by sudden environment change for the octahedra at the interface, and associated to localized electronic states; on the other hand, for larger n, less localized interfacial states and increased polarity of the LaNiO_3 layers contribute to metallicity. We discuss how the interplay between double and super-exchange interaction via complex structural and charge redistributions results in interfacial magnetism. While (LaNiO_3)_n/(CaMnO_3)_m superlattices are chosen as prototype and for their experimental feasibility, our approach is generally applicable to understand the intricate roles of interfacial states and exchange mechanism between magnetic ions towards the overall response of a magnetic interface or superlattice.

Quadrupole deformation signatures in elastic electron scattering from oriented odd-A nuclei

Elastic electron scattering from oriented odd-A axially deformed nuclei is studied in the plane-wave Born approximation. The nuclear structure is described within a microscopic selfconsistent Skyrme deformed Hartree-Fock approximation with pairing correlations. The interference form factors between monopole and quadrupole Coulomb terms that characterize the nuclear response with aligned nuclear targets are shown to increase or decrease the unpolarized cross-section, depending on the sign of the quadrupole deformation. This feature provides valuable information on the nuclear deformation that can be used as a signature of the oblate or prolate character of the nuclear shape. Some selected cases of nuclei with different spins are presented that exemplify the scope of the method.

State Observer Based on an Accelerometer for an Elastic Joint with Nonlinear Friction

This paper presents a state observer for an elastic joint with nonlinear friction via the information from an acceleration sensor. In order to avoid discontinuities, the nonlinear friction of the motor, which includes static, coulomb, and viscous terms, is considered a smooth function. In addition, it uses an acceleration sensor to obtain the information about the link with high uncertainty. The proposed state observer guarantees that the estimation error for the position and velocity of the link connected via an elastic joint containing a nonlinear stiffness (elasticity) converges to zero. In addition, it is shown that the observer gain can be designed by LMI (linear matrix inequality) optimization. Finally, to verify the performance of the proposed observer, the method proposed in this paper is tested by experiments on a two-inertia system with an elastic shaft.