Classical Coulomb Interaction Research Articles

Random phase approximation for gapped systems: Role of vertex corrections and applicability of the constrained random phase approximation

The many-body theory of interacting electrons poses an intrinsically difficult problem that requires simplifying assumptions. For the determination of electronic screening properties of the Coulomb interaction, the Random Phase Approximation (RPA) provides such a simplification. Here, we explicitly show that this approximation is justified for band structures with sizeable band gaps. This is when the electronic states responsible for the screening are energetically far away from the Fermi level, which is equivalent to a short electronic propagation length of these states. The RPA contains exactly those diagrams in which the classical Coulomb interaction covers all distances, whereas neglected vertex corrections involve quantum tunneling through the barrier formed by the band gap. Our analysis of electron-electron interactions provides a real-space analogy to Migdal's theorem on the smallness of vertex corrections in electron-phonon problems. An important application is the increasing use of constrained Random Phase Approximation (cRPA) calculations of effective interactions. We find that their usage of Kohn-Sham energies already accounts for the leading local (excitonic) vertex correction in insulators.

Electronic Structure and Stability of [B12X12]2- (X = F-At): A Combined Photoelectron Spectroscopic and Theoretical Study.

The stability and electron loss process of numerous multiply charged anions (MCAs) have been traditionally explained in terms of the classical Coulomb interaction between spatially separated charged groups. An understanding of these processes in MCAs with not well-separated excess charges is still lacking. We report the surprising properties and physical behavior of [B12X12]2-, X = F, Cl, Br, I, At, which are MCAs with not well-separated excess charges and cannot be described by the prevailing classical picture. In this series of MCAs, comprising a "boron core" surrounded by a "halogen shell", the sign of the total charge in these two regions changes along the halogen series from X = F-At. With the aid of experimental photoelectron spectroscopy and highly correlated ab initio electronic structure calculations, we demonstrate that the trend in the electronic stability of these MCAs is determined by the interplay between the Coulomb (de)stabilization originating from the "boron core" and "halogen shell" and the extension of the overlap between the orbitals from both regions. The second excess electron is always taken from the most positively charged region, viz., the "boron core" for X = F, Cl, and the surrounding "halogen shell" for X = I, At. This change in the physical behavior is attributed to the position of the highest occupied molecular orbital, which dwells in a region that is spatially separated from the one containing the excess negative charge. The unusual intrinsic electronic structure of the [B12X12]2- MCAs provides the basis for a molecular level understanding of their observed unique physical and chemical properties and a new paradigm for understanding the properties of these MCAs with not well-separated charges that departs from the prevailing model used for spatially separated charges that is based on their classical Coulomb interaction.

Förster Resonance Energy Transfer between Fluorescent Proteins: Efficient Transition Charge-Based Study

Toward a better understanding of the Forster resonance energy transfer (FRET) utilized in genetically encoded biosensors we theoretically examined the excitonic coupling between cyan fluorescent protein (CFP) and yellow FP (YFP) with time-dependent density functional theory (TD-DFT). Going beyond the dipole–dipole (dd) approximation in the original Forster theory, we adopted a transition charge from the electrostatic potential (TrESP) method that approximates the excitonic coupling as classical Coulomb interaction between the transition charges derived from the transition density for each FP fluorophore. From the TD-DFT calculations with embedded point charges for the trajectory generated by classical molecular dynamics (MD) simulations we found that the thermal fluctuation of the fluorophore geometry in FP and the protein electrostatic interactions do not significantly affect the Coulomb interaction between the FP pairs. The TrESP calculations utilizing the Poisson equation indicate that the screening an...

A multipolar approach to the interatomic covalent interaction energy.

Interatomic exchange-correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp) expansion is customary used in biomolecular modeling to approximate the classical Coulomb interaction between two charge densities ρA(r) and ρB(r), we examine in this work the mp approach to approximate the interatomic exchange-correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1-2 pairs) albeit it works reasonably well most times for 1- n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to l1+l2=2 usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole-monopole xc mp term and the inter-atomic bond order, as measured by the delocalization index of the quantum theory of atoms in molecules, is also established. © 2017 Wiley Periodicals, Inc.

Ab Initio Potential for H3O+ → H+ + H2O: A Step to a Many-Body Representation of the Hydrated Proton?

We report a new potential energy surface (PES) for hydronium that dissociates to H+ + H2O. The PES is a permutationally invariant fit to a data set of nearly 100,000 electronic energies, of which most are CCSD(T)-F12/aug-cc-pVQZ, plus a small set of MRCI-aug-cc-pVTZ diabatic energies in the region where the CCSD(T) method fails. The long-range part of the PES is described accurately by a classical Coulomb interaction between the proton and H2O using partial charges obtained from an accurate, full-dimensional dipole moment surface. A switching function connects the fitted PES to this long-range interaction.The fidelity of this global PES is determined by a combination of standard geometry and harmonic analyses at the minimum and inversion saddle point. In addition, VSCF/VCI calculations of the fundamentals and tunneling splittings are reported; all of these are within 3 cm-1 or less of experimental values. A diffusion Monte Carlo calculation is also reported for the zero-point state. The PES is used in a two-body representation of the interaction of the proton with two water molecules, including a 2-body H2O-H2O interaction, and is shown to give a realistic description of the Zundel cation H5O2+. This demonstrates that the PES may be usable as a component in a many-body potential describing the hydrated proton, especially for vibrational calculations of protonated water clusters.

Role of nonlinearity in non-Hermitian quantum mechanics: Description of linear quantum electrodynamics from the nonlinear Schrödinger-Poisson equation

In this paper we consider a basic two-level nonlinear quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrodinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant \( \alpha\) is provided within 99.95% accuracy by the present first-order non-relativistic and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).

ELECTRON-ELECTRON INTERACTION IN THE NON-RELATIVISTIC LIMIT

The electron-electron potential in the one-photon exchange approximation with the omission of the spin-spin interaction, leads to the classical Coulomb interaction, but the inclusion of the latter results in the Møller interaction. Bethe and Fermi showed that the latter interaction leads to the Breit potential, if a few of the terms in the expansion of the retardation effect are considered. In this article, it is shown that the higher order terms omitted in the Bethe-Fermi treatment reduces to terms of the same order in Dirac's alpha-matrices considered by Bethe and Fermi. This raises questions whether the Breit interaction is the appropriate first order correction to the Coulomb potential in the non-relativistic limit. It is pointed out that the nature of the interaction between two bound (1s) electron derived by Brown using the Schwinger formalism of the quantum electrodynamics but proposed empirically in 1929 by Gaunt could be a better correction to the Coulomb potential for bound electrons in atoms. The calculated energies using these matrix elements plus the vacuum polarization energies are in reasonable agreement with the data. For comparison, calculated energies using the Breit interaction plus vacuum polarization energies are also presented.

Hydrogen adsorption in HKUST-1: a combined inelastic neutron scattering and first-principlesstudy

Hydrogen adsorption in high surface area nanoporous coordination polymers has attracteda great deal of interest in recent years due to the potential applications in energy storage. Herewe present combined inelastic neutron scattering measurements and detailed first-principlescalculations aimed at unraveling the nature of hydrogen adsorption in HKUST-1 (Cu3(1,3,5-benzenetricarboxylate)2), a metal–organic framework (MOF) with unsaturated metal centers. We revealthat, in this system, the major contribution to the overall binding comesfrom the classical Coulomb interaction which is not screened due to theopen metal site; this explains the relatively high binding energies and shortH2–metal distances observed in MOFs with exposed metal sites as compared to traditional ones.Despite the short distances, there is no indication of an elongation of the H–H bond for the boundH2 molecule at the metal site. We find that both the phonon and rotational energy levelsof the hydrogen molecule are closely similar, making the interpretation of theinelastic neutron scattering data difficult. Finally, we show that the orientation ofH2 has a surprisingly large effect on the binding potential, reducing the classical bindingenergy by almost 30%. The implication of these results for the development of MOFmaterials for better hydrogen storage is discussed.

Nature and Tunability of Enhanced Hydrogen Binding in Metal−Organic Frameworks with Exposed Transition Metal Sites

Metal−organic framework (MOF) compounds with exposed transition-metal (TM) sites were recently found to exhibit significantly larger experimental heats of adsorption of H2 than classical MOFs, thus attracting greater attention. Here we show that the hydrogen binding in Mn4Cl−MOF is not of the expected Kubas type because there is (a) no significant charge transfer from TM to H2, (b) no evidence of any H2-σ* Mn-d orbital hybridization, (c) no significant H−H bond elongation, and (d) no significant shift in H−H stretching mode frequency. We make predictions for the magnetic superexchange interactions in Mn4Cl−MOF and determined low- and high-spin states of the Mn ion as local minima with very different hydrogen binding energies. We show that, by replacing Cl with F or Br, one can tune the H2 binding energy. We further reveal that the major contribution to the overall binding comes from the classical Coulomb interaction which is not screened due to the open-metal site and explains the relatively high binding energies and short H2−TM distances observed in MOFs with exposed metal sites compared to traditional ones. Finally, we show that the orientation of H2 has a surprisingly large effect on the binding potential, reducing the classical binding energy by almost 30%.

Temperature-dependent cyclotron resonance in a hybridized electron–hole system in InAs/GaSb heterostructures

Cyclotron resonance measurements are performed as a function of temperature on InAs/GaSb quantum well structures. The effects of electron–hole hybridization on cyclotron resonance are found to be strongly temperature dependent. As the temperature increases, the cyclotron resonance spectra narrow dramatically and multiple splittings due to electron–hole hybridizations disappear. This phenomenon is believed to be due to the classical Coulomb interaction between electrons with different cyclotron effective masses. The influence of the minigap formed due to electron–hole coupling is shown to be particularly important in narrower gap structures where strong thermal excitation of carriers is observed across the minigap. The influence of the minigap on the system is confirmed by the application of large parallel magnetic fields which decouple the electron and hole bands.

Designable electron transport features in one-dimensional arrays of metallic nanoparticles: Monte Carlo study of the relation between shape and transport

We study the current and shot noise in a linear array of metallic nanoparticles taking explicitly into consideration their discrete electronic spectra. Phonon assisted tunneling and dissipative effects on single nanoparticles are incorporated as well. The capacitance matrix which determines the classical Coulomb interaction within the capacitance model is calculated numerically from a realistic geometry. A Monte Carlo algorithm which self-adapts to the size of the system allows us to simulate the single-electron transport properties within a semiclassical framework. We present several effects that are related to the geometry and the one-electron level spacing like e.g. a negative differential conductance (NDC) effect. Consequently these effects are designable by the choice of the size and arrangement of the nanoparticles.

Analysis of low-momentum correlations with Cartesian harmonics

Exploiting final-state interactions and/or identity interference, analysis of anisotropic correlations of particles at low-relative velocities yields information on the anisotropy of emission sources in heavy-ion reactions. We show that the use of Cartesian surface-spherical harmonics in such analysis allows for a systematic expansion of the correlations in terms of real angular-moment coefficients dependent on relative momentum. The coefficients are directly related to the analogous coefficients for emission sources. We illustrate the analysis with an example of correlations generated by classical Coulomb interaction.

The dynamical equation of the spinning electron

We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when quantized. It is shown that the dynamics can be described in terms of the evolution of the point charge which satisfies a fourth-order differential equation or, alternatively, as a system of second-order differential equations by describing the evolution of both the centre of mass and centre of charge of the particle. As an application of the found dynamical equations, the Coulomb interaction between two spinning electrons is considered. We find from the classical viewpoint that these spinning electrons can form bound states under suitable initial conditions. Since the classical Coulomb interaction of two spinless point electrons does not allow for the existence of bound states, it is the spin structure that gives rise to new physical phenomena not described in the spinless case. Perhaps the paper may be interesting from the mathematical point of view but not from the point of view of physics.

Electronic structure and many-body effects in self-assembled quantum dots

A detailed model for the electronic properties of self-assembled InAs/GaAs quantum dots (SADs) is presented, with emphasis on inter-level transitions and many-body effects. The model is based on the self-consistent solution of three-dimensional Poisson and Schrödinger equations within the local (spin-) density approximation. Nonparabolicity of the band structure and a continuum model for the strain between GaAs and InAs results in position- and energy-dependent effective mass. The electronic spectra of SADs of various shapes have been determined with intraband level transitions and mid-infrared optical matrix elements. Shell structures obeying Hund's rule for various occupation numbers in pyramidal SADs agree well with recent capacitance measurements. It is shown that many-body interactions between orbital pairs of electrons are determined in a first approximation by classical Coulomb interaction.

Electron-electron interactions between orbital pairs in quantum dots

We derive a simple model for the estimates of the orbital-pair interaction in self-assembled dots and show that many-body interactions between all orbital pairs for a few electrons are determined in a first approximation by the classical Coulomb interaction between the first two electrons. The estimated values are within 35% of the accurate results derived from local density functional theory. We extend the model to electrostatically defined planar quantum dots and find a better agreement (20%). This is a result of the weakening of the individual orbital-pair interactions with the number of electrons in the dot caused by the screening of the confining potential.

Theoretical modeling of a weak correlation effect in a nonideal plasma

Weak correlation effect in a nonideal plasma system has been modeled within a fluid description by an average classical Coulomb interaction potential in dynamic momentum equation of the electrons. This is the lowest order correction and models the small deviation from the ideal gas behavior of the plasma. Numerical solution of the Poisson equation shows a reasonably good agreement with the earlier calculation based on the statistical formulation of the particle correlation in plasmas. Effects of the particle correlation may be displayed through the modification in the dispersion characteristics of the plasma waves/sheath potential at a surface in contact with the nonideal plasma.

Evidence for influence of the interactions between electrons on the chemical potential of a two-dimensional electron gas

It is shown experimentally that the interactions between electrons strongly influence the chemical potential of the two-dimensional electron gas. At sufficiently low temperatures and in high magnetic fields regions of filling factor appear where (i) the chemical potential diminishes with increasing carrier density, and (ii) the rate of increase of the chemical potential with magnetic field is much higher than the maximum value for a noninteracting gas. Using these results we have estimated the energy of the electron-electron interaction in Si inversion layers which appears to be an order of magnitude less than the classical Coulomb interaction calculated for Si-MOSFET's.

Classical Coulomb interaction between undistorted atoms of arbitrary symmetry

Abstract A general expression is obtained for the classical electrostatic interaction between undistorted atomic charge distributions constructed through one-electron Hartree-Fock wave functions. The original two-center problem is uncoupled by working in Fourier space leading to one-center integrals. The results of this work are suitable for applications of the independent atom model (IAM) in the study of molecule formation.

Evidence for the influence of electron-electron interaction on the chemical potential of the two-dimensional electron gas.

It is shown experimentally that the interaction between electrons strongly influences the chemical potential of the two-dimensional (2D) electron gas. At sufficiently low temperatures and in high magnetic fields, regions of filling factor appear where (i) the chemical potential \ensuremath{\mu} diminishes with increasing carrier density, i.e., the thermodynamic density of states is negative; (ii) the derivative \ensuremath{\partial}\ensuremath{\mu}/\ensuremath{\partial}H (H is the magnetic field) is considerably higher than the maximum value for a noninteracting 2D electron gas. Using these results, we have estimated that the energy of the e-e interaction in Si inversion layers in a magnetic field is about 1 order of magnitude less than the classical Coulomb interaction calculated for Si metal-oxide-semiconductor field-effect transistors.

Dynamical properties of a two-dimensional Coulomb fluid

Simplified expressions for the fourth-frequency-moment sum rules for the longitudinal- and transverse-current correlation functions have been obtained for a two-dimensional classical Coulomb fluid interaction with a logarithmic potential. The numerical results for these sum rules are presented as a function of wavenumber k for Gamma =2, 10 and 40. Using the exact result for the triplet correlation function for Gamma =2, it is found that the error involved in the use of the superposition approximation is about 5% for 0.4<or=k<or=4.0. Sum rules and a simple mean-field theory are used to study the plasma wave dispersion for Gamma =72. Results are in close agreement with recent molecular dynamics calculations.