Electron-electron Interaction Energy Research Articles

Hydrogen-like impurities in Si and Ge quantum dots in connection with 5 nm and beyond metal-oxide-semiconductor technologies

The industrial drive towards smaller semiconductor devices is at less than 10 nano-meters. In the next few years a three-dimensional quantum confined device structure is expected. We have studied the electronic structure of hydrogen-like donor impurities in Si and Ge quantum dots with varied shape of the confinement potential. These calculations are carried out within the Density-Functional-Effective-Mass Theory (DF-EMT). We have paid particular attention to the electron-electron interaction energy in a negative charge state of the donor impurity. The effect of electron correlation on the binding energy has been explored. In addition to these, we show that the second order correction to the ground state energy obtained through perturbative approach agrees well with the DF-EMT based numerical results, down to very small sizes of the quantum dots when the depth of the confinement is moderate or small. A non-monotonic shallow-deep transition of the binding energy of neutral and charged donors of hydrogen-like impurities is expected to occur with the reduction in the size of the quantum dot. A similar effect is expected for hydrogen-like acceptor impurities as well. Furthermore, the optical gap also shows non-monotonic shallow-deep behaviour with the quantum dot size reduction. Deepening of shallow donor or acceptor level implies that the carriers will freeze out at small sizes of the dot. We believe this is quite important in the context of metal-oxide-semiconductor (MOS) devices beyond 5 nm technologies, based on Si, Ge or a combination (SiGe). We also point out possible variabilities in the binding energy of donors and acceptors if there are variations in the size of host quantum dots in a large assembly of devices in future integrated circuits. This will lead to the variabilities in the characteristics from device to device. These results should be incorporated in the Technology Computer Aided Design (TCAD) simulation of less than or equal to 5 nm MOS devices.

Resonant photoemission studies on Fe-Ni alloys

This paper investigates the electronic structure of Fe1−xNix (x = 0.32, 0.36, 0.4, 0.5) alloys employing high resolution photoelectron spectroscopy using synchrotron radiation. The valence bands and the core levels have been recorded at various on-resonance and off-resonance photon energies of Fe and Ni. An anti-resonance dip observed in the valence bands taken at Fe 3p → 3d resonance lies closer to the Fermi level compared to that observed at Ni 3p → 3d resonance, indicating larger density of itinerant Fe 3d electrons. Whereas, Ni 3d states are comparatively less itinerant in these alloys. The hybridization effects increase with increase of Fe content in the alloy system. The intensity of Ni L3M4,5M4,5 Coster-Cronig Auger transition observed with 853 eV (Ni 2p → 3d resonance) photon energy, drops down drastically for the Invar alloy (Fe0.64Ni0.36) as compared to other Fe-Ni alloys due to the existence of Ni in more than one local chemical surroundings as expected for Invar alloy. The electron-electron interaction energy (Udd) of Ni 3d shell is found to decrease with the decrease of Ni concentration. The 3p and 3s core levels of Fe and Ni recorded at 707 eV (Fe 2p → 3d resonance) are overwhelmed by various intense resonant Auger features such as Fe L3M2,3M2,3, Fe L3M2,3M4,5 and Fe L3M1M4,5. The 1S state of Fe L3M2,3M2,3 is greatly enhanced in the Invar alloy as compared to other alloys. The microscopic compositional in-homogeneity present in Invar alloy plays a crucial role in the screening of holes in Ni sites but does not contribute in screening the holes in Fe sites.

High harmonic generation in fullerene molecules

Using dynamical Hartree-Fock mean-field theory, we study the high harmonic generation (HHG) in the fullerene molecules ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ under strong pump wave driving. We consider a strong-field regime and show that the output harmonic radiation exhibits multiple plateaus, whose borders are defined by the molecular excitonic lines and cutoff energies within each plateau scale linearly with the field strength amplitude. In contrast to atomic cases for the fullerene molecule, with the increase of the pump wave photon energy the cutoff harmonic energy is increased. We also show that with the increase of the electron-electron interaction energy overall the HHG rate is suppressed. We demonstrate that the ${\mathrm{C}}_{70}$ molecule shows richer HHG spectra and a stronger high harmonic intensity than the ${\mathrm{C}}_{60}$.

A new approach to estimate atomic energies.

A new approach to estimate atomic energies is introduced. The method is based on utilization of experimental ionization energies as well as conversion of "n-electron atomic systems" to n "one-electron systems." Sample detail calculations are presented with typical graphs to show the distribution of different types of energy within an atom. The breakdown of atomic energies into kinetic, electron-nucleus attraction, and electron-electron repulsion is shown within an atom as well the total of energies of each type for elements. Then in a following step, the variations in kinetic, electron-electron, and electron-nucleus interaction energies of electrons as evidence for atomic shell changes are presented. Furthermore, the article overviews the spatial gaps between orbitals as an added evidence for existence of electronic shells. The findings in this article have significant implications for the structure of atoms and the layout of periodic table. Graphical abstractElectronic energy variations of barium (Ba) for kinetic, electron-electron repulsion, and electron-nucleus energies versus electron number.

Phase dilemma in natural orbital functional theory from the N-representability perspective

Any rigorous approach to first-order reduced density (1RDM) matrix functional theory faces the phase dilemma, that is, having to deal with a large number of possible combinations of signs in terms of the electron-electron interaction energy. This problem was discovered by reducing a ground-state energy generated from an approximate N-particle wavefunction into a functional of the 1RDM, known as the top-down method. Here, we show that the phase dilemma also appears in the bottom-up method, in which the functional E[1RDM] is generated by progressive inclusion of N-representability conditions on the reconstructed two-particle reduced density matrix. It is shown that an adequate choice of signs is essential to accurately describe model systems with strong non-dynamic (static) electron correlation, specifically, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, the Piris natural orbital functional 7 (PNOF7), with phases equal to -1 for the inter-pair energy terms containing the exchange-time-inversion integrals, agrees with exact diagonalization results.

Variationally fitting the total electron-electron interaction

Density fitting is used throughout quantum chemistry to simplify the electron-electron interaction energy (EE). A fundamental property of quantum chemistry, and DFT in particular, is that a variational principle connects the EE to a potential. Density fitting generally does not preserve this connection. Herein we describe the construction of a robust EE that is variationally connected to fitted potentials in all electronic structure methods. For DFT, this results in fitting equations that are satisfied at an energy saddle point in multidimensional fitting space.

Impurity with two electrons in the spherical quantum dot with Unite confinement potential

Two-electron states in a spherical QD with the hydrogenic impurity located in the center and with a finite height confinement potential barrier are investigated. The effective mass mismatch have been taken into account. The dependence of ground state energy and Coulomb electron-electron interaction energy correction on the QD size is studied. The problem of the state exchange time control in QD is discussed, taking into account the spins of the electrons in the Russell-Saunders approximation. The effect of quantum emission has been shown.

Propagating two-particle reduced density matrices without wave functions

Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density matrix (2-RDM). We develop a closed equation of motion for the 2-RDM employing a novel reconstruction functional for the three-particle reduced density matrix (3-RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing $N$-representability during time evolution is essential for achieving stable solutions. As a prototypical test case which features long-range Coulomb interactions we employ the one-dimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both one-particle observables such as the time-dependent dipole moment and two-particle observables such as the pair density and mean electron-electron interaction energy. Our results are in very good agreement with numerically exact solutions for the $N$-electron wavefunction obtained from the multiconfigurational time-dependent Hartree-Fock method.

Grain Boundary Controlled Electron Mobility in Polycrystalline Titanium Dioxide

Grain Boundary Controlled Electron Mobility in Polycrystalline Titanium Dioxide

A new method of calculation in the Fractional Quantum Hall Effect regime

AbstractThe electron-electron and electron-background interaction energies are calculated analytically for systems with up to N = 6 electrons. The method consists of describing the position vectors of electrons using complex coordinates and all the interaction energies with complex notation, whereby simplifications become possible. As is known, in this type of calculation, complicated expressions involving integrals over many variables are encountered and the trick of using complex coordinates greatly facilitates the exact calculation of various quantities. Contrary to previous analytical calculations, using complex coordinates avoids complicated trigonometric functions from appearing in the integrand, simplifying the exact evaluation of the integrals. The method we have used can be straightforwardly extended to larger systems with N > 6 electrons.

Equation of State for Electron-Electron Interaction Energy by Padé Approximation

Describing the electron-electron interaction contribution to the Helmholtz free energy, we obtained a new fitting formula by revising the electronic exchange contribution to the Helmholtz free energy of the previous fitting formula. Using Fortran program, we calculated the curves with some sensitive parameters like the electron-electron interaction contribution to the free energy and the Coulomb coupling parameter , temperature , the mean distance between the electrons making a comparison between the revised fitting formula and the formers. It is concluded that the theoretical value of the revised fitting formula basically has agreement with the previous theoretical value at , when , the revised value completely has a consistent with the previous results. It is illustrated that the curve of the revised fitting formula is more smooth, perfect, and we obtained a very good agreement between the theoretical result of the revised Helmholtz free energy and the theoretical result of the former Padé formulas, which illustrates us to get a more accurate fitting formula and result. Therefore, the revised fitting formula is a more complete and accurate description of the thermodynamic properties of the electron-electron interaction contribution to the Helmholtz free energy.

Extension of the search region of pair densities by means of the scaling of the electron coordinates

We present a scheme for correcting the pair density (PD) to get it close to the ground state one. The search region of PDs is efficiently extended by adding the uniformly-scaled PDs to its elements. The key point is that the search region of PDs is kept within the set of N-representable PDs. The validity of this scheme is confirmed by numerical calculations of neutral neon atom. It is shown that the root-mean-square error of the electron-electron interaction and external potential energies, which can be a benchmark for the error of the PD, is reduced to about two-third without additional heavy calculations.

Why is the ground-state electron configuration for lithium 1s22s?

The electronic ground state for lithium is 1s22s, and not 1s22p. The traditional argument for why this is so is based on a screening argument that claims that the 2p electron is better shielded by the 1s electrons, and therefore higher in energy than the configuration that includes the 2s electron. We show that this argument is flawed, and in fact the actual reason for the ordering is because the electron-electron interaction energy is higher for the 2p-1s repulsion than it is for the 2s-1s repulsion.

Correction method for obtaining the variationally best ground-state pair density

We present a correction method for the pair density (PD) to get close to the ground-state one. The PD is corrected to be a variationally best PD within the search region that is extended by adding the uniformly scaled PDs to its elements. The corrected PD is kept $N$-representable and satisfies the virial relation rigorously. The validity of the present method is confirmed by numerical calculations of neon atom. It is shown that the root-mean-square error of the electron-electron interaction and external potential energies, which is a good benchmark for the error of the PD, is reduced by 69.7% without additional heavy calculations.

Approximations for the interparticle interaction energy in an exactly solvable two-electron model atom

The capability of different ansatz kernels, denoted as K(r,r{sup '}), in the calculation of the electron-electron interaction energy is investigated here for an exactly solvable two-electron model atom proposed by Moshinsky. The model atom is in the spin-compensated, paramagnetic ground state. The exact expression for the interaction energy in this state, derived by the diagonal of the second-order density matrix, is used as a rigorous background for comparison. It is found that the form of K{sub M}(r,r{sup '})=2rho(r)rho(r{sup '})-gamma{sup p}(r,r{sup '})gamma{sup q}(r{sup '},r), expressed via the rho(r) density distributions and operator powers of the one-body density matrix gamma(r,r{sup '}), results in the exact value for the interparticle interaction energy of the two-electron model atom if and only if p=q=1/2. Approximate forms with p=qnot =1/2 and with pnot =q at (p+q)=1 give deviations from the exact expression.

Necessary and sufficient conditions for theN-representability of density functionals

It is well known that variational optimization of the energy using approximate density functionals can give results below the true ground-state energy. This can be attributed to the fact that many approximate density functionals are not N-representable. This paper presents a general method for deriving N-representability conditions in density-functional theory and presents specific results for the kinetic energy, the electron-electron interaction energy, the Hohenberg-Kohn functional, and the exchange-correlation energy functional. The method can be extended to energy densities, and specific results are presented for two different choices of the kinetic-energy density. Max-min variational principles for minimizing the energy subject to N-representability constraints are presented. Some constraints on exchange-correlation density functionals are among our secondary findings. In particular, we construct an exact meta-generalized-gradient-approximation meta-GGA functional using a Legendre transform and use this expression to show that a meta-GGAs should be convex functionals of the kinetic-energy density and b the sum of the Coulomb energy and the meta-GGA exchangecorrelation energy should be a convex functional of the electron density.

Significant Reduction of On‐Site Coulomb Energy U due to Short‐Range Correlation in an Organic Mott Insulator

By carrying out a first-principles T-matrix calculation on multiple scatterings between electrons, we show that the intramolecular electron-electron interaction energy U, of a Mott insulator of the organic radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) is significantly reduced from the naive expectation value of the Coulomb interaction (7.3 eV and 5.3 eV, respectively, for the bare and screened Coulomb interactions) to 2.9 eV due to the short-range correlation. This result together with the intermolecular interaction energy D=1.3 eV explains the experimental optical gap (1.5 eV). The associated two-particle wavefunction clearly shows the Coulomb hole indicating that two electrons with antiparallel spins cannot approach because of the Coulomb repulsion. We also discuss the energetics and magnetics of this system.

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.

Atomistic Simulation of the Electronic Transport in Organic Nanostructures: Electron-Phonon and Electron-Electron Interactions

This paper show a novel implementation of the GW correction applied to DFTB method and show its applications to molecular systems sandwiched in-between electrodes to obtain a first-principle correction of the electron-electron interaction energy. The resulting self-energy is used to correct the system GF and to obtain a correction of the tunneling current, behind DFT.

Bound states in a quantized Hall ferromagnet

We report on a study of the quasielectron-quasihole and skyrmion-antiskyrmion bound states in the $\nu=1$ quantum Hall regime. The short range attraction potential is assumed to be determined by a point magnetic impurity. The calculations are performed within the strong field approximation when the binding energy and the characteristic electron-electron interaction energy are smaller than the Landau level spacing. The Excitonic Representation technique is used in that case.