One-electron Model Research Articles

Entropy and Negative Specific Heat of Doped Graphene: Topological Phase Transitions and Nernst's Theorem Revisited.

This study explores the thermodynamic properties of doped graphene using an adapted electronic spectrum. We employed the one-electron tight-binding model to describe the hexagonal lattice structure. The dispersion relation for graphene is expressed in terms of the hopping energies using a compositional parameter that characterizes the different dopant atoms in the lattice. The focus of the investigation is on the impact of the compositions, specifically the presence of dopant atoms, on the energy spectrum, entropy, temperature, and specific heat of graphene. The numerical and analytical results reveal distinct thermodynamic behaviors influenced by the dopant composition, including topological transitions, inflection points in entropy, and specific heat divergences. In addition, the use of Boltzmann entropy and the revision of Nernst's theorem for doped graphene are introduced as novel aspects.

Demonstrating the Connection between the Nonvalence Correlation-Bound Anions of Polyaromatic Hydrocarbons and the Image Potential States of Graphene Using a One-Electron Model Hamiltonian.

The ground and excited state nonvalence correlation-bound (NVCB) anion states of the hexagonal polycylic aromatic hydrocarbons and of hexagonal graphene nanoflakes are characterized using a one-electron model Hamiltonian which incorporates atomic electrostatic moments up to the quadrupole, coupled inducible charges and dipoles, and atom-centered Gaussians to describe the short-range repulsive interactions. Extrapolation of the calculated electron binding energies of the lowest energy symmetric and antisymmetric (with respect to the molecular plane) NVCB anions of both the polycylic aromatic hydrocarbons and the carbon nanoflakes to the n → ∞ limit yields binding energies that are in good agreement with those of the most stable symmetric and antisymmetric image potential states of freestanding graphene as determined from two-photon photoemission spectroscopy (2PPE) experiments.

Quantitative reconstruction of atomic orbital densities of neon from partial cross sections

The approach of photoemission orbital tomography, i.e., the orbital density reconstruction from photoemission of planar molecular layers by using a formalism equivalent to a Fourier transformation, is transferred to free atoms. Absolute radial orbital densities of neon 1s, 2s, and 2p orbitals are reconstructed with a central-field one-electron model, using well-known atomic photoionization data. The model parameters are optimized by a Markov chain Monte Carlo method with Bayesian inference from which uncertainties for the reconstructed orbital densities are derived. The presented model opens the path for photoemission orbital tomography as a powerful tool, as well as for a quantitative analysis. Published by the American Physical Society 2024

Zeeman spectroscopy and crystal-field analysis of low symmetry centres in Nd3+ doped Y2SiO5

We report on infrared to visible Zeeman absorption spectroscopy and parameterised crystal-field modelling of Nd3+ centres in Y2SiO5 through the use of experimentally inferred crystal-field energy levels and Zeeman directional electronic g values. We demonstrate that good agreement between the calculated and experimental crystal-field energy levels as well as directional Zeeman g values along all three crystallographic axes can be obtained. Further, we demonstrate that the addition of correlation crystal field effects successfully account for discrepancies that arise between the calculated and experimental values relevant to the 2H(2) multiplet in a one-electron crystal field model.

Rigorous analysis of the effects of electron–phonon interactions on magnetic properties in the one-electron Kondo lattice model

The Kondo lattice model (KLM) is a typical model describing heavy fermion systems. In this paper, we consider the interaction of phonons with the system described by the one-electron KLM. Magnetic properties of the ground state of this model are revealed in a rigorous form. Furthermore, we derive the effective Hamiltonian in the strong coupling limit (\(J\rightarrow \infty \)) for the strength of the spin-exchange interaction J; we examine the magnetic properties of the ground state of the effective Hamiltonian and prove that the Aizenman–Lieb theorem concerning the magnetization holds for the effective Hamiltonian at finite temperatures. Generalizing the obtained results, we clarify a mechanism for the stability of magnetic properties of the ground state in the one-electron KLM system.

Surface Electrons: Theory and Electrohydrodynamic Applications

The paper presents the theory of surface electronic states induced by a high-voltage field and considers applications of the theory of surface electrons to electrohydrodynamic flows. Theoretical considerations were carried out within the framework of a one-electron quantum mechanical model. It is shown that surface electrons initiate the injection of negative charg-es from the cathode into a liquid dielectric containing an electron-withdrawing impurity, for example, molecular iodine. Comparison of the theoretic and experimental data is satisfacto-ry

Progress toward a one-electron model for the non-valence correlation-bound anions of polycyclic aromatic hydrocarbons

A one-electron model Hamiltonian is used to characterize the non-valence correlation-bound (NVCB) anions of hexagonal polycyclic aromatic hydrocarbons (PAHs) (n = 3–7). The model incorporates atomic electrostatic moments up to the quadrupole, coupled inducible charges and dipoles, and atom-centered repulsive Gaussians to describe the interaction between the excess electron and PAH. These model components are parameterized on and validated against all-electron calculations. Good agreement is found between the static dipole polarizabilities obtained from the model and those from PBE0 density functional theory and second-order Møller–Plesset perturbation theory calculations. In the model, charge flow dominates the in-plane polarizability of PAHs larger than C54H18, yielding an approximately quadratic scaling of the mean polarizabilty with the number of carbon atoms. Inclusion of electrostatic interactions decreases the electron binding energies for the largest PAHs considered by about 20% and shift charge distribution from above and below the plane of the ring system toward the periphery. Analysis of the electrostatic and polarization interactions provides insight into qualitative trends in the electron binding energy and the charge distribution of the lowest energy NVCB anion.

Polarons on Dimerized Lattice of Polyacetilene. Continuum Approximation

A one-electron model is proposed to describe a polaron on a dimerized polyacetylene lattice. Within the framework of the formulated model, the dynamics of a freely moving polaron is considered. The results obtained are compared with the many-electron model that takes into account all π-electrons of the valence band. Polaron can move at subsonic and supersonic speeds. The subsonic polaron is stable. A supersonic polaron loses stability at times ∼ 6 000 fs. A supersonic polaron has a forbidden speed range. An analytical solution to the continual approximation helps to understand the reason for the existence of forbidden speeds. The dynamics of a free polaron is similar to the dynamics of a polaron in an electric field. The proposed one-electron approximation significantly expands the possibilities of numerical simulation in comparison with the traditional many-electron model.

Molecular theory considering nuclear potential wells.

This article introduces potential wells around nuclei and their roles in chemical bonds. The approach uses one-electron Bohr atomic model concept. Multi-electron atoms are converted to one-electron atoms by grounding all inactive, non-reacting electrons using the Apparent Nuclear Charge (ANC) and Electron Shielding Effect (ESE) concepts introduced in earlier publications. Then, the resulting two one-electron atoms and their potential wells are utilized to obtain the related chemical bond length. The methodology is applicable to all elements of periodic table without a need for any additional tool. To test the concept, calculated bond lengths were compared to experimental ones for about 90 different bonds, which showed an average error of less than 5%. The article discusses some nontraditional views for chemical bonds which may contradict the traditional beliefs in chemistry. Hopefully, readers would consider the calculated results in support of the presented views. Attached to this article is a computer software program which was prepared with sample input and output files for readers. The software can be utilized to obtain any interested bond length. The software is applicable to all elements in the periodic table up to the element Hassium with the atomic number of 108. Nuclear potential well associated with the electron of hydrogen atom.

Инфракрасное фотоотражение полупроводниковых материалов A-=SUP=-3-=/SUP=-B-=SUP=-5-=/SUP=- ( О б з о р )

Photoreflectance is a contactless type of modulation optical spectroscopy. It is used to study the band structure features of monocrystalline semiconductors, their doping level, the composition of alloys, as well as surface and interface band bending. Using high-quality GaAs as an example, the possibilities of describing the photoreflectance lineshape by one-electron and exciton models are demonstrated. The spectra of ultrapure samples of this material exhibit an oscillating structure well described by excitonic effects. For III-V alloys, a review of photoreflectance results concerning the effect of composition and temperature on the band gap and spin-orbit splitting is carried out. Determination of the position of the Fermi level on the surface (Fermi level pinning) for III-V crystals is considered. The currently developing technique for measuring photoreflectance in the mid-infrared range (photomodulation Fourier transform infrared spectroscopy) is described in detail. It is shown that phase correction plays a decisive role in such measurements. Original results demonstrate the capabilities of this method in a wide wavelength range.

The Universe Can Be an Elementary Particle?

The dimension of our space outside the boundaries of the atom - the Solar System, gradually decreases to unity. But, the Universe is an n-dimensional continuum filled with a specific form of matter. Consequently, the space-time continuum is closed at the micro and macro levels, since in both cases it is a one-dimensional world. Given the one-electron model of the Universe, we conclude that the Universe is an elementary particle: an electron.

ARC 3.0: An expanded Python toolbox for atomic physics calculations

ARC 3.0 is a modular, object-oriented Python library combining data and algorithms to enable the calculation of a range of properties of alkali and divalent atoms. Building on the initial version of the ARC library (Šibalić et al., 2017), which focused on Rydberg states of alkali atoms, this major upgrade introduces support for divalent atoms. It also adds new methods for working with atom–surface interactions, for modelling ultracold atoms in optical lattices and for calculating valence electron wave functions and dynamic polarisabilities. Such calculations have applications in a variety of fields, e.g., in the quantum simulation of many-body physics, in atom-based sensing of DC and AC fields (including in microwave and THz metrology) and in the development of quantum gate protocols. ARC 3.0 comes with an extensive documentation including numerous examples. Its modular structure facilitates its application to a wide range of problems in atom-based quantum technologies. Program summaryProgram Title: ARC 3.0CPC Library link to program files:https://doi.org/10.17632/c4z4n2cdf7.1Licencing provisions: BSD-3-ClauseProgramming language: PythonExternal Routines: NumPy [1], SciPy [1], Matplotlib [2], SymPy [3], LmFit [4]Nature of problem: The calculation of atomic properties of alkali and divalent atoms including energies, Stark shifts and dipole–dipole interaction strengths using matrix elements evaluated through a variety of means.Solution method: Dipole matrix elements are calculated using an analytical semi-classical approximation or wave functions obtained by numerical integration of the radial Schrödinger equation for a one-electron model potential. Interaction energies and shifts due to external fields are calculated using second order degenerate perturbation theory or exact diagonalisation of the interaction Hamiltonian, yielding results valid even at large external fields or small interatomic separation.Additional comments including restrictions and unusual features: External electric and magnetic field must be parallel to the quantisation axis. The accuracy of short range (≲1μm) atom - atom interaction potentials is limited by the truncation of the basis. Only weak magnetic fields are supported as only linear Zeeman shifts are taken into account. Calculations for divalent atoms use a single-electron approximation and calculation of their wave functions is not supported.

Hydrogen Atom Transfer Reaction Free Energy as a Predictor of Abiotic Nitroaromatic Reduction Rate Constants: A Comprehensive Analysis.

A linear free energy model is presented that predicts the second-order rate constant for the abiotic reduction of nitroaromatic compounds (NACs). Previously presented models use the one-electron reduction potential of the NAC reaction . If is not available, it has been proposed that be computed directly or estimated from the gas-phase electron affinity (EA). The model proposed uses the Gibbs free energy of the hydrogen atom transfer (HAT) reaction as the parameter in the linear free energy model. Both models employ quantum chemical computations for the required thermodynamic energies. The available and proposed models are compared using experimentally determined second-order rate constants from 5 investigations from the literature in which a variety of NACs were exposed to a variety of reductants. A comprehensive analysis utilizing all the NACs and reductants demonstrate that the HAT energy model and the experimental one-electron reduction potential model have similar root mean square errors and residual error probability distributions. In contrast, the model using the computed EA has a more variable residual error distribution with a significant number of outliers. The results suggest that a linear free energy model utilizing computed HAT reaction free energy produces a more reliable prediction of the NAC abiotic reduction second-order rate constant than previously available methods. The advantages of the proposed HAT energy model and its mechanistic implications are discussed as well. Environ Toxicol Chem 2020;39:1678-1684. © 2020 SETAC.

Subsonic and supersonic polarons in one-electron model of polyacetylene

Free-moving polarons are investigated in the framework of new one-electron model of conjugated polymers. It is shown that on a dimerized lattice there exist free (in the absence of an external force like an electric field) stationary polarons, both subsonic and supersonic. Subsonic free polarons are observed in the velocity range from 0 to the speed of sound. Supersonic free polarons are observed in a limited range of velocities. There is a range of forbidden velocities between subsonic and supersonic free polarons. An analytical expression for the free polaron shape at different velocities is derived and confirmed in molecular dynamics simulations. The dynamics of subsonic and supersonic polarons in an electric field is different. It is shown that the subsonic polaron motion is not stationary and the velocity oscillations are associated with the periodic emission of tensile impulses in front of the polaron, taking away the energy received from the electric field. The supersonic polaron motion is stationary and the energy gained from the electric field is permanently transformed into oscillations behind the polaron.

Rydberg spectrum of a single trapped Ca+ ion: A Floquet analysis

We compute the Rydberg spectrum of a single Ca$^+$ ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in Ca$^+$, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for e$^-$+Ca$^{2+}$, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of Ca$^+(23P)$ and Ca$^+(52F)$ Rydberg lines.

Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene.

We consider the effect of atomic impurities on the energy spectrum and electrical conductance of graphene. As is known, the ordering of atomic impurities at the nodes of a crystal lattice modifies the graphene spectrum of energy, yielding a gap in it. Assuming a Fermi level within the gap domain, the electrical conductance diverges at the ordering of graphene. Hence, we can conclude about the presence of a metal–dielectric transition. On the other hand, for a Fermi level occurring outside of the gap, we see an increase in the electrical conductance as a function of the order parameter. The analytic formulas obtained in the Lifshitz one-electron strong-coupling model, describing the one-electron states of graphene doped with substitutional impurity atoms in the limiting case of weak scattering, are compared to the results of numerical calculations. To determine the dependence of the energy spectrum and electrical conductance on the order parameter, we consider both the limiting case of weak scattering and the case of finite scattering potential. The contributions of the scattering of electrons on a vapor of atoms to the density of states and the electrical conductance of graphene with an admixture of interstitial atoms are studied within numerical methods. It is shown that an increase in the electrical conductance with the order parameter is a result of both the growth of the density of states at the Fermi level and the time of relaxation of electron states. We have demonstrated the presence of a domain of localized extrinsic states on the edges of the energy gap arising at the ordering of atoms of the admixture. If the Fermi level falls in the indicated spectral regions, the electrical conductance of graphene is significantly affected by the scattering of electrons on clusters of two or more atoms, and the approximation of coherent potential fails in this case.

Effect of impurities ordering in the electronic spectrum and conductivity of graphene

By carrying out a computation in the Lifshitz tight-binding one-electron model, we obtain the energy spectrum and electrical conductance of graphene, in the presence of substitutional impurity atoms, thus assessing the influence of the latter. In the weak-scattering approximation, we study specific features of the electron energy spectrum in the gap region having width η|δ| and centered at the point yδ, arising because of the ordering of substitutional impurity atoms on nodes of the crystal lattice. Here η is the parameter of ordering, δ is the difference of the scattering potentials of impurity atoms and carbon atoms, and y is the impurity concentration. It is shown that if the ordering parameter η is close to ηmax=2y,y<1/2, the plot of the density of electron states has peaks on the edges of the energy gap. Those peaks correspond to impurity levels. As the ordering parameter η decreases, the impurity levels split into the impurity bands. The regions of localization of electron impurity states, which arise at the edges of the spectrum and edges of the energy gap, are investigated.

The energy spectrum and the electrical conductivity of graphene with substitution impurity

The effect of substitution atoms on the energy spectrum and the electrical conductivity of graphene was investigated in a Lifshitz one-electron tight-binding model. It is established that the ordering of impurity atoms results in a gap in the energy spectrum of electrons whose width depends on the order parameter and on the magnitude of the scattering potential. It is shown that if the order parameter is close to its maximum value, there are peaks associated with localized impurity states on the energy curve of the electron states density at the edges of the energy gap. At the electron concentration at which the Fermi level enters the gap region, the electrical conductivity is zero, and the metal-dielectric transition occurs. If the Fermi level falls in the region of the energy band, the electron relaxation time and electrical conductivity tend to infinity when the order parameter reaches its maximum value. The analytical calculations of the electron density and of the electrical conductivity of graphene, made in the limiting case of weak scattering, are compared with the results of the numerical calculations for different scattering potentials.

Excluded-volume descriptors for dipole-bound anions: Amine N-oxides as a test case.

Dipole-bound anions can be theoretically characterized at three fundamentally different levels. The highest are ab initio calculations, which themselves range from fairly approximate, say, Koopmans's Theorem (KT) or second-order Møller-Plesset perturbation theory, to highly sophisticated, say, the electron affinity equation-of-motion couple-cluster with single, double, and perturbative triple substitutions, which rivals experiments in reliability. The next level down is represented by one-electron model Hamiltonians. Again, one-electron model Hamiltonians can be fairly approximate, especially if the molecular system is modeled by a simple point-dipole and point-polarizable site; however, very reliable models have been developed for specific systems, for example, water clusters. At the lowest level, one can qualitatively explain trends in classes of dipole-bound anions in terms of the dipole moment, μ, the polarizability, α, and the so-called excluded volume, Vx. This project aims at the qualitative level. While the dipole moment and the polarizability possess clear-cut definitions, the excluded volume must-similar to all molecular volumes-remain a rather vaguely defined term, and so far, we are unaware of any quantitative definition in the literature. Here, we introduce and investigate three descriptors for Vx. To this end, we first establish a dataset with consistent ab initio results for 25 amine N-oxides structures. Then, we demonstrate that the descriptors are indeed able to explain trends for sets of isomers and conformers and investigate to what extent the descriptors are able to predict electron binding energy of dipole-bound states using simple quantitative structure-property relationship-like models. It turns out that μ and Vx provide a reasonably accurate prediction of the electrostatic part of the electron bind energy (the KT value) and that the polarizability α provides an acceptable prediction of the electron correlation contribution.

The one-electron self-interaction error in 74 density functional approximations: a case study on hydrogenic mono- and dinuclear systems.

The self-interaction error (SIE), i.e. unphysical interactions of electrons with themselves, has plagued developers and users of Density Functional Approximations (DFAs) since the inception of Density Functional Theory (DFT). Formally, it can be separated into the one-electron and many-electron SIE; herein we present one of the most comprehensive studies of the first. While we focus mostly on the total SIE, we also make use of two different decompositions. The first is a separation into functional and density-driven errors as championed by Sim, Burke and co-workers [J. Phys. Chem. Lett., 2018, 9, 6385-6392]; the second separates the error into exchange, correlation, and one-electron components, with the latter being a density error that has not been discussed in this form before. After investigating the familiar hydrogen atom and dihydrogen cation, we establish a relationship between the SIE and the nuclear charge with the help of a series of heavier hydrogenic analogues. For the mononuclear systems and the diatomics at the dissociation limit, this relationship is linear in nature with prominent exceptions, mostly belonging to the Minnesota and range-separated (double-)hybrid DFAs. For the first time, we also show how the magnitude of the SIE depends on the underlying atomic-orbital basis set and how DFAs that rely on a popular van-der-Waals DFT type London-dispersion term exhibit "self-dispersion". We find that range separation is not a panacea for solving the one-electron SIE. DFAs that have been developed to be one-electron SIE free for one system, such as the hydrogen atom, show larger errors for heavier hydrogenic systems. Often, one-electron SIE-free DFAs rely on fortuitous error cancellation between their exchange and correlation components. An analysis of the most robust methods for general applications to date reveals that they suffer moderately from the one-electron SIE, while DFAs that are nearly SIE-free do not perform well in applications. Implicit in the continued existence of the one-electron SIE is that well-performing DFAs continue to suffer insufficiencies at their fundamental levels that are being compensated for by the SIE. Our analysis includes more than 250 000 datapoints, resulting in multiple insights that may drive future developments of new DFAs or SIE corrections.