Study of an approximate relation between the energy of an atom and the electronic potential at the nucleus

This paper provides an analysis of the reasons for the approximate validity of the relation \documentclass{article}\pagestyle{empty}\begin{document}$ E = \frac{3}{7}NV(0) $\end{document}, between the total energy E of a neutral atom, the number N of electrons, and the electronic potential at the nucleus V(0). Using the density functional formalism we find that the right-hand side of the above equation also appears (and is the leading term) in density functional approximations more sophisticated than the Thomas–Fermi (TF ) approximation (the above equation is exact in the TF approximation). Systematic improvements to the equation appear to be difficult because the main corrections come from those terms which are more difficult to handle in the density functional formalism. After this analysis we propose a kinetic energy functional for neutral atoms in the Hartree–Fock approximation. The first term of this new functional is a rescaled Thomas–Fermi term , where γ = ?0.0063 for light atoms and γ = 0.0085 for the others. The second term is the first gradient correction due to Kirzhnits . For lithium to krypton atoms, this new functional gives an average error of 0.22%.     

A density functional study of the electronic spectrum of permanganate

Multiplet splittings for six excited electronic configurations of the permanganate ion, MnO₄⁻, are calculated. Earlier density functional calculations on the same subject are improved upon by the numerical evaluation of some two-electron integrals to resolve certain multideterminantal states. Excellent agreement with the experimental spectrum is obtained, and a reassignment of bands in the 25,000–35,000 cm⁻¹ range is proposed. Fully symmetric (a₁) vibrational frequencies are calculated, and the origin and magnitude of the most significant Jahn-Teller distortions of the excited states are discussed. © 1996 John Wiley & Sons, Inc.     

Atomic resolution density maps reveal secondary structure dependent differences in electronic distribution

The X-ray crystal structure of the flavoenzyme cholesterol oxidase, SCOA (Streptomyces sp.SA-COO) has been determined to 0.95 A resolution. The large size (55kDa) and the high-resolution diffraction of this protein provides a unique opportunity to observe detailed electronic effects within a protein environment and to obtain a larger sampling for which to analyze these electronic and structural differences. It is well-known through spectroscopic methods that peptide carbonyl groups are polarized in alpha-helices. This electronic characteristic is evident in the sub-Angstrom electron density of SCOA. Our analysis indicates an increased tendency for the electron density of the main chain carbonyl groups within alpha-helices to be polarized toward the oxygen atoms. In contrast, the carbonyl groups in beta-sheet structures tend to exhibit a greater charge density between the carbon and oxygen atoms. Interestingly, the electronic differences observed at the carbonyl groups do not appear to be correlated to the bond distance of the peptide bond or the peptide planarity. This study gives important insight into the electronic effects of alpha-helix dipoles in enzymes and provides experimentally based observations that have not been previously characterized in protein structure.     

On the relationship between the electron-pair distribution function and the correlation energy of an atom

The pair distribution function h(r₁₂;r₁, γ) and the virial theorem are used to derive a general expression for the local contributions to the total correlation energy of an atom. A direct link between correlation effects and the correlation energy is obtained by use of G(r₁, γ) and Γ(r₁, y). The former is the probability associated with a given choice of r₁ and γ, while the latter describes the local contribution to the correlation energy. Explicit calculations for the ground state of helium indicate that the angular dependence of the local contribution to the correlation energy is essentially independent of r₁, whereas the local correlation energy shows a strong r₁ dependence. The maximum contribution to the correlation energy occurs at intermediate values of γ where there is close agreement between the Hartree–Fock and exact densities.     

Lithium atom spin density from the Hiller-Sucher-Feinberg identity

Summary The electronic spin density, which determines the observed Fermi contact hyperfine splitting, is usually represented by a delta function operator at the nucleus. Approximate wavefunctions determined by overall energetic considerations may show large errors for such a highly localized property. Hiller, Sucher, and Feinberg (HSF) have shown that the delta function operator can be replaced by a global operator. The possibility that this may lead to an improved method for calculation of the spin density is examined for the ground and first excited states of the lithium atom. Particular attention is given to simple spin polarization wavefunctions that provide the leading contributions to the spin density. It is found that the delta function and HSF formulations give very nearly the same results when the wavefunctions are determined by essentially exact numerical methods. However, the HSF approach shows clear advantages in calculations carried out with finite Slater or contracted Gaussian type basis sets.     

Radial intensity distribution of atom and ion lines in an argon ICP

Summary The measured radial intensity distribution of atom and ion lines of four elements (Be, Mg, Zn and Li) with ionization energies varying from 5–9 eV are compared with theoretically calculated radial intensity distributions of analyte based on a one-dimensional model. The model simulated the distributions satisfactorily when the radius ranged between 1 and 3 mm.

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Radiale Intensitätsverteilung von Atom- und Ionenlinicn in einem Argon-ICP

Zusammenfassung Die gemessene radiale Intensitätsverteilung der Atom- und Ionenlinien von 4 Elementen (Be, Mg, Zn, Li) mit lonisierungsenergien von 5 bis 9 eV wurden mit theoretisch berechneten Verteilungen verglichen, die auf einem eindimensionalen Modell beruhen. Im Radiusbereich von 1 bis 3 mm entsprach das Modell den Messungen zufriedenstellend.

     

A density functional study on the electronic structures of TiN solid

The electronic structures of TiN bulk have been studied by using different theoretical formalisms, and the DFT method, especially the BLYP method can produce reasonable results. The band structure of TiN (001) surface is also investigated and two a type surface states are presented in our results. The state located at 2.9 eV below EF in angle resolved photoemis-sion in (ARPES) is well reproduced in this work, which consists essentially of 2pz orbital of surface N atom. Another surface state is associated with the bands originated from 3d orbital of surface Ti atom. Furthermore, the elastic constants of TiN are also calculated by using BLYP method.     

Resonances in angular distribution of secondary photons from an excited atom in the (e +A +) recombination

Resonances in the angular distribution of secondary photons from an excited atom which are formed during the electron-ion recombination process are considered. The interference between the radiation and dielectronic recombination branches leads to sharp changes in the fluorescence angular anisotropy in the region of autoionization states. The concrete calculations have been carried out for the helium ion recombination.     

Towards an exact orbital-free single-particle kinetic energy density for the inhomogeneous electron liquid in the Be atom

Holas and March [Phys. Rev. A51, 2040 (1995)] wrote the gradient of the one-body potential V(r) in terms of low-order derivatives of the idempotent Dirac density matrix built from a single Slater determinant of Kohn–Sham orbitals. Here, this is first combined with the study of Dawson and March [J. Chem. Phys. 81, 5850 (1984)] to express the single-particle kinetic energy density of the Be atom ground-state in terms of both the electron density n(r) and potential V(r). While this is the more compact formulation, we then, by removing V(r), demonstrate that the ratio t(r)/n(r) depends, though non-locally, only on the single variable n′(r)/n(r), no high-order gradients entering for the spherical Be atom.     

Current density distribution,limiting current density and saturation current density in an ion-exchange membrane electrodialyzer

The current density distribution in a seawater electrodialyzer is approximated by a quadratic equation. The equation is solved using a three-dimensional simultaneous equation, and the current density distribution and the coefficients expressing the current density distribution are calculated. The method for estimating the limiting current density and the saturation current density of an electrodialyzer is established using the current density distribution coefficients. Electrodialytic conditions (current density, solution velocity and electrolyte concentration in desalting cells, the thickness and flow-pass length of a desalting cell, the standard deviation of the solution velocity ratio in desalting cells and the overall osmotic coefficient of a membrane pair) versus the current density distribution coefficients, limiting current density and saturation current density are obtained. Electrodialytic conditions at which current density reaches the limiting current density or saturation current density are determined.     

Accurate electron density and one-electron properties for the beryllium atom

An accurate analytical electron density for the beryllium atom is obtained by using a fast and systematic method recently developed and tested for the neon atom. Asymptotic conditions both at the nucleus and at large distances are obeyed. A point-by-point comparison between our density and the one obtained from an almost “exact” configuration interaction wave function shows that differences are less than 0.5% for r between 0 and 5 bohrs and less than 1 % up to 9 bohrs. The accuracy of the density is also assessed by comparing results of density moments and x-ray scattering factors.     

Distribution of electronic density in n-mononitroalkanes

In the framework of ??quantum theory of atoms in molecule?? (QTAIM) was distribution of electronic density analyzed and inductive effect studied in trans- and gauche-isomers of n-mononitroalkanes CH₃(CH₂) _n NO₂ with n ?? 8. Influence of NO₂ is demonstrated to spread on the four neighboring NO₂ groups. Association of gauche-effect with the electronic density distribution has been given adequate consideration. Definitions were formulated for the standard NO₂ group and perturbed CH₂ groups. It has been suggested the refinements of additive procedures for properties calculation of n-nitroalkanes as well as of big molecules containing the nitroalkane substituents.     

Theoretical study of lithium ionic conductors by electronic stress tensor density and electronic kinetic energy density

We analyze the electronic structure of lithium ionic conductors, and , using the electronic stress tensor density and kinetic energy density with special focus on the ionic bonds among them. We find that, as long as we examine the pattern of the eigenvalues of the electronic stress tensor density, we cannot distinguish between the ionic bonds and bonds among metalloid atoms. We then show that they can be distinguished by looking at the morphology of the electronic interface, the zero surface of the electronic kinetic energy density. © 2016 Wiley Periodicals, Inc.     

Non-unitary classification of molecular electronic structures and other atom clusters

Molecules or reacting assemblies of an isomeric set of atoms become related to each other regardless of any spatial symmetry by the principle of linear covariance and the valency dyad field introduced in two previous papers by the author. Crucial electronic indices characterize certain equivalence classes into which molecules get classified under transformations which are in general non-unitary.     

Ground state electronic structures of some metal atom cluster compounds

The ground state electronic structures of several metal atom cluster compounds, Re₃Cl₉, Re₃Cl^3?₁₂ and Mo₆Cl^2?₁₄, have been calculated by the SCF Xα SW method. The results are consistent with the earlier d-orbital overlap patterns and with the reported spectroscopic properties.