General variation method for the relativistic calculations of atoms and molecules

Use of the general variation method of Weinstein and MacDonald for the relativistic calculation of atoms and molecules is proposed. It is shown from the numerical calculations for hydrogenlike atomic systems that this method is useful in judging an accuracy of energies and wave functions obtained with a relativistic Hamiltonian whose spectra are not bounded. It is also shown that this method can be used to find spurious solutions such as 1p_½ or 2d_3/2 appearing in atomic systems. Problems in extending the method to many-electron atoms and molecules are discussed.     

X-ray and electron scattering factors for many-electron atomic system

Analytical expressions are developed for the x-ray and electron scattering factors for a many-electron atomic system when the single configuration wave function of the system is written as a sum of Slater determinants of spin orbitals. The radial part of the orbital is expanded in terms of Slater-type orbitals (STO 's). The expressions so developed have been used to calculate the coherent and incoherent x-ray and electron scattering factors and intensities for all the neutral atoms up to krypton (Z = 36) and for some positive and negative ions of chemical interest. The results obtained are used to test the value of Hartree–Fock wave functions for the evaluation of “one-electron properties” of many-electron atomic systems.     

Determination of the parameters of atomic pair correlations in nickel oxide films by the electron energy loss fine structure method

The electron energy loss extended fine structure (EELFS) spectra were obtained from the pure nickel surface (M _2,3 EELFS) of a stoichiometric NiO film (NiM _2,3 and OK EELFS spectra) and the “nonhomogeneous” oxide film on the surface of nickel Ni-O (NiM _2,3 and OK EELFS spectra). The amplitudes and intensities of electron transitions for the core levels of atoms were calculated with regard for the multiplicity of electron impact excitation of the corresponding core levels of atoms. The corresponding normalized oscillating terms were isolated using the results of calculations based on the experimental EELFS spectra. Agreement between the experimental and calculated (on Ni and NiO test objects) data showed that the theoretical approaches used and the calculated data for describing the EELFS spectra are good approximations. Using the results of calculations and the parameters of secondary electron elastic scattering (FEEF-8 data) we obtained the atomic pair correlation functions from the experimental normalized oscillating parts of the EELFS spectra by Tikhonov’s regularization method.     

X-ray single crystal study of reversible thermochromism and the pecularities of atomic thermal motion in n,n-diphenylguanidinium(1+) hexabromotellurate (IV)

Peculiarities of the atomic structure of N,N-diphenylguanidium (1+) hexabromotellurate (IV), (C₁₃H₁₄N₃)₂[TeBr₆], which has reversible thermochromic properties, have been studied by X-ray single crystal method at different temperatures. It has been revealed that temperature-dependent distortions of the geometry of the thermochrom compound are not expressed anyhow substantially; therefore, the temperature behavior of thermal parameters of Br atoms was studied in detail. For the first time the interrelation between the thermochromic properties of the complex and peculiarities of atomic thermal vibrations has been disclosed: abnormally great increase in the deflection angle of the axis σ₃ of the ellipsoid of thermal vibrations of apical bromine atoms from Te-Br bond direction under the temperature reduction reflects the decrease of vibronic interaction between the ground and the first excited state of Te(IV) (the display of Jahn-Teller dynamic effect of the second order) and, correspondingly, results in asymmetry lessening of the band A in the absorption spectrum and causes the change in compound color determined by it. There has been revealed the presence of C-H…Br hydrogen bond via hydrogen atoms of phenyl rings of diphenylguanidium. Basing on the analysis of atomic thermal parameters, it has been established that the apical atom Br(4) having the shortest distance in the octahedron is linked with the central atom relatively weaker than other atoms.     

Zn or O? An Atomic Level Comparison on Antibacterial Activities of Zinc Oxides

For the first time, the influence of different types of atoms (Zn and O) on the antibacterial activities of nanosized ZnO was quantitatively evaluated with the aid of a 3D‐printing‐manufactured evaluation system. Two different outermost atomic layers were manufactured separately by using an ALD (atomic layer deposition) method. Interestingly, we found that each outermost atomic layer exhibited certain differences against gram‐positive or gram‐negative bacterial species. Zinc atoms as outermost layer (ZnO?Zn) showed a more pronounced antibacterial effect towards gram‐negative E. coli (Escherichia coli), whereas oxygen atoms (ZnO?O) showed a stronger antibacterial activity against gram‐positive S. aureus (Staphylococcus aureus). A possible antibacterial mechanism has been comprehensively discussed from different perspectives, including Zn²⁺ concentrations, oxygen vacancies, photocatalytic activities and the DNA structural characteristics of different bacterial species.     

Left-right asymmetry in superelastic collisions of polarized electrons with unpolarized laser-excited sodium atoms

Polarized electrons have been scattered superelastically from laser-excited unpolarized sodium atoms (deexcitation of the 3² P _1/2 or 3² P _3/2 states). The left-right scattering asymmetry, which results from an interplay of the atomic charge cloud orientation, atomic fine-structure interaction and exchange processes, has been measured for energies between 6 and 20 eV and scattering angles ranging from 40 to 120°. Within the experimental uncertainty the Percival-Seaton hypothesis, which is the basis of current theoretical calculations for electron-sodium collisions, has been confirmed. However, the quantitative agreement between experimental and numerical results is satisfactory only for a 2-state close-coupling calculation of Moores.     

The Valence-Bond (VB) Model and Its Intimate Relationship to the Symmetric or Permutation Group

VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent entity built up of electrons and nuclei and characterized by its molecular structure. Nevertheless, there is a much more fundamental difference between these two models which is only revealed when the symmetries of the many-electron Hamiltonian are fully taken into account: while the VB and MO wave functions exhibit the point-group symmetry, whenever present in the many-electron Hamiltonian, only VB wave functions exhibit the permutation symmetry, which is always present in the many-electron Hamiltonian. Practically all the conflicts among the practitioners of the two models can be traced down to the lack of permutation symmetry in the MO wave functions. Moreover, when examined from the permutation group perspective, it becomes clear that the concepts introduced by Pauling to deal with molecules can be equally applied to the study of the atomic structure. In other words, as strange as it may sound, VB can be extended to the study of atoms and, therefore, is a much more general model than MO.     

Nonadiabatic theory of electron–vibrational coupling: New basis for microscopic interpretation of superconductivity

A systematic procedure has been developed to construct an electronic energy matrix for diatomics in the basis of antisymmetrized products of atomic wave functions represented as linear combinations of coupled momenta eigenfunctions. The exchange matrix element is expanded in powers of electronic interchange between atoms. General expressions of many-electron angular coefficients have been obtained for all types of products of one- and two-electron and overlap integrals in energy matrix elements. © 1992 John Wiley & Sons, Inc.     

Gaussian expansions from STOs by the distance between subspaces

Expansions of STO orbitals with GTO s for the first-row atoms have been obtained by the method of the distance between subspaces. The expansion coefficients and exponential parameters were simultaneously varied when the distance between subspaces, which are generated from STO and GTO functions, is minimized. The ζ; exponents (or scale factors) for the atomic orbitals that are optimized for these atoms are also shown to be almost independent of the number of Gaussian functions. Comparisons carried out with Stewart's least-squares method produce equivalent results when exponents for 2s and 2p functions are different. Some examples and applications for several atomic properties of the first-row atoms are included: energies and expectation values of rⁱ and pⁱ for the several expansions. These new minimal basis sets were tested for diatomic and polyatomic molecules containing these atoms. © 1993 John Wiley & Sons, Inc.     

Structure of the electron momentum density of atomic systems

The present paper addresses the controversial problem on the nonmonotonic behavior of the spherically-averaged momentum density γ(p) observed previously for some ground-state atoms based on the Roothaan-Hartree-Fock (RHF) wave functions of Clementi and Roetti. Highly accurate RHF wave functions of Koga et al. are used to study the existence of extrema in the momentum density γ(p) of all the neutral atoms from hydrogen to xenon. Three groups of atoms are clearly identified according to the nonmonotonicity parameter μ, whose value is either equal to, larger, or smaller than unity. Additionally, it is found that the function p^?α γ(p) is (i) monotonically decreasing from the origin for α ≥ 0.75, (ii) convex for α ≥ 1.35, and (iii) logarithmically convex for α ≥ 3.64 for all the neutral atoms with nuclear charges Z = 1–54. Finally, these monotonicity properties are applied to derive simple yet general inequalities which involve three momentum moments 〈p ^t≥. These inequalities not only generalize similar inequalities reported so far but also allow us to correlate some fundamental atomic quantities, such as the electron-electron repulsion energy and the peak height of Compton profile, in a simple manner.     

Matrix elements of multi-electron operator in restricted Hartree-Fock theory

A theorem has been established for the matrix elements of a general t-electron operator between N-dimensional determinantal wave functions arising in the solution of the atomic and molecular multi-electron problem by the restricted Hartree-Fock (RHF) method (1 ≤ t ≤ N). The required matrix elements of this operator are sums of matrix elements over t-dimensional basic determinantal wave functions. The final results are especially useful in the determination of multi-electron properties for atoms and molecules when the Hylleraas approach in RHF theory is employed.     

Generalized exponential functions applied to atomic calculations

The use of a generalized exponential function r ^v?1 exp(?ζr ^μ ) as a radial basis function in atomic calculations is studied with our special interest in the variationally optimum value of the parameter μ, since special cases of μ = 1 and μ = 2 correspond respectively to the radial parts of commonly-used Slater-type and Gaussian-type functions. Roothaan-Hartree-Fock calculations are performed for ground-state neutral atoms with atomic number Z = 2–54, singly-charged cations with Z = 3–55, and anions with Z = 1–53 within the single-zeta (or minimal basis) framework. For all the species examined, the optimtum μ values are found to be smaller than unity and increase towards unity as the atomic number increases. The present results support the use of Slater-type functions when μ is restricted to be an integer, but suggest from the variational point of view that even the exponential decay of Slater-type functions is too “strong” within the single-zeta approximation.     

Atomic transferability within the exchange‐correlation density

Starting from either the exchange or the exchange‐correlation density together with Bader's definition of an atom in a molecule, an atomic hole density function can be defined. Contour maps of atomic hole density functions are able to show how the electron density of each atom in a molecule is partially delocalized into the rest of atoms in the molecule. The degree of delocalization of the atomic density ultimately depends on the nature of the atom studied and its environment. Atomic hole density functions are also used to define an atomic similarity measure, which allows for the quantitative assessment of the degree of atomic transferability in different molecular environments. In this article, contour maps for the N atom in the (N₂, CN⁻, NO⁺) series and the O atom in the (CO, H₂CO, and HCOOH) series are presented at the Hartree–Fock and CISD levels of theory. Moreover, the transferability of N and O within the two series is studied by means of atomic similarity measures. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1361–1374, 2000     

The effect of low earth orbit atomic oxygen exposure on phenylphosphine oxide-containing poly(arylene ether)s

Unoriented thin films of phenylphosphine oxide-containing poly(arylene ether)s were exposed to low Earth orbit aboard the space shuttle Atlantis (STS-51) as part of a flight experiment designated Limited Duration Candidate Exposure (LDCE 4–5). The samples were exposed to primarily atomic oxygen (!10,\7×10¹⁹ atoms/cm²). Based on post-flight analyses using atomic force microscopy, X-ray photoelectron spectroscopy, gel permeation chromatogrpahy and weight loss data, it was proposed that atomic oxygen exposure of these materials produces a phosphate layer at the surface of the samples, apparently by the reaction of atomic oxygen with the phosphorus in the polymer backbone. Ground-based oxygen plasma exposure experiments have previously shown that this phosphate layer provides a barrier against further attack by atomic oxygen [1]. The results obtained from these analyses compare favorably with those obtained from samples exposed to an oxygen plasma in ground-based exposure experiments [1]. © 1998 John Wiley & Sons, Ltd.     

Shake up and shake off probabilities for L-, M-, and N-electrons in atoms with Z=3 to 60

In sudden approximation, the probabilities of shake up and shake off processes upon ionization of atomic inner shells are calculated for outer-shell L-, M-, and N-electrons in atoms with Z=3–60. The relative role of the shake off processes increases with the atomic number. Within the same shell of the same atom, the shake off processes are relatively more probable for the nl electrons with smaller l.     

Population analyses that utilize projection operators

Several different methods have been explored that partition the 3‐D space of a molecule into its atomic components using Hermitian one‐electron position‐space projection operators, P_A. Previously, we defined P_A so that hard interatomic boundaries between atoms are observed. This idea has been extended to allow softer boundaries that have a region of overlap between atoms that can be controlled through an iterative process. Functions that determine the shape of the atomic volume are also discussed. The atomic electron populations of 17 different systems are presented as a function of these two factors. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 384–394, 2003     

Electron spin-spin contact interaction in many-electron atoms

A general formulation has been developed for the evaluation of the total electron spin-spin contact interaction in many-electron atoms, including both the intra- and inter-shell contributions. Calculations have been carried out, using existing analytical Hartree-Fock functions, for the positive ions, neutral systems, and negative ions for all the atoms from He to Kr.

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Zusammenfassung Es wird ein allgemeiner Formalismus zur Berechnung der gesamten Elektronen-Spin-Spin-Kontakt-Wechselwirkung in Vielelektronen-Atomen angegeben, der sowohl die Anteile der Wechselwirkung innerhalb einer Schale als auch zwischen einzelnen Schalen berücksichtigt. Berechnungen wurden unter Benutzung vorhandener analytischer Hartree-Fock-Funktionen für die positiven Ionen, die neutralen Systeme und die negativen Ionen aller Atome von He bis Kr durchgeführt.

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This work has been supported in part by the National Research Council of Canada.     

The accuracy of hyperfine integrals in relativistic NMR computations based on the zeroth-order regular approximation

The accuracy of the hyperfine integrals obtained in relativistic NMR computations based on the zeroth–order regular approximation (ZORA) is investigated. The matrix elements of the Fermi contact operator and its relativistic analogs for s orbitals obtained from numerical nonrelativistic, ZORA, and four–component Hartree–Fock–Slater calculations on atoms are compared. It is found that the ZORA yields very accurate hyperfine integrals for the valence shells of heavy atoms, but performs rather poorly for the innermost core shells. Because the important observables of the NMR experiment—chemical shifts and spin–spin coupling constants—can be understood as valence properties it is concluded that ZORA computations represent a reliable tool for the investigations of these properties. On the other hand, absolute shieldings calculated with the ZORA might be substantially in error. Because applications to molecules have so far exclusively been based on basis set expansions of the molecular orbitals, ZORA hyperfine integrals obtained from atomic Slater-type basis set computations for mercury are compared with the accurate numerical values. It is demonstrated that the core part of the basis set requires functions with Slater exponents only up to 10⁴ in the case where errors in the hyperfine integrals of a few percent are acceptable.     

Relativistic theory of an inhomogeneous electron liquid in relation to atomic binding energies

Experimentally determined ionization potentials in the literature are used to plot the binding energies for neutral atoms as a function of atomic number Z for Z?=?2–30, 32, 36, 42. From this pretty smooth plot we have subtracted non-relativistic Hartree–Fock binding energies, using both available numerical values and the almost analytical result, based on the non-relativistic Thomas–Fermi statistical theory valid for large Z. The difference is still relatively smooth. For Mo, with Z?=?42, the difference is about 70 atomic units. This difference is then analyzed using first relativistic theory of an inhomogeneous electron liquid and then the Local Density Approximation (LDA), and for Mo their results yield approximately 88 and 67 atomic units respectively. We infer that a highly accurate relativistic many-electron theory will therefore be needed before reliable electron correlation energies can be extracted from the experimental binding energies for atoms heavier than Argon. This fact has prompted us to use available LDA calculations to confront three theoretical predictions of the Z dependence of non-relativistic electron correlation energies at large Z.