Calculation of the Electron Binding Energies and X-Ray Energies for the Superheavy Elements 114, 126, and 140 Using Relativistic Self-Consistent-Field Atomic Wave Functions

1968 ◽  
Vol 174 (1) ◽  
pp. 118-124 ◽  
Author(s):  
Thomas C. Tucker ◽  
Louis D. Roberts ◽  
C. W. Nestor ◽  
Thomas A. Carlson ◽  
F. B. Malik
Keyword(s):  
Superheavy Elements ◽  
Binding Energies ◽  
Wave Functions ◽  
X Ray ◽  
Atomic Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Electron Binding Energies ◽  
Electron Binding

Core Electron Binding Energies in Solids from Periodic All-Electron Δ-Self-Consistent-Field Calculations

2021 ◽  
Vol 12 (38) ◽  
pp. 9353-9359
Author(s):  
J. Matthias Kahk ◽  
Georg S. Michelitsch ◽  
Reinhard J. Maurer ◽  
Karsten Reuter ◽  
Johannes Lischner
Keyword(s):  
Binding Energies ◽  
Core Electron ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Electron Binding Energies ◽  
Electron Binding

SCATTERING FACTORS FOR SOME OF THE HEAVIER ATOMS

1959 ◽  
Vol 37 (9) ◽  
pp. 967-969 ◽  
Author(s):  
Beatrice H. Worsley
Keyword(s):  
Wave Functions ◽  
Radial Wave ◽  
X Ray ◽  
University Of Toronto ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Atomic Scattering ◽  
Approximate Wave ◽  
The University

A program for calculating X-ray atomic scattering factors from the radial wave functions has been written for the IBM 650 installation at the University of Toronto. It has been applied to the results of self-consistent field calculations previously performed at this University on the FERUT computer. Results are given for Ne, V++, Kr, Ag+, and Pb+++. The results for Ne and V++ are compared with those calculated by Freeman using Allen's wave functions for Ne and Hartree's approximate wave functions for V++.

scholarly journals Multi-reference Approach to the Computation of Double-Core-Hole Spectra

2021 ◽  
Author(s):  
Bruno Nunes Cabral Tenorio ◽  
Piero Decleva ◽  
Sonia Coriani
Keyword(s):  
Small Molecules ◽  
Ground State ◽  
Binding Energies ◽  
Wave Functions ◽  
Correlation Effects ◽  
Core Hole ◽  
Active Space ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Double-Core Hole (DCH) states of small molecules are assessed with the restricted<br>active space self-consistent field (RASSCF) and multi-state restricted active space perturbation<br>theory of second order (MS-RASPT2) approximations. To ensure an unbiased<br>description of the relaxation and correlation effects on the DCH states, the neutral<br>ground state and DCH wave functions are optimized separately, whereas the spectral<br>intensities are computed with a biorthonormalized set of molecular orbitals within the<br>state-interaction (SI) approximation. Accurate shake-up satellites binding energies and<br>intensities of double-core-ionized states (K<sup>-2</sup>) are obtained for H<sub>2</sub>O, N<sub>2</sub>, CO and C<sub>2</sub>H<sub>2n</sub><br>(n=1–3). The results are analyzed in details and show excellent agreement with recent<br>experimental data.

Wave functions for the normal states of Ne+3 and Ne+4

1957 ◽  
Vol 53 (3) ◽  
pp. 663-668 ◽  
Author(s):  
Charlotte Froese ◽  
D. R. Hartree
Keyword(s):  
Atomic Number ◽  
Wave Functions ◽  
The Self ◽  
Atomic Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Normal States ◽  
Mathematical Laboratory

ABSTRACTSolutions of Fock's equations for the self-consistent field with exchange have been carried out for Ne+4, using the EDSAC at the Mathematical Laboratory, Cambridge. The initial estimates for the calculation were made by a simplified version of a method previously suggested for interpolating atomic wave functions with respect to atomic number. This gave good estimates for Ne+4, and it is probable that estimates for Ne+3, obtained similarly, are already accurate enough for practical use. Such wave functions for Ne+3 are given. The results have application in astrophysical contexts.

scholarly journals Multi-reference Approach to the Computation of Double-Core-Hole Spectra

2021 ◽  
Author(s):  
Bruno Nunes Cabral Tenorio ◽  
Piero Decleva ◽  
Sonia Coriani
Keyword(s):  
Small Molecules ◽  
Ground State ◽  
Binding Energies ◽  
Wave Functions ◽  
Correlation Effects ◽  
Core Hole ◽  
Active Space ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Double-Core Hole (DCH) states of small molecules are assessed with the restricted<br>active space self-consistent field (RASSCF) and multi-state restricted active space perturbation<br>theory of second order (MS-RASPT2) approximations. To ensure an unbiased<br>description of the relaxation and correlation effects on the DCH states, the neutral<br>ground state and DCH wave functions are optimized separately, whereas the spectral<br>intensities are computed with a biorthonormalized set of molecular orbitals within the<br>state-interaction (SI) approximation. Accurate shake-up satellites binding energies and<br>intensities of double-core-ionized states (K<sup>-2</sup>) are obtained for H<sub>2</sub>O, N<sub>2</sub>, CO and C<sub>2</sub>H<sub>2n</sub><br>(n=1–3). The results are analyzed in details and show excellent agreement with recent<br>experimental data.

scholarly journals Results of calculations of atomic wave functions. II.—Results for K + and Cs +

1934 ◽  
Vol 143 (850) ◽  
pp. 506-517 ◽  
Keyword(s):  
Wave Functions ◽  
The Self ◽  
Numerical Accuracy ◽  
Atomic Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Approximate Wave ◽  
High Degree

In a recent papers I presented the results of calculations of approximate wave functions of two atoms, based on the method of the “self-consistent field”, these calculations having been carried out to a fairly high degree of numerical accuracy (for work of this kind) as regards both precision of the work and the approximation to the self-consistent field attained, in order that the results published should be quite dependable. I also gave a survey of the situation which led to such calculations being undertaken, and mentioned other atoms for which they were being made. This paper presents a second instalment of such results, namely, those for the atoms K + and Cs + . Of these atoms, Cs is the heaviest for which calculations of the self-consistent field have so far been completed, though work on a still heavier atom, namely, mercury, has been started, and it is hoped that rough results, at least, will be available before long.

Self-Consistent Field Calculations of X-Ray Emission Spectra of Surface Adsorbates and Polymers

1997 ◽  
Vol 7 (C2) ◽  
pp. C2-515-C2-516
Author(s):  
H. Agren ◽  
L. G.M. Pettersson ◽  
V. Carravetta ◽  
Y. Luo ◽  
L. Yang ◽  
...  
Keyword(s):  
Emission Spectra ◽  
X Ray ◽  
Consistent Field ◽  
Self Consistent ◽  
Surface Adsorbates ◽  
Self Consistent Field

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

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