Atomic Self-consistent Field Research Articles

Hierarchical Basis Sets for the Calculation of Nuclear Magnetic Resonance Spin-Spin Coupling Constants Involving Either Selenium or Tellurium Nuclei.

New basis sets, acvXz-J (X = 2, 3, 4), were designed for tellurium and selenium atoms for the calculation of indirect nuclear spin-spin coupling constants involving selenium or tellurium nuclei. Saturation of angular spaces was performed in an even-tempered manner till achieving the convergence of spin-spin coupling constants under consideration. The high-accuracy correlated SOPPA(CCSD) method was employed in this procedure. Saturated basis sets were contracted by approximately 30% using the coefficients obtained from the atomic self-consistent field (SCF) closed-shell calculations of selenium and tellurium anions, Se2- and Te2-. Final basis sets of acvXz-J showed sufficiently high accuracy in comparison with previous special basis sets.

Jj-Coupling-based atomic self-consistent-field calculations with relativistic effective core potentials and two-component spinors

A self-consistent-field (SCF) program for the calculation of atomic energies and wave functions defined in jj-coupling using two-component atomic spinors and relativistic effective core potentials (RECPs) is described. The code is based on the linear combination of atomic orbitals SCF algorithm for atomic states defined in LS-coupling developed by Roothaan and Bagus. Hamiltonian matrix elements with respect to one- and two-electron operators, including RECPs, are calculated for two-component atomic spinor basis functions of either Gaussian-type orbitals (GTOs) or Slater-type orbitals (STOs). Electronic states are defined as eigenfunctions of the total angular momentum squared operator and tables of the required vector coupling coefficients that define such pure states are provided. In addition, one or more GTO expansions of large- and small-core RECPs and their corresponding GTO basis sets are supplied for all elements Z=3 through Z=118. Optimized two-component basis sets of STOs or GTOs can be calculated for use in molecular structure codes based on RECPs and relativistic electronic structure theory. Atomic asymptotic state energies at the SCF level of theory for analysis of molecular dissociation limits can be studied. Program summaryProgram title: jjatomProgram Files doi:http://dx.doi.org/10.17632/zs4twp8r67.1Licensing provisions: GPLv3Programming language: Fortran 90Nature of problem: Relativistic atomic energies and wave functions; optimization of two component spinor basis sets.Solution method: Atomic spinors defined in jj-coupling and expansions in two-component spinor basis functions of Gaussian- or Slater-type functions. Self-consistent field optimization of the total energy. Used for optimization of two-component atomic spinor basis sets and calculations of valence spectra of heavy elements.

RELATIVISTIC AND NONRELATIVISTIC APPROACHES IN THEORY OF PERMITTED BETA-TRANSITIONS: AN EFFECT OF ATOMIC FIELD ON FERMI AND INTEGRAL FERMI FUNCTIONS VALUES

Within a new optimized gauge-invariant Dirac-Fock approach it is considered a problem of computing the permitted beta transition probabilities and estimating a quality of computing the Fermi and integral Fermi functions in dependence upon the type of the atomic self-consistent field. It is shown that for small and middle values for the nuclear charge (Z<40) the difference between data obtained from other methods is low (hundredths of %). At the large Z (till Z~ 95; for example the beta decay 241Pu-241Am) calculation in a case of the HFSrel field gives 0.5% lower value for F, and respectively in a case of the GIDF field - 0.8%, compared with the non-relativistic HFSnerel value. This difference is explained by an effect of the squeezing for relativistic orbitals.

Björn O. Roos: 1937–2010. Mentor, colleague, innovator

Björn O. Roos: 1937–2010. Mentor, colleague, innovator

Photonionization and radiative recombination of Br——Comparison of rate coefficients deduced form the average atom and detailed configuration models

For practical purposes, the ionic stage and populations of hot dense plasma are often described by the average atom(AA) model instead of the detailed average configuration accounting(DCA) model, which is more close to the reality. According the atomic self-consistent field theory, we calculate the DCA reduced photonionization cross-sections of every subshell of Br ions in different ionic stages. Comparing these DCA reduced cross-sections with the reduced photonionization cross-secion of the corresponding average electronic orbital in the AA model, we deduce the inherent rules between the reduced cross-sections. Based on the AA reduced photonionization cross-section, the DCA reduced photonionization cross-sections and detailed configuration rate coefficients of photonionizaiton and radiative recombination can be calculated. This work is a necessary preparation for accurate description of non-local thermal equilibrium(n-LTE) plasma.

Chemical shifts in X-ray and photo-electron spectroscopy: a historical review

A review with historical emphasis is given of the discovery and evaluation of chemical shifts in X-ray and photo-electron spectroscopy. The discovery and interpretation of the shifts in the X-ray spectra in the early 1920s are treated as an introduction and general background. The discovery of the shifts in photo-electron spectra, discovered in the late 1950s, and its interpretation, which led to the invention of the electron spectroscopy for chemical analysis (ESCA) method in the early 1960s, are then reviewed. Various methods of evaluating the core-electron binding energies and chemical shift are discussed—from atomic self-consistent field calculations in the early 1960s to quite sophisticated many-body and density-functional calculation in the late 1990s.

Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals

A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic minimal-basis-set orbitals that deviate as little as possible from free-atom SCF minimal-basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed "quasiatomic minimal-basis-sets" is independent of the calculational atomic orbital basis used. The resulting resolution of molecular orbitals in terms of quasiatomic minimal basis set orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimal-basis orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn-Sham density functional theory orbitals and is easily generalized to valence MCSCF orbitals.

Accurate relativistic Gaussian basis sets determined by the third-order Douglas–Kroll approximation with a finite-nucleus model

Highly accurate relativistic Gaussian basis sets with a finite-nucleus model are developed for the 103 elements from H (Z=1) to Lr (Z=103). The present GTO sets augment the relativistic basis sets with a point-charge model proposed in the first paper of this series. The relativistic third-order Douglas–Kroll approach is adopted in optimizing the orbital exponents of a basis set by minimizing the atomic self-consistent field (SCF) energy. The basis sets are designed to have equal quality and to be appropriate for the incorporation of relativistic effects. The performance of the present basis sets is tested by calculations on a prototypical molecule, gold dimer using SCF and the singles and doubles coupled-cluster model with perturbative triples [CCSD(T)]. Several spectroscopic constants are calculated for the ground state of Au2. At the basis set superposition error (BSSE) corrected CCSD(T) level, the deviation from experiment is ΔRe=0.018 Å, Δωe=−3 cm−1, and ΔDe=−0.17 eV. The finite-size nucleus effect makes Re, ωe, and De smaller by 0.004 Å, 1 cm−1, and 0.05 eV, respectively. The application shows that the present relativistic Gaussian-type orbitals (GTO) basis sets with a finite-nucleus model are accurate and reliable.

Accurate core electron binding energy calculations using small 6-31G and TZV core hole optimized basis sets

A procedure for optimizing basis sets for core hole binding energies is described. Contracted Gaussian basis sets are optimized for ground state and core hole state atomic configurations, exponents and contraction coefficients being determined by a minimization of the atomic self-consistent field state within a simulated annealing procedure. The basis sets are used in connection with Δself-consistent field, ΔMøller–Plesset and ΔKohn–Sham theory calculations of core electron binding energies and chemical shifts of high accuracy. Whatever the method, the small basis sets optimized in this way give results with an accuracy comparable to that obtained using very extended normal basis sets close to the complete basis set limit. They provide an excellent alternative to treat large molecular systems and push the accuracy of the ΔKohn–Sham technique for binding energy computations even further, exhibiting only small (a few tenths of an electron volt) deviations from experimental data.

Accurate relativistic Gaussian basis sets for H through Lr determined by atomic self-consistent field calculations with the third-order Douglas–Kroll approximation

Highly accurate relativistic Gaussian basis sets are developed for the 103 elements from H(Z=1) to Lr (Z=103). Orbital exponents are optimized by minimizing the atomic self-consistent field (SCF) energy with the scalar relativistic third-order Douglas–Kroll approximation. The basis sets are designed to have equal quality and to be appropriate for the incorporation of relativistic effects. The basis set performance is tested by calculations on prototypical molecules, hydrides, and dimers of copper, silver, and gold using SCF, Møller–Plesset theory, and the singles and doubles coupled-cluster methods with and without perturbative triples [CCSD, CCSD(T)]. Spectroscopic constants and dissociation energies are reported for the ground state of each species. The effects of relativity, electron correlation, and the basis set superposition error (BSSE) are investigated. At the BSSE corrected CCSD(T) level, the mean absolute error relative to experiment in De for three dimers (hydrides) is 0.13 (0.09) eV; for Re the error is 0.024 (0.003) Å, and for ωe it is 2 (13) cm−1. These illustrative calculations confirm that the present basis sets fulfill their design objectives.

Fully optimized contracted Gaussian basis sets for atoms Li to Kr

Various contracted Gaussian basis sets for atoms up to Kr are presented which have been determined by optimizing atomic self-consistent field ground state energies with respect to all basis set parameters, i.e., orbital exponents and contraction coefficients.

Single-electron ionisation of Ar 3s2subshell by slow electrons

The effect of the self-consistent atomic field and atomic-electron correlations upon the magnitude and the form of the total cross section is considered theoretically. The calculations were performed in the Hartree-Fock approximation taking account of many-electron correlations for the incoming electron energy region from the ionisation threshold up to 100 eV. It has been found that consideration of the action of the atomic self-consistent field upon the incoming and scattered electrons, the exchange effects and the final-state configuration interaction is more essential than the correlation corrections within the RPAE.

L1-L23M Coster-Kronig transition energies

A non-relativistic atomic Hartree-Fock self-consistent field method has been used to demonstrate that L1-L23M Coster-Kronig transition energies are highly dependent upon the state of multiple ionization of the atom. The limiting atomic number values for energetically allowed processes corresponding to selected initial defect configurations have been determined. The calculated Coster-Kronig energy values are in acceptable agreement with the limited experimental results available. They are however significantly smaller than the empirical values commonly used in transition rate studies. The importance of the present findings for the interpretation of X-ray and Auger satellite spectra and for the interpretation of experimental data on the variation of fluorescence yield with atomic configuration is discussed. It is concluded that similar behaviour for Coster-Kronig processes associated with other shells in heavy atoms should be possible.

A Theoretical and Experimental Study of fe XIX to fe XXIV Solar-Flare Spectra and Isoelectronic Spectra in Sulfur

view Abstract Citations (31) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Theoretical and Experimental Study of Fe XIX to Fe XXIV Solar-Flare Spectra and Isoelectronic Spectra in Sulfur Fawcett, B. C. ; Cowan, R. D. ; Hayes, R. W. Abstract Atomic self-consistent field calculations are used to predict wavelengths and oscillator strengths of the - 13d transitions in Fe xix to Fe xxiv. The validity of these calculations is checked through comparison with new experimental data in the isoelectronic sequences. In particular, sulfur classifications are correlated and new S ix identifications reported. The application of the results in Fe XIX to xxiv, combined with some observational and theoretical considerations affecting expected solar line intensities, leads to a more definitive analysis of solar-flare spectra of these ions. Data of value to the analysis of improved solar-flare spectrograms are also presented. Subject headings: atomic processes - flares, solar - line identifications - spectra, X-ray - transition probabilities Publication: The Astrophysical Journal Pub Date: January 1974 DOI: 10.1086/152642 Bibcode: 1974ApJ...187..377F full text sources ADS |

Nonorthogonal atomic self-consistent field orbitals

A method is presented for determining nonorthogonal linear combinations of accurate self-consistent field atomic orbitals which are analogous to nodeless minimal-basis-set Slater-type atomic orbitals. The utility of such nonorthogonal basis orbitals is discussed in terms of applications to molecular calculations.

New classifications of highly ionized Ni, Co, Cr, V and isoelectronic spectra (Solar spectra)

The far ultraviolet spectra of the highly ionized solar-abundant element nickel is analysed on the basis of new observations of laser produced plasmas. The transitions involved are mainly between principal quantum numbers 3 and 4 and their spectra are observed and classified in isoelectronic elements in the period between nickel and scandium with the aid of atomic self-consistent field calculations. Recent solar iron identifications are supported and the data provide information about configurations which can account for solar forbidden lines.

The non-expansion of the octet

Analysis of effective potential functions for the 3d orbitals of sulphur and oxygen, obtained from atomic selfconsistent field calculations, indicate a possible origin for the non-expansion of the octet amongst first-row atoms of the Periodic Table.

Inner-electron rearrangement in the Hartree-Fock scheme

Atomic self-consistent field calculations are performed by numerical solution of the Hartree-Fock equations on each of the atoms in the third row of the periodic system, both with all the valence electrons present and with all the valence electrons absent. Ionization energies resulting when the inner shells are not allowed to relax, as well as the contributions to the ionization energies from the relaxation of the inner shells, are evaluated along that series for the first time, and are separately examined: contributions shown by the 1s, 2s and 2p orbitals upon stripping off of the valence electrons are not all of the same sign. The same is true of the changes in the mean radii of these orbitals. These results are explained in terms of exchange and Coulomb interactions between inner and valence (outer) shells, and as a consequence of the variations in the nuclear screening. The accuracy of Koopmans' theorem for monovalent species is tested by comparison with the Hartree-Fock contribution to the ionization potential of the valence electron. Hartree-Fock and experimental ionization potentials are also compared along the above-mentioned series of third-row elements.

RELATION BETWEEN ELECTRONS AND HOLES, AND THE VECTOR-COUPLING COEFFICIENTS FOR pmfq AND dnfq CONFIGURATIONS

The electrostatic energy of an atomic state arising from a configuration involving holes differs by ΔW from the energy expression of the same state arising from the configuration involving electrons where ΔW can be expressed in terms of Slater's integrals.General formulas for ΔW are given for the pmfq and dnfq configurations. In addition, the vector-coupling (VC) coefficients useful for atomic self-consistent field (SCF) calculations are presented for all the states arising from the pmfq and dnfq configurations.

Vector Coupling Coefficients for Atomic Self-Consistent-Field (SCF) Calculations

General formulas are derived for the vector-coupling coefficients useful in atomic self-consistent-field (SCF) calculations. Tables of these coefficients for all the states arising from atomic configurations consisting of any combination of s, p, and d shells and for a single f shell have been prepared and are available for atomic SCF calculations.