Physical properties of many-electron atomic systems evaluated from analytical Hartree-Fock functions

Numerical values are presented for the electric field gradients (q) and nuclear quadrupole coupling constants (eqQ) for a series of neutral atoms and their positive and negative ions. The angular dependence of the field gradient integrals is tabulated for configurations involving equivalent p and d electrons, for LS-coupling and central-force-field functions (e.g., Hartree-Fock functions).

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Zusammenfassung Für eine Reihe neutraler Atome und ihre positiven und negativen Ionen werden Zahlenwerte für die elektrischen Feldgradienten (q) und die Kernquadrupolkopplungskonstanten (eqQ) berechnet. Für Konfigurationen, die gleichwertige p- und d-Elektronen enthalten, wird für LS-Kopplung und Zentralkraftfeldfunktionen (z. B. Hartree-Fock-Funktionen) die Winkelabhängigkeit der Feldgradientenintegrale in Tabellenform angegeben.

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Résumé On présente les valeurs numériques pour les gradients de champ (q) et les constantes de couplage quadrupolaire (eqQ) pour des atomes neutres et leurs ions positives et négatives. On a calculé les valeurs des intégrales qui donnent la dependence angulaire du gradient de champ pour des configurations avec des électrons p et d équivalents, pour le couplage LS et fonctions de champ central (par exemple, fonctions de Hartree-Fock).

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

Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2

Ab initio accurate all-electron relativistic molecular orbital Dirac–Fock self-consistent field calculations are reported for the linear symmetric XeF₂ molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₂ at various internuclear distances. The relativistic correction to the electronic energy of XeF₂ was calculated as ～ ?215 hartrees (?5850 eV) by using the Dirac–Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac–Fock–Breit self-consistent field and perturbation methods. The calculated Breit correction is ～6.5 hartrees (177 eV) for XeF₂. The relativistic Dirac–Fock as well as the nonrelativistic HF wave functions predict XeF₂ to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF₂ by using various ab initio post Hartree–Fock methods. The calculated dissociation energy obtained using the MP 2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ～ ?2 hartrees (?54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe—F distance of 1.979 Å in XeF₂. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (D_e) close to experimental value for XeF₂. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF₂. © 1995 John Wiley & Sons, Inc.     

Acoustic soft modes of Nb3Sn in high magnetic fields

In single crystal Nb₃Sn the effect of a magnetic field upon the soft sound velocity v_s (110, 1$\text{1}$0) was measured at different temperatures above the structural phase transition point. The observed quadratic variation with field is in accordance with theory. But the magnitude of the field dependence is much smaller than expected and can only be explained by existing theories if the magnetic moment of the electron would vary by as much as a factor of two within an energy interval of some 100 K.     

Dissociation energy of ekaplutonium fluoride E126F: the first diatomic with molecular spinors consisting of g atomic spinors

Our ab initio all-electron fully relativistic Dirac-Fock (DF) and nonrelativistic (NR) Hartree-Fock (HF) self-consistent field (SCF) calculations predict the superheavy diatomic ekaplutonium fluoride E126F to be bound with the calculated dissociation energy of 7.44 and 10.46 eV at the predicted E126-F bond lengths of 2.03 and 2.18 Angstroms, respectively. The antibinding effects of relativity to the dissociation energy of E126F are approximately 3 eV. The predicted dissociation energy with both our NR HF and relativistic DF SCF wave functions is fairly large and is comparable to that for very stable diatomics. This is the first case, where in a diatomic, an atom has g orbital (l = 4) occupied in its ground state electronic configuration and such superheavy diatomics would have occupied molecular spinors (orbitals) consisting of g atomic spinors (orbitals). This opens up a whole new field of chemistry where g atomic spinors (orbitals) may be involved in electronic structure and chemical bonding of systems of superheavy elements with Z> or =122.     

Les conditions d'orthonormation dans la méthode SCF de champ auto-cohérent

Sans résumé     

Validity of first-order perturbation theory for relativistic energy corrections

First-order relativistic calculations give a relative error in the estimate of the total correction which increases like Z² from 0.26% for neon to 8% for xenon.     

Physical properties of many-electron atomic systems evaluated from analytical Hartree-Fock functions

Diamagnetic susceptibilities _dhave been calculated for all positive ions, neutral atoms, and negative ions up to Krypton. It is pointed out that the electrons in the outermost orbitals give the maximum contribution to _d.

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Zusammenfassung Die diamagnetische Suszeptibilität _dsind für alle positiven Ionen, neutrale Atome und negativen Ionen bis zum Krypton (Z=36) berechnet worden. Dabei zeigt es sich, daß die äußersten Schalen den größten Beitrag liefern.

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Résumé Les susceptibilités diamagnetiques _dont été calculées pour tous les ions positives, les atomes neutres et les ions négatives jusqu'au Krypton (Z=36). On montre que les couches électroniques exterieures donnent la contribution la plus importante.

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

Thirty years of relativistic self-consistent field theory for molecules: relativistic and electron correlation effects for atomic and molecular systems of transactinide superheavy elements up to ekaplutonium E126 with g-atomic spinors in the ground state configuration

Relativistic Hartree–Fock–Roothaan (RHFR) self-consistent field theory for molecules developed by Malli and Oreg (J Chem Phys 63, 830, 1975) is reviewed. Ab initio all-electron fully relativistic Dirac–Fock and the corresponding nonrelativistic Hartree–Fock calculations for a number of molecular systems of heavy and superheavy elements are discussed in order to asecrtain relativistic effects. It is pointed out for the first time that there are dramatic antibinding effects of relativity for diatomics of the superheavy elements ekagold and ekaastatine. These are first results of antibinding effects of relativity in relativistic quantum chemistry. Moreover, in order to take into account the relativistic and electron correlation effects simultaneously for these systems, relativistic Moeller Plesset second order (RMP2), coupled-cluster singles doubles (RCCSD) and RCCSD with inclusion of triple corrections perturbationally (RCCSD(T)) calculations performed by the author for a number of atomic and molecular systems of superheavy elements (SHE) including the primordial SHE ekaplutonium E126 (Z = 126) (with g atomic spinors occupied in the ground state atomic configuration) are reported. Such calculations and results have not been reported before for systems of superheavy elements. Contribution to the Serafin Fraga Memorial Issue. An erratum to this article can be found at