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  • 1
    Electronic Resource
    Electronic Resource
    Ab initio all-electron fully relativistic Dirac–Fock self-consistent field calculations for molecules of superheavy elements: Seaborgium hexabromide (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 5476-5480 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Gargantuan ab initio all-electron fully relativistic Dirac–Fock (DF) and nonrelativistic (NR) Hartree–Fock (HF) limit self-consistent field (SCF) molecular calculations are reported for SgBr6 at various Sg–Br bond distances assuming an octahedral geometry. Our fully relativistic Dirac–Fock and nonrelativistic HF calculations predict for SgBr6 bond distance of 2.52 and 2.59 Å, respectively. Both our DF and NR HF SCF calculations predict the ground state of SgBr6 to be bound, with the predicted atomization energy of 18.75 and 11.53 eV, respectively. A relativistic Dirac–Fock wave function predicts for SgBr6∼63% larger atomization energy than the corresponding NR HF calculation. The vertical ionization potential of SgBr6 calculated with our DF and HF wave functions is almost the same, viz., 10.60 and 10.78 eV, respectively. This is due to the fact that the HOMO consists entirely of the combination of the 4p AOs of the six Br ligands, for which relativistic effects are nominal. However, the vertical electron affinity calculated with our HF and DF wave function for SgBr6 is 5.35 and 3.80 eV, respectively. The calculated HF HOMO–LUMO gap of 7.74 eV is in fairly close agreement with that of 8.91 eV obtained from the corresponding DF relativistic MOs for SgBr6. These results can be understood in terms of the nature of the HOMOs and LUMOs calculated in our HF and DF calculations for SgBr6. Mulliken population analysis of our relativistic DF and HF wave functions yields a charge of 1.26 and 0.70, respectively on Sg in SgBr6; our DF wave function predicts SgBr6 to be more ionic (and less volatile) than that by the corresponding HF wave function. Our prediction of the bond dissociation energy of 44 and 72 kcal mol−1 with our NR HF and relativistic DF wave functions, respectively for SgBr6 is a first for a species of a superheavy transactinide element, as is our prediction of a positive electron affinity for SgBr6 with both our HF and DF wave functions. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1453959
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  • 2
    Electronic Resource
    Electronic Resource
    Ab initio all-electron Dirac–Fock–Breit calculations for ThF4 using relativistic universal Gaussian basis set (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 10736-10745 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Ab initio all-electron fully relativistic Dirac–Fock–Breit calculations are reported for ThF4 assuming the experimental tetrahedral geometry with the Gaussian nuclear model for the Th and F nuclei. The calculations were performed with our relativistic universal Gaussian basis set, which has been shown to be of Dirac–Fock accuracy for all atoms. The calculated relativistic correction to the total electronic energy of ThF4 is −2150.5 hartrees (−58 518 eV) which is about 9% of its total Hartree–Fock energy. There are also major relativistic corrections to the binding energies of the molecular orbitals, especially for the inner (core) orbitals of ThF4. The magnetic part of the Breit interaction is calculated to be 38.8 hartrees (1056 eV) for ThF4. The results of our ab initio all-electron relativistic calculations, predict the molecule ThF4 to be bound with respect to dissociation into one Th and four F Dirac–Fock atoms. The dissociation energy predicted by our relativistic calculations for ThF4 of 19.34 eV is 70% of the experimental value (27.7 eV) reported by Lau et al. [J. Chem. Phys. 90, 1158 (1989)]. This result is quite remarkable in view of the fact that it was obtained by using single configuration Dirac–Fock self-consistent field wave function for the tetrahedral ThF4. Our NR HF calculations for the tetrahedral ThF4 also predict the molecule to be bound with the predicted dissociation energy of 19.11 eV, which is only 0.23 eV less than that predicted by our relativistic wavefunction. Therefore, although the relativistic correction to the total electronic energy of ThF4 is very significant, its contribution to the binding energy of the molecule is almost negligible (0.23 eV). This is due to the cancellation of the relativistic corrections for the ThF4 molecule and its constituent atoms. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467886
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  • 3
    Electronic Resource
    Electronic Resource
    Dirac scattered-wave study of trigonal bipyramidal silver clusters Ag5q+ (q=0, 2–4) (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 6610-6622 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The electronic structure of the neutral and cationic pentaatomic silver bare clusters is investigated by the Dirac scattered-wave (DSW) method. The results indicate that there is significant 5s1/2–4d5/2 hybridization in the bonding molecular orbitals, due to relativistic effects. Molecular hyperfine interactions (hfi) are calculated for the paramagnetic species Agq+5 (q=0, 2, and 4) through a first-order perturbation to the Dirac Hamiltonian. The ground state (2E') orbital degeneracy of Ag5 in D3h geometry is removed by spin-orbit interaction leading to Kramers degeneracy, and consequently the D3h geometry of Ag5 will not distort due to Jahn–Teller effect. It is found that the hyperfine coupling constants calculated by using a four-component wave function for the Ag2+5 and Ag4+5 clusters differ significantly from previously computed hfi using a second-order perturbation to the Schrödinger Hamiltonian. First ionization potentials and excitation energies are predicted for all the species as calculated by the spin-restricted transition state method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451443
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  • 4
    Electronic Resource
    Electronic Resource
    Dirac scattered-wave calculations for Ag2+3, Auq+3, and Auq+4 (q=1, 2) clusters (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 5891-5897 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Dirac scattered-wave (DSW) calculations are presented for the Ag2+3, Au+3, Au2+3, Au+4, and Au2+4 clusters. The results show that relativistic effects in bonding are not negligible for the silver cluster; whereas for the gold clusters these are very significant and lead to appreciable s–d hybridization in the bonding molecular orbitals. Zeeman and hyperfine tensors have been calculated for the Ag2+3, which are in very good agreement with the experimental results. These tensors are also predicted for the Au2+3 cluster. First ionization potentials and excitation energies are predicted for all these cationic clusters using the spin-restricted transition state method. Contour diagrams which clearly reveal the significant relativistic effects in bonding are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449900
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  • 5
    Electronic Resource
    Electronic Resource
    The generator coordinate Dirac–Fock method for open-shell atomic systems (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 8759-8763 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Recently we developed generator coordinate Dirac–Fock and Dirac–Fock–Breit methods for closed-shell systems assuming finite nucleus and have reported Dirac–Fock and Dirac–Fock–Breit energies for the atoms He through Nobelium (Z=102) [see Refs. 〈citeref RID="R10" STYLE="ONLINE"〉10〈citeref RID="R11" STYLE="ONLINE"〉11〈citeref RID="R12" STYLE="ONLINE"〉12〈citeref RID="R13" STYLE="ONLINE"〉13]. In this paper, we generalize our earlier work on closed-shell systems and develop a generator coordinate Dirac–Fock method for open-shell systems. We present results for a number of representative open-shell heavy atoms (with nuclear charge Z〉80) including the actinide and superheavy transactinide (with Z〉103) atomic systems: Fr (Z=87), Ac (Z=89), and Lr (Z=103) to E113 (eka-thallium, Z=113). The high accuracy obtained in our open-shell Dirac–Fock calculations is similar to that of our closed-shell calculations, and we attribute it to the fact that the representation of the relativistic dynamics of an electron in a spherical ball finite nucleus near the origin in terms of our universal Gaussian basis set is as accurate as that provided by the numerical finite difference method. The DF SCF energies calculated by Desclaux [At. Data. Nucl. Data Tables 12, 311 (1973)] (apart from a typographic error for Fr pointed out here) are higher than those reported here for atoms of some of the superheavy transactinide elements by as much as 5 hartrees (136 eV). We believe that this is due to the use by Desclaux of much larger atomic masses than the currently accepted values for these elements. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477545
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  • 6
    Electronic Resource
    Electronic Resource
    Ab initio all-electron Dirac–Fock–Breit calculations for UF6 (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 1012-1017 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Ab initio all-electron Dirac–Fock, Dirac–Fock–Breit, and Hartree–Fock calculations are reported for UF6, assuming the experimental octahedral geometry. The spin–orbit (S–O) splitting is calculated for all the ground state levels of UF6 and the calculated S–O splittings for the 4d, 5d, and 4f levels are in excellent agreement with those reported experimentally by Martensson et al. [J. Chem. Phys. 80, 5456 (1984)]. The magnetic part of the Breit interaction for UF6 is calculated via perturbation theory as 42 hartrees (1145 eV). Our Hartree–Fock, Dirac–Fock, and Dirac–Fock–Breit wave functions predict UF6 to be bound with dissociation energy of 13.71, 23.53, and 23.27 eV, respectively. Relativistic effects lead to about 70% increment in the predicted dissociation energy of UF6. Our calculations show that the relativistic effects are so large for UF6 that it is imperative to treat them using Dirac's fully relativistic equation. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.470825
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  • 7
    Electronic Resource
    Electronic Resource
    Ab initio all-electron fully relativistic Dirac–Fock–Breit calculations for molecules of the superheavy transactinide elements: Rutherfordium tetrachloride (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 4448-4455 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Ab initio all-electron fully relativistic molecular spinor (RMS) Dirac–Fock (DF) self-consistent field (SCF) and nonrelativistic limit Hartree–Fock (HF) calculations are reported at four Rf–Cl bond distances for the ground state of tetrahedral (Td) rutherfordium tetrachloride (RfCl4) with our universal Gaussian basis set. The optimized Rf–Cl bond distance computed from our relativistic and nonrelativistic SCF wave functions for RfCl4 (Td) is 2.39 and 2.45 Å, respectively. The relativistic correction to the total electronic energy of RfCl4 was calculated as ∼−4355 hartrees (−118 504 eV) at the Dirac–Fock level. The dominant magnetic part of the Breit interaction correction for RfCl4 is estimated by perturbation method as 66.8509 hartrees. Our Hartree–Fock, Dirac–Fock, and Dirac–Fock–Breit calculations predict the tetrahedral RfCl4 to be bound with the calculated dissociation energy of −14.14, −15.56, and −15.53 eV, respectively. Mulliken population analysis of our Dirac–Fock wave function indicates RfCl4 (Td) to be more volatile than that estimated from the corresponding Hartree–Fock wave function. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477048
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  • 8
    Electronic Resource
    Electronic Resource
    Les conditions d'orthonormation dans la méthode SCF de champ auto-cohérent (1966)
    Springer
    Theoretical chemistry accounts 5 (1966), S. 446-448 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00527048
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  • 9
    Electronic Resource
    Electronic Resource
    Physical properties of many-electron atomic systems evaluated from analytical Hartree-Fock functions (1966)
    Springer
    Theoretical chemistry accounts 6 (1966), S. 54-63 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: 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.
    Abstract: 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).
    Notes: Abstract 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).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00528291
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  • 10
    Electronic Resource
    Electronic Resource
    Self-consistent-field theory for positive ions (1966)
    Springer
    Theoretical chemistry accounts 6 (1966), S. 122-130 
    Details
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Die Untersuchung der Stabilitätseigenschaften von Hartree-Fock-Funktionen führt zu Schlußfolgerungen, die von Interesse sind im Zusammenhang mit Funktionen für positive Ionen. Diese Betrachtungen, in Verbindung mit einem veränderten SCF-Formalismus, machen es möglich, die SCF-Methode umzuformulieren, um sie der Bestimmung von Hartree-Fock-Funktionen für positive Ionen anzupassen.
    Abstract: Résumé L'étude de la stabilité des fonctions de Hartree-Fock mène à des conclusions présentant un intérêt par rapport aux fonctions des ions positifs. Ces considérations, liées à un formalisme SCF modifié, permettent de reformuler la méthode SCF en l'adaptant à la déterminantion des fonctions de Hartree-Fock des ions positifs.
    Notes: Abstract Investigation of the stability characteristics of Hartree-Fock functions leads to conclusions of interest in relation to the functions of positive ions. These considerations, in conjunction with an existing modified SCF formalism, make it possible to reformulate the SCF method in order to adapt it to the determination of Hartree-Fock functions for positive ions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00526943
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