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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2Presented in part as an invited talk at the Satellite meeting of the 8th International Congress of Quantum Chemistry on “Electron Correlation in Atoms and Molecules: New Methods and Applications,” June 15-18, 1994, Smolenice Castle and Bratislava, Slovakia. (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 55 (1995), S. 213-225 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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 MP2(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 (De) 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.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560550302
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  • 9
    Electronic Resource
    Electronic Resource
    Electron correlation and relativistic effects in xenon tetrafluoride (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 55 (1995), S. 227-235 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio all-electron fully relativistic Dirac-Fock self-consistent field and Dirac-Fock-Breit calculations are reported for the XeF4 molecule at various internuclear distances assuming the experimental D4h geometry with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree-Fock calculations were also performed for XeF4 at various internuclear distances. The calculated relativistic correction to the total energy of molecule at the Dirac-Fock level is ∼ -5856 eV, whereas the magnetic part of the Breit correction to the electron-electron interaction is calculated as ∼ 177 eV. The electron correlation effects were included in the nonrelativistic Hartree-Fock calculations using the second-order Møller-Plesset (MP2) theory, and the calculated correlation energy for XeF4 is -71 eV. The basis-set superposition error (BSSE) was estimated by using the counterpoise method for Xe and F. The inclusion of both the relativistic and electron correlation effects in the calculated total energies of F, Xe, and XeF4 predicts the Xe - F bond length and dissociation energy of XeF4 as 1.952 Å and 5.59 eV, respectively, which are in excellent agreement with the experimental values of 1.953 Å and 5.69 eV, respectively, for XeF4. The contribution of the electron correlation and relativistic effects to the dissociation energy of XeF4 is 8.11 and 0.05 eV, respectively. The Breit interaction, however, contributes only 0.02 eV to the dissociation energy of XeF4. Electron correlation is most significant for the prediction of an accurate value of dissociation energy, whereas relativistic effects are very important for the prediction of spin-orbital splitting as well as the energies of the orbitals, especially the inner orbitals of XeF4. © 1995 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560550303
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  • 10
    Electronic Resource
    Electronic Resource
    Relativistic all-electron Dirac-Fock-Breit calculations on xenon fluorides (XeFn, n = 1, 2, 4, 6) (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 18 (1997), S. 601-608 
    Details
    ISSN: 0192-8651
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The MOLFDIR package of programs is used to perform fully relativistic all-electron Dirac-Fock and Dirac-Fock-Breit calculations for the the XeFn (n = 1, 2, 4, 6) molecules assuming experimental symmetries. The Xe-F bound length for XeF2, XeF4, and XeF6 is optimized and the total ground-state energies are reported. The variation of the relativistic energy and the Breit correction with the internuclear distance is plotted. The role of relativistic corrections in the proper prediction of the Xe-F distance and the dissociation energy of the molecule is discussed. The problem of the reduction of the number of scalar two-electron integrals is studied. Our results illustrate the possibilities, difficulties, and limitations of the finite basis Dirac-Fock calculations for polyatomic molecules of different symmetries. © 1997 by John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
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