Single-Fock-operator method for matrix Dirac-Fock self-consistent-field calculations on open-shell atoms

Koc, Konrad; Ishikawa, Yasuyuki

doi:10.1103/physreva.49.794

Cited by 44 publications

(14 citation statements)

References 44 publications

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“…18 For oxygen basis sets, we optimized the contraction coefficients at the four-component multiconfigurational Dirac-Coulomb Hartree-Fock ͑MCDCHF͒ level using the exponents of Roos' double-zeta atomic natural orbital ͑ANO͒ basis sets. 19 We optimized the contraction coefficients at the four-component MCDCHF level for fluorine and chlorine, 20 using the exponents of the third-order DouglasKroll-Hess basis sets. 21 The lowest one or two exponents of these basis sets were added as primitive basis sets to give these basis sets to be valence double-zeta ͑DZ͒ or triple-zeta ͑TZ͒ quality, respectively.…”

Section: Computational Detailsmentioning

confidence: 99%

Ligand effect on uranium isotope fractionations caused by nuclear volume effects: An ab initio relativistic molecular orbital study

Abe

Suzuki

Fujii

et al. 2010

The Journal of Chemical Physics

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We have calculated the nuclear volume term ͑ln K nv ͒ of the isotope fractionation coefficient ͑͒ between 235 U-238 U isotope pairs by considering the effect of ligand coordination in a U͑IV͒-U͑VI͒ reaction system. The reactants were modeled as ͓UO 2 Cl 3 ͔ − and ͓UO 2 Cl 4 ͔ 2− for U͑VI͒, and UCl 4 for U͑IV͒. We adopted the Dirac-Coulomb Hartree-Fock method with the Gaussian-type finite nucleus model. The result obtained was ln K nv = 0.001 90 at 308 K, while the experimentally estimated value of ln K nv is 0.002 24. We also discuss how the ligand affects the value of ln K nv , especially for the various structures of different compounds, and different ligands within the halogen ion series ͑F, Cl, and Br͒.

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Section: Computational Detailsmentioning

confidence: 99%

Ligand effect on uranium isotope fractionations caused by nuclear volume effects: An ab initio relativistic molecular orbital study

Abe

Suzuki

Fujii

et al. 2010

The Journal of Chemical Physics

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“…The no-pair Hamiltonian H ‡ DC , often modi® ed to account for ® nite-nuclear-size e ects, is the basis of modern relativistic calculations beyond Hartree± Fock [30,32,33]. H ‡ DC is bounded from below by de® nition: positive kinetic energy and mass operator, bounded nuclear± electron potential and positive electron± electron repulsion.…”

Section: …9 †mentioning

confidence: 99%

Justification of relativistic Dirac-Hartree-Fock and configuration interaction

Bunge

Ley‐Koo²,

Jáuregui

2000

Molecular Physics

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Before knowing that the relativistic Hamiltonian H does allow the existence of bounded states (H is unbounded from below and from above), the existence of SCF and beyond SCF solutions had to be assumed as an act of faith vindicated by consistent numerical results. A recent theorem showing the existence of such bounded states furnishes a rigorous framework for the relativistic theory of electronic bounded states. IntroductionThe atomic physics community sees Charlotte Froese Fischer as the mother of Hartree± Fock methodology, both at the independent particle model (IPM) level of approximation and beyond the IPM [1, 2], without demerit of grandfather Douglas Hartree [3]. Why? For many reasons: she was the ® rst (i) to show how to handle`di cult' con® gurations [4] against prevailing scepticism, (ii) to develop e ectively convergent and ecient numerical self-consistent-® eld (SCF) procedures [5] when analytical methods were reigning supreme [6, 7], (iii) to reliably apply SCF methods beyond the IPM [1,8], when most connoisseurs thought they would not work, and (iv) to write and to make public the most used and useful computer programs for ab initio calculations of atomic structures [9, 10]. Not surprinsigly, she is now playing an important role in leading the new generations into the relativistic realm [11]. In this context, we present some recent work on the foundations of multicon® guration Dirac± Hartree± Fock theory, with special emphasis on the IPM.As one goes from the non-relativistic Schro È dinger equation into Dirac's relativistic theory of the electron, the Hamiltonian becomes unbounded: upon variation in a trial function within Hilbert space, the expectation value h D ,

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“…): Here \documentclass{article}\pagestyle{empty}\begin{document}$\mbox{\mathversion{bold}$\mathit{\alpha}$}$\end{document} and β are the 4×4 Dirac vector and scalar matrices, respectively. V nuc ( r ) is the nuclear potential, which for each nucleus takes the form The nuclei are modeled as spheres of uniform proton‐charge distribution 10; Z is the nuclear charge. R (bohr) is the radius of the nucleus and is related to the atomic mass, A (amu), by R =2.2677×10 −5 A 1/3 .…”

Section: Theorymentioning

confidence: 99%

“…Given a trial orthonormal set of one‐particle radial spinors {ϕ

_{italicn_{italicq} κ_{italicq}}^{(0)}

( r )} (∈ D (+) ∪ D (−) ), the optimum occupied electronic radial spinors {ϕ

_{italicn_{italicp} κ_{italicp}}^{(+)}

( r )} (∈ D (+) ) can be found by a unitary transformation U =1+ T via Here the summation extends over both N κ negative and N κ positive energy spinors. P

_{italicn_{italicp} κ_{italicp}}

( r ) and Q

_{italicn_{italicp} κ_{italicp}}

( r ) are the large and small radial components and are expanded in N κ G spinors, {χ

_{κ italici}^{italicL}

} and {χ

_{κ italici}^{italicS}

}, that satisfy the boundary conditions associated with the finite nucleus 10, Here {ξ

_{italicki}^{italicL}

} and {ξ

_{italicki}^{italicS}

} are linear variation coefficients. The MCDF energy [Eq.…”

Section: Theorymentioning

confidence: 99%

Relativistic multireference M�ller-Plesset perturbation theory calculations for siliconlike ions

Ishikawa¹,

Vilkas²,

Koc³

2000

Int. J. Quant. Chem.

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Single-Fock-operator method for matrix Dirac-Fock self-consistent-field calculations on open-shell atoms

Cited by 44 publications

References 44 publications

Ligand effect on uranium isotope fractionations caused by nuclear volume effects: An ab initio relativistic molecular orbital study

Ligand effect on uranium isotope fractionations caused by nuclear volume effects: An ab initio relativistic molecular orbital study

Justification of relativistic Dirac-Hartree-Fock and configuration interaction

Relativistic multireference M�ller-Plesset perturbation theory calculations for siliconlike ions

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