On the accuracy of Dirac-Hartree-Fock calculations using analytic basis sets

Quiney, Harry M.; Grant, I P; Wilson, Stephen

doi:10.1088/0953-4075/22/2/001

Cited by 44 publications

(26 citation statements)

References 21 publications

(6 reference statements)

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“…We set up a 108-term CI singles expansion, solve for the lowest bounded state, viz., N ¡ ‡ 1= 63, and generate a process [46] to annihilate the 107 CI coe cients apart from the reference con-® guration. After convergence, our DHF energy coincides with the ® nite-di erence result [49] in seven decimals of au, and the CI coe cient of the reference con® guration is 1 £ 10 ¡12 . Also, the 108 by 108 H DC singles CI matrix is block-diagonal on account of the annihilation of singly excited coe cients: one block has dimension 1 and the other dimension 107.…”

Section: Self-consistent ® Eld Equations and Theirsupporting

confidence: 58%

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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Section: Self-consistent ® Eld Equations and Theirsupporting

confidence: 58%

Justification of relativistic Dirac-Hartree-Fock and configuration interaction

Bunge

Ley‐Koo²,

Jáuregui

2000

Molecular Physics

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“…TABLE II. Theoretical (RCICP) energies (ε in Hartree) and separated mass-corrected E1 ( E (1) ) and E2 ( E (2) ) decay rates (in seconds −1 ) for several eigenstates of hydrogen. Underscores of the calculated energies (ε I ) denote digits which are different from the exact value [37].…”

Section: Numerical Test: Energy Of Closed-shell Atomsmentioning

confidence: 99%

“…The core electrons are represented by orbitals obtained from Dirac-Fock (DF) calculations. The wave function for the valence electrons is computed by expanding the wave function as a linear combination of Laguerre function spinors (L-spinors) and Slater function spinors (S-spinors) [1][2][3]. The direct and exchange interactions between the core and the valence electrons can be computed without approximation.…”

Section: Introductionmentioning

confidence: 99%

Relativistic semiempirical-core-potential calculations ofSr+using Laguerre and Slater spinors

et al. 2016

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A relativistic description of the structure of heavy alkali-metal atoms and alkali-like ions using S-spinors and L-spinors is developed. The core wave function is defined by a Dirac-Fock calculation using an S-spinor basis. The S-spinor basis is then supplemented with a large set of L-spinors for calculation of the valence wave function in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a Z = 60 hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the 5s, 4d, and 5p states of Sr +. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the 5s → 4d 3

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“…Attempts 8, 9 to use the algebraic approximation in solving the relativistic atomic and molecular electronic structure problem during the 1960s and 1970s exposed certain difficulties, which were termed “the finite basis set disease.” It was not until the early 1980s that the “disease” was cured 10–15. Consequently, it was demonstrated that the solutions of the Dirac equation and the Dirac–Hartree–Fock equations could be approximated successfully within the algebraic approximation, or finite basis set expansion technique 10–23. This approach has been employed routinely in nonrelativistic molecular electronic structure studies since the work of Hall 24 and of Roothaan 25, 26 during the early 1950s.…”

Section: Introductionmentioning

confidence: 99%