Hartree-Fock-Roothaan calculations for many-electron atoms and ions in neutron-star magnetic fields

Engel, D.; Wunner, Günter

doi:10.1103/physreva.78.032515

Cited by 18 publications

(17 citation statements)

References 25 publications

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“…These orbitals are products of a spatial wave function ψ i (r) and a spin function χ i (s). In a previous version of the Hartree-Fock-Roothaan method [29,30], the single-electron wave functions were taken in the form of a product,…”

Section: A Two-dimensional-hartree-fock-roothaan Equationsmentioning

confidence: 99%

Atomic ground states in strong magnetic fields: Electron configurations and energy levels

2013

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Using a combination of a fast two-dimensional-Hartree-Fock-Roothaan method and highly accurate fixed-phase diffusion quantum Monte Carlo simulations, we analyze the electronic structure and calculate the energy of the ground states of atoms with nuclear charges Z = 2-26 in very strong magnetic fields B = 10 7 -5 × 10 8 T, relevant for astrophysical problems, e.g., the thermal emission of strongly magnetized isolated neutron stars.

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Section: A Two-dimensional-hartree-fock-roothaan Equationsmentioning

confidence: 99%

Atomic ground states in strong magnetic fields: Electron configurations and energy levels

2013

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“…The comparison of oscillator strengths of transitions to the carbon ground state in Table V of Ref. [49] and of transitions to the ground states of iron ions in Table VI shows that the improvements are large only for transitions with very small oscillator strengths, while for large oscillator strengths taking into account more Landau levels does not significantly change the values calculated in adiabatic approximation. Thus it may be concluded that the energies and oscillator strengths calculated using the HFFEM code already well reproduce the general features of the exact level scheme.…”

Section: Results and Accuraciesmentioning

confidence: 93%

“…[49,50] where they are compared with the results of more advanced (but slower) methods as a function of magnetic field strength and nuclear charge.…”

Section: Results and Accuraciesmentioning

confidence: 99%

“…[49] the HFFEM wave functions were used to initialize a multi-configurational Hartree-Fock approach in which up to 8 Landau levels were taken into account. That method also allows for the calculation of excited states and oscillator strengths.…”

Section: Results and Accuraciesmentioning

confidence: 99%

“…Moreover, even at magnetic field strengths where the adiabatic approximation becomes poor (B ∼ Z 2 B 0 ) these values still provide valuable estimates for the correct energies and oscillator strengths. In addition, the wave functions can be used to initialize more sophisticated methods which go beyond the adiabatic approximation, such as Hartree-Fock-Roothaan calculations [48,49], or serve as guiding wave functions in quantum Monte Carlo simulations of heavy atoms and ions in strong magnetic fields [50].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A fast parallel code for calculating energies and oscillator strengths of many-electron atoms at neutron star magnetic field strengths in adiabatic approximation

Engel

Klews

Wunner

2009

Computer Physics Communications

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A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Lehtola

2019

Int J of Quantum Chemistry

102

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The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly used approach for all-electron electronic structure calculations in general-the linear combination of atomic orbitals (LCAO) method-is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, for example, finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform allelectron Hartree-Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.atomic calculations, density functional theory, diatomic calculations, fully numerical electronic structure theory, Hartree-Fock | INTRODUCTIONThanks to decades of development in approximate density functionals and numerical algorithms, density functional theory [1,2] (DFT) is now one of the cornerstones of computational chemistry and solid-state physics. [3][4][5] Since atoms are the basic building block of molecules, a number of popular density functionals [6][7][8][9][10] have been parametrized using ab initio data on noble gas atoms; these functionals have been used in turn as the starting point for the development of other functionals. A comparison of the results of density-functional calculations to accurate ab initio data on atoms has, however, recently sparked controversy on the accuracy of a number of recently published, commonly used density functionals. [11][12][13][14][15][16][17][18][19][20][21] This underlines that there is still room for improvement in DFT even for the relatively simple case of atomic studies.The development and characterization of new density functionals require the ability to perform accurate atomic calculations. Because atoms are the simplest chemical systems, atomic calculations may seem simple; however, they are in fact sometimes surprisingly challenging. For instance, a long-standing discrepancy between the theoretical and experimental electron affinity and ionization potential of gold has been resolved only very recently with high-level ab initio calculations. [22] Atomic calculations can also be used to formulate efficient starting guesses for molecular electronic structure calculations via either the atomic density [23,24] or the atomic potential as discussed in Ref. [25].

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Hartree-Fock-Roothaan calculations for many-electron atoms and ions in neutron-star magnetic fields

Cited by 18 publications

References 25 publications

Atomic ground states in strong magnetic fields: Electron configurations and energy levels

Atomic ground states in strong magnetic fields: Electron configurations and energy levels

A fast parallel code for calculating energies and oscillator strengths of many-electron atoms at neutron star magnetic field strengths in adiabatic approximation

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

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