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

Engel, D.; Klews, M.; Wunner, Günter

doi:10.1016/j.cpc.2008.09.008

Cited by 16 publications

(8 citation statements)

References 51 publications

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“…For instance, Flores et al have calculated correlation energies with Møller‐Plesset perturbation theory truncated at the second order, while Sundholm and coworkers have relied on highly accurate multiconfigurational self‐consistent field (MCSCF) methods to study the ground state of the beryllium atom, electron affinities, excitation energies and ionization potentials, hyperfine structure, nuclear quadrupole moments, the extended Koopmans' theorem, and the Hiller–Sucher–Feinberg identity . Braun and Engel and coworkers have in turn reported finite‐element calculations of atoms in strong magnetic fields. Approaches based on FEM‐DVR have also been developed: Hochstuhl and Bonitz have implemented a restricted active space procedure for modeling photoionization of many‐electron atoms .…”

Section: Applicationsmentioning

confidence: 99%

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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Section: Applicationsmentioning

confidence: 99%

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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“…Elsewhere, Engel and Schimeczek and co-workers, working with Günter Wunner, investigated atoms in strong and intense magnetic fields using two separate approaches. First, they carried out fixed-phase QMC calculations and arrived at estimates for the ground states of atoms from Z = 2 to 26 (Meyer et al, 2013) as well as a Hartree-Fock-Roothan method with a fast parallel implementation using finite-element techniques (Schimeczek et al, 2012;Engel and Wunner, 2008;Engel et al, 2009), in all cases obtaining beautifully accurate results for the ground states of atoms as well as for oscillator strengths. They expand the wave function as…”

Section: Light Atoms: Two and Few-electron Systemsmentioning

confidence: 99%

Energy Levels of Light Atoms in Strong Magnetic Fields

Thirumalai

2014

Advances in Atomic, Molecular, and Optical Physics

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In this review article we provide an overview of the field of atomic structure of light atoms in strong magnetic fields. There is a very rich history of this field which dates back to the very birth of quantum mechanics. At various points in the past significant discoveries in science and technology have repeatedly served to rejuvenate interest in atomic structure in strong fields, broadly speaking, resulting in three eras in the development of this field; the historical, the classical and the modern eras. The motivations for studying atomic structure have also changed significantly as time progressed. The review presents a chronological summary of the major advances that occurred during these eras and discusses new insights and impetus gained. The review is concluded with a description of the latest findings and the future prospects for one of the most remarkably cutting-edge fields of research in science today.

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“…Mori et al [26,27] have studied mid-Z atoms in strong to intense magnetic fields using perturbation theory as well, obtaining results consistent with previous findings. In recent years Engel and Wunner and co-workers [70][71][72][73][74] have computed accurate results for several atoms in magnetic fields relevant to neutron stars with a variety of techniques involving finite-element methods with B-splines both in the adiabatic approximation and beyond the adiabatic approximation with more than one Landau level. These highly accurate formulations employ a fast parallel Hartree-Fock-Roothan code, in which the electronic wave functions are solved for along the z−direction, with Landau orbitals (and combinations of more than one level in the latter studies) describing the remaining parts of the wave functions.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional pseudospectral Hartree-Fock method for low-Zatoms in intense magnetic fields

Thirumalai

2014

Phys. Rev. A

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The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to ≈ 10 8 − 10 9 T are calculated in this study. A pseudospectral method is employed for the computational procedure. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these two-and three-electron systems in a self-consistent manner. The method exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. It is seen that the results obtained here for a few of the most tightly bound states of each of the atoms, helium and lithium, are in good agreement with findings elsewhere. In this regard, we report new data for two new states of lithium that have not been studied thus far in the literature. It is also seen that the pseudospectral method employed here is considerably more economical, from a computational point of view, than previously employed methods such as a finite-element based approach. The key enabling advantage of the method described here is the short computational times which are on the order of seconds for obtaining accurate results for heliumlike systems.

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

Cited by 16 publications

References 51 publications

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

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

Energy Levels of Light Atoms in Strong Magnetic Fields

Two-dimensional pseudospectral Hartree-Fock method for low-Zatoms in intense magnetic fields

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