High‐precision atomic computations from finite element techniques: Second‐order correlation energies for Be, Ca, Sr, Cd, Ba, Yb, and Hg

Arguments are presented that accurate second-order Møller-Plesset (MP2) energies, evaluated in calculations involving extensive radial and angular basis sets, followed by careful angular extrapolations (referred to as MP2/CA energies), provide reliable approximations to the correlation energies for the ground states of closed-shell atomic systems. MP2/CA energies are calculated for the members of the Cu ϩ isoelectronic series (Cu ϩ , Zn 2ϩ , Ge 4ϩ , and Kr 8ϩ ), which belong to the simplest atomic system containing the 3d 10 configuration. The most accurate ab initio correlation energies for a 28-electron isoelectronic series are reported. To exemplify the applicability of the total nonrelativistic energies, obtained as a sum of these energies and accurate Hartree-Fock energies, in examinations of density functionals, density functional theory energies are calculated for various functionals and basis sets and compared with their MP2/CA counterparts. An evaluation of the performance of these functionals is presented. The impact of the limited basis set size on the energy results is estimated.

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“…For the remaining systems discussed in this work these energies are compiled from Refs. [33] and [34].…”

Section: Computational Detailsmentioning

confidence: 98%

Application of accurate MP2 energies for closed‐shell atoms in examinations of density functionals for 3d¹⁰ electron ions

Jankowski

Nowakowski

Słupski

et al. 2004

Int J of Quantum Chemistry

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“…In addition to enabling variational calculations—approaching the converged value strictly from above—and making sure orbital orthonormality is always honored, the use of an explicit radial basis set instead of the implicit basis set of the finite‐difference method also enables the straightforward use of post‐HF methods . 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.…”

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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Toward improved density functionals for the correlation energy

Thakkar

McCarthy

2009

The Journal of Chemical Physics

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Eleven density functionals, including some of the most widely used ones, are tested on their ability to predict nonrelativistic, electron correlation energies for the 17 atoms from He to Ar, the 17 cations from Li(+) to K(+), and 11 (1)S state atoms from Ca to Rn. They all lead to relatively poor predictions for the heavier atoms. Reparametrization of these functionals improves their performance for light atoms but does not alleviate their problems with the heavier, closed-shell atoms. Several novel, few-parameter, density functionals for the correlation energy are developed heuristically. Four new functionals lead to qualitatively improved predictions for the heavier atoms without unreasonably compromising accuracy for the lighter atoms. Further progress would be facilitated by reliable estimates of electron correlation energies for more atoms, particularly heavy ones.

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High‐precision atomic computations from finite element techniques: Second‐order correlation energies for Be, Ca, Sr, Cd, Ba, Yb, and Hg

Cited by 8 publications

References 43 publications

Application of accurate MP2 energies for closed‐shell atoms in examinations of density functionals for 3d¹⁰ electron ions

Application of accurate MP2 energies for closed‐shell atoms in examinations of density functionals for 3d¹⁰ electron ions

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

Toward improved density functionals for the correlation energy

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High‐precision atomic computations from finite element techniques: Second‐order correlation energies for Be, Ca, Sr, Cd, Ba, Yb, and Hg

Cited by 8 publications

References 43 publications

Application of accurate MP2 energies for closed‐shell atoms in examinations of density functionals for 3d10 electron ions

Application of accurate MP2 energies for closed‐shell atoms in examinations of density functionals for 3d10 electron ions

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

Toward improved density functionals for the correlation energy

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Product

Resources

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Application of accurate MP2 energies for closed‐shell atoms in examinations of density functionals for 3d¹⁰ electron ions

Application of accurate MP2 energies for closed‐shell atoms in examinations of density functionals for 3d¹⁰ electron ions