Density functional theory of field theoretical systems

Engel, E.

doi:10.1002/qua.560560405

Cited by 4 publications

(2 citation statements)

References 20 publications

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“…With very few exceptions [273,274], one treats the multi-electron Dirac equation within mean-field theory, that is either at the D-HF (Dirac-Hartree-Fock) level or by using D-DFT (Dirac density functional theory) [275,276], with the latter method being more popular in molecular calculations. It is fair to say that the accuracy of current density functional approximations cannot compete with wave-function-based methods (for a recent critical analysis on DFT see Ref.…”

Section: Experimental Perspective: Heavy-ion Collisionsmentioning

confidence: 99%

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Smits,

Indelicato,

Nazarewicz

et al. 2023

Preprint

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We review the progress in atomic structure theory with a focus on superheavy elements and the aim to predict their ground state configuration and element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is important to correctly solve the Dirac equation in strong Coulomb fields, and also to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge Z crit ≈ 170, where levels such as the 1s shell dive into the negative energy continuum (E nκ < −m e c 2 ). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.* Here we define the starting point of the superheavy element region at the transactinides, Z ≥ 103

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Section: Experimental Perspective: Heavy-ion Collisionsmentioning

confidence: 99%

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Smits,

Indelicato,

Nazarewicz

et al. 2023

Preprint

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“…On the theoretical side things have apparently not been completely straightened out, as witnessed by a number of misunderstandings in the literature. After an initial overview of the relativistic many-electron Hamiltonian in section 1., we therefore give a variational formulation of QED in the semiclassical limit, that is with continuous electromagnetic fields, in section 2.. At this level of theory a true minimization principle is assumed to exist [7], and this puts the discussion of the variational stability of the relativistic many-electron Hamiltonian on firm grounds. The separate basis set expansion of the large and small components needed to solve the second problem above leads to increased computational cost.…”

Section: Introductionmentioning

confidence: 99%

Four-Component Electronic Structure Methods for Molecules

Saue

Visscher

2003

Theoretical Chemistry and Physics of Heavy and Superheavy Elements

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In this chapter we consider the extension of 4-component relativistic methods from atomic to molecular systems, in particular the chaIIenges arising from the introduction of the algebraic approximation. In order to analyze the variational stability of the relativistic many-electron Hamiltonian we derive a variational theory of QED in the semiclassicaI limit using the second quantization formalism and exponential parametrization. In QED the negative-energy orbitals are fiIIed leading to a true minimization principle for the electronic ground state, whereas in the standard 4-component approach these orbitals are empty and treated as an orthogonal complement, thus leading to a minimax principle. We emphasize the non-uniqueness of the resulting no-pair Hamiltonian of the standard approach. 4-component methods allow the continuous update of the Hamiltonian and thereby complete relaxation of the electronic wave function. We also discuss more practical aspects of the implementation of 4-component relativistic methods. We carefuIly analyze their computational cost and conclude that the difference with respect to non-relativistic methods constitute a prefactor and not a difference in order. We furthermore discuss how computational cost may be reduced while staying at the 4-component level, e.g. by exploiting the atomic nature of the small component density.

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Relativistic all-electron density functional calculations

Wüllen

1999

J. Comput. Chem.

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Density functional theory of field theoretical systems

Cited by 4 publications

References 20 publications

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Pushing the Limits of the Periodic Table -- A Review on Atomic Relativistic Electronic Structure Theory and Calculations for the Superheavy Elements

Four-Component Electronic Structure Methods for Molecules

Relativistic all-electron density functional calculations

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