High-accuracy relativistic coupled-cluster calculations for the heaviest elements

Ephraim Eliav, Anastasia Borschevsky, Uzi Kaldor

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


High-accuracy calculations of atomic properties of the heaviest elements, up to element 122, are reviewed. The properties discussed include ionization potentials, electron affinities, and excitation energies, which are associated with the spectroscopic and chemical behavior of these elements and are therefore of considerable interest. Accurate predictions of these quantities require highorder inclusion of relativity and electron correlation, as well as large, converged basis sets. The Dirac-Coulomb-Breit Hamiltonian, which includes all terms up to second order in the fine-structure constant α, serves as the framework for the treatment; higher-order Lamb shift terms are considered in some selected cases. Electron correlation is treated by the Fock-space coupled cluster method, enhanced by the intermediate Hamiltonian scheme, allowing the use of large, converged model (P) spaces. The quality of the calculations is assessed by comparison with available experimental information. Very good agreement is obtained, usually within a few hundredths of an eV, and similar accuracy is expected for the superheavy elements (SHEs), with Z≥104, for which experimental values are scarce. Many of the properties predicted for these species differ significantly from what may be expected by straightforward extrapolation of lighter homologs, demonstrating that the structure and chemistry of SHEs are strongly affected by relativity. The major scientific challenge of the calculations is to find the electronic structure and basic atomic properties of the SHE and assign its proper place in the periodic table. Significant recent developments include joint experimental-computational studies of the ionization energies of At and Lr, with excellent agreement of experiment and theory. For Lr, calculations were required not only for comparison with experiment; the extraction of the ionization potential from experimental data depended on reliable estimates of atomic excitation energies, obtainable from theory.

Original languageEnglish
Title of host publicationHandbook of Relativistic Quantum Chemistry
PublisherSpringer Berlin Heidelberg
Number of pages31
ISBN (Electronic)9783642407666
ISBN (Print)9783642407659
StatePublished - 1 Jan 2016


  • Coupled cluster methods
  • Electron correlation
  • Heavy elements
  • Relativity


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