Accuracy of relativistic energy-consistent pseudopotentials for superheavy elements 111–118: Molecular calibration calculations

Abstract

Relativistic energy-consistent pseudopotentials modelling the Dirac-Coulomb-Breit Hamiltonian with a finite nucleus model for the superheavy elements with nuclear charges 111-118 were calibrated in atomic and molecular calculations against fully relativistic all-electron reference data. Various choices for the adjustment of the f-potentials were investigated and an improved parametrization is recommended. Using the resulting pseudopotentials relativistic all-electron reference data can be reproduced at the self-consistent field level with average absolute (relative) errors of 0.0030 Å (0.15%) for bond lengths and 2.79 N m(-1) (1.26%) for force constants for 24 diatomic test molecules, i.e., neutral or singly charged monohydrides, monofluorides, and monochlorides with closed-shell electronic structure. At the second-order Møller-Plesset perturbation theory level the corresponding average deviations are 0.0033 Å (0.15%) for bond lengths and 2.86 N m(-1) (1.40%) for force constants. Corresponding improved f-potentials were also derived for the pseudopotentials modelling in addition the leading contributions from quantum electrodynamics.

Relativistic and quantum electrodynamic effects in superheavy elements

“…Prime examples are the Klein paradox [100,101], the fact that deviating from a Coulomb potential can lead to a completely continuous spectrum of the Dirac operator [102], or the possibility of the 1s state diving into the negative energy continuum [101,103]. The appearance of these negative energy states and the consequence that vacuum fluctuation can cause electron-positron pair creation forces us to cope with an indefinite number of particles described by quantum electrodynamics (QED).…”

Generalized relativistic effective core potentials for superheavy elements

“…All the calculations presented in the table were carried out by the coupled cluster method with accounting for the spin‐orbit interactions, single and double cluster amplitudes, and some corrections for the higher cluster amplitudes. The results for CnH + obtained with the use of the second order Møller‐Plesset perturbation theory instead of the coupled cluster method and without accounting for the spin‐orbit interactions can be found in the cited papers. Because of different (and not complete enough) basis sets, different numbers of correlated electrons, slightly dissimilar versions of the coupled cluster method, different treatment of Breit interactions and a finite nuclear size used in the studies listed in the table, the results of all‐electron calculations cannot be directly used as the reference values to estimate the RECP errors.…”

“…Large number of electrons in SHE atoms and necessity to account for huge relativistic effects for them leads to enormous computational demands in the case of all‐electron calculations already for few‐atom systems containing one SHE atom. Examples of all‐electron calculations of SHE compounds with Dirac‐Coulomb (DC) or Dirac‐Coulomb‐Gaunt Hamiltonians can be found in papers . Up to our knowledge, no ab initio correlation calculations on SHE‐containing molecules using the full Dirac‐Coulomb‐Breit (DCB) many‐electron Hamiltonian have been reported.…”

“…The shape‐consistent RECPs for SHEs are available in paper . There have also been published many versions of the energy‐consistent (semilocal) PP parameters for SHEs which demonstrate non‐trivial difficulties of deriving continuous functions (radial components of the semilocal SHE pseudopotential) from a finite discrete data set (energy differences). Some examples of calculations on SHE compounds with the above mentioned semilocal PPs (RECPs) are presented in papers .…”

Relativistic energy-consistent pseudopotentials for superheavy elements 119 and 120 including quantum electrodynamic effects

“…21,22 As recently shown for the elements with nuclear charges 111 to 118 not only the major relativistic effects, but also the Breit and QED contributions can be treated by PPs in a one-or two-component way. 23,24 The number of treated electrons is drastically reduced by replacing the core electrons by PPs. 21,22,[25][26][27] Additionally, the required basis sets are reduced due to the simplified nodal structure of the valence orbitals.…”