Simon Verdebout

Hyperfine structures and Landé gJ-factors for n=2 states in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations

Abstract Energy levels, hyperfine interaction constants, and Lande g J -factors are reported for n = 2 states in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations. Valence, core–valence, and core–core correlation effects are taken into account through single and double-excitations from multireference expansions to increasing sets of active orbitals. A systematic comparison of the calculated hyperfine interaction constants is made with values from the available literature.

A partitioned correlation function interaction approach for describing electron correlation in atoms

The traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis. For atoms with many closed core shells, or complicated shell structures, a large orbital basis is needed to saturate the different electron correlation effects such as valence, core-valence and correlation within the core shells. The large orbital basis leads to massive configuration state function (CSF) expansions that are difficult to handle, even on large computer systems. We show that it is possible to relax the orthonormality restriction on the orbital basis and break down the originally very large calculations into a series of smaller calculations that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The expansion coefficients of the PCFs are determined from a low dimensional generalized eigenvalue problem. The interaction and overlap matrices are computed using a biorthonormal transformation technique (Verdebout et al 2010 J. Phys. B: At. Mol. Phys. 43 074017). The new method, called partitioned correlation function interaction (PCFI), converges rapidly with respect to the orbital basis and gives total energies that are lower than the ones from ordinary MCHF and CI calculations. The PCFI method is also very flexible when it comes to targeting different electron correlation effects. Focusing our attention on neutral lithium, we show that by dedicating a PCF to the single excitations from the core, spin- and orbital-polarization effects can be captured very efficiently, leading to highly improved convergence patterns for hyperfine parameters compared with MCHF calculations based on a single orthogonal radial orbital basis. By collecting separately optimized PCFs to correct the MR function, the variational degrees of freedom in the relative mixing coefficients of the CSFs building the PCFs are inhibited. The constraints on the mixing coefficients lead to small off-sets in computed properties such as hyperfine structure, isotope shift and transition rates, with respect to the correct values. By (partially) deconstraining the mixing coefficients one converges to the correct limits and keeps the tremendous advantage of improved convergence rates that comes from the use of several orbital sets. Reducing ultimately each PCF to a single CSF with its own orbital basis leads to a non-orthogonal CI approach. Various perspectives of the new method are given.

Exploring biorthonormal transformations of pair-correlation functions in atomic structure variational calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core–valence correlation effects. This in turn leads to huge numbers of configuration state functions (CSFs), many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the multiconfiguration Hartree–Fock (MCHF) method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double-excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional complete active space (CAS)-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations.

Isotope shifts in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations

Energy levels, normal and specific mass shift parameters as well as electronic densities at the nucleus are reported for numerous states along the beryllium, boron, carbon, and nitrogen isoelectronic sequences. Combined with nuclear data, these electronic parameters can be used to determine values of level and transition isotope shifts. The calculation of the electronic parameters is done using first-order perturbation theory with relativistic configuration interaction wavefunctions that account for valence, core–valence, and core–core correlation effects as zero-order functions. Results are compared with experimental and other theoretical values, when available.

Spectral properties of Sb IV from MCDHF calculations

We report on extensive relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) spectrum calculations for Sb IV. Energies, LS-compositions and Land´ e gJ-factors for 60 oddand even-parity states are computed along with lifetimes and rates for transitions between these states. Results for the 5s 21 S0–5s5p 3 P o hyperfine-induced transition are also presented. Valence and core-valence electron correlation effects are accounted for by explicit configuration interaction. The calculated energies agree very well with experiment, but the labelling of some of the odd states is ambiguous due to close degeneracies between the 5p5d, 5s7p and 5p6s configurations. Computed lifetimes of the excited states are compared with values from cascade-corrected beam-foil measurements.

From atoms to biomolecules: A fruitful perspective

We present a summary of the research activities of the “Quantum Chemistry and Atomic Physics” theoretical group of the “Chimie Quantique et Photophysique” Laboratory at Université Libre de Bruxelles. We emphasize the links between the three orientations of the group: theoretical atomic spectroscopy, structure, and molecular dynamics and list the perspectives of our collaboration.

Interaction of Variational Localized Correlation Functions for Atomic Properties

XXVII International Conference on Photonic, Electronic and Atomic Collisions Belfast, (Northern Ireland, UK), July 27 – August 2, 2011.

Ab-initio multi-configuration Dirac-Hartree-Fock calculation on the lifetimes of levels in 2p53s configuration of neutral neon

Large-scale calculations have been performed using the GRASP2K package to accurately determine the lifetime of levels in 2p53s configuration of neutral neon. In particular, we calculated the hyperfine-induced transition rates from two metastable levels 3P20,0 to the ground state for odd Ne isotopes. It was found that hyperfine interactions drastically quench the lifetime of these two levels.