Relativistic radial electron density functions and natural orbitals from GRASP2018

Schiffmann, Sacha; Li, Ji‐Guang; Ekman, Jörgen; Gaigalas, Gediminas; Godefroid, Michel; Jönsson, P.; Bieroń, Jacek

doi:10.1016/j.cpc.2022.108403

Cited by 5 publications

(6 citation statements)

References 44 publications

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“…Since their introduction in 1955 by Löwdin [30], natural orbitals have been used in quantum chemistry to obtain more compact representations of correlated wave functions [31]. The electron density and natural orbitals of relativistic multiconfiguration expansions can be computed using the RDENSITY program [32]. Introducing, for each relativistic symmetry κ, the density matrix ρ κ with elements…”

Section: Transformation To Natural Orbitalsmentioning

confidence: 99%

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Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations

Ma,

Li,

Godefroid

et al. 2024

Atoms

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Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron correlation effects. In multiconfiguration calculations, the wave functions are expanded in terms of configuration state functions (CSFs) built from sets of one-electron orbitals. The orbital sets are typically enlarged within the layer-by-layer approach. The calculations are energy-driven, and orbitals in each new layer of correlation orbitals are spatially localized in regions where the weighted total energy decreases the most, overlapping and breaking up different closed core subshells in an irregular pattern. As a result, hyperfine structure constants, computed as expectation values of the hyperfine operators, often show irregular or oscillating convergence patterns. Large orbital sets, and associated large CSF expansions, are needed to obtain converged values of the hyperfine structure constants. We analyze the situation for the states of the {2s22p3,2s22p23p,2s22p24p} odd and {2s22p23s,2s2p4,2s22p24s,2s22p23d} even configurations in N I, and show that the convergence with respect to the increasing sets of orbitals is radically improved by introducing separately optimized orbital sets targeted for describing the spin- and orbital-polarization effects of the 1s and 2s core subshells that are merged with, and orthogonalized against, the ordinary energy-optimized orbitals. In the layer-by-layer approach, the spectroscopic orbitals are kept frozen from the initial calculation and are not allowed to relax in response to the introduced layers of correlation orbitals. To compensate for this lack of variational freedom, the orbitals are transformed to natural orbitals prior to the final calculation based on single and double substitutions from an increased multireference set. The use of natural orbitals has an important impact on the states of the 2s22p23s configuration, bringing the corresponding hyperfine interaction constants in closer agreement with experiment. Relying on recent progress in methodology, the multiconfiguration calculations are based on configuration state function generators, cutting down the time for spin-angular integration by factors of up to 50, compared to ordinary calculations.

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Section: Transformation To Natural Orbitalsmentioning

confidence: 99%

“…where ν ij nn ′ are angular coefficients, the computation of which are described in [32], the natural orbitals vector ϕ κ with elements ϕ nκ are obtained from the eigenvectors U κ of the density matrix…”

Section: Transformation To Natural Orbitalsmentioning

confidence: 99%

Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations

Ma,

Li,

Godefroid

et al. 2024

Atoms

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“…There are also some graphical utilities. The application programs and tools, along with the underlying theory, are described in the original write-ups [4][5][6][7][8][9][10][11][12][13][14][15][16]. The present manual updates the previous version (GRASP2018 [4]), to include also the most recent application programs.…”

Section: Features Of the Packagementioning

confidence: 99%

“…Synthesizes spectral profiles, see [11] and TP Section 3.6. 14. rdensity -compute the radial electron density function and transform to natural orbitals, see [16] and TP Section 3.4.…”

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GRASP Manual for Users

Jönsson

Gaigalas

Fischer

et al. 2023

Atoms

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grasp is a software package in Fortran 95, adapted to run in parallel under MPI, for research in atomic physics. The basic premise is that, given a wave function, any observed atomic property can be computed. Thus, the first step is always to determine a wave function. Different properties challenge the accuracy of the wave function in different ways. This software is distributed under the MIT Licence.

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Relativistic effects on electronic pair densities: A perspective from the radial intracule and extracule probability densities

Rodríguez‐Mayorga

Keizer

Giesbertz

et al. 2022

The Journal of Chemical Physics

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While the eﬀect of relativity in the electronic density has been widely studied, the eﬀect on the pair probability, intracule, and extracule densities has not been studied before. Thus, in this work, we unveil new insights related to changes on the electronic structure caused by relativistic eﬀects. Our numerical results suggest that the mean inter-electronic distance is reduced (mostly) due to scalar-relativistic eﬀects. As a consequence, an increase of the electron-electron repulsion energy is observed. Preliminary results suggest that this observation is also valid when electronic correlation eﬀects are considered.

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Relativistic radial electron density functions and natural orbitals from GRASP2018

Cited by 5 publications

References 44 publications

Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations

Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations

GRASP Manual for Users

Relativistic effects on electronic pair densities: A perspective from the radial intracule and extracule probability densities

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