Second-order Rayleigh–Schrodinger perturbation theory for the GRASP2018 package: Valence–valence correlations

The accurate description of electron correlations remains a major challenge in atomic calculations. In order to perform accurate calculations, it is necessary to consider various types of electron correlations and this often leads to extensive configuration state function (CSF) expansions. This work presents further development of the method based on the second-order perturbation theory to identify the most significant CSFs that have the greatest influence on core–valence, core, core–core and valence–valence correlations. This method is based on a combination of the relativistic configuration interaction method and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form [G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the Grasp2018 package: core–valence correlations, Lith. J. Phys. 64 (1), 20–39 (2024),https://doi.org/10.3952/physics.2024.64.1.3, G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the Grasp2018 package: core correlations, Lit. J. Phys. 64 (2), 73–81 (2024), https://doi.org/10.3952/physics.2024.64.2.1, and G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the Grasp2018 package: core–core correlations, Lith. J. Phys. 64 (3), 139–161 (2024), https://doi.org/10.3952/physics.2024.64.3.1]. The method is extended to include additionally valence–valence electron correlations. It can be applied for an atom or ion with any number of valence electrons for the calculation of energy spectra and other properties. Meanwhile, the correlations which cannot be included according to perturbation theory are taken into account in a regular way. The use of the developed method allows a significant reduction of CSFs especially for complex atoms and ions. As an example of its application, the atomic calculations of the energy structure for Se III ion are presented.