Second-Order Rayleigh-Schrödinger Perturbation Theory for the Grasp2018 Package: Valence-Valence Correlations

Abstract: The accurate description of electron correlations remains a major challenge in atomic calculations. In order to perform accurate calculations, it is necessary to consider the various types of electron correlations what often leads to extensive 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, L. Kitovienė, Lithuanian Journal of Physics, 64, No. 1, 20-39 (2024) (https://doi.org/10.3952/physics.2024.64.1.3), G. Gaigalas, P. Rynkun, L. Kitovienė, Lithuanian Journal of Physics, 64, No. 2, 73-81 (2024) (https://doi.org/10.3952/physics.2024.64.2.1) and G. Gaigalas, P. Rynkun, L. Kitovienė, Lithuanian Journal of Physics, 64, No. 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 calculation of energy spectra and other properties. Meanwhile, the correlations which can not be included according to perturbation theory are accounted for 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.