Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

SECOND-ORDER RAYLEIGH–SCHRÖDINGER PERTURBATION THEORY FOR THE GRASP2018 PACKAGE: VALENCE–VALENCE CORRELATIONS
Gediminas Gaigalas, Pavel Rynkun, and Laima Kitovienė
Institute of Theoretical Physics and Astronomy, Faculty of Physics, Vilnius University, Saulėtekio 3, 10257 Vilnius, Lithuania
Emails: gediminas.gaigalas@tfai.vu.lt; pavel.rynkun@tfai.vu.lt; laima.radziute@tfai.vu.lt

Received 22 November 2024; accepted 2 December 2024

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.
Keywords: configuration interaction, spin-angular integration, perturbation theory, tensorial algebra, valence–valence correlations, core–valence correlations, core correlations, core–core correlations

ANTROSIOS EILĖS RELĖJAUS IR ŠRĖDINGERIO TRIKDYMŲ TEORIJA, SKIRTA GRASP2018 PROGRAMINIAM PAKETUI: VALENTINĖS–VALENTINĖS KORELIACIJOS
Gediminas Gaigalas, Pavel Rynkun, Laima Kitovienė

Vilniaus universiteto Fizikos fakulteto Teorinės fizikos ir astronomijos institutas, Vilnius, Lietuva

Vienas pagrindinių uždavinių atomo struktūros skaičiavimuose yra tikslus elektronų koreliacijų įskaitymas. Norint atlikti tikslius skaičiavimus, būtina atsižvelgti į įvairių tipų elektronų koreliacijas, o tai dažnai veda prie didelės konfigūracinių būsenų funkcijų (KBF) erdvės. Šiame darbe toliau plėtojamas antrosios eilės trikdymų teorija grįstas metodas, siekiant nustatyti svarbiausias KBF, kurios daro didžiausią įtaką kamieno–valentinėms, kamieno, kamieno–kamieno ir valentinėms–valentinėms koreliacijoms. Šis metodas paremtas reliatyvistinės superpozicijos ir stacionariosios antrosios eilės Relėjaus ir Šrėdingerio daugelio kūnų trikdymų teorijos neredukuotinėje tensorinėje formoje (G. Gaigalas, P. Rynkun, 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, L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core correlations, Lith. J. Phys. 64(2), 73–81 (2024), https://doi.org/10.3952/physics.2024.64.2.1), (G. Gaigalas, P. Rynkun, 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) metodų deriniu. Metodas yra išplėstas norint papildomai įtraukti valentines–valentines koreliacijas. Šį metodą galima taikyti atomo ar jono energijos spektro ir kitų charakteristikų skaičiavimui, esant skirtingiems valentinių sluoksnių pagrindiniams, orbitiniams kvantiniams skaičiams bei užpildymams. O koreliacijos, kurių negalima įtraukti pagal trikdymų teoriją, yra įtraukiamos naudojant įprastą būdą. Sukurtas metodas leidžia žymiai sumažinti KBF erdvę, tai ypač aktualu sudėtingiems atomams ir jonams. Darbe, kaip metodo taikymo pavyzdys, taip pat pateikiami Se III energijos struktūros skaičiavimai.

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