Abstract
The purpose of this work was to develop a Screened Hydrogenic Model (SHM) to accurately calculate the electron energies for light atoms and ions with up to ten electrons for atomic numbers up to 18. The total energy of an atom or ion was calculated with effective nuclear charges and screening parameters for each electron type (1s, 2s and 2p) within a specific electron configuration. Multiple energy states, centered at the total energy, were calculated for electron configurations that have Russell-Saunders coupling. The energy of each electron included its relativistic energy, EREL, but close overall agreement between the calculated and experimental energies of multi-electron configurations required that the one-electron expression for EREL be modified in a simple manner. In the present work, 98% of the 587 calculated energies for light atoms/ions have a relative error within ±0.1% of the corresponding experimental energies. The effective nuclear charges described in this work allow hydrogen-like wave functions to be defined for the electrons within a multi-electron configuration. The SHM, described in this work, is available for future calculations involving light atoms and ions.
Highlights
It is well known that the energy levels of a one-electron atom or ion have been determined by solving the Schrӧdinger equation
The experimental energies, computed in this work from spectroscopic data for the neutral atoms of helium through neon, were compared to the corresponding experimental total energies listed by Veillard [24]. The energies of these nine atoms each agreed within ±0.001 a.u., except for oxygen that agreed within ±0.02 a.u
The 587 energy levels correspond to 293 different electron configurations
Summary
It is well known that the energy levels of a one-electron atom or ion have been determined by solving the Schrӧdinger equation. One theoretical approach for determining the energy of complex atoms and ions is the self-consistent field (SCF) method. This process is repeated until the potential energy values for the electrons are the same as the potential energies that were used to calculate them. This approach, which can be applied to molecular calculations, gives increasingly better agreement as the basis set is expanded and the complexity of the calculation is increased
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