Electronic Structure Problem of Alkaline Earth Metals

Purpose: The present study is to resolve the problem in electronic structure of alkaline earth metals bydifferent calculations and conceptual theories. Methodological concept: All discovered alkaline earth metals occur in nature. Experiments have beenconducted to attempt the synthesis of element 120, the next potential member of the group, but they have allmet with failure. The electronic structure of alkaline earth metals determines all their physical properties.Effective electron Eigen value problem of the singly charged alkaline earth metal ion with a single valenceelectron. This valence electron moves in one particle model potential to reproduce the valence excitationenergies of the monocation. Results: The radial degree of freedom of the electronic wave function in a finite element basis set from thesolution of the one electron problem. Using the Lanczos-based package ARPACK, we calculate-for eachvalid combination of angular momentum quantum numbers l and j-the first 18 eigen functions outside thecore shells. In other words, solutions associated with inner shells are skipped. Thus, the selected valence-electron solutions display correct nodal behavior.