Atomic Variational Calculations: Hydrogen to Boron

Abstract: Relatively simple quantum mechanical calculations are described for atoms and ions up to boron. The calculations employ scaled hydrogenic orbitals and can be completed with or without the aid of a computer. Given the simplicity of the trial wave functions the agreement with experiment is satisfactory. Noting the absence of simple multielectron calculations in the pedagogical literature, Saleh-Jahromi and Moebs [1] recently described a one-parameter variational calculation on three-electron atomic species (Li, Be+, B2+) that gave reasonable agreement with experimental data. The purpose of the present manuscript is to demonstrate that it is easy to extend their calculation to four- and five-electron systems. Thus, without an unreasonable amount of mathematical effort it is possible to develop a set of one-parameter variational calculations on the elements from hydrogen to boron. In this study one-, two-, and three-electron variational calculations will be reviewed and then extended to four- and five-electron systems. The scaled hydrogenic orbitals [2] that will be used are given below: