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 multi-electron 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 develope a set of one-parameter variational calculation 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. Because the 1s, 2s, and 2pz orbitals contain the same variational parameter (alpha) they remain orthogonal under the variational procedure. This prevents the need for an anti-symmetric wave function and greatly reduces the mathematical complexity of the calculations. As we shall see later, this one-parameter simplicity comes at a price and the comparison between model and experiment deteriorates rapidly by the time we reach boron.

Reference:

1. Saleh-Jahromi, A.; Moebs, W.Eur. J. Phys 1998, 19, 355.

Back to Frank Rioux's homepage.