A Variational Monte Carlo Approach to Atomic Structure

Abstract

A simple version of the variational Monte Carlo method is applied to the electronic structure of atomic hydrogen, helium, lithium, and beryllium. For simplicity, the trial functions are taken as products of hydrogenic orbitals for which Z is treated as a variable parameter. The variationally optimized values of these parameters are interpreted as effective nuclear charges. These ab initio calculations are done using only spreadsheets that are straightforward enough for students to construct and use. The results are used to explicate several features of many electron atoms, including electron shielding in the ground state of helium, singlet�triplet splitting in the first excited state of helium, the difference in 2s and 2p penetration in lithium, and the trends in ionization energies for Be, Be+, and Be2+.