A variational Monte Carlo approach to atomic structure

This paper has demonstrated the practicality and usefulness of variational Monte Carlo calculations at the undergraduate level. Using only a commonly available spreadsheet program such as Microsoft Excel, it is possible for students to obtain numerical energies for states of simple, many-electron atoms. In order to keep the method as transparent as possible, a simple rejection method is used to generate the required random positions. In spite of the low efficiency of such a method, it easily succeeds in quantitatively illustrating a number of key concepts in atomic structure theory. These concepts include electron shielding, effective nuclear charge, l-dependence of the orbital energies, singlet-triplet energy splitting, and ionization energy trends. Though not presented in this paper, this spreadsheet approach can also be successfully used to obtain quantitative estimates of the L-S term energies in the ground state of carbon and the bond energy and equilibrium bond distance in H2+. Usually these concepts are introduced merely qualitatively, but VMC calculations allow students to see them emerge from numerical results they can obtain for themselves using only familiar tools. Another pedagogical advantage of this VMC approach is that it reinforces the idea of the wave function as a probability distribution. Seeing the actual generation of a random sample of properly distributed electron positions helps make concrete the concept of the electron cloud"."