Convergence of the orbital expansion in a correlated system: A test study on positronium

Positronium, the bound state of an electron and a positron, is an exactly soluble quantum system, similar to a light isotope of hydrogen. It can be studied using the finite basis quantum chemistry codes developed for atoms and molecules. In fact, positronium can be mimicked by two electrons with opposite spins, in the absence of any nucleus and having the sign of the Coulomb interaction reversed. The exact wave function has a cusp in the points of coalescence of the two particles (a “Coulomb peak”), and this fact makes the convergence of the total energy, as a function of the basis set size, extremely slow. For this reason, positronium can be used to test the convergence properties of the quantum chemistry methods used to describe the dynamic correlation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001