Rate of Convergence of the Configuration Interaction Model for the Helium Ground State

Abstract

The rate of convergence of a CI calculation on the ground state of the helium atom is rigorously derived under suitable assumptions on the regularity of the exact wavefunction. For bases consisting of all partial waves with angular momentum less than or equal to L, the large L asymptotic energies are found to obey the well-known formula $E_L-E=CL^{-3}+o(L^{-3})$, where C is an explicit constant defined in terms of the exact wavefunction.