Two-body Schroedinger Wave Functions in a Plane-wave Basis via Separation of Dimensions

Using a combination of ideas, the ground and several excited electronic states of the helium atom are computed to chemical accuracy---i.e., to within 1--2 millihartree or better. The basic strategy is very different from the standard electronic structure approach, in that the full, two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock (HF) approximation. Electron correlation is thus treated \emph{exactly}, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full- dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted---as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's Rule, which states that the lower energy of the higher spin- multiplici