Natural Expansions of Exact Wavefunctions. III. The Helium-Atom Ground State

A wavefunction similar to the Kinoshita function has been analyzed into natural orbitals. As it was for the hydrogen molecule, the first natural orbital for helium is very nearly the SCF function. The first three natural orbitals describe the atom quite well. These three terms give an energy of —2.8974 hartrees and an overlap with the exact wavefunction of 0.99979. Beyond these three terms, the natural expansion converges slowly with many terms required to even approximately fit the cusp in the correlation hole.