Convergence of the partial wave expansion of the He ground state

The configuration interaction (Cl) method, using a very large Laguerre orbital basis, is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each l ranging from 0 to 12, resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron delta-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite angular momentum using expansions of the type Delta X-J = A(X)[J + 1/2](-p) + B-X[J + 1/2](-mu-1) +..., gave an energy accurate to 10(-7) Hartree and a value of <delta > accurate to about 0.5%. Improved estimates of < E > and <delta >, accurate to 10(-8) Hartree and 0.01%, respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J -> infinity limit. Round-off errors were the main impediment to achieving even higher precision, since determination of the radial and angular limits required the manipulation of very small energy and <delta > differences. (c) 2006 Wiley Periodicals, Inc.