Convergence of the partial wave expansion of the He ground state

Abstract

The configuration interaction (CI) 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 δ-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 ΔXJ = AX[J + 1/2] -p + BX[J + 1/2]-p-1 + ..., gave an energy accurate to 10-7 Hartree and a value of 〈δ〉 accurate to about 0.5%. Improved estimates of 〈E〉 and 〈Δ〉, 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 → ∞ 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 〈δ〉 differences. © 2006 Wiley Periodicals, Inc.