Accurate CI expansion in a spline basis of the helium ground‐state wave function

Careful study of radial spline basis‐set convergence on the angular limits of the He 1s 2 state has been performed. Improvement of algorithm allows reaching the full ci limit in a large radial (79 spline functions) and angular (Imax=80) expansion. A variational energy of − 2.903724299061 au, with an error of 7.8 × 10−8 au is obtained, improving by over two orders of magnitude the previous available limit. Accurate angular momentum limits (1 × 10−8 au) are obtained up to l = 25. Analysis of the behavior of two‐particle radial wave functions reveals a sharply peaked behavior which allows effective truncation of the two‐electron radial basis for high angular momentum values. A reasonable estimate of computational resources required indicate that an accuracy below 1 × 10−8 au is presently feasible and about 1 × 10−9 au possible in the near future.