Linear dependence in Hylleraas configuration-interaction calculations of He atom

The explicitly-correlated basis sets are much easier to be linearly dependent than the product type bases constructed by one-electron orbitals due to the explicit inclusion of interelectronic coordinates in system wave functions. In this work, we apply Lowdin's canonical orthogonalization method to study the linearly dependent problems arising from the variational calculations based on Hylleraas configuration-interaction (Hy-CI) basis functions. Both the ground and excited states of He atom are calculated with increasingly large basis sets. Our results show that the linear dependence in Hy-CI basis sets can be successfully overcome by employing Lowdin's canonical orthogonalization method, yet without using extended higher-precision arithmetic in numerical implementations. Therefore, the computational effort can be reduced considerably. It is expected that the present method can be applied to other types of explicitly correlated basis functions.