Abstract
Abstract New sets of functions with arbitrarily large finite cardinality are constructed for two-electron systems. Functions from these sets exactly satisfy Kato’s cusp conditions. The new functions are particular linear combinations of Hylleraas- and Kinoshita-type terms. The energies of the system can be calculated by a standard variational calculation, leading to a matrix eigenvalue problem. There is no need for a constrained optimization to satisfy the cusp conditions. In the numerical examples, the ground state energies of the He atom and the H − ion are considered and several expectation values are calculated for the He.