ABSTRACT In previous studies we have established a new basis‐set expansion method, called the kinetic energy partition (KEP) method, for solving general quantum eigenvalue problems, and applied it to several one‐body or two‐body systems, such as the dihydrogen cation and helium‐like atoms. Extending this method to larger atomic and molecular systems, although straightforward, confronts additional technical problems. Some of the difficulties are associated with the Coulomb interactions, so here we study several model atoms, such as the harmonium (Hookium), the Dirackium, and the Moshinsky atoms, in which a partial or full substitution of Coulomb interactions among charges with model potentials yields a simplifying solution scheme. In this way we can clearly identify the main technical issues associated with the KEP method, with the hope to point toward a streamlined solution procedure. Our results show that with a variety of complexity of interaction patterns, the calculation procedure is still well under control and the resulting errors are all within the required accuracy level. The purpose of this paper is, therefore, to advocate the utility of the KEP method in front‐line researches in quantum chemistry problems.
Wu et al. (2026) studied this question.