Cusps and Derivatives for Wave-Functions Expanded in Slater Orbitals: A Density Study

摘要

This article recalls basic properties of Slater type Orbital (STO) basis sets, in particular, with respect to satisfying Kato's electron-nucleus cusp condition. It is shown that a suitable starting point is the set of hydrogen-like orbitals or, more flexibly, their generalization as Coulomb Sturmians. A case study is presented on the Hartree-Fock density obtained for a water molecule, N-2, and CO2 showing that the nuclear cusp condition may be easily accounted for near the heavier nuclei, but only with difficulties at the hydrogen center. In particular, bond stretching affects the expected cusp condition on hydrogen atoms. Some indications are given on the improvement of STO basis sets.