Sturmian approach to one-electron many-center systems: integrals and iteration schemes

The Sturmian hydrogenoid orbitals form a basis set (complete with no need for inclusion of the continuum) which can be usefully exploited for the solution of atomic and molecular structure problems. They are connected in momentum space with hyperspherical harmonics and in configuration space with Slater-type orbitals. In this work we give exact formulas and computational recipes for nuclear attraction integrals involving both the polar and the parabolic (or Stark) Sturmian set. These integrals are needed for the matrix elements entering the secular problem for the construction of molecular orbitals within the Born–Oppenheimer scheme. Such a secular problem can be formulated at different iteration levels for the one-electron Schrödinger equation, and their relative performances against truncation are quantitatively assessed.