d-Dimensional Kepler–Coulomb Sturmians and Hyperspherical Harmonics as Complete Orthonormal Atomic and Molecular Orbitals

Sturmian basis sets are increasingly finding applications to the description of atomic and molecular structure, because of their mathematical properties and their flexibility regarding the ability to describe features of specific physical problems. However, their nature and properties have not been fully exploited in quantum chemistry. In this work we present a classification of Kepler-Coulomb Sturmian sets, where notations, symmetry properties, useful formulae, and relationships are described in detail, so to provide support for their applications to physical problems. The mathematical solution of Schrodinger equation is given for these sets both in configuration and momentum space, where Sturmian eigenfunctions coincide with hyperspherical harmonics and connections between different sets manifestly appear as elements of angular momentum algebra. Applications of the considered sets and some of their generalizations are also briefly accounted for.