Sturmian orbitals and molecular structure

Abstract

In this paper, we introduce the basic steps of a computational scheme for molecular structure problems, where Sturmian orbitals appear as building blocks in a valence-bond type of approach. The Sturmian basis set approach to the solution of quantum chemical problems is the configuration space counterpart of hyperspherical analysis in momentum space and leads to promising algorithms alternative to the usual SCF-plus-configuration interaction hierarchies. The mathematical ingredients are considered, particularly the possibility of exploiting relationships with Slater-type orbitals in order to circumvent the bottleneck of calculation of matrix elements. We also propose a procedure to solve two-center overlap integrals between Sturmians based on a momentum-space approach. The example of the electronic structure of the hydrogen molecule is worked out and results of computations are given. The optimal choice of scaling parameters for Sturmian sets is also discussed.