Analysis of the segmented contraction of basis functions using density matrix theory.

A particular formulation based on density matrix (DM) theory at the Hartree-Fock level of theory and the description of the atomic orbitals as integral transforms is introduced. This formulation leads to a continuous representation of the density matrices as functions of a generator coordinate and to the possibility of plotting either the continuous or discrete density matrices as functions of the exponents of primitive Gaussian basis functions. The analysis of these diagrams provides useful information allowing: (a) the determination of the most important primitives for a given orbital, (b) the core-valence separation, and (c) support for the development of contracted basis sets by the segmented method.

Exact Gaussian expansions of Slater-type atomic orbitals.

Three exact Slater-type function (STO) integral transforms are presented. The STO-NG basis set can then be developed using either only 1s Gaussian functions, the same Gaussian exponents for each shell, or using the first Gaussian of each symmetry. The use of any of these three alternatives depends only on appropriate numerical integration techniques.