Slater and Gaussian basis functions and computation of molecular integrals

Basis functions and molecular integrals are critical components utilized in electronic structure (ab initio and density functional theory) calculations. In this chapter, a mathematical overview is provided about the construction of basis functions and computation of molecular integrals. Included is a discussion about the selection of basis functions for use in computational chemistry calculations, providing insight about factors that should be considered. The behavior of energies and properties with increasing basis set size, as well as extrapolation schemes are presented. Also, a discussion of the computational scaling and more efficient approaches, such as pseudopotential basis sets and the density fitting, are described.