4.5. Basis sets

The spatial wave functions, , in the integrals of Section 4.4, Molecular Hamiltonian in the Hartree-Fock orbitals basis, are approximated by linear combinations of several independent basis functions. The form of these functions is inspired by the atomic orbitals of hydrogen-like systems that we introduced in Section 2.1.1, Spherical harmonic functions, which have a radial part as shown in Section 2.2.1, Computing the radial wave functions.

Two classes of approximate basis orbitals that are commonly used are Slater-type orbitals (STOs) based on the Slater determinant introduced in Section 4.2, Fock space, and Cartesian Gaussian-type orbitals (GTOs). These two types of basis functions can be combined as STO-nG, where n is the number of Gaussians used to make the approximation. Ab Initio electronic structure computations are conducted numerically using a basis set of orbitals.

We now detail the structure of these two classes and illustrate them with Python plots...