Hydrogen atom with Gaussian functions

A basis set is used to express the unknown MOs in terms of a set of known functions. The more basis functions used, the more accurate the description of the MOs. Any type of function can be used, but most efficient are basis functions with a physical behavior (e.g., approach zero for large distances between electrons and nuclei) and which make the integral evaluation easy. Slater-type orbitals (STOs) are related to the exact solutions for the hydrogen atom, but Gaussian-type orbitals (GTOs) are preferable for computational ease ... 

The presence of a single polarization function (either a full set of the six Cartesian Gaussians dxx, d z, dyy, dyz and dzz, or five spherical harmonic ones) on each first row atom in a molecule is denoted by the addition of a. Thus, STO/3G means the STO/3G basis set with a set of six Cartesian Gaussians per heavy atom. A second star as in STO/3G implies the presence of 2p polarization functions on each hydrogen atom. Details of these polarization functions are usually stored internally within the software package. 

Sometimes it turns out that we need to include a number of polarization functions, not just one of each type. The notation 4-31G(3d, 2p) indicates a standard 4-31G basis set augmented with three d-type primitive Cartesian Gaussians per centre and two p-type primitives on every hydrogen atom. Again, details of the... 

Electron Affinity of Hydrogen, Deuterium, and Tritium Atoms Obtained with 300 Explicitly Correlated Gaussian Functions ... 

---