## Basis sets STO (slater-type orbital, hydrogenic orbitals) basis sets are very natural choice, For it follows our chemical intuitions, they are "*real*" orbitals and easy to depict to actual chemical process. But STO integrals are difficult to compute, so people use GTO (Gaussian type orbital) as basis functions. They're easy to compute, and having one common factor, $e^{-\alpha r^{2}}$, which can be computed and stored for multiple uses. Single function in GTO behaves differently from STO, so we use multiple GTO functions to fit STO, this is called [STO-nG](https://en.wikipedia.org/wiki/STO-nG_basis_sets). Besides computational aspects, chemically STO (or GTO) basis sets might not be enough to describe some cases, Like when polarization affects geometry, or electrons are weakly bonded. Under these scenarios, we add: - Polarization functions: Add one more group (e.g., $d$ to $f$) of BS, marked as $*$. - Diffuse function: To model weekly bonded electrons, or polarized electrons, or excited electrons, marked as $+$ or $++$. Although increasing number of basis sets get better results, but remember, it scales with $N^{4}$, which could be very large! So a good way to approach to the [[Hartree-Fork method#^ed2c7d|HF limit]] is extrapolate/curve fitting of some smaller basis sets. >[!Info] >See more on: >Basis set: https://en.wikipedia.org/wiki/Basis_set_(chemistry) >STO: https://en.wikipedia.org/wiki/Slater-type_orbital >STO-nG: https://en.wikipedia.org/wiki/STO-nG_basis_sets >GTO: https://en.wikipedia.org/wiki/Gaussian_orbital >CP2K basis sets: https://www.cp2k.org/basis_sets