Notation for Gaussian-type basis functions

The term STO-3G denotes a minimal Gaussian basis set in which each Slater-type atomic orbital (s, p or d) is approximated by a fixed block of three Gaussian functions189, 

Although the use of split-valence basis functions introduces larger flexibility, this may be further increased by the addition of so-called polarization functions, which consist of five or six 3d orbitals for elements of the second row of the periodic table and of three 2p orbitals for hydrogen. The first case is marked by the addition of one asterisk, i.e. 6-31G 194. Two asterisks, i.e. 6-31G 194 or 6-311G 193, indicate the additional presence of polarization 2p orbitals on hydrogens. 

Especially for negatively charged systems, diffuse s- or p-type functions of high quantum numbers may be necessary. These are marked by + signs, i.e. 3-21 + G or 6-31 +G.  

Optimizations of molecular geometries may be performed with a simpler basis set followed by a single-point Hartree-Fock (HF) calculation with a larger basis set for that derived geometry. This is indicated by double slashes, i.e. 6-31G //3-21G. 

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