I am a little confused about how to decide how many basis functions that are used in a particular basis set for a given molecule.
STO-3G is a so-called "minimal basis set", meaning that only one basis function is used for each atomic orbital in the atoms of which the molecule is made from.
The water molecule has two H atoms and one O atom, with 1s1 and 1s2 2s2 2p6 electron configurations, respectively. When STO-3G is used, would that then mean that three 1s type basis functions, one 2s type basis function, and 3 p-type basis functions are used, totalling at 7 basis functions that are used, each being made up from a linear combination (LC) of three simple Gaussian functions?
The 6-31+G** is a split-valence basis set, which includes both diffuse and polarisation functions. The two asterisks tell that polarization functions are used for both the H atom and the O atom, p and d polarization functions respectively. I am not sure "how many" polarization functions are used per atom - just 1, or one for each of the p-orbitals? (Some basis sets are of the form 6-31G(3pd); does that mean that 3 p and 1 d polarization functions are used, or 9 p functions?) The single "+" sign means that just one diffuse function is used for the O atom.
So, I think that the 6-31+G** for the water molecule equates to a total of 16 basis functions:
- 1s in oxygen: one LC of 6 GTOs
- 2s in oxygen: one LC of 3 GTOs + 1 GTO
- 2p in oxygen: one LC of 3 GTOs + 1 GTO (for each of px, py, and pz)
- 1s in hydrogen 1: one LC of 3 GTOs + 1 GTO
- 1s in hydrogen 2: one LC of 3 GTOs + 1 GTO
- Diffuse: one diffuse basis function for the oxygen atom
- Polarization: one polarised basis function for the oxygen atom
- Polarization: one polarised basis function for the hydrogen atom
- Total: 16
Is this correct? I do not feel confident carrying out this analysis, especially the point concerning how many polarization functions for the p/d-orbitals that should be used.