Counting basis sets in quantum chemistry

Question

I have to use STO-nG (a "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). Let's take the example of a water molecule.

The water molecule has two H atoms and one O atom. Thus, we have a total of 7 orbitals (two 1s of H, one 1s of O, one 2s of O and three 2p of O). So when using STO-nG, 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, each being made up from a linear combination (LC) of n simple gaussians?

Possible duplicate of How many basis functions used in STO-3G and 6-31+G** for the water molecule? — Tyberius, Mar 27 '19 at 14:11
@Tyberius Yes. But if you see the answers, this has not been answered. — hhsomething69, Mar 27 '19 at 16:34
Sorry I missed that they never explicitly answered that. But you are correct, STO-nG for water will have 7 basis functions, each of which is formed from n-Gaussians. As an aside, you could always check this using a free electronic structure program like Psi4 or ORCA. @hhsomething69 — Tyberius, Mar 27 '19 at 16:50

score 6 · Accepted Answer · answered Mar 27 '19 at 19:49

Yes, you have counted the number of basis functions correctly:

    #1s    #2s    #2px    #2py    #2pz    #Total
H1   1                                      1
H2   1                                      1
O    1      1       1       1       1       5

Which as you also counted is 7 basis functions. As you also correctly state, each of the basis functions will be a linear combination of $n$ primitive Gaussians:

$$\phi(r)=\sum_{i=1}^nc_i\exp\left(-\alpha_i\left(r-r_0\right)^2\right)$$

As you have observed that is what the $n$ in STO-$n$G denotes.

Counting basis sets in quantum chemistry

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