I'm quite curious about this:
In a basis set (I'll just use minimal-basis STO-nG basis sets for convenience), the basis functions are written as a linear combination of primitive GTOs. Are the GTOs normalised first, like this:
$$\Psi^\mathrm{STO} = \sum_i N_i c_i \phi_i^\mathrm{GTO}$$
where $\phi_i^\mathrm{GTO}$ are un-normalised GTO functions, and $N_i^{2} \left<\phi_i\left|\phi_i\right.\right> = 1$
or are they normalised like this (GTOs are not normalised):
$$\Psi^\mathrm{STO} = N_\mathrm{STO} \sum_i c_i \phi_i^\mathrm{GTO}$$
where $N_\mathrm{STO}^{2} \left<\Psi^\mathrm{STO}\left|\Psi^\mathrm{STO}\right.\right> = 1$?
I thought it was the former and not the latter, but after poking around the internet I'm not so sure anymore.
