I was very interested in the following question and answer about the Slater- and Gaussian-type orbitals (STO and GTO) used in quantum chemistry and a practical calculation.
After reading this discussion, I am further interested in the critical difference and roles of these STO and GTO orbitals, because I have considered (or misunderstood!) that the STO is actually hard to calculate but always outperforms the GTO in computational accuracy.
My question is that, does the GTO simply represent the STO by using many Gaussians, or not?
Intuitively, it would be better to use many GTOs to represent the molecular orbitals in a many electron system in a flexible way, because it is not bound by the form of the hydrogen atom wavefunction. However, the GTO does not have a cusp and so... I'm very wondering how to understand this problem.