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Gaussian-type-orbitals (GTOs) are the work horse of modern molecular quantum chemistry calculations. They are computationally efficient and allow for analytic evaluation of integrals. However, there's an increasing number of ab initio packages that choose to use other alternatives for molecular calculations. One particular example being the numerical atomic orbitals (NAOs).

For example, here's a similar discussion comparing GTOs and Slater-type-Orbitals (STOs). That brings me to my question: What's the advantage of using a NAOs or other approaches that use numerically evaluated integrals?

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In some cases at least, NAO give smaller BSSE (basis set superposition error).

Here is the figure from the FHI-aims paper:

enter image description here

The BSSE here is the difference between red and black lines. It is small, and moreover, it converges to zero with basis set growth, that is really convenient.

The integration of NAO is more complicated that for GTO, but there are some advanced numerical algorithms. Probably advances in numerical integration contributed to the emergence of NAO codes.

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