Natural minimal basis accuracy

Thus, these orbitals can be used to represent exactly any property of the system in localized terms. The NAOs divide naturally into a leading high-occupancy set (the natural minimal basis ) and a residual low-occupancy set (the natural Rydberg basis ), where the occupancies of the latter orbitals are usually quite negligible for chemical purposes. Thus, even if the underlying variational basis set is of high dimensionality (6-311++G for the applications of this book), a perturbative analysis couched in NAO terms has the simplicity of an elementary minimal-basis treatment without appreciable loss of chemical accuracy. 

There have been a few basis sets optimized for use with DFT calculations, but these give little if any increase in efficiency over using EIF optimized basis sets for these calculations. In general, DFT calculations do well with moderate-size HF basis sets and show a significant decrease in accuracy when a minimal basis set is used. Other than this, DFT calculations show only a slight improvement in results when large basis sets are used. This seems to be due to the approximate nature of the density functional limiting accuracy more than the lack of a complete basis set. 

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