Real-space Basis Sets
On the same principle as the plane waves but in real space, there are basis sets whose functions are centered on a uniform mesh in real space. This is the case for the finite difference, the functions sinc or wavelets. In the case of the latter, it is possible to have an adaptive mesh closer to the nucleus using the scaling properties of wavelets. These methods use functions that are localized which allow the development of order N methods.
Read more about this topic: Basis Set (chemistry)
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