Basis Sets for Electronic Wave Functions

The standard strategy to tackle this problem is to select a set of basis functions 0y(r)) for the KS orbitals t/t/, 

Of course, the basis set 0y(r) cannot be complete in practical computations (as the Hilbert space H is of infinite dimension), and there are two possibilities to optimize the overlap of the subspace spanned by 0y(r) with the low-energy portion of H, 

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