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Properties of the weighted Löwdin orthogonalization procedure are thoroughly discussed. It is shown that its flexibility might be very useful in the construction of optimal truncated basis sets in approximate theories of the electronic structure of molecules and solids. The relevance of pairwise nonorthogonal (hybrid) basis functions is pointed out

Construction of Optimal Basis Sets in Approximate Theories of the Electronic Structure of Molecules: Weighted Löwdin Orthogonalization