Unifying General and Segmented Contracted Basis Sets. Segmented Polarization Consistent Basis Sets.

We propose a method, denoted P-orthogonalization, for converting a general contracted basis set to a computationally more efficient segmented contracted basis set, while inheriting the full accuracy of the general contracted basis set. The procedure can be used for any general contracted basis set to remove the redundancies between general contracted functions in terms of primitive functions. The P-orthogonalization procedure is used to construct a segmented contracted version of the polarization consistent basis sets, which are optimized for density functional theory calculations. Benchmark calculations show that the new pcs-n basis sets provide uniform error control of the basis set incompleteness for molecular systems composed of atoms from the first three rows in the periodic table (H-Kr) and for different exchange-correlation functionals. The basis set errors at a given zeta quality level are lower than other existing basis sets, and the pcs-n basis sets are furthermore shown to be among the computationally most efficient. The pcs-n basis sets are available in qualities ranging from (unpolarized) double-zeta to pentuple zeta quality and should therefore be well suited for both routine and benchmark calculations using density functional theory methods in general.