Polarization consistent basis sets. II. Estimating the Kohn–Sham basis set limit

The performance of the previously proposed polarization consistent basis sets is analyzed at the Hartree–Fock and density functional levels of theory, and it is shown that each step up in basis set quality decreases the error relative to the infinite basis set limit by approximately an order of magnitude. For the largest pc-4 basis set the relative energy error is approximately ${10}^{\text{−7}},$ and extrapolation further improves the results by approximately a factor of 2. This provides total atomization energies for molecules with an accuracy of better than 0.01 kJ/mol per atom. The performance of many popular basis sets is evaluated based on 95 atomization energies, 42 ionization potentials and 10 molecular relative energies, and it is shown that the $\mathrm{pc}\mathrm{-n}$ basis sets in all cases provides better accuracy for a similar or a smaller number of basis functions.