Polarization consistent basis sets: Principles

The basis set convergence of Hartree–Fock energies for the ${\mathrm{H}}_{\mathrm{2}},$ ${\mathrm{H}}_3^{+},$ ${\mathrm{C}}_{\mathrm{2}},$ ${\mathrm{N}}_{\mathrm{2}},$ ${\mathrm{N}}_{\mathrm{4}},$ ${\mathrm{O}}_{\mathrm{2}},$ ${\mathrm{O}}_{\mathrm{3}},$ ${\mathrm{F}}_{\mathrm{2}},$ HF, and ${\mathrm{CH}}_{\mathrm{4}}$ molecules is analyzed using optimized basis functions. Based on these analysis a sequence of polarization consistent basis sets are proposed which should be suitable for systematically improving Hartree–Fock and density functional energies. Analogous to the correlation consistent basis sets designed for correlation energies, higher angular momentum functions are included based on their energetical importance. In contrast to the correlation consistent basis sets, however, the importance of higher angular momentum functions decreases approximately geometric, rather than arithmetic. It is shown that it is possible to design a systematic sequence of basis sets for which results converge monotonic to the Hartree–Fock limit. The primitive basis sets can be contracted by a general contraction scheme. It is found that polarization consistent basis sets provide a faster convergence than the correlation consistent basis sets. Results obtained with polarization consistent basis sets can be further improved by extrapolation.