Uniformly convergent n-tuple-ζ augmented polarized (nZaP) basis sets for complete basis set extrapolations. I. Self-consistent field energies

We present a sequence of n-tuple-zeta augmented polarized (nZaP) basis sets designed for extrapolations of both self-consistent field (SCF) and correlation energies to the complete basis set (CBS) limit. These nZaP basis sets (n=2-6) are formulated to give consistent errors throughout the Periodic Table (e.g., a consistent of similar to 1 mhartree/electron error for the 2ZaP SCF energy and a consistent of similar to 1.4 mu hartree/electron error for the 6ZaP SCF energy). The SCF energy exhibits systematic convergence to the CBS limit: E(SCF)(nZaP)approximate to E(SCF)(CBS)+Ae(-)an. A single parameter, a=6.30, describes the 2ZaP through 6ZaP errors of H through Xe within 10%. The SCF rms basis set truncation errors of H through Xe are 33.5mE(h), 4.58mE(h), 0.82mE(h), 0.18mE(h), and 0.047mE(h) for 2ZaP, 3ZaP, 4ZaP, 5ZaP, and 6ZaP, respectively. Linear extrapolations of the (2,3)ZaP, (3,4)ZaP, (4,5)ZaP, and (5,6)ZaP calculations (all with a=6.30) reduce these errors by an order of magnitude to 0.24mE(h), 0.056mE(h), 0.020mE(h), and 0.005mE(h), respectively. A test set of 34 atoms, ions, and molecules gives similar results, and the associated test set of 25 chemical energy differences also gives comparable absolute accuracy. However, the cancellation of errors between reactant and product is lost by extrapolation. As a result, these chemical energy differences show a more modest two-to-fourfold improvement with extrapolation.