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-ζ 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 ∼1 mhartree/electron error for the 2ZaP SCF energy and a consistent of ∼1.4 μhartree/electron error for the 6ZaP SCF energy). The SCF energy exhibits systematic convergence to the CBS limit: ESCF(nZaP)≈ESCF(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 33.5mEh, 4.58mEh, 0.82mEh, 0.18mEh, and 0.047mEh 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 0.24mEh, 0.056mEh, 0.020mEh, and 0.005mEh, respectively. A test set o...