On the accuracy limits of orbital expansion methods: Explicit effects of k-functions on atomic and molecular energies

For selected first- and second-row atoms, correlation-optimized Gaussian k functions have been determined and used in the construction of septuple-ζ basis sets for the correlation-consistent cc-pVXZ and aug-cc-pVXZ series. Restricted Hartree–Fock (RHF) and second-order Møller–Plesset (MP2) total and pair energies were computed for H, N, O, F, S, H2, N2, HF, H2O, and (H2O)2 to demonstrate the consistency of the new septuple-ζ basis sets as extensions of the established (aug)-cc-pVXZ series. The pV7Z and aug-pV7Z sets were then employed in numerous extrapolation schemes on the test species to probe the accuracy limits of the conventional MP2 method vis-à-vis explicitly correlated (MP2-R12/A) benchmarks. For (singlet, triplet) pairs, (X+12)−n functional forms with n=(3, 5) proved best for extrapolations. The (mean abs. relative error, std. dev.) among the 73 singlet pair energies in the dataset is (1.96%, 0.54%) and (1.72%, 0.51%) for explicit computations with the pV7Z and aug-pV7Z basis sets, respectively, but only (0.07%, 0.09%) after two-point, 6Z/7Z extrapolations with the (X+12)−3 form. The effects of k functions on molecular relative energies were examined by application of the septuple-ζ basis sets to the barrier to linearity and the dimerization energy of water. In the former case, an inherent uncertainty in basis set extrapolations persists which is comparable in size to the error (≈20 cm−1) in explicit aug-pV7Z computations, revealing fundamental limits of orbital expansion methods in the domain of subchemical accuracy (0.1 kcal mol−1).