Basis-set convergence of the energy in molecular Hartree–Fock calculations

The basis-set convergence towards the numerical limit of the Hartree–Fock total energy and binding energy is investigated for the correlation-consistent cc-pVXZ basis sets. For both energies, solid improvements are obtained with each increment in X. The basis-set errors for the total energy (ΔE) fit an exponential form better than a power form, and the total energy is better fitted than the binding energy. It is difficult to find generally reliable extrapolation schemes for the total energy. In most cases, the most successful scheme gives results extrapolated beyond a given X that are comparable to the cc-pV(X+1)Z results, but occasionally it fails dramatically for large X. Indeed, explicit calculation of the energy in a larger basis set, especially the cc-pV6Z set for which ΔE⩽0.1 mEh, gives the most reliable estimate of the basis-set limit.