Results from different sets of band calculations for undoped and doped HgBa2CuO4 show that small changes in localization can lead to very different ground states. The normal LDA results are compared with ‘modified' LDA results, in which different linearization energies make the O p band more localized. The ground states in the normal calculations are far from the anti-ferromagnetic ones, while nearly AFM states are found in the modified calculations. The proximity of an AFM state in the doped system leads to increased λsf, and the modified band structure has favourable conditions for spin–phonon coupling and superconductivity mediated by spin fluctuations.