The effective Hamiltonian is obtained by using a reverse-engineered inverse density functional theory (iDFT), or more precisely an inverse site occupation function theory (iSOFT) as in the iDFT. The off diagonal elemts, i.e. the hopping elements are taken from evaluating the Fock terms as in iHF. The determination of the the local potentials utilizes a steepest-descent gradient search. In order to avoid problems due to degeneracies a finite inverse temperature \(\beta\) is applied. The default value is \(\beta=10^4\).