Orbital choice in constructing model Hamiltonians

Abstract: Model Hamiltonians (e.g., the Hubbard or Heisenberg models) provide a simple yet physically meaningful description of complex electronic phenomena through a small number of parameters, such as electron hopping integrals or magnetic exchange couplings. Their construction typically exploits the local nature of electron correlation effects and therefore relies on localized orbitals. Although many localization schemes are available, the resulting localized orbitals depend not only on the chosen localization functional but also on the orbital space to which the localization procedure is applied. These choices are often treated as technical details and are rarely discussed explicitly. Here, we demonstrate that different, chemically reasonable choices of localized orbitals can lead to substantially different model Hamiltonian parameters, even when they produce nearly identical electronic energies. Using Density Matrix Downfolding, we systematically investigate how the localization functional and, more importantly, the choice of model orbital space affect effective Hamiltonians derived from ab initio calculations for representative $π$-conjugated systems and transition metal complexes.