What about U on surfaces? Extended Hubbard models for adatom systems from first principles

Electronic correlations together with dimensional constraints lead to some of the most fascinating properties known in condensed matter physics. As possible candidates where these conditions are realized, semiconductor (111) surfaces and adatom systems on surfaces have been under investigation for quite some time. However, state-of-the-art theoretical studies on these materials that include many-body effects beyond the band picture are rare. First principles estimates of inter-electronic Coulomb interactions for the correlated states are missing entirely, and usually these interactions are treated as adjustable parameters. In this work, we report on calculations of the interaction parameters for the group IV surface-adatom systems in the alpha-phase series of Si(111):C, Si, Sn, Pb. For all systems investigated, the inter-electronic Coulomb interactions are indeed large compared to the kinetic energies of the states in question. Moreover, our study reveals that intersite interactions cannot be disregarded. We explicitly construct an extended Hubbard model for the series of group IV surface-adatom systems on silicon, which can be used for further many-body calculations.