Tight-binding Møller-Plessed theory for phosphorus arrays in silicon.

The distribution of electrons in lattice structures can reveal complex quantum phenomena and new matter states, also serving as the foundation for quantum simulations of the Fermi-Hubbard model. Dopant-based silicon devices realize such lattice models thanks to the near-atomic precision in the impurity placement and electrical control. Numerical studies on the electronic structure are needed to validate such quantum simulations and to interpret the electric and electromagnetic response of these systems. In this talk, we introduce a numerical approach, the TB-MP method, that combines atomistic tight-binding electronic calculations, Hartree-Fock theory, and Møller-Plesset perturbation theory to compute the electron distribution and spin configuration of multielectron systems. In particular, we consider phosphorus arrays in silicon consisting of up to seven atoms and up to half filling, in linear, triangular, and other lattices. We also compute binding and charging energies, comparing the predictions with full configuration interactions in cases with a few sites or electrons. Our results show that the TB-MP method accurately models multielectronic states of large arrays in silicon, incorporating electron correlation energy when relevant for describing interactions between electrons and fully describing electron lattice physics.