# Partition Density Functional Theory for Semi-Infinite and Periodic Systems

Partition Density Functional Theory (P-DFT) is a formally exact method to find the ground-state energy and density of molecules via self-consistent calculations on isolated fragments. It is being used to improve the accuracy of Kohn-Sham DFT (KS-DFT) calculations and to lower their computational cost. Here, the method has been extended to be applicable to semi-infinite and periodic systems. This extension involves the development of new algorithms to calculate the exact partition potential, a central quantity of P-DFT. A novel feature of these algorithms is that they are applicable to systems of constant chemical potential, and not only to systems of constant electron number. We illustrate our method on one-dimensional model systems designed to mimic metal-atom interfaces and atomic chains. From extensive numerical tests on these model systems, we infer that: 1.) The usual derivative discontinuities of open-system KS-DFT are reduced (but do not disappear completely) when an atom is at a nite distance from a metallic reservoir; 2.) In situations where we do not have chemical potential equalization between fragments of a system, a new constraint for P-DFT emerges which relates the fragment chemical potentials and the combined system chemical potential; 3.) P-DFT is an ideal method for studying charge transfer and fragment interactions due to the correct ensemble treatment of fractional electron charges; 4.) Key features of the partition potential at the metalatom interface are correlated to well-known features of the underlying KS potential; and 5.) When there is chemical potential equalization between an atom and a metal surface it is interacting with, there is strong charge transfer between the metal and atom. In these cases of charge transfer the density response to an innitesimal change in the chemical potential is located almost exclusively around the atom. On the other hand, when the fragment chemical potentials do not equalize, the density response only aects the surface Friedel oscillations in the metal.