Partition density functional theory and its extension to the spin-polarized case

Partition density functional theory (PDFT) [P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, Phys. Rev. A 82 (2), 024501 (2010)] is a formally exact method for obtaining molecular properties from Kohn–Sham calculations on isolated fragments. Here, we express the partition energy of PDFT as an implicit functional of the molecular spin-densities for a given choice of fragmentation, and use the principle of von Barth and Hedin to formulate the spin-decomposed version of PDFT. We introduce a partition energy functional of the spin-up and spin-down electronic densities and derive the associated polarized partition potentials, which are found to be global quantities that influence every fragment in the molecule. Along with the formal theory, we propose a simplified approach to computing the spin-partition potentials, and illustrate its utility and accuracy with two simple examples. Finally, we propose a viable approach to including external electric and magnetic fields in the framework of spin-PDFT.