Density functional partition theory with fractional occupations

Partition theory (PT) is a formally exact methodology for calculating the density of any molecule or solid via separate calculations on individual fragments. Just as Kohn-Sham density functional theory (DFT) introduces noninteracting fermions in an effective potential that is defined to yield the exact density of the interacting problem, in PT a global effective potential is found that ensures that the sum of the fragment densities is that of the full system. By combining the two, density functional partition theory (DFPT) produces a DFT scheme that yields the (in principle) exact molecular density and energy via Kohn-Sham calculations on fragments. We give the full formalism and illustrate DFPT in the general case of noninteger fragment occupations.