Fragment Electron Populations in Partition Density Functional Theory

Partition Density Functional Theory (P-DFT) is a density-based embedding method that partitions a system into fragments by minimizing the sum of fragment energies subject to two constraints: (1) That the sum of fragment densities equals the density of the system; (2) That the sum of fragment electron populations equals the total number of electrons. To perform this constrained minimization, we study a two-stage procedure in which the sum of fragment energies is lowered when electrons flow from fragments of lower electronegativity to fragments of higher electronegativity. The global minimum is reached when all electronegativities are equal. The non-integral fragment electron populations are dealt with in two different ways: (1) by using fractionally occupied orbitals (FOO) and (2) ensemble (ENS) treatments. Although these two methods lead to the same total energy and density, they lead to different fragment properties and partial charges. We compare exact P-DFT calculations with results obtained from the Local-Density Approximation (LDA) for heteronuclear diatomic molecules. We find that the electron numbers transferred in ENS are generally smaller than that in FOO, and explain why.