Fragment occupations in partition density functional theory

Abstract

The exact ground-state energy and density of a molecule can in principle be obtained via Partition Density Functional Theory (PDFT), a method for calculating molecular properties from Kohn–Sham calculations on isolated fragments. For a given choice of fragmentation, unique fragment densities are found by requiring that the sum of fragment energies be minimized subject to the constraint that the fragment densities sum to the correct molecular ground-state density. We investigate two interrelated aspects of PDFT: the connections between fragment densities obtained via different choices of fragmentation, for which we find “near-additivity”, and the nature of their corresponding fragment occupations. Whereas near-integer occupations arise for very large inter-fragment separations, strictly integer occupations appear for small inter-fragment separations. Cases where the fragment chemical potentials cannot be equalized lead to fragment occupations that lock into integers.