Is an interacting ground state (pure state) v-representable density also non-interacting ground state v-representable by a Slater determinant? In the absence of degeneracy, yes!

Publication date: Available online 13 March 2019Source: Physics Letters AAuthor(s): A. GonisAbstractIt is shown that in the absence of degeneracy a density, n(r), describing the probability of finding a particle in a small volume at position, r, that is known to be pure-state v-representable in terms of the ground state of an interacting system of particles evolving under an external potential, v(r), is also pure state v-representable in terms of a single Slater determinant describing the ground state of a system of non-interacting particles under a potential, vs(r). This establishes the validity of the Kohn–Sham formalism of density functional theory. An explicit form of vs(r) is derived. We also derive the exact form of the correlation functional and the corresponding potential, μc(r), that lead to the exact density and energy of an interacting system's ground state. Finally, we demonstrate that practical implementations of the Kohn–Sham formalism can generate neither the exact density nor energy of an interacting system's ground state, a feature that is particularly true in the case of the so-called exact exchange, in which the correlation functional and potential are set equal to zero.

Source: Physics Letters A - March 15, 2019 Category: Physics Source Type: research