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!

Journal Article · Wed Mar 13 00:00:00 EDT 2019 · Physics Letters. A

DOI:https://doi.org/10.1016/j.physleta.2019.03.007· OSTI ID:1566790

Gonis, A. ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

It 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, $$v_s(r)$$ . This establishes the validity of the Kohn–Sham formalism of density functional theory. An explicit form of $$v_s(r)$$ is derived. We also derive the exact form of the correlation functional and the corresponding potential, $$\mu_c(r)$$, that lead to the exact density and energy of an interacting system's ground state. In addition, we demonstrate the existence of a one-to-one mapping between the ground-state densities of non-degenerate interacting and non-interacting systems. Finally, we show 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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1566790
• Alternate ID(s): OSTI ID: 1636850
• Report Number(s): LLNL-JRNL--750479; 934666
• Journal Information: Physics Letters. A, Journal Name: Physics Letters. A Journal Issue: 23 Vol. 383; ISSN 0375-9601
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Kohn-Sham density functional theory
Proof of Kohn-Sham conjecture
pure state interacting v-representable
pure state non-interacting v-representable
v-representability