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!
Abstract
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.
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1566790
- Alternate Identifier(s):
- OSTI ID: 1636850
- Report Number(s):
- LLNL-JRNL-750479
Journal ID: ISSN 0375-9601; 934666; TRN: US2000996
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics Letters. A
- Additional Journal Information:
- Journal Volume: 383; Journal Issue: 23; Journal ID: ISSN 0375-9601
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Proof of Kohn-Sham conjecture; Kohn-Sham density functional theory; v-representability; pure state interacting v-representable; pure state non-interacting v-representable
Citation Formats
Gonis, A. 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!. United States: N. p., 2019.
Web. doi:10.1016/j.physleta.2019.03.007.
Gonis, A. 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!. United States. https://doi.org/10.1016/j.physleta.2019.03.007
Gonis, A. Wed .
"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!". United States. https://doi.org/10.1016/j.physleta.2019.03.007. https://www.osti.gov/servlets/purl/1566790.
@article{osti_1566790,
title = {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!},
author = {Gonis, A.},
abstractNote = {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.},
doi = {10.1016/j.physleta.2019.03.007},
journal = {Physics Letters. A},
number = 23,
volume = 383,
place = {United States},
year = {Wed Mar 13 00:00:00 EDT 2019},
month = {Wed Mar 13 00:00:00 EDT 2019}
}
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