N-representability of two-electron densities and density matrices and the application to the few-body problem

Pistol, Mats‐Erik

doi:10.1016/j.cplett.2004.11.014

Cited by 60 publications

(45 citation statements)

References 14 publications

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“…One has to be, however, extremely careful in the construction because of the N-representability problem. 10,15,[30][31][32][33][34][35][36][37][38][39][40][41][42][43] Dal Ri et al 19 derived density matrices from Jastrowtype trial wave functions. The pair density used in this work can be considered as the lowest-order approximation to the general N-representable pair density presented by Dal Ri et al Consequently, our pair density is, at least approximately, N-representable.…”

Section: Discussionmentioning

confidence: 99%

Modeling the Pauli potential in the pair density functional theory

Amovilli

Nagy

2008

The Journal of Chemical Physics

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In the ground state the pair density can be determined by solving a single auxiliary equation of a two-particle problem. A novel method for determining the Pauli potential entering this equation is presented and, starting from a reliable description of the pair density, an analytical expression is derived for atomic systems. Test calculations are presented for Be and isoelectronic C 2+ and O 4+ions.

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Section: Discussionmentioning

confidence: 99%

Modeling the Pauli potential in the pair density functional theory

Amovilli

Nagy

2008

The Journal of Chemical Physics

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“…6,7,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] Our strategy is to restrict the search region within the set of PDs that are constructed from the single Slater determinants ͑SSDs͒. It prevents the solution from being unphysical, in other words, it guarantees the solution to be necessarily N-representable.…”

Section: ͑6͒mentioning

confidence: 99%

Pair density functional theory utilizing the noninteracting reference system: An effective initial theory

Higuchi

2008

Phys. Rev. B

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We present a pair density ͑PD͒ functional scheme utilizing the noninteracting reference system. In order to check to what extent this scheme can express the correlation effects, actual calculations are performed for the neutral neon atom. It is shown that this scheme reproduces about 20% of the correlation energy through use of noninteracting single determinants with an approximate correlating kinetic energy functional. Thus, since it obviously provides the N-representable and correlated PD, this scheme can be positioned as an effective initial theory in the field of the PD functional theory, just like the position of the Hartree-Fock approximation in the field of the wave function theory.

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“…This problem is attributed to the lack of practical knowledge about the necessary and sufficient conditions for the N -representability of PDs [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. This problem is very important because the variational principle may possibly lead to an unphysical solution as the best PD unless we devise some practical method to avoid this problem.…”

Section: Introductionmentioning

confidence: 99%

Scaling method for the pair-density-functional theory in combination with energy functionals satisfying the virial theorem: Checking the validity via atomic-structure calculations

Higuchi

2013

Phys. Rev. A

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We perform atomic-structure calculations for the neutral Ne, Mg, and Ar atoms on the basis of the recently proposed correction method (scaling method) for the pair-density (PD) -functional theory [Phys. Rev. A 84, 044502 (2011)]. The formal features of the scaling method are that the search region of PDs is substantially extended and that the resultant variationally best PD, which can be obtained without the heavy calculation tasks, satisfies the virial theorem rigorously. To enjoy the benefit of these features, we also develop the approximate form of the kinetic energy functional. It is shown by the atomic-structure calculations that the scaling method can improve well not only various energy functionals but also the spatial profiles of the electron density and exchange-correlation hole. Especially it is found that the scaling method makes preferential modifications to the energetically effective regions of the electron density and exchange-correlation hole. These results suggest that the scaling method efficiently puts the PD close to the correct ground-state PD.

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N-representability of two-electron densities and density matrices and the application to the few-body problem

Cited by 60 publications

References 14 publications

Modeling the Pauli potential in the pair density functional theory

Modeling the Pauli potential in the pair density functional theory

Pair density functional theory utilizing the noninteracting reference system: An effective initial theory

Scaling method for the pair-density-functional theory in combination with energy functionals satisfying the virial theorem: Checking the validity via atomic-structure calculations

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