The pair density functional of the kinetic energy and its simple scaling property

Levy, Mel; Ziesche, P.

doi:10.1063/1.1413976

Cited by 73 publications

(74 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The theory presented above is free from the Nrepresentability problem [42,[44][45][46][47][48][49][50][51][52][53][54][55][56]. However, the exact form of the Pauli potential is not known even for the ground state.…”

Section: Discussionmentioning

confidence: 99%

Excited-state pair-density-functional theory

Nagy

2014

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

Section: Discussionmentioning

confidence: 99%

Excited-state pair-density-functional theory

Nagy

2014

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…8 Let us start with the scaling relation of ⌬T c ͓␥ ͑2͒ ͔. We have 8,13 ⌬T c ͓␥ ͑2͒ ͔ = 2 ⌬T c ͓␥ ͑2͒ ͔. ͑A1͒…”

Section: Discussionmentioning

confidence: 99%

“…͑11͔͒, the approximate form of ⌬T c ͓␥ ͑2͒ ͔ is absolutely necessary. Utilizing the scaling properties of the kinetic energy functionals, 8,13 we develop an approximate form…”

Section: ͑8͒mentioning

confidence: 99%

“…8 Of course, due to the above-mentioned merit of the PD, a lot of works concerning the PD functional theory have been done. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] They are expected to provide a possible way to go beyond the conventional density-functional theory, 25,26 and have gotten a lot of attention recently. The PD functional theory is yet a developing field.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Higuchi

2008

Phys. Rev. B

View full text Add to dashboard Cite

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.

show abstract

“…As for the second strategy, two kinds of relations and bounds for the KE functional of the PD theory have been derived so far [11,24]. Several approximate KE functionals have been developed by requiring them to fulfill two relations and bounds [24,25].…”

Section: Introductionmentioning

confidence: 99%

Coupling-constant expression and exact relations for the kinetic-energy functional in pair-density-functional theory

Higuchi

2012

Phys. Rev. A

View full text Add to dashboard Cite

We derive the coupling-constant expression for the kinetic energy (KE) functional of the pair-density-functional theory. Such the expression can be effectively used in developing the approximate KE functional. Indeed, on the basis of this expression, we present an approximate form of the KE functional by means of the perturbation theory. Furthermore, as the first step of an alternative way of obtaining the approximate KE functional, we derive several relations and bounds for the KE functional by investigating how the KE functional changes with the nonuniform scaling, rotation, and translation of electron coordinates. Such relations and bounds can be utilized as restrictive conditions on the approximate form. Thus, the coupling-constant expression, relations and bounds obtained here provide useful tools for devising various types of the approximate KE functional that is indispensable for advancing the pair-density-functional theory.

show abstract

The pair density functional of the kinetic energy and its simple scaling property

Abstract: For electronic systems, a simple property of the recently introduced kinetic energy T as a functional of the pair density n(r1,r2)is derived. Approximate explicit expressions for T[n] are presented.

Cited by 73 publications

References 33 publications

Excited-state pair-density-functional theory

Excited-state pair-density-functional theory

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

Coupling-constant expression and exact relations for the kinetic-energy functional in pair-density-functional theory

Contact Info

Product

Resources

About