Attempts toward a pair density functional theory

Ziesche, P.

doi:10.1002/(sici)1097-461x(1996)60:7<1361::aid-qua18>3.0.co;2-7

Cited by 83 publications

(101 citation statements)

References 72 publications

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“…The PD functional theory was first proposed by Ziesche. 6,7 After his proposal, many workers have studied it extensively, so that we have comprehended that there exist two kinds of problems for the development of the PD functional theory.…”

Section: Introductionmentioning

confidence: 99%

Computational pair density functional theory: A proposal for the kinetic energy functional

Higuchi

2010

Phys. Rev. B

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We present a computational pair density ͑PD͒ functional theory using multiple Slater determinants in constructing the PD. Compared to the effective initial scheme ͓M. Higuchi and K. Higuchi, Phys. Rev. B 78, 125101 ͑2008͔͒, the search region for the ground-state PD is substantially extended within the set of N-representable PDs. The merit of the present scheme is to guarantee the resultant PD to be N-representable and to describe correlation effects beyond the effective initial scheme, which enables us to tackle with the development of the approximate form of the kinetic energy functional. We derive two restrictive conditions on the kinetic energy functional. With the aid of these restrictive conditions, we also propose several types of approximate functionals of the kinetic energy. To check the abilities and limitations of the present scheme including such approximate functionals, actual calculations are performed for the neutral neon atom. The results show that the present scheme provides the N-representable and correlated PDs, though it would have some limitations. What we need to do first for improvement of the computational PD functional theory is that the development of the approximate functional of the kinetic energy is further advanced along the present scheme.

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Section: Introductionmentioning

confidence: 99%

Computational pair density functional theory: A proposal for the kinetic energy functional

Higuchi

2010

Phys. Rev. B

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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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“…Due to the Hohenberg-Kohn theorem with respect to the PD [7,8], the ground-state wave function can be denoted as | [γ (2) ] , where γ (2) is the ground-state PD of the system. The KE functional of the PD-functional theory is given by…”

Section: Coupling-constant Expression For the Ke Functionalmentioning

confidence: 99%

“…Therefore, the PD-functional theory , which can reproduce the ground-state PD, has recently attracted particular interest as a potential scheme that goes beyond the conventional density-functional theory (DFT) [45,46]. The PD-functional theory was first proposed by Ziesche [7,8]. Since then, two kinds of problems make it difficult for us to perform actual calculations of the PD-functional theory.…”

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

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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.

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Attempts toward a pair density functional theory

Cited by 83 publications

References 72 publications

Computational pair density functional theory: A proposal for the kinetic energy functional

Computational pair density functional theory: A proposal for the kinetic energy functional

Modeling the Pauli potential in the pair density functional theory

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

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