Pair density functional theory — a generalized density functional theory

2012

Phys. Rev. A

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.

Section: Coupling-constant Expression For the Ke Functionalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2012

Phys. Rev. A

“…8,27,28) 3. These restrictive conditions are effectively used in developing approximate forms of T [γ (2) ]. Several types of approximate functionals have been proposed.…”

Section: Recent Progress Of the Computational Pd Functional Theorymentioning

confidence: 99%

Density Functional Approach for Calculating the Diagonal Elements of the Second-Order Reduced Density Matrix: Restrictive Conditions on the Kinetic Energy Functional

2011

J. Phys. Soc. Jpn.

“…Using this universal functional, the Hohenberg-Kohn theorem can be proven in the extended form. 1,8,9,15 The variational principle of this theorem is given by…”

Section: Pd Functional Theory Using the Noninteracting Reference mentioning

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%

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

2008

Phys. Rev. B

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.