Exact single-particle kinetic energy functional for general two-level and model<i>n</i>-level one-dimensional systems: Dependence only on electron density and its gradient

Kozlowski, P.M.; March, N. H.

doi:10.1103/physreva.39.4270

Cited by 8 publications

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“…However, for this particular model the expression for single-particle kinetic energy is known for an arbitrary number of levels [12, 131, with and, as we demonstrated previously, this equation contains as limit both the Weizsäcker form for N = 1 and the Thomas-Fermi limit as N oo [12]. Of course, the above relations hold only for a particular harmonic oscillator model which is known to be local [14].…”

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On the Single-Particle Kinetic Energy Density Functional in Hyper-spherical Reprezentation

Kozlowski

1991

Acta Phys. Pol. A

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The properties of hyperspherical representation where the one-body orbitals are expressed in terms of the square root of the electron density, p(r) and the angle functions {θi(r)}i=1 . N-1 , (R.F. Nalewajski, P.M. Kozlowski, Acta Phys. Pol. Α74, 287 (1988)) are discussed, and the expression for the kinetic energy density functional is analyzed. This expression contains the Weizsäcker term plus a correction determined by the angle functions: Taking into account both the limit of only one occupied level and the slowly varying electron density with large N, it is shown that the kinetic energy density functional interpolates correctly between the known results. Finally, an example of a linear harmonic oscillator is given and the relation between the usual orbital pictures is discussed.PACS numbers: 02.90.+ρ, 31.20.Sy Density Functional Theory (DFT) has some advantages in the theory of many body systems such as atoms, molecules and the solid state. One of the most important problems in DFT is to derive the single-particle kinetic energy density functional Ts [p(r)] in terms of the electron density p(r) and its lowest derivatives. The simplest and most basic formulation of DFT is embodied in Thomas-Fermi (TF) theory, since the kinetic energy is approximated by that corresponding to a free electron gas e.g. a homogeneous system [1]. Construction of an adequate kinetic energy density functional is closely related to the problem of N-representability, namely, for a given density p(r) with p(r) ≥ 0 and f p(r)dr = N, is it always possible to find antisymmetric, N-electron wave function leading to this density? The usual approach is based on construction of a set of orthonormal functions which are continuous, smooth, and extended over all space. This approach has been discussed in the literature by many authors, for example Macke [2], Gilbert (655)

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“…For only two-hevels occupied the density is In terms of this density and angle function the first and second orbitals become, with the angle function It should be pointed out that the above phase is solely determined by the density and its first derivative as the solution of the following differential equation [12] .…”

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On the Single-Particle Kinetic Energy Density Functional in Hyper-spherical Reprezentation

Kozlowski

1991

Acta Phys. Pol. A

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The N‐particle wave function as a homogeneous functional of the density

Gál

2007

Int J of Quantum Chemistry

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ABSTRACT:It is shown that requiring consistency with the structure of the equation that determines the wave function associated to a density ͑r ៝͒ by density-functional theory, yields the N-particle wave function as a degree-half homogeneous functional of the density, and leads to a separation A͓N, ͔ of N dependence (with N ϭ ͵ ͑r ៝͒ dr ៝) of density functionals A͓͔ ϭ A͓ ͵ , ͔ for which A͓ ͵ , ͔ ϭ A͓ ͵ , ͔; as a consequence of the linearity of quantum mechanical operators. This implies that the ground-state value of any quantum mechanical observable arises naturally as a degree-one homogeneous N-particle density functional. This general scheme for the structure of density functionals can be considered as the conceptual generalization of the Weizsäcker functional, which is the exact degree-one homogeneous one-particle kinetic-energy density functional.

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Theory of phase factors for a one-body potential of arbitrary symmetry

Kozlowski

March

1990

Journal of Molecular Structure: THEOCHEM

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Exact single-particle kinetic energy functional for general two-level and modeln-level one-dimensional systems: Dependence only on electron density and its gradient

Cited by 8 publications

References 7 publications

On the Single-Particle Kinetic Energy Density Functional in Hyper-spherical Reprezentation

On the Single-Particle Kinetic Energy Density Functional in Hyper-spherical Reprezentation

The N‐particle wave function as a homogeneous functional of the density

Theory of phase factors for a one-body potential of arbitrary symmetry

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