### Abstract

On the basis of the equation obtained by differentiating the virial theorem with respect to the density and the homogeneity property of the non- interacting kinetic energy functional T[ρ], a generalized Weizsacker kinetic energy functional is shown to be the only possible form for T[ρ], provided T[ρ] = ∫ t(ρ(r̄), ♀ρ(r̄)) dr̄, which has the consequence that the exact functional T[ρ] cannot have a form of this kind. The presented method, with the proposed mathematical formalism to treat multiple spatial derivatives of p in functional differentiations simply, can be used to get more general analytical expressions for T[ρ] making less restrictive assumptions about its form (allowing dependence on higher-order derivatives of ρ as well) and involving further relations. (C) 2000 Elsevier Science B.V.

Original language | English |
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Pages (from-to) | 167-171 |

Number of pages | 5 |

Journal | Journal of Molecular Structure: THEOCHEM |

Volume | 501-502 |

DOIs | |

Publication status | Published - Apr 28 2000 |

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### Keywords

- Functional differentiation
- Generalized Weizacker functional
- Homogeneity property
- Non-interacting kinetic energy density functional
- Virial theorem

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Computational Theory and Mathematics
- Atomic and Molecular Physics, and Optics

### Cite this

**A method to get an analytical expression for the non-interacting kinetic energy density functional.** / Gál, T.; Nagy, A.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A method to get an analytical expression for the non-interacting kinetic energy density functional

AU - Gál, T.

AU - Nagy, A.

PY - 2000/4/28

Y1 - 2000/4/28

N2 - On the basis of the equation obtained by differentiating the virial theorem with respect to the density and the homogeneity property of the non- interacting kinetic energy functional T[ρ], a generalized Weizsacker kinetic energy functional is shown to be the only possible form for T[ρ], provided T[ρ] = ∫ t(ρ(r̄), ♀ρ(r̄)) dr̄, which has the consequence that the exact functional T[ρ] cannot have a form of this kind. The presented method, with the proposed mathematical formalism to treat multiple spatial derivatives of p in functional differentiations simply, can be used to get more general analytical expressions for T[ρ] making less restrictive assumptions about its form (allowing dependence on higher-order derivatives of ρ as well) and involving further relations. (C) 2000 Elsevier Science B.V.

AB - On the basis of the equation obtained by differentiating the virial theorem with respect to the density and the homogeneity property of the non- interacting kinetic energy functional T[ρ], a generalized Weizsacker kinetic energy functional is shown to be the only possible form for T[ρ], provided T[ρ] = ∫ t(ρ(r̄), ♀ρ(r̄)) dr̄, which has the consequence that the exact functional T[ρ] cannot have a form of this kind. The presented method, with the proposed mathematical formalism to treat multiple spatial derivatives of p in functional differentiations simply, can be used to get more general analytical expressions for T[ρ] making less restrictive assumptions about its form (allowing dependence on higher-order derivatives of ρ as well) and involving further relations. (C) 2000 Elsevier Science B.V.

KW - Functional differentiation

KW - Generalized Weizacker functional

KW - Homogeneity property

KW - Non-interacting kinetic energy density functional

KW - Virial theorem

UR - http://www.scopus.com/inward/record.url?scp=4244194108&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4244194108&partnerID=8YFLogxK

U2 - 10.1016/S0166-1280(99)00425-X

DO - 10.1016/S0166-1280(99)00425-X

M3 - Article

AN - SCOPUS:4244194108

VL - 501-502

SP - 167

EP - 171

JO - Computational and Theoretical Chemistry

JF - Computational and Theoretical Chemistry

SN - 2210-271X

ER -