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Studies of the energy density functional approach. I. Kinetic energy
Author(s) -
Tal Y.,
Bader R. F. W.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560140813
Subject(s) - kinetic energy , orbital free density functional theory , quantum , density functional theory , charge density , range (aeronautics) , hartree–fock method , atom (system on chip) , hybrid functional , limiting , chemistry , charge (physics) , limit (mathematics) , basis (linear algebra) , local density approximation , atomic physics , statistical physics , physics , quantum mechanics , materials science , mathematics , mechanical engineering , mathematical analysis , geometry , computer science , engineering , composite material , embedded system
The quantum kinetic energy density is defined and its properties discussed. Its limiting values, at the nucleus of an atom and at large distances from it, are both shown to be proportional to the corresponding values of the charge density. The properties of existing kinetic energy density functionals are analyzed with respect to their local behavior and compared with the quantum results at the Hartree‐Fock level. Their local behavior is found to be unsatisfactory. It is shown that the higher‐order terms in the general gradient expansion, which may be considered as the basis for these models, diverge in the long‐range limit. In view of these findings, a model of the kinetic energy density functional is proposed which possesses the correct limiting values for an exact as well as for a Hartree‐Fock charge density. Its local behavior is found to be in good agreement with the quantum results. Thus, the integrated values of this kinetic energy density functional are in excellent general agreement with Hartree‐Fock values, the percentage error in the estimate for argon, for example, being 0.04%. The basis for this model is a partitioning of the charge density into corelike and valence components. The charge density itself is not modeled, as the proposed partitioning scheme may be applied to any density, including the exact one. Consequently, the present model should be useful in the energy density functional approach to the study of the physical properties of atoms, molecules, and solids.