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Introduction of the shell structure with gradient expansion corrections into the Thomas‐Fermi‐Dirac energy density functional for neutral atoms
Author(s) -
Csavinszky P.
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.560200841
Subject(s) - wave function , thomas–fermi model , atom (system on chip) , dirac (video compression format) , kinetic energy , physics , fermi–dirac statistics , electron , atomic physics , shell (structure) , fermi energy , energy (signal processing) , quantum mechanics , materials science , computer science , neutrino , composite material , embedded system
Considering the Na atom as an example, an approximation to the electron number density is constructed from H‐like wavefunctions. Using this electron density the Thomas‐Fermi‐Dirac energy density functional, with the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term, is optimized with respect to the Z in the wavefunctions. The total energy obtained for the Na atom is −170.1 a.u., while the energy calculated by the Roothan‐Hartree‐Fock method is −161.8 a.u. The Weizsäcker and Hodges corrections are found significant, with values of +9.8 a.u. and +1.4 a.u., respectively.