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On the conjoint gradient correction to the Hartree—Fock kinetic and exchange energy density functionals
Author(s) -
Gázquez José L.,
Robles Juvencio
Publication year - 1996
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/(sici)1097-461x(1996)57:1<3::aid-qua1>3.0.co;2-1
Subject(s) - kinetic energy , dirac (video compression format) , range (aeronautics) , physics , energy (signal processing) , order (exchange) , mathematical physics , hybrid functional , chemistry , quantum mechanics , density functional theory , materials science , finance , neutrino , economics , composite material
The kinetic and the exchange energy functionals are expressed in the form T [ρ] = C TF ∫ drρ 5/3 (r) f t (s) and K[ρ] = C D ∫ drρ 4/3 (r) f K ( s ), where C TF = (3/10)(3π 2 ) 2/3 and C D = −(3/4)(3/π) 4/3 are the Thomas‐Fermi and the Dirac coefficients, respectively, and s = |∇ρ(r)|/ C s ρ 4/3 (r), with C s = 2(3π 2 ) 1/3 . These expressions are used to perform a comparison of f T (s) and f K (s) in terms of their generalized gradient expansion approximations. It is shown that f κ (s) and is congruent to f T (s) in the range characteristic of the interior regions of atoms and many solids and that the second‐order gradient expansion of the kinetic energy provides a rather reasonable approximation to the generalized gradient expansion approximation of both the kinetic and the exchange energy functionals. © 1996 John Wiley & Sons, Inc.