On the conjoint gradient correction to the Hartree—Fock kinetic and exchange energy density functionals

✍ Scribed by José L. Gázquez; Juvencio Robles

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 266 KB
• Volume: 57
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1996)57:1<3::aid-qua1>3.0.co;2-1

✦ Synopsis

The kinetic and the exchange energy functionals are expressed in the form T [ p ] = CTFj drp5/3(r)f.,(s) and K [ p ] = C,/drp4/3(r)fK(s), where C,, = (3/10)(3.rr2)2/3 and C , = -(3/4)(3/7~)'/~ are the Thomas-Fermi and the Dirac coefficients, respectively, and s = lVp(r)l/C, p4l3(r), with C, = 2 ( 3 ~' ) ' / ~. These expressions are used to perform a comparison of fT(s) and fK( s) in terms of their generalized gradient expansion approximations. It is shown that fK(s) = fT(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.