Exchange energy density in density-functional theory via the Dirac density matrix for a nonrelativistic 10-electron atomic ion compared with Becke's proposal for a gradient-corrected local-density-approximation result
Faculty of Sciences. Physics
Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015
, p. 042506,1-042506,7
University of Antwerp
Especially in atomic systems, it is now well established that exchange energy generally dominates correlation effects. Therefore we focus here on the exchange energy density x(r) as given in terms of the idempotent Dirac density matrix. This is then brought into contact with the one-parameter form of Becke's functional, which corrects the local-density-approximation form −cx[n(r)]4/3 with n(r) as the ground-state electron density, cx=(3/4)e2(3/)1/3, by terms involving the dimensionless gradient ratio |n(r)|/n4/3(r). A particular nonrelativistic model of the 10-electron Ne-like atomic ions, with large atomic number Z, is then compared to Becke's approximation to x(r).